[wittmann, andreas] high-performance quantum casca

DISS. ETH Nr. 18363

HIGH-PERFORMANCE QUANTUM CASCADE LASER

SOURCES FOR SPECTROSCOPIC APPLICATIONS

A dissertation submitted to

ETH ZURICH

for the degree of

DOCTOR OF SCIENCES

presented by

ANDREAS WITTMANN

M.Sc., Technische Universität München

born January 2nd, 1974

citizen of Zurich/ZH, Switzerland

accepted on the recommendation of

Prof. Dr. J. Faist, supervisor

Prof. Dr. M. W. Sigrist, co-examiner

Prof. Dr. J. Wagner, co-examiner

2009

To my wife Nadia

Abstract

Quantum cascade (QC) lasers are semiconductor lasers based on intersubband

transitions in multi quantum well heterostructures, which rely on epitaxial growth

techniques. They are very versatile mid-infrared sources for the realization of ultra-

sensitive and selective sensors for spectroscopic applications in the fields of

environmental monitoring, industrial processes, security and military. However, for

many applications, like the determination of isotopic ratios (e.g. of CO2), a high spectral

resolution (in the MHz range) is an absolute necessity, which requires the laser source to

operate in continuous wave (CW) mode. Cheap measurement systems for large volume

applications also benefit from CW operating lasers since they can be combined with

inexpensive dc current drivers, instead of pulse shaping electronics needed for pulse

operated lasers. In addition, applications like breath analysis would profit from portable,

low-power consuming devices allowing the realization of hand-held, battery-operated

systems. Furthermore, broadly tunable sources with narrow linewidth are desirable for

the detection of multiple absorption lines or mixtures with very broad resonances, as

found in clinical medicine for non-invasive detection of glucose levels. Their broad

frequency coverage combined with their higher spectral resolution (compared with

Fourier transform infrared spectrometers) makes them very interesting for the detection

of a variety of chemicals.

In this work, low power consuming distributed feedback (DFB) based single mode QC

lasers were developed, operating at !~9 µm in CW up to a temperature of 150 °C, which

is the highest value reported in literature. Such devices are tunable by 1.3 % of its center

wavelength. Low electrical power consumption of 1.6 W and 3.8 W for an optical output

power of 16 mW and 100 mW has been demonstrated.

The relatively small tuning range of a single DFB device, smaller than or equal to

approximately 1 % of the wavelength, usually limits its efficiency for the detection of

complex mixtures with multiple absorption lines. By using a broad-gain active region

design and monolithic integration of different DFB gratings, high-performance devices

Abstract

ii

were realized with single-mode emission between 7.7 and 8.3 µm at a temperature of

+30 °C. This corresponds to 8 % of the center wavelength. Some of these lasers have

been selected for the NASA Mars Science Laboratory Mission to evaluate whether Mars

was ever inhabitable.

The combining of two of these broad-gain active region designs in the same device

resulted in heterogeneous high performance QC lasers for broad-gain applications. They

were tested in an external cavity setup, with single-mode tuning of the center wavelength

at room temperature of 25 % in pulsed mode and 18 % in CW operation, which is the

widest reported tuning range in literature. These devices are commercially available at

Daylight Solutions, Poway, CA.

Furthermore, a model to a priori calculate the temperature and field dependent

intersubband linewidth in QC laser designs is presented; the same was experimentally

verified with devices having different linewidths. This model constitutes a useful tool for

the development of novel narrow gain and high wallplug efficiency active region designs

or designs for broad gain applications.

Kurzfassung

Quantenkaskaden-Laser sind Halbleiterlaser, die auf Intersubband-Übergängen in

Multi-Quantentopf-Schichtstrukturen basieren und mit Hilfe von epitaktischen

Wachstumsverfahren hergestellt werden. Mit ihnen lassen sich sehr empfindliche und

selektive Sensoren für spektroskopische Anwendungen in den Bereichen Industrie,

Umwelt, Sicherheit und Militär realisieren.

In vielen Fällen, wie beispielsweise für die Bestimmung von Isotop-Verhältnissen (etwa

von CO2), ist eine hohe spektrale Auflösung (im MHz-Bereich) nötig, was Laserquellen

im Dauerstrich-Betrieb erfordert. Aber auch die preiswerten Messsysteme für die

Massenproduktion würden von dauerstrichbetriebenen Lasern profitieren, da diese mit

Gleichstromquellen betrieben werden können, die im Vergleich zu Pulsgeneratoren

relativ günstig sind. Zudem braucht es stromsparende batteriebetriebene Laserquellen,

um tragbare Systeme zu realisieren, welche beispielsweise für die Atemanalyse mit

portablen Geräten von Vorteil wären. Des Weiteren sind Breitband-Laserquellen mit

schmaler Linienbreite sehr interessant für die Messung von Substanzen mit mehreren

Absorptionslinien oder Mischungen mit breiten Absorptionsresonanzen, wie etwa zur

nichtinvasiven Messung von Glukose. Der grosse Abstimmbereich zusammen mit einer,

verglichen mit Fourier-Transformierten-Infrarot Spektrometern, viel höheren

spektralen Auflösung macht diese Laserquellen sehr interessant für die Messung einer

Vielzahl von chemischen Substanzen.

In dieser Arbeit wurden Laser mit verteilter Rückkopplung (DFB-Laser) für eine

Emissionswellenlänge von 9 µm entwickelt, welche bis zu einer Temperatur von 150 °C

im Dauerstrichbetrieb arbeiten, was die höchste publizierte Temperatur darstellt. Solche

Laser sind um 1.3 % der Zentralwellenlänge durchstimmbar. Der elektrische

Leistungsverbrauch eines solchen Lasers für optische Ausgangsleistungen von 16 mW

bzw. 100 mW liegt bei 1.6 W bzw. 3.8 W.

Der relativ kleine Abstimmbereich eines einzelnen DFB-Lasers von etwa 1 % oder

weniger schränkt den Anwendungsbereich für Messungen von komplexen Mischungen

Kurzfassung

iv

mit mehreren Absorptionslinien ein. Durch den Einsatz eines Breitband-

Verstärkermediums und der Integration mehrerer DFB-Gitter konnten

Hochleistungslaser realisiert werden, die einen Wellenlängenbereich von 7.7 bis 8.3 µm

bei einer Temperatur von 30 °C abdecken. Dies entspricht einem Durchstimmbereich

von 8 % der Zentralwellenlänge. Einige von diesen Lasern wurden für die NASA Mars

Science Laboratory Mission ausgewählt, deren Ziel es ist, herauszufinden, ob der Planet

Mars jemals bewohnbar war.

Die Kombination zweier solcher Breitband-Verstärkermedien im selben Bauteil

erlaubte die Realisierung eines heterogenen Hochleistungs-Quantenkaskaden-Lasers,

welcher mit Hilfe einer externen Kavität durchgestimmt wurde. Der Abstimmbereich

eines solchen Lasers über 25 % der Zentralwellenlänge im Pulsbetrieb und 18 % im

Dauerstrichbetrieb stellt den höchsten publizierten Wert für Quantenkaskaden-Laser

dar. Diese Laser sind kommerziell bei Daylight Solutions (Poway, Kalifornien)

erhältlich.

Darüber hinaus wurde ein Modell für die Berechnung der temperatur- und feld-

abhängigen Intersubband-Linienbreite in Quantenkaskaden-Lasern erstellt und

experimentell mit Lasern unterschiedlicher Linienbreite verifiziert. Dieses Modell stellt

ein nützliches Werkzeug für die Entwicklung neuer aktiver Zonen mit schmalen

Linienbreiten und hohem Gesamtwirkungsgrad oder neuartiger Designs für Breitband-

Anwendungen dar.

Table of content

Abstract........................................................................................................................... i!

Kurzfassung .................................................................................................................iii!

1.! Introduction .............................................................................................................. 1!

1.1.!Motivation ..................................................................................................................... 1!

1.2.!Scope and organization of this thesis......................................................................... 2!

1.3.!Continuous wave mid-infrared sources...................................................................... 4!

1.3.1.!Lead salt-based diode lasers............................................................................... 5!

1.3.2.!Antimonide-based diode lasers.......................................................................... 6!

1.3.3.!Interband cascade lasers..................................................................................... 7!

1.3.4.!Sources based on optical parametric frequency conversion............................ 8!

1.4.!The quantum cascade laser ...................................................................................... 13!

1.4.1.!Historical review of first intersubband laser ................................................... 13!

1.4.2.!Intersubband laser versus interband laser ...................................................... 17!

1.4.3.!Different architectures of active region designs............................................. 19!

1.4.4.!Material aspects and growth techniques ......................................................... 21!

1.4.5.!Continuous wave operation above room temperature .................................. 25!

1.4.6.!Broad-gain quantum cascade laser sources .................................................... 27!

1.4.7.!Tunable single-mode devices ........................................................................... 29!

1.4.7.1.! Distributed feedback quantum cascade lasers ................................. 29!

1.4.7.2.! External cavity tuned quantum cascade lasers ................................. 31!

2.!Theory...................................................................................................................... 35!

2.1.!Fundamentals ............................................................................................................. 35!

2.1.1.!Electronic states in multi-quantum well heterostructures............................. 35!

2.1.2.!Intersubband absorption and gain................................................................... 40!

2.1.3.!Inter- and intrasubband scattering processes ................................................. 45!

2.1.4.!Intersubband linewidths ................................................................................... 49!

Table of content

vi

2.1.5.!Rate equation approach ................................................................................... 53!

2.2.!Design Parameters ..................................................................................................... 56!

2.2.1.!Electrical point of view ..................................................................................... 56!

2.2.2.!Optical point of view......................................................................................... 60!

2.2.3.!Thermal point of view....................................................................................... 68!

2.3.!Mode control in QC lasers ........................................................................................ 73!

2.3.1.!Distributed feedback cavity .............................................................................. 74!

2.3.2.!External cavity feedback................................................................................... 80!

3.!Technology .............................................................................................................. 84!

3.1.!Introduction ................................................................................................................ 84!

3.1.1.!Epitaxial growth................................................................................................. 84!

3.1.2.!Processing and assembly................................................................................... 86!

3.2.!Buried distributed feedback gratings....................................................................... 88!

3.3.!Advanced waveguide etching I................................................................................... 89!

3.4.!Buried heterostructures............................................................................................. 91!

3.4.1.!Investigation of epitaxial blocking layers ........................................................ 92!

3.4.2.!Selective growth on non-planar structures...................................................... 96!

3.5.!Epi-side down mounting ............................................................................................ 98!

3.6.!Advanced waveguide etching II ................................................................................. 99!

4.!Two-phonon resonance versus bound-to-continuum design............................ 105!

4.1.!Introduction .............................................................................................................. 105!

4.2.!Design and experiment ............................................................................................ 105!

4.3.!Intersubband linewidth............................................................................................ 107!

4.4.!Laser performance ................................................................................................... 110!

4.4.1.!Pulsed and CW laser characteristics.............................................................. 110!

4.4.2.!Transport.......................................................................................................... 111!

4.4.3.!Waveguide losses............................................................................................. 112!

4.4.4.!Differential gain .............................................................................................. 114!

4.4.5.!Threshold current density and slope efficiency ............................................ 114!

4.5.!Conclusion................................................................................................................. 115!

Table of content

vii

5.!Low power consumption laser sources............................................................... 117!

5.1.!Introduction .............................................................................................................. 117!


5.3.!Laser performance of moderately coupled devices ............................................... 118!

5.3.1.!CW laser characteristic ................................................................................... 118!

5.3.2.!Thermal resistance and temperature tuning................................................. 120!

5.3.3.!Cavity losses ..................................................................................................... 121!

5.3.4.!Longitudinal and lateral mode discrimination ............................................. 122!

5.4.!Laser performance of strongly coupled devices..................................................... 124!

5.5.!Conclusion................................................................................................................. 125!

6.!Quantum cascade lasers with widely spaced operation frequencies............... 126!

6.1.!Introduction .............................................................................................................. 126!


6.3.!Laser performance ................................................................................................... 128!

6.3.1.!CW laser characteristic ................................................................................... 128!

6.3.2.!Thermal resistance and tuning properties .................................................... 130!

6.3.3.!Coupling strength and mode discrimination ................................................ 132!

6.3.4.!Extrapolated gain spectrum and differential gain........................................ 133!

6.4.!Evaluation of reliability for NASA Mars mission project .................................... 135!

6.5.!Conclusion................................................................................................................. 136!

7.!Broadly tunable heterogeneous quantum cascade laser sources .................... 138!

7.1.!Introduction .............................................................................................................. 138!


7.2.1.!Active region design........................................................................................ 139!

7.2.2.!Waveguide and thermal design...................................................................... 141!

7.2.3.!Single mode control in external cavity setup ................................................ 142!

7.3.!Device characterization............................................................................................ 143!

7.3.1.!Gain chip performance ................................................................................... 143!

7.3.2.!Extrapolated gain spectrum ........................................................................... 147!

7.3.3.!Broadband tuning in external cavity setup.................................................... 147!

7.4.!Conclusion................................................................................................................. 150!

Table of content

viii

8.!Conclusion and Outlook...................................................................................... 151!

List of abbreviations................................................................................................. 154!

References.................................................................................................................. 156!

Acknowledgement ..................................................................................................... 172!

Curriculum vitae....................................................................................................... 175!

Publications............................................................................................................... 176!

Chapter 1

1. Introduction

1.1. Motivation

The monitoring and control of our environment, as well as maintaining a high quality of

life of an aging population has become one of the major challenges of today’s society

and is of profound importance with regard to the technological development of the

industrialized world. The diversity of applications include fields such as the

environmental monitoring of important carbon gases in global warming (e.g. CH4, CO,

CO2 and H2CO), urban (e.g. automobile traffic, power generation) and rural emissions

(e.g. rice agro-ecosystems, horticultural greenhouses and fruit storage), industrial

emissions, chemical analysis and process control for manufacturing processes (e.g. food,

semiconductor and pharmaceutical), as well as toxic gases and explosives relevant to law

enforcement and public safety. An important field in clinical medicine is the analysis of

breath metabolites (e.g. NO, CO, CO2, C2H6 and NH3) for the early detection of ulcers,

cancer and diabetes. Breath analysis is very attractive because it is a non-invasive way to

monitor a patient’s physiological status. All these applications require the precise

determination of concentration levels, for which several methods exist. Those based on

chemical reactions are generally classified as electrochemical, measuring a change in

output voltage due to a chemical interaction of the analyte with the sensing element.

Other methods are based on changes of physical properties (thermal, mechanical or

optical). Optical absorption techniques allow the realization of non-invasive and highly

sensitive and selective measurement systems for both gases and analytes dissolved in

liquids. Furthermore, they are fast, consume no material (as in the case of

electrochemical methods), and can be employed in harsh environments. Optical

Introduction

2

absorption techniques also enable the probing of the overtone and fundamental

rotational-vibrational frequencies of target molecules, most of which are located in the

near-infrared (0.7–3 µm) and mid-infrared (3–24 µm) range, and also allow the

obtaining of an unambiguous signature of the investigated gas or liquid. Optical

techniques are well established in chemistry, but instruments such as the Fourier

transform infrared (FTIR) spectrometer are bulky, expensive, power-consuming and

limited in spectral resolution. Recent progress in the telecommunication industry allows

the fabrication of semiconductor optical sources with very high performance levels, low

electrical power consumption and low manufacturing costs. The invention of the

quantum cascade (QC) laser and recent improvements of its room temperature

performance allow the generation of single-mode emission at room temperature across

the mid-infrared (MIR) wavelength range, where most of the relevant target molecules

have absorption lines several orders of magnitudes stronger than in the near-infrared

(NIR). Concentrations in the parts-per-billion (ppb) and parts-per-trillion (ppt) ranges

are detectable. Furthermore, the two atmospheric transmission windows in the MIR at

3–5 µm and 8–12 µm allow remote sensing. However, one needs portable, low power-

consuming, selective and sensitive measurement systems, which are capable of analyzing

the chemical composition of small quantities in reasonable time. Furthermore, broadly

tunable room temperature operated sources with narrow linewidth, compared with the

well-established FTIR techniques, would open new prospects in chemistry.

1.2. Scope and organization of this thesis

The objective of this work is the development of high performance quantum cascade

lasers for spectroscopic applications. For one part, the focus was on the development of

low-power consumption laser sources suited for portable applications. They should

possess sufficient tunability, preferably without cooling, to identify a specific gas by its

fingerprint spectra. For the other part, the goal was to develop broadly tunable single

mode laser sources for the detection of complex mixtures with multiple absorption lines,

or mixtures with very broad lines - typically those with a liquid phase matrix. The

challenge is to build sources with a narrow linewidth (10-4–10-5 cm-1), which makes

continuous wave (CW) operation necessary, without the need of cryogenic cooling.

Scope and organization of this thesis

3

Furthermore, for broadband tunability, a broad gain spectrum is required, which results

in a lower differential gain. These demand on three totally different physical aspects that

have to be considered, namely the electrical, the optical and finally the thermal design.

Unfortunately, these three aspects cannot be regarded as independent and must all be

solved.

First of all, a short introduction on alternative mid-IR coherent sources will be given.

After a brief review of the history of the first intersubband laser, an overview of today’s

state-of-the-art quantum cascade lasers will be given. Chapter II describes the

theoretical framework and design parameters of quantum cascade lasers. Chapter III

describes the technological aspect. In Chapter IV, the two most promising active region

designs for high performance operation are compared. Low power- consumption single-

mode devices are the topic of Chapter V. The results for realizing broadly tunable

quantum cascade lasers are presented in Chapters VI and VII. Finally, Chapter VIII

concludes this work and gives an outlook.

The material published by the author in the following papers and conference

proceedings has been used in the different chapters of this work:

Chapter 2:

• Appl. Phys. Lett. 93, 141103 (2008)

Chapter 3:

• IEEE J. Quantum Electron. 44, 36 (2008)

Chapter 4:

• Appl. Phys. Lett. 93, 141103 (2008)

Chapter 5:

• Photon. Techn. Lett., accepted for publication

Chapter 6:

• Appl. Phys. Lett. 89, 201115 (2006)

• Proc. SPIE 6485, 64850P (2007)

Chapter 7:

• IEEE J. Quantum Electron. 44, 1083 (2008)

Introduction

4

1.3. Continuous wave mid-infrared sources

Numerous trace gas species are detectable in the NIR from 1.3 to 3 µm using reliable,

room temperature, single mode lasers, that were primarily developed for

telecommunication, with output powers of tens of mW. However, these lasers access

molecular overtone or combination band transitions that are typically a factor of 30-300

weaker than the fundamental transitions in the mid-IR [1]. The spectral region of

fundamental vibrational molecular absorption bands from 3 to 24 µm is the most

suitable for high sensitivity trace gas measurement. Fig. 1.1 shows the fingerprint spectra

of spectroscopically interesting molecules within the two atmospheric transmission

windows in the MIR.

Fig. 1.1 Fingerprint spectra of several gas molecules in the two atmospheric

transparent windows [HITRAN 2000 database].

However, the usefulness of laser spectroscopy in this spectral range is limited by the

availability of convenient tunable sources. Real world applications require the laser

sources to be compact, efficient, reliable and operating close to room temperature. The

Continuous wave mid-infrared sources

5

quantum cascade laser is not the only coherent source in the mid-infrared spectral

region (see Fig. 1.2). In this section, the advantages and disadvantages of relevant

alternative continuously tunable mid-IR sources are briefly discussed. Since this work

focuses on lasers emitting with a narrow linewidth, I restricted the overview on

continuous wave operating sources. Although CO and CO2 gas lasers are very popular

for photoacoustic spectroscopy, which is due to its large output power (several hundreds

of watts in CW operation), they will not be discussed here, since they are only line-

tunable on the rotational-vibrational transitions of the molecule (with gaps of 1-3 cm-1).

A good overview on different solid-state mid-infrared laser sources is given in the book

edited by Sorokina and Vodopyanov [2] and a follow-up edited by Ebrahim-Zadeh and

Sorokina [3].

Fig. 1.2: Mid-infrared CW laser sources. The blue shaded areas represent the two

atmospheric transmission windows at 3–5 and 8–12 µm [1].

1.3.1. Lead salt-based diode lasers

Such sources have been developed since mid-1960s for the operation between 3 and

30 µm. Lead salt diode lasers are based on semiconductor IV-VI materials like PbTe,

PbSe, and PbS. The active region is either realized as homojunction, grown by liquid

phase epitaxy (LPE), or heterostructure, grown by molecular beam epitaxy (MBE),

using the mentioned materials as barrier and the same materials combined with Cd, Eu,

Sn or Yb for the active region. In contrast to most optoelectronic materials, the direct

Introduction

6

bandgap is not located at the ! point but at the L point of the Brillouin zone. Laser

action is based on the injection of electrons and holes across a forward biased pn-

junction. Although the effective electron and hole masses are very similar which results

in a reduced Auger recombination rate, the very small bandgap of these Pb-based

materials and the low T0 value of such devices require cryogenic cooling for reaching

population inversion in CW operation. This in turn demands on the entire laser

packaging that makes such lasers rather large in size. The highest reported CW

operation temperature of such devices is 223 K [4]. Since the emission energy depends

on the temperature-dependent energy bandgap, the frequency of such devices can be

shifted up to 100 cm-1 by direct temperature tuning or tens of cm-1 by current tuning.

However, since those devices are normally Fabry-Pérot devices, both tuning mechanisms

produce only continuous wavelength coverage of 1-2 cm-1 before the wavelength jumps

to another longitudinal mode. A relatively large tuning coefficient of 2-5 cm-1/K is

achieved but since the complete laser package must be heated, this mechanism is rather

slow (in the order of seconds). On the other hand, since typical linewidths of many

applications are in the 0.001 cm-1 range, stable operations requires temperature control

to better than 1 mK over long times. In contrast to direct temperature tuning, current

tuning is very fast and allows to employ high frequency modulation techniques in the

kHz and MHz regime. Typical linewidths of 0.6-25 MHz (full-width at half maximum,

FWHM) have been achieved [5]. Temperature cycling reduces the reliability of such

devices in terms of wavelength stability and spatial mode quality and leads to a reduction

of output power. Output power levels in the range of 0.1-0.5 mW are relatively small

compared to quantum cascade lasers.

1.3.2. Antimonide-based diode lasers

Type-I quantum well (QW) lasers based on compressively-strained InGaAsSb QWs

incorporated in AlGaAsSb barriers on GaSb substrates provide hundreds of mW output

power at room temperature in CW within the spectral range of "=2.3 to 2.8 µm [6-8].

The wavelength in such devices is mainly adjusted by the amount of Indium in the QW.

For longer wavelengths, this has to be accompanied by increasing the Arsen content in

the QW in order to avoid strain-relaxation. However, this significantly reduces the hole


7

confinement and results in degrading the laser efficiency. Using quinternary

AlInGaAsSb allows the increase of the barriers. This resulted in type-I devices at

!=3.0 µm with an output power of 130 mW [9] and !=3.36 µm with 15 mW [10] at room

temperature. Another successful approach is to use GaSb barriers instead of Al-

containing barriers. The lower barrier height results in lower quantization energies and

consequently a red-shift of the emission wavelength at constant In content in the QW.

Although this results in a reduced hole confinement, it should allow for a more

homogeneous pumping of the multi-QWs. DFB devices incorporating GaSb barriers

lased up to room temperature with 3 mW output power at !=3.0 µm [11].

1.3.3. Interband cascade lasers

Interband cascade (IC) lasers with a Sb-type-II “W” active region design [12] are very

promising for sources in the first atmospheric window between 3 and 5 µm [13, 14]. They

take advantage of the broken bandgap alignment in Sb-based type-II quantum wells to

re-use injected electrons in cascade stages for photon generation, first proposed by Yang

et al. [15]. Fig. 1.3 shows the band diagram of such a device. Electrons injected into the

InAs QW emit a photon while undergoing a diagonal transition (E1"H1) to the valence

band of the InGaSb hole QW. The second InAs QW (“W”-shaped active region)

increases the matrix element of the optical transition due to a strong overlap of

wavefunctions (shown in upper part of Fig. 1.3). Electrons tunnel then via hole states

from the InGaSb QW into the GaSb well, following resonant interband tunneling into

the InAs well of the n-doped chirped InAs-(In)AlSb superlattice. The function of the

GaSb well and second AlSb barrier is to prevent electron escape from the active region

by tunneling. The electrons are finally injected into the active region of the next cascade.

In contrast to QC lasers, IC lasers use interband optical transitions without involving fast

phonon scattering and the reduced Auger recombination by eliminating inter-valence

resonances (between the bandgap energy and split-off band energy #0) [16], making it

possible to achieve very low threshold current densities (<10 A/cm2 at 80 K). However,

such devices show rather small values of T0=40-60 K associated primarily with Auger

recombination, increasing internal losses and decreasing internal efficiencies with

Introduction

8

temperature. Nevertheless, CW operation on a Peltier cooler was demonstrated for

!=3.3, 4.05, and 4.1 µm [17-19]. The highest CW operation temperature to date for an

IC laser is 319 K, using a 5-stage active region, which emits at !=3.75 µm. At 300 K, this

device emits 10 mW of optical power [20].

Fig. 1.3: Band diagram of type-II “W” interband cascade (IC) laser, reprinted

from [14]. Shown are the moduli squared of the relevant wavefunctions in the

conduction band (E1) and valcence band (H1).

1.3.4. Sources based on optical parametric frequency conversion

Another well established way to generate mid-IR coherent light sources is the use of

frequency conversion in a nonlinear optical material. There are in principle two

arrangements for this process: In difference frequency generation (DFG), two optical

beams customarily called pump (highest frequency) and signal (intermediate frequency),

are focused into a nonlinear optical crystal to generate (in a single pass) idler (lowest

frequency) radiation which equals the energy difference of signal and pump (Fig. 1.4a).

In an optical parametric oscillator (OPO), the incoming (pump) beam is converted into

two (signal and idler) beams and the phase matching condition defines which

frequencies are generated (Fig. 1.4b). Before discussing the specifics of DFGs and

OPOs, common properties are discussed.


9

In both cases, pump, signal and idler frequencies are related by the energy conservation:

!!

pump= !!

signal+ !!

idler. In this process, momentum conservation is needed, i.e.

!k = k

pump" k

signal" k

idler= 0 , where !k is the so-called phase mismatch. If the phase

matching condition is not met, after each coherence length lc=!/!k, the newly generated

light will destructively interfere with the light generated in the previous coherence

length. Thus after twice the coherence length all generated light will be destroyed. The

phase matching condition can be satisfied in birefringent materials, like "-BaB2O4

(BBO) and LiB3O5 (LBO), where the ordinary and extraordinary polarization axis

exhibit different dispersions. However, the limited transparency in the mentioned

materials confine them to idler wavelengths below 2 µm.

Fig. 1.4: a) Schematics for difference frequency generation (DFG) and b) optical

parametric oscillator (OPO).

Newer materials (like KTP, KTA and RTA) offer improved effective nonlinearities and

deeper transparencies up to 5 µm. Unfortunately, these materials show non-optimal

phase-matching conditions. The breakthrough came with advent of quasi-phase-matched

(QPM) nonlinear crystals, particularly periodically-poled LiNbO3 (PPLN), which is

Introduction

10

today’s most used material for sources based on optical parametric frequency

conversion. In these materials, the phase mismatch is compensated by a periodical

change of the polarization by 180° after each coherence length (poling period !QPM=2lc)

by means of a relatively high dc external electric field. Thus, the light will constructively

interfere with the light from the previous coherence length and a build-up of the

generated light is observed. For a quasi-phase-matching process, the phase mismatch

!k = 2" / #

QPM= k

pump$ k

signal$ k

idler. PPLN is transparent up to "4-5 µm and is therefore

the material of choice for wavelengths between 2 and 5 µm. Above 5 µm, the crystal is

strongly absorbing. For higher wavelength ranges, there exist orientation-patterned

GaAs (OP-GaAs) and birefringent materials like AgGaS2, AgGaSe2 and ZnGeP2.

However, the short wavelength absorption cutoff well above 1 µm precludes the direct

use of widespread solid-state Nd pump lasers (#"1.06 µm) in many of these crystals, so

that successful implementation often requires cascaded two-step pumping arrangements

to extend the pumping wavelength into the material transparency. GaAs has excellent

characteristics for parametric frequency conversion since it is widely transparent (0.9-

17 µm), has a high thermal conductivity, low optical dispersion that leads to a large

coherence length and a huge effective nonlinear optical coefficient (94 pm/V at #=4 µm,

which is 5 times larger compared with PPLN) [21, 22]. QPM in OP-GaAs cannot be

achieved by periodically poling since this material is not ferroelectric, but by regrowth of

laterally orientation-patterned GaAs films, fabricated using GaAs/Ge/GaAs

heteroepitaxy [23, 24]. Another approach to obtain QPM in GaAs and other

semiconductors, like InP or ZnSe, is to use the Fresnel phase shift at total internal

reflections (TIR-QPM) in a plane-parallel crystal where each leg of the zigzag path is

approximately an odd number of lc. Parallel and perpendicular polarized waves display

different reflection coefficients. A large differentiating mechanism between the two

waves can be achieved which allows large tuning and alleviates the phase matching

condition [25, 26]. In the following, the particular features of the DFG and OPO are

discussed.


11

Difference frequency generation (DFG)

The combination of a PPLN nonlinear crystal, telecommunication diode lasers and/or

advanced optical fiber lasers allow the realization of very compact and robust sensors

[27, 28]. The narrow linewidths of pump and signal laser convolve during the frequency

conversion process, resulting in a similarly narrow linewidth for the idler. Moreover, the

frequency tuning range of pump and signal wave is transferred to the idler wave

resulting in a large total tuning range. This is mainly limited by the phase-matching

bandwidth but can be extended by integrating several poling periods in the nonlinear

crystal or by using a fan-out geometry. Another approach involves changing the

temperature of the crystal and tuning both the pump and signal wavelength. Richter et

al. report a multi-component gas senor based on a fiber coupled tunable near-IR

external cavity (EC) diode laser (814-870 nm) and an Yb-fiber-amplified distributed

Bragg reflector (DBR) diode laser (1083 nm) [29]. Using a fan-out-type PPLN, a large

tuning range from 3.3 to 4.4 µm (28 % of center frequency) was achieved. However, the

relatively low output power of 2.9 µW forbids the use of advanced detection techniques

such as dual-beam detection. The low output powers (typically below 100 µW) and low

optical conversion efficiencies (0.2 %W-1) can be markedly increased by fabricating

PPLN ridge waveguides. Denzer et al. reported conversion efficiencies of 45 %W-1,

resulting in an output power of 0.26 mW at !=3.3 µm [30]. Recently, an output power of

65 mW was reported. This resulted from the high damage resistance of Zn-doped PPLN

waveguide which allowed input powers of 444 mW (from a YDFA amplified 1.064 µm

diode laser) and 558 mW (from a EDFA amplified 1.55 µm EC diode laser) resulting in

a conversion efficiency of 35 %W-1 [31]. Vasilyev et al. demonstrated a DFG sensor

based on OP-GaAs, which could be widely tuned from 7.6 to 8.2 µm (7.6 % of center

frequency) with an output power of 0.5 mW using 1.5 and 2 µm fiber laser sources [32].

Optical parametric oscillator (OPO)

As in a conventional laser oscillator, the OPO is characterized by a threshold condition,

defined by the pumping intensity at which the growth of the parametric wave in one

round trip in the optical cavity just compensates the total losses. Unfortunately, the low

Introduction

12

differential gain (in CW mode operation) necessitates the use of high-power CW pump

lasers with Watt to tens of Watt level. Doubly resonant oscillators (for both, idler and

signal wave), triply resonant oscillators (for all three waves) or pump-enhanced (PE-)

singly resonant oscillators (SRO) substantially reduce the threshold compared with

SRO. Typical CW pump power threshold of 100 mW are reported for PE-SROs [33].

However, this is achieved at the expenses of increased spectral and power instabilities in

the idler output arising from the difficulty in maintaining resonance for more than one

optical wave in a single cavity. Therefore, PE-SROs require active stabilization

techniques to control output power and frequency stability. As a consequence, most of

the OPO-based systems use PPLN, which shows lower thresholds compared with other

materials, in combination with singly resonant cavities. An etalon within the cavity serves

as a frequency-selective element enhancing stable single mode operation. Coarse tuning

is achieved by selection of poling period and fine-tuning is performed by varying

temperature, pump frequency, cavity length or etalon. With the use of a 3 W CW single

mode diode-pumped Nd:YAG laser at 1.064 µm, van Herpen et al. demonstrated a

tuning range from 3.0 to 3.8 µm by using a fan-out PPLN crystal in a singly resonant

cavity. The oscillator threshold was found to be 3 W and an idler power of 1.5 W (at

!=3.3 µm) was achieved for a pump power of 9 W [34]. Using a multi-grating PPLN

crystal, together with the same pump laser, provided an extended tuning range from 3.7-

4.7 µm. Unfortunately, in this spectral range the absorption of the idler wave in PPLN is

significant, causing the oscillator threshold to increase from 5 to 7.5 W and the output

power to decrease from 1.2 W at !=3.9 µm to 120 mW at !=4.7 µm [35]. Although

these tuning ranges are fairly broad, the spectrum is not always continuous. Ngai et al.

reported a continuous tuning over 450 cm-1 per poling period [36]. With a fiber-

amplified DFB diode laser, the same group demonstrated a continuous spectral

coverage of 16.5 cm-1 by pure pump source tuning [37].

The quantum cascade laser

13

1.4. The quantum cascade laser

1.4.1. Historical review of first intersubband laser

More than 35 year ago, very important developments set the basis for today’s success of

the quantum cascade laser: In 1971, Kazarinov and Suris proposed light amplification in

intersubband transitions by photon-assisted tunneling when electrons are transported

vertically through a superlattice in a multi-QW heterostructure [38, 39]. In their

proposal, electrons tunnel from the ground state of a QW to the excited state of the

neighboring QW, with the simultaneous emission of a photon (see Fig. 1.5). After a non-

radiative relaxation to the ground state, electrons are injected into the next state by

sequential tunneling. Population inversion is realized by the relative long scattering time

associated with the diagonal transition between wells (inter-well) compared with very

short intra-well relaxation.

Fig. 1.5: Principle of the first proposal of light amplification in intersubband

transitions by Kzarinov and Suris in 1971.

In the same year, A. Y. Cho and J. R. Arthur invented the molecular beam epitaxy

enabling the growth of such superlattices, where layers as thin as several monolayers can

be grown with atomic precision [40, 41]. A superlattice, first described by Esaki and Tsu

[42] in 1970, is a periodic repetition of two materials of different composition, for

example a repeated quantum well and barrier. Dingle et al. demonstrated that electrons

confined in such structures show quantization effects [43]. However, intersubband

absorption was already discovered in 1966 [44] from a two-dimensional electron gas in a

Si MOS transistor [45]. In 1976, Gornik et al. showed intersubband emission using such a

Introduction

14

structure [46]. It took a decade after the invention of the MBE until intersubband

absorption was demonstrated in a GaAs/AlGaAs multi-quantum well structure [47], and

the first observation of sequential resonant tunneling in a superlattice by Capasso et al.

in 1986 [48]. Helm et al. were the first to observe intersubband emission in the terahertz

frequency (2.2 THz), initially pumped by thermal excitation [49] and then by resonant

tunneling [50]. At that time it was assumed that intersubband lasers with a radiative

energy smaller than the optical phonon energy would be easier to realize, since ultra-fast

non-radiative relaxations via LO phonon emission would be energetically forbidden,

resulting in lifetimes two orders of magnitude larger, limited by acoustic phonons.

However, as we know today, it is much easier to operate an intersubband laser in the

mid-infrared, where the large subband energy separation makes the establishment of

population inversion less difficult and where free-carrier absorption in the waveguide is

much lower. The original proposal of Kazarino and Suris turned out to be inapplicable

for laser action due to the difficulty of obtaining population inversion and the tendency

to break up into high-field domains. The breakthrough came in 1994 at Bell Labs in the

group of Federico Capasso, where Jérôme Faist and co-workers developed the first

intersubband laser. This was the birth of the quantum cascade (QC) laser [51]. Since

then there has been an incredible fast development of QC lasers. The most significant

achievements to date are summarized in the following sections.

Operation principle of first quantum cascade laser

The first device was grown by MBE in the Ga0.47In0.53As-Al0.48In0.52As heterojunction

material system lattice matched to InP and operated at a wavelength of 4.2 µm. Lasing

took only place in pulsed mode at cryogenic temperatures with a threshold current

density of 14 kA/cm2. The bandstructure and the moduli squared of the relevant wave

functions are depicted in Fig. 1.6 for two out of 25 cascades. Each cascade consists of an

active part and a relaxation/injector region. The active part, composed of three coupled

quantum wells, is a three-level system in which population inversion between level 2 and

3 is achieved by engineering of lifetimes and optical matrix element.


15

Fig. 1.6: Bandstructure and moduli squared of the relevant wavefunctions of the

first quantum cascade laser at an electric field of 95 kV/cm, reprinted from Ref.

[51]. Each cascade of the structure consists of an active part and a

relaxation/injection region. In this three-level system, the lifetime of the optical

transition (3!2) has to be longer than the lifetime of level 2 in order to realize

population inversion.

The wavy arrow indicates the optical transition in the active part between level 3 and 2,

which is diagonal in real space. The reduced spatial separation of the overlap of the

wavefunctions increases the non-radiative relaxation time between these levels.

Depopulation of the lower laser level 2 is realized by designing the subband spacing

between level 1 and 2 equal to the optical phonon resonance energy (see Fig. 1.7), which

very efficiently empties the lower laser level 2 via electron-phonon inelastic scattering

(with nearly zero momentum transfer). This scattering is much more efficient than the

non-radiative relaxation between level 3 and 2 due to the necessary large in-plane

momentum exchange (which was also the reason for choosing the wavelength of 4.2 µm

( !!

=300 meV) since the momentum exchange decreases at higher transition energies). In

addition, the diagonal laser transition decreases also the escape rate of electrons into the

continuum.

Introduction

16

Fig. 1.7: Schematic dispersion of the subband levels 1, 2 and 3 parallel to the layers,

reprinted from [51]. The quasi-Fermi energy EFn corresponds to the population

inversion at threshold. The radiative transitions, indicated by the wavy arrows, have

essentially the same wavelength. Straight lines indicate the non-radiative LO

phonon scattering process. Ultra-fast relaxation is possible between subband levels

2 and 1 due to negligible momentum transfer.

The active part is left undoped since doping broadens the laser transition by

introducing a tail of impurity states [52]. The injector/relaxation region consists of a

digitally graded alloy superlattice (with constant period shorter than the electron de

Broglie wavelength, and varying duty cycle) to obtain a graded gap pseudoquaternary

alloy. On one hand, its purpose is to collect the carriers from level 2 and to cool down

the electron distribution by non-radiative phonon processes. On the other hand, its

function is to inject carriers into the excited state 3 of the downstream cascade by

resonant tunneling through the injection barrier. Furthermore, the injector introduces

an additional energy drop between the lower laser level and the ground state of the

cascade which is important to reduce thermal backfilling of carriers into the lower laser

level. Finally, the injector is also used as electron reservoir, ensuring that the total

negative charge is compensated by positive donors, thus avoiding the formation of

space-charge domains. Therefore, the injector region is partly n-doped with Si. The

structure is embedded in a waveguide (for details see [51]) that ensures an overlap of the

active region with the optical TM mode (which is due to the intersubband selection rules

normal to the layers polarized).


17

1.4.2. Intersubband laser versus interband laser

Intersubband lasers differ in many ways from conventional diode lasers:

• Interband semiconductor lasers (semiconductor diode lasers) rely on transitions

between energy bands in which conduction band electrons and valence band holes,

injected into the active region through a forward biased pn-junction, radiatively

recombine across the band gap (see Fig. 1.8). In contrast, the quantum cascade laser

is an unipolar device, operating with only one kind of carriers (in our case electrons),

and the optical transitions between subband states arise from size quantization

within the same band (in our case the conduction band) of semiconductor

heterostructures (see Fig. 1.6). So far, no QC lasers relying on confined states in the

valence band could be realized and only electroluminescence has been demonstrated

in p-type QC structures [53]. The unipolar property results also in a higher device

reliability (no damage due to electron-hole recombination at the facets).

Fig. 1.8: Schematic bandstructure of an interband diode laser relying on transitions

between conduction and valence band.

• Due to the opposite curvature of conduction band and valence band in interband

semiconductor lasers and Pauli’s exclusion principle, which ensures a broadly

distributed population inversion, the resulting gain spectrum is relatively broad and

asymmetric (see Fig. 1.9a). In contrast, intersubband transitions have an atomic-like

joint density of states (delta-like function when broadening is neglected) because the

subbands have same curvature resulting in narrow and essential symmetric linewidths

(see Fig. 1.9b). As will be shown later, the linewidth of a single transition of a MIR-

QC laser is mainly a result of lifetime-broadening and interface roughness scattering.

Introduction

18

Fig. 1.9: Band diagram, in-plane energy dispersion and gain spectrum of a) an

interband and b) an intersubband transition.

• In quantum cascade lasers, the emitting wavelength is not related to the band-gap of

the quantum well material. Therefore, mature materials like GaAs and InP-based

heterostructures, which are technologically mastered, can be used and one has not to

rely on temperature-sensitive small-gap semiconductors. The lower limit for the

wavelength is the conduction band offset (!50 % of its value). In principle, there is

no limit on the long-wavelength side (except within the Reststrahlen region).

• Threshold currents are intrinsically very high in quantum cascade lasers compared to

diode lasers, which is due to the ultra-short non-radiative lifetime (in the picosecond

range) of the upper state level. However, quantum cascade lasers are less sensitive to

temperature (large characteristic T0 of 130-200 K) because the upper laser state

relaxation time based on the emission of an optical phonon is less temperature

dependent compared to Auger recombination in diode lasers and the gain is only

indirectly broadened by temperature due to collisions.

• The cascade concept recycles electrons by re-injecting them into the upper laser state

of a subsequent cascade (see Fig. 1.6). Therefore, an electron can trigger more than

one photon while passing the gain material. The external quantum efficiency scales

therefore with the number of cascades and an efficiency greater than one is possible.

Furthermore, the threshold current density is inversely proportional to the number

of cascades. This is contrast to interband multi-QW lasers where adding more QWs


19

will result in an increased threshold current since a larger active region volume must

reach transparency.

• In order to avoid the formation of space-charge domains, the QC laser has to be

doped. The amount of doping defines the maximum injectable current density. This

is in contrast to interband lasers where the maximum injectable current is limited by

thermal issues or the catastrophic optical mirror damage (COMD) at the front facet.

• A very small linewidth enhancement factor is the consequence of the symmetric gain

spectrum (see Fig. 1.9b) because the Kramers-Kronig relation predicts no variation

of the real part of the refractive index for a symmetric gain shape [54-56]. This

results in a narrow laser linewidth (of a single optical transition), which should be as

narrow as predicted by the Shawlow-Townes formula modified by Henry [57, 58].

• For transition energies larger than the optical phonon resonance, the emission of

optical phonon is the dominant scattering mechanism, with (upper state) lifetimes in

the picosecond-range. The ultra-short lifetime of the upper state allows in principle

high frequency modulation in the order of 100 GHz without relaxation oscillations.

1.4.3. Different architectures of active region designs

After the birth of the quantum cascade lasers, several new active region proposals were

realized, which resulted in a dramatic improvement in performance:

• Faist et al. demonstrated a new active region design relying on a vertical transition

combined with a Bragg confinement of the upper state. In this two-well active region

design the aim of the vertical transition, i.e., with the upper and final laser state

centered in the same well, was to be less sensitive to interface roughness and

impurity fluctuations. They also introduced a new injector design that acts as Bragg

reflector at higher energies, which suppresses electrons from tunneling out of the

excited state 3 into the continuum. This device resulted in a threshold current density

of 3 kA/cm2 at 100 K [59].

• In 1996, Faist et al. presented an active region design relying still on a vertical

transition but using three coupled wells. The very thin additional well selectively

pushes the upper laser state’s wavefunction into the injector region which maximizes

the injection efficiency by increasing the overlap between the upper laser states and

Introduction

20

the ground state wavefunction of the preceding cascade. At the same time, this

narrow well reduces the overlap of the ground state with the lower laser states

reducing unintentional injection (leakage) into these states. Lasers using such a

design worked up to a temperature of 320 K [60].

• In 1997, Scamarcio et al., also at Bell Labs, used a completely different concept for

achieving gain by using a superlattice (SL) active region rather than establishing gain

between discrete energy levels. In this concept, electrons emit photons

corresponding to the energy gap (minigap) between two superlattice conduction

bands (minibands). A distinctive design feature of this concept is the high oscillator

strength of the optical transition at the mini-Brillouin zone boundary of the

superlattice. Population inversion is automatically ensured due to the very short

lifetime at the top of the first miniband (!0.1 ps) compared to the relative long

scattering time (!10 ps) from the second miniband to the first miniband, resulting

from the much larger momentum transfer for interminiband optical phonon

emission. The large oscillator strength and the high current capacity of this designs

(no level misalignment when the applied voltage is increased) favors high optical

powers (750 mW at 80 K). However, the need to dope the active SL region for

maintaining a flat SL band profile under external bias resulted in higher optical

losses, broadening of the linewidth and reduced population inversion at higher

temperatures which limited the maximum operation temperature to 240 K [61]. A

year later, Tredicucci et al. presented a chirped SL active region design which

overcomes the need to dope the active region and the doping is restricted to the

injector region. Thus room temperature operation in pulsed mode was achieved [62,

63]. This SL active region design is especially interesting at long wavelength.

Colombelli et al. showed laser operation up to 24 µm [64].

However, none of the above mentioned designs could be operated in CW at room

temperature which was the result of different reasons: Although the three-quantum-well

design demonstrates high injection efficiency into the upper laser level, it suffers from

insufficient extraction from the lower laser level. The SL active region design


21

demonstrates excellent extraction due to the very fast intraminiband scattering time but

lacks efficient current injection in the upper laser miniband. In 2001, new active region

designs were demonstrated in the Faist group addressing these deficiencies:

• The bound-to-continuum design [65] utilizes resonant tunneling injection into the

upper laser state (like in the three quantum well design) and a SL type lower laser

miniband (like in the SL active region design).

• The two-phonon resonance design [66] utilizes also resonant tunneling injection into

the upper laser level but the active part consists of four-quantum wells realizing three

lower levels that are spaced by the energy of the LO phonon resonance energy which

efficiently reduces backfilling into the lower laser state.

Today, these two designs are the most promising for high performance operation, we

will focus on them in the following.

1.4.4. Material aspects and growth techniques

As already mentioned, the realization of an intersubband lasers is not fundamentally

bound to a specific material system. Besides the original InGaAs/AlInAs/InP material

system, devices were demonstrated very soon in other heterostructure material systems

(see Fig. 1.10). Here is a brief discussion of material systems that have been explored for

QC lasers:

• In the lattice matched InGaAs/InAlAs/InP material system, used throughout the

present work, the large conduction band discontinuity of 0.52 eV allows wavelengths

as low as 4.3 µm. Furthermore, the electron masses are relatively small (InGaAs:

m*= 0.043m

0) compared with the GaAs/AlGaAs material system (GaAs:

m

*= 0.067m

0). This permits to use larger quantum well widths Lw making thickness

fluctuations less critical and leads to a larger matrix element z

ij

2! L

w

2!1 / m

* , longer

non-radiative relaxation lifetimes ! "1 / m

* and consequently a higher differential

gain g

d!" # z

ij

2!1 / m

*3 , which is about a factor of two larger than in the

GaAs/AlGaAs material system. This explains the better performance achieved with

the InGaAs/InAlAs/InP-based system for the mid-IR spectral range. The lower

Introduction

22

refractive index of InP compared with both InGaAs and InAlAs makes this material

an ideal candidate for a waveguide cladding layer. Furthermore, the binary nature of

InP provides a good thermal transport compared to ternary materials. Lasers

emitting at 3.4 µm were realized using strain compensated layers [68], where the

band offset can be extended to about 0.72 eV. Wavelengths as long as 85 µm are

presently achieved with this material system [69].

Fig. 1.10: Conduction band offset !Ec," at the " point and effective band offset

!Ec,eff of different material systems. Inset: "-valley conduction band edges of the

(Ga,In)As, and Al(As,Sb) material systems (reprinted from [67]).

• QC lasers based on GaAs/AlxGa1-xAs have been demonstrated [70]. While the

shortest possible wavelength in this system is around 8 µm, this material system is

very popular for long-wavelength QC lasers in the THz region. The main advantage

of this system is the property that regardless of the Al fraction, this material is lattice

matched to GaAs, enabling more flexible designs and somewhat relaxed growth

requirements (an Al content x=0.33-0.45 results in a !Ec," #0.3-0.4 eV). While the

higher effective mass is a penalty in terms of gain (compared with the InP-based


23

system), this results in lower free-carrier losses !

fc" #

2/ m

e

* , particularly important

for longer wavelengths. It was this material system in which the first THz laser at

67 µm was realized by Köhler et al., using a chirped superlattice design [71]. The

longest wavelength, achieved to date (without magnetic field enhancement but using

shallow barriers with x=0.1), was demonstrated by Walther et al. at 250 µm

(1.2 THz) [72].

• An alternative for short wavelengths is the lattice matched InGaAs/AlAsSb/InP

material system, which exhibits a large conduction band discontinuity !Ec,"#1.6 eV.

However, intervalley scattering ("$X) at higher transition energies results in an

effective band discontinuity !Ec,eff#0.53 eV (see Fig. 1.10). The main advantage is the

lattice matching to InP, which provides a low refractive index cladding, high thermal

conductivity and compatibility with well established quantum cascade laser

fabrication technologies. Lasers operating up to 310 K in the 3.7–3.9 µm wavelength

range have been demonstrated [73]. Laser action at 3.05 µm was observed at 20 K

[74]. Using strain balanced active region (containing more Indium in the InGaAs

layers) should result in a !Ec,eff#0.6 eV [75].

• The quasi-lattice-matched (slightly mismatched) InAs/AlSb material system grown

on InAs or GaSb substrates with !Ec,"#2.1 eV and !Ec,eff#0.73 eV ("$L) is very

promising for short wavelength QC lasers to cover the 3-5 µm atmospheric window.

Neglecting non-parabolicity, the very low effective mass m

e

*= 0.023m

0 (InAs) should

result in gain 2.5 times higher than in the InGaAs/AlInAs/InP material system [76-

78]. In the early stages, the realization of short wavelength InAs-based QCLs was

hampered by the lack of suitable waveguides [79], but finally, InAs plasmon

enhanced cladding layers and InAs/AlSb superlattice spacers enabled the fabrication

of InAs/AlSb QC lasers emitting below 3.5 µm [80]. Recently, QC lasers based on

this material system (on a InAs substrate) pushed the short wavelength frontier down

to 2.7 µm [81]. Devices operating at 3.3 µm operate in pulsed mode up to 400 K with

about 1 W of peak power at room temperature [82].

Introduction

24

• Another approach uses the strain-compensated InxGa1-xAs/AlxIn1-xAs/AlAs material

system on InP, which is closer to the original material system, and results in a

!Ec"1.3 eV at the #-point for x=0.70. The thickness of the AlAs needs to be about

1/3 that of Ga0.27In0.73As. The InAs-AlAs system grown pseudomorphically strained

on InP would result in !Ec"1.5 eV, however InAs is very challenging to grow on InP

and has the tendency to form self-organized nanostructures. Lasers based on this

material system work up to 330 K in pulsed mode (using two-component

Al0.45In0.55As-AlAs barriers in addition to pure AlAs barriers which allows to tune the

barrier thicknesses and the net strain almost independently) [83]. Recently, lasers

emitting at 3.05 µm (at 80 K) were realized using a very spatial diagonal transition

and different well materials for the upper and lower laser level [84]. This design is

beneficially because it results in a increased transition energy due to the electrical

field induced stark-shift (diagonal transition), enables the use of different well

materials for the upper (In0.55Al0.45As) and lower (In0.73Ga0.27As) laser level which

further increase the transition energy, and suppresses leakage from the upper laser

state into L or X [85].

• Optical communication would potentially benefit from the high frequency

modulation properties of QC lasers. Intersubband transitions in group-III nitrides

are of great interest for optical devices operating at telecommunication wavelengths

at $=1.3 and 1.55 µm, thanks to the large conduction band offset of ~2 eV [86, 87].

Wavelengths as short as $=1.08 µm have been observed in AlN/GaN

heterostructures grown on sapphire [88].

• While silicon diode lasers are impossible to realize due to the indirect bandgap,

Si/SiGe quantum cascade lasers are in principle possible and would pave the road for

integrated active optical components into silicon-based technology. Furthermore,

this material system should allow operation in the 20-50 µm range, not easy to access

with InP or GaAs based devices (reststrahlen band). In contrast to the other material

systems, the optical transition is designed in the valence band, which is a result of the

much lighter effective hole mass. Intersubband electroluminescence from silicon-

based quantum cascade structures was reported in 2000 [53]. However, no Si-based


25

QC laser has been realized so far. The main obstacles are accommodation of the

large built-in strain (4 % mismatch between Si and Ge lattices), the physically more

complex valence band (coupled heavy and light hole, larger effective masses),

smaller band offsets and interface roughness.

So far, the heterostructure of the active region has been grown by either solid source

[51] or gas source [89] MBE. An alternative is the metal organic vapor phase epitaxy

(MOVPE) growth technique. This technology is a widely established platform for high-

volume production of reliable semiconductor lasers since it offers several advantages:

reactors can be scaled for multi-wafer deposition; it does not require elaborate baking

cycles to recover from atmospheric contamination, resulting in long down times of the

system; growth of phosphide materials is simplified; wide range of growth rates (~1-

5 µm/h) significantly reduces growth times. In 2003, Roberts et al. demonstrated the first

atmospheric pressure MOVPE grown QC laser based on the AlGaAs/GaAs material

system [90]. In a follow-up work they demonstrated room temperature operation of a

QC laser, emitting at !=8.5 µm, based on the three-quantum-well design in the

InGaAs/AlInAs/InP material system, using low-pressure MOVPE. In order to obtain the

necessary interface abruptness and layer thicknesses, the growth rate was kept at

~0.8 µm/h (which is comparable to that of an MBE system) while the growth rate was

increased to 3 µm/h for the waveguide layers [91]. The laser performance is comparable

to that of similar MBE grown structures.

1.4.5. Continuous wave operation above room temperature

For many applications, high spectral resolution (in the MHz range) is an absolute

necessity. Therefore, the devices must be operated in CW operation in order to avoid

thermal chirp (shifting of the emission wavelength by thermal heating of the device

during the pulse). However, for almost one decade CW operation was just feasible at

cryogenic temperatures. The main limitation was bad thermal management of the

device, leading to an overheating of the active region that resulted in a reduction of

differential gain and high waveguide losses. After 2001, device performance

Introduction

26

improvements (in terms of CW operation) were mainly achieved by improving the

thermal management and optimization of the injector doping levels.

• In 2002, Beck et al. demonstrated the first QC laser operating in CW at room

temperature (up to a temperature of 312 K) with an output power of 17 mW at

292 K using the two-phonon resonance active design, emitting at 9 µm [92]. This was

facilitated by burying the waveguide in undoped InP and epi-down mounting on

diamond, resulting in a dramatic reduction of the thermal resistance of the device.

• One year later, Yu et al. reported CW operation up to 308 K of a laser emitting at

6 µm. The device was grown in a single step using gas source MBE. The active region

is based on a two-phonon extraction design similar to [66]. Instead of a buried

waveguide, they processed double-channel ridge waveguide and electroplated a

5 µm-thick Au layer on top of the ridge for heat-removal. Finally, the device was

mounted epi-up on copper submounts [93].

• In 2006, Prof. Capasso’s group at Harvard University in collaboration with AdTech

Optics Inc., Palo Alto, CA, demonstrated CW operation up to 380 and 400 K and

output powers at 300 K of 312 and 204 mW at !=5.3 and 8.4 µm, respectively [94,

95]. These outstanding results were achieved by using a combination of dry and wet

etching for producing very narrow ridges and by using Iron-doped InP for burying

the ridges. The two-phonon resonance active region design [66] was grown by

MOVPE.

• The previous mentioned results are based on the two-phonon resonance design,

which exhibits a relative small gain width of <165 cm-1 (FWHM) [96]. Spectroscopic

applications need tunable devices, preferably over a large frequency range. This

necessitates an active region design with a broad gain spectrum. In this respect, the

relative small gain width, which favors high performance operation, is a drawback. In

contrast to this, the bound-to-continuum design exhibits a FWHM of 200–300 cm-1.

Wittmann et al. presented high-performance bound-to-continuum quantum cascade

lasers, tailored for emission at !=8.6 µm, that operated CW up to 383 K [97]. This

was achieved by selective and non-selective multi-etching of the waveguide and


27

subsequent burying with Fe-doped InP. Finally, the devices were mounted epi-down

on diamond submounts. Details are shown in subsequent chapter.

• Recently, watt-level output power has been demonstrated at !=4.6 µm,

independently by two research groups: Bai et al. demonstrated 1.3 W output power at

room temperature by epi-down mounting a buried strain-balanced QC laser on

diamond. This accomplishment was achieved by optimizing the core doping and the

width of the waveguide. [98]. Lyakh et al. reached similar results by introducing a

five-quantum well active region design aiming to improve efficient injection and

extraction into/from the active region. In addition, they mounted the devices with

buried waveguides epi-down on AlN [99].

• Free carrier absorption and thermal population of the lower laser state force a strong

downward trend of the wallplug efficiency in QC lasers with increasing wavelength

[100]. However, progress has been made in increasing wallplug efficiencies in QC

lasers. Recently, Bai et al. demonstrated a record wallplug efficiency at room

temperature of 12.5 % for a MOVPE grown QC laser, emitting at !=4.6 µm, which

was processed into a 4.8 mm-long double-channel ridge waveguide device and

subsequent epi-down mounted on a diamond submount. The emitted power of this

device was 2.5 W at room temperature [101].

1.4.6. Broad-gain quantum cascade laser sources

As was already mentioned, gain in quantum cascade lasers is essentially narrow. For

many applications, a broader gain width would be desirable. However, since

differential gain is inversely proportional to the gain width, realizing a broad gain

spectrum results in higher threshold current densities. As will be shown later, the

linewidth mainly results from interface roughness scattering, which is primarily

related on the type of the transition (diagonal/vertical):

• The first QC laser, emitting at 4.2 µm and based on a diagonal transition, shows

an electroluminescence linewidth of 21 meV (FWHM) at 10 K [52].

• As expected, the electroluminescence linewidth is much narrower in a design with

a vertical transition (two-quantum-well design), resulting in only 12.4 meV

(FWHM) at 10 K [59].

Introduction

28

• The three-quantum well design, which is more a vertical than a diagonal

transition, shows a similar linewidth of 16 meV at 10 K. The linewidth increases

to 28 meV (FWHM) at 300 K.

• The two-phonon resonance design shows linewidths that are mainly bias

independent and approximately 20 meV (FWHM) at room temperature [96,

102].

• The bound-to-continuum design [65, 103] exhibits a broader gain spectrum of 18–

38 meV (FWHM), which is strongly bias depending [102]. The temperature and

bias dependent linewidths of the two-phonon resonance and bound-to-continuum

design will be discussed in detail in this thesis.

Four characteristics of intersubband transition can be combined to engineer a broad-

gain spectrum: a peak energy that can be freely selected (only limited by the choice

of material), an optical dipole matrix element that can be similarly tailored,

transparency for frequencies on either side of the laser transition, and the possibility

of cascading:

• Gmachl et al. demonstrated a so-called super-continuum QC laser, which shows

laser action between 6 and 8 µm at cryogenic temperatures. The active region

consists of 36 cascades with dissimilar optical transitions of the three-quantum

well design [60]. The peak gain was kept constant by bandstructure engineering

and the waveguide-dependent losses were compensated with the confinement

factor and the number of stacks. A broad electroluminescence spectrum of

93 meV (FWHM) centered at 6.5 µm was attained at cryogenic temperature

[104].

• Maulini et al. used a different approach: They combined two bound-to-

continuum designs resulting in a heterogeneous QC laser with an

electroluminescence width of 43 meV (FWHM). The center wavelength of the

individual stacks (20 cascades of each design) was designed for emission at

8.4 µm and 9.6 µm ensuring a spectral overlap [105]. This is in contrast to the

supercontinuum laser [104] where the individual gain regions are not overlapping

resulting in an inhomogeneous gain spectrum. In principle, an even broader gain


29

width can be engineered by combining several bound-to-continuum designs.

However, in order to end up with a homogeneous gain spectrum, both a spectral

and spatial overlap of the individual gain media is required.

1.4.7. Tunable single-mode devices

Spectroscopic applications require tunable single-mode sources. For this reason, a

frequency selective element is necessary that favors one longitudinal mode against the

others.

1.4.7.1. Distributed feedback quantum cascade lasers

Most applications use a distributed feedback (DFB) grating along the waveguide forcing

the laser to emit on the so-called Bragg frequency. A side-mode suppression ratio

(SMSR) of 47 dB (which approaches that of NIR telecom lasers) was measured from

residual transmission measurements of a CW operated DFB QC laser, emitting at

!=5.3 µm [106]. The frequency can be tuned continuously by a heat-induced change of

the refractive index. Heating can be direct by changing the device temperature ("#/"T=-

0.05 to -0.15 cm-1/K) or indirect by current heating ("#/"I=$-0.02 cm-1/mA).

• Distributed feedback quantum cascade lasers were first demonstrated by Faist et al.

in 1997 [107]. Feedback was achieved mainly by loss-coupling using the top metal

after etching the first order grating in the top waveguide cladding layer.

• One year later, Gmachl et al. presented an index coupled DFB QC laser where the

grating was etched in the upper InGaAs cladding layer of the active region which was

subsequently overgrown with InP [108]. Most of todays DFB QC lasers rely on this

concept.

• Two years after the first demonstration of CW at room temperature by Beck et al.

[92], Aellen et al. demonstrated the first CW DFB-QC laser operating on a Peltier

cooler (up to a temperature of 260 K) using the same active region design, emitting

at 9 µm [109].

• Northwestern University demonstrated CW DFB QC lasers operating up to 60 °C at

4.8 µm [110], 40 °C at 7.8 µm [111] and 50 °C at 9.6 µm [112]. This was achieved by

Introduction

30

processing double-channel ridge waveguides and electroplating them with thick Au.

The long-wavelength device was further mounted epi-down on AlN submounts.

• The relatively small temperature tuning range on a Peltier cooler of a single device

usually limits the possibilities of gas analysis. This is particularly true for complex

mixtures with multiple absorption lines or with very broad lines (typically those with

a liquid phase matrix). By using a bound-to-continuum broad-gain active region and

integrating several different DFB gratings on the same piece of gain material,

Wittmann et al. demonstrated stable single mode emission over 100 cm-1 in CW

above RT, that is from !=7.7 to 8.3 µm [113]. In the gain center, a temperature of

63 °C was attained [114]. These high-performance devices are discussed in detail

later on. Some of these lasers have been selected for the NASA Mars Science

Laboratory Mission with the goal to evaluate whether Mars was ever inhabitable.

• Based on the same concept, Lee et al. demonstrated a QC laser spectrometer which

works in pulsed mode from !=8.7 to 9.4 µm using an array of 32 buried DFB

gratings monolithically integrated into the same epi-layer [115]. They performed

absorption spectroscopy on isopropanol, acetone and methanol. The results compare

favorably with spectra obtained by a conventional FTIR spectrometer.

• Recently, single-mode QC lasers for low-power consumption applications operating

at !!9 µm in continuous wave up to 423 K (150 °C) were demonstrated. This was

achieved by the combination of strong distributed feedback coupling, a narrow gain

active region design, low intersubband and free-carrier losses as well as a good

thermal management. Tuning of 10 cm-1 was achieved by heating the device. The

threshold current density varies from 1.1 kA/cm2 at 303 K to 2.4 kA/cm2 at 423 K.

Other devices with low electrical power consumption of 1.6 W and 3.8 W for an

optical output power of 16 mW and 100 mW have been demonstrated [116]. Details

are shown in subsequent chapter.


31

1.4.7.2. External cavity tuned quantum cascade lasers

As we have seen, the tuning range of a thermo-opto-tuned DFB QC laser on a Peltier

cooler is limited and the frequency coverage can be extended by arrays of DFB lasers.

However, some applications, such as the detection of complex organic molecules or the

analysis of multi-component gases, will benefit from more broadly tunable sources.

Therefore, it is more convenient to use a broad gain Fabry-Pérot QC laser source in an

external cavity configuration, although setups are getting more complicate and bulky. In

such a setup, an external grating acts as a spectral filter and the selected wavelength is

fed-back into the laser, forcing the device to emit there. Furthermore, a good anti-

reflection (AR) coating is needed for suppressing the chip modes for extended off-gain

peak operation. In an ideal setup, the tuning range is then only limited by the bandwidth

of the gain medium.

• The first realization of an EC tuned QC laser was shown by Luo et al. The QC laser

gain chip [117] is based on the three-quantum-well design with a vertical transition

[60]. The EC setup used the Littrow configuration [118] and the uncoated chip (no

AR coating) was mounted in a cryostat with an AR coated window. Tuning ranges in

pulsed operation of 32 cm-1 and 33 cm-1 have been achieved at 80 K for two lasers

emitting at !~4.5 µm and 5.1 µm, respectively. Increasing the heat sink temperature

to 203 K reduced the tuning range to only 10 cm-1 [119]. One year later, Luo et al.

demonstrated the results of an AR coated 5.1 µm laser, with a residual reflectivity of

3-5 %. The mode discrimination was good enough to allow tuning between the FP

modes and the tuning range at 243 K could be extended to 49 cm-1 [120].

• The first Peltier cooled EC tuned QC laser was reported by Totschnig et al. [121]

using a 10.4 µm QC laser from Alpes Lasers SA. At -30 °C, they achieved a tuning

range of 7 cm-1 without using an antireflection coating.

• Maulini et al. demonstrated tuning over 150 cm-1, which is 15 % of center wavelength

(10 µm) in pulsed mode at room temperature [122]. The front facet was coated with

a quarter wave of ZnS, which resulted in a residual reflectivity of 4 %. The broad

tunability was mainly achieved by the broader gain spectrum (297 cm-1) of the bound-

to-continuum design compared with the three-quantum well and two-phonon

Introduction

32

resonance design. Due to the fact that all transitions share the same upper state,

laser action at a particular wavelength results in a homogeneous gain clamping.

However, the SMSR is very poor (<25 dB) since at the beginning of each pulse, the

chip FP modes are present.

• A year later, Maulini et al. presented a gain chip that can be operated in CW at

-30 °C in an EC setup [122]. The gain chip is based on the bound-to-continuum

design with a center wavelength of 5.15 µm. The chip could be tuned over 140 cm-1 in

single-mode operation with a SMSR>30 dB (limited by the instrument). The output

power was in excess of 10 mW over 100 cm-1. The linewidth of this laser was

examined by heterodyning it with a reference laser. The superimposed beams were

detected using high-speed room temperature mercury cadmium telluride (MCT)

detector. The beat note on the spectrum analyzer showed a width of 5 MHz

(FWHM). Although this is sufficient for most of the applications, this relatively large

value is a consequence of temperature and current fluctuations of the reference

laser. Wysocki et al. demonstrated direct absorption spectroscopy of nitric oxide

(NO) and water (H2O) with this gain chip [123]. Their setup allows mode-hop-free

tuning by simultaneous tuning of cavity length, current and angle. The narrow laser

linewidth allowed resolving two spectral peaks in NO which are separated by

0.006 cm-1.

• Using the heterogeneous QC laser structure as mentioned in 1.4.6 and applying a

broadband AR coating, consisting of YF3 and ZnSe, with very low residual

reflectivity, Maulini et al. demonstrated tuning from 8.2 to 10.4 µm (265 cm-1 or

24 %), in pulsed mode near room temperature [105]. The strong spectral and spatial

overlap of the individual gain spectra resulted in a clamping of the total gain

spectrum. However, the broad gain spectrum combined with a relatively high doping

level resulting in a large threshold current and an insufficient thermal management

disallowed CW operation.

• So far, CW operation of a gain chip in an EC configuration was limited to cryogenic

or very low temperatures on a Peltier element which makes is necessary to operate

the setup in a closed environment resulting in complicate and bulky setups.


33

Wittmann et al. developed a gain chip for high-performance broad-gain

applications, emitting at 8.4 µm [97]. Arun et al. used such a gain chip, mounted epi-

up on copper, and achieved room temperature CW operation of an EC tuned QC

laser. Single-mode tuning from 7.96 to 8.84 µm (over 126 cm-1 or 10 %), was archived

[124]. However, the extracted power was only 1.2 mW in the gain center. The output

power could be increased by a modified Littrow setup with back extraction of the

light that resulted in a power of 20 mW at the gain center. It was later found that the

submount temperature must have been much higher than room temperature due to

the large thermal resistance between submount and Peltier. Mounting the gain chip

epi-down on diamond, as described in [97], resulted in a large output power of

137 mW in gain maximum and more than 40 mW over 85 cm-1 (temperature was now

measured on the submount). However, the higher residual reflectivity of the AR

coating resulted in a reduced tuning range.

• Wysocki et al. used the gain chip developed by the group of Capasso in collaboration

with AdTech Optics (described above) [95], in their mode-hop-free EC setup. At

-30 °C, they demonstrated tuning from 7.77 to 9.05 µm (182 cm-1 or 15 %) in CW and

a maximum output power of 50 mW. Nitrous oxide (N2O), methane (CH4), sulfur

dioxide (SO2), and ammonia (NH3) are within this tuning range. This result is

attributed to the combination of a high performance QC laser gain chip, a very high

quality AR coating (residual reflectivity of 0.046 %) and a strong EC feedback [125].

• In 2008, Wittmann and Hugi et al. presented a heterogeneous high performance gain

chip for ultra-broad tuning in an EC configuration. A coarse tuning of 292 and

201 cm-1 (25 and 18 % of center frequency) was achieved in pulsed and CW operation

at room temperature, respectively. At gain maximum, 135 mW could be extracted in

CW. This gain chip represents a very promising solution for laser photoacoustic

spectroscopy (L-PAS) since it can be tuned over 172 cm-1 with output powers in

excess of 20 mW along with a room temperature operated EC setup [126]. This gain

chip is discussed in details later on. Fig. 1.11 shows tuning ranges of EC systems in

pulsed operation available from Daylight Solutions, Poway, CA. The heterogeneous

QC laser gain chips presented in this work (red curve in Fig. 1.11, marked with an

Introduction

34

arrow) have been sold by Alpes Lasers SA to Daylight Solutions, which confirmed

our measurement (see press release of Daylight Solutions [127]).

Fig. 1.11: Tuning ranges of different EC tuned QC laser gain chips. The

heterogeneous high-performance QC laser gain chip shows a tuning of 25 % in

pulsed mode with a peak power of 480 mW (red curve) [Courtesy of Daylight

Solutions].

Chapter 2

2. Theory

2.1. Fundamentals

The success of quantum cascade lasers is based on the knowledge of band structure

engineering. In the first section of this chapter, the relevant quantum mechanical models

are sketched, especially the simplifications, which are sufficient to accurately model our

devices. This includes a model to a priori calculate the temperature and field dependent

intersubband linewidth in quantum cascade laser designs. In the last section, the rate

equation approach will be presented which leads to the macroscopic accessible

quantities such as threshold current density and slope efficiency.

2.1.1. Electronic states in multi-quantum well heterostructures

The quantum cascade laser is composed of several hundred of layers of alternating

materials (indicated by A and B) that have different band-edge profiles, forming an

alternating potential V

c(z) of wells and barriers. Moreover, the layer thicknesses are in

the order of the de Broglie wavelength resulting in quantization of energy states along

the growth direction. The problem that has to be solved is the computation of these

electronic states in (planar) heterostructures. In a very efficient and elegant manner this

can be done by using the envelope function approximation [128] which allows to

separate the three-dimensional wave function ! into a slowly varying “envelope” and a

fast varying unit cell (Bloch function):

!(r) = Fl ,k!

A,B (r)l

" #ul ,k=0

A,B (r) (2.1)

Theory

36

where F

l ,k!

A,B (r) is the envelope function, u

l ,k=0

A,B (r) is the Bloch function and l is the index

of the considered bands. Furthermore, we assume that the Bloch functions are identical

in both materials, i.e. u

l ,k=0

A (r) = ul ,k=0

B (r) .

Because of the in-plane translational invariance, the envelope function can be written as:

Fl ,k!

(r) =1

Sact

eik!r!!

l(z)

(2.2)

where Sact is the sample area, k!= (k

x,k

y) is the in-plane wavevector and

!

l(z) is the

l-component envelope function. In the general case, this involves the conduction band,

the heavy-hole, light-hole, split-off valence bands and results in an eight bands model

(taking into account the spin). While it is essential to solve the full model for the

valence band, fortunately, simplification can be made if one is only interested in the

conduction band.

We start with a simple pure one-band model (Ben-Daniel Duke model) [129]. The

Schrödinger equation reads:

!!

2

2m*(z)

"2

"z2+V (z)

#

$%%

&

'(()

c(z) = E)

c(z)

(2.3)

Here, the bands are assumed to have parabolic curvatures, given by the effective mass

m*= m

0Eg/ (E

g+ E

P) . Since the Kane’s energy

E

P is very similar for different materials

(around 22 eV) and E

P! E

g, the effective mass depends mainly on the band-gap

E

g

resulting in a very low effective mass m* for low band-gap materials. Of course, the

effective mass has to be dependent on the position z, since the heterostructure is

composed by different materials. Equation (2.3) can be solved by introducing the

boundary conditions at the interface between materials A and B:

!

c

A(z) = !c

B (z) (2.4)

1

mA

* (z)

!"c

A(z)

!z=

1

mB

* (z)

!"c

B (z)

!z

(2.5)

Fundamentals

37

Including the effective mass in (2.5) ensures probability current conservation. However,

the conduction band wavefunction has a discontinuity of the slope at each interface

when the effective mass is discontinuous.

This pure one-band model works surprisingly well for thick QWs in the conduction

band, when the confinement energies E are much smaller than Eg

(or for isolated

bands like the heavy hole valence band). However, it fails to predict the levels in our

laser devices since at least the upper laser state lies close to the top of the barrier.

We now want to refine our model by taking into account an effective valence band

(substituting the light hole, heavy hole and split-off bands). Neglecting the in-plane

momentum k!= 0 , the wavefunction for this two-band model reads:

!(r) = "c(z) #u

c,k=0(r) + "

v(z) #u

v ,k=0(r) (2.6)

Instead of treating this model now as a full two-band model, only the conduction band

wavefunction !

c(z) has to satisfy the modified Schrödinger equation:

!!

2

2

""z

1

m*(E, z)

""z

+V (z)#

$%%

&

'(()

c(z) = E)

c(z)

(2.7)

whereas the contribution of the valence band is taken into account by an energy

dependent effective mass [130]:

m*(E, z) = m

*(z) 1+E !V (z)

Eg,eff

"

#$

%

&'

(2.8)

where the effective band gap E

g,eff= !

2 / (2!m*(z)) is related to the nonparabolicity

coefficent ! . This model is called effective one-band model, since we finally end up again

with a one-band model but considering the valence band by the energy dependent mass.

Note that this energy dependent mass causes non-parabolicity since the energy

dispersion E

c(k) = E

c(k = 0) + !2

k2 / (2m

*(E, z)) (which is the solution of (2.7)) is not

anymore parabolic. The edge of the well material is taken as zero point for the electron

energy E. V (z) will be replaced by zero in case of a well and by the conduction band

Theory

38

discontinuity in case of a barrier. Of course, the boundary conditions are the same as for

the one band model but now taking into account an energy dependent mass. However,

the conduction band wavefunction !

c(z) is not the complete envelope function.

Therefore, the conduction band wavefunction must be normalized, taking into account

the valence band [131]:

!c1+E " E

c(z)

E " Ev(z)

!c

= 1 (2.9)

The effective one-band model, which is used in our calculations, is accurate enough to

predict the resonance energies Ei (i is the subband index) with a typical error of a few

meV, which is less than the uncertainty introduced by growth fluctuations. A comparison

with the pure one-band model is shown in Fig. 2.1.

Fig. 2.1: Computation of the energy levels E

i and conduction band wavefunctions

!

c,i in a 90 nm-wide QW applying the pure one-band model (dashed lines) and the

effective one-band model (solid lines) using m

InGaAs

* =0.0427 m

0,

m

AlInAs

* =0.076 m

0

and a non-parabolicity coefficient ! =1.13 x 10-18 m2.

Fundamentals

39

The influence of the valence band also has to be considered when calculating the matrix

element zij= !

iz !

j of the optical transition between an initial | i! and a final state

| j! [131]:

zij=

!i!

2(Ei! E

j)

"c,i

pz

1

m*(E

i, z)

+1

m*(E

j, z)

pz"

c, j

(2.10)

where the momentum operator is defined as p

z= !i! "

"z.

In order to drive current through the laser structure, an external bias !V (z) has to be

added to the pure heterostructure band-edge profile V

c(z) . Furthermore, the Hartree

potential V

H(z) must be considered for accurate predictions:

V (z) =V

c(z) + !V (z) +V

H(z) (2.11)

The Hartree potential results from ionized donors (that are needed to avoid the

formation of space-charge domains) and conduction electrons that result in a local

charge density:

!(z) = q0

ND

(z) " ni#

i(z)

2

i

$%

&'

(

)*

(2.12)

where N

D(z) is the doping profile of ionized dopants and

n

i is the sheet carrier density

in the ith subband. The Hartree potential is computed from !(z) using Poisson’s

equation:

!2V

H(z)

!z2

= "#(z)

$$0

(2.13)

The electonic densities n

i on the subbands depend on the transport through the device

and are therefore not known. However a good approximation is to assume that the

electron distribution is thermal, based on a Fermi-Dirac distribution and a common

chemical potential ! (measured from the ground state of each period), and that charge

neutrality is achieved in each period:

Theory

40

ni=

i

! Di(E) f

dist(E) dE"

i

! (electrons)

= N

D(z) dz = n

s! (dopants)

(2.14)

where the density of states Di(E) = m*(E) / (!!2 ) "#(E $ E

i) is the density of states in the

ith subband and !(E " E

i) is the Heavyside function, f

dist(E) = (1+ exp([E ! !] / kT )!1 is

the Fermi distribution function, and n

s is the total carrier sheet density. Since the

Hartree potential is a function of the conduction band wavefunction and therefore of

the solution of the Schrödinger equation, both Schrödinger’s and Poisson’s equation

must be solved iteratively until convergence is achieved.

2.1.2. Intersubband absorption and gain

In this section we consider possible transitions within quantized states and derive an

expression for the intersubband absorption, which will be further used for the

calculation of gain in QC structures. The interaction between the electronic system and

a polarized electromagnetic (EM) field gives rise to scattering events of electrons from

one state to another and results in absorption (or emission) of photons. We start from

Fermi’s golden rule for the transition rate from a state | i,k

!! to a state | j,k

!

' ! .

W

ij ,k!k!

'=

2!

""

i,k!

H ' "j ,k!

'

2

# Ej(k!

' ) $ Ei(k!) ± "%( )

(2.15)

where the upper sign is for emission and the lower sign for absorption of a photon and

H ' is the perturbation Hamiltonian. This is schematically illustrated in Fig. 2.2a. To

calculate the absorption rate from state | i! to all possible final states | j! , one has to sum

over all electronic states:

Wabs,i

=2!

!"i,k"

H ' "j ,k"

'

2

# Ej(k"

' ) $ Ei(k") $ !%( )

k"k"

'

&j

& ' fdist,i

1$ fdist, j( )

(2.16)

where the Fermi-Dirac function f

dist,i= f

dist(E

i(k!)) represents the probability that the

initial state is occupied and 1! fdist, j( ) the probability that the final state is empty. The

Fundamentals

41

corresponding emission rate W

em can be simply derived by inverting the probability

functions.

Fig. 2.2: Schematics of a scattering event a) from an initial state | i,k

!! to a final

state | j,k

!

' ! and b) from an initial | i! to a final state | j! having same momentum.

The absorption coefficient is defined through the ratio of the absorbed energy per unit

volume and time !! "W

net/ V (with the net total rate

W

net=W

abs!W

em) and the average

intensity I, where the volume V = S

act! L

p (

L

p is the length of one period of the QC laser

active region). The absorption coefficient !

ISB= !" #W

net/ (S

act# L

p# I ) summed over all

occupied initial and empty final states results in:

!ISB!"( ) =

!"

LpSactI

2#

!$i,k"

H ' $j ,k"

'

2

% Ej(k"

' ) & Ei(k") & !"( )

k"k"

'

'ij

' ( fdist,i

& fdist, j( )

(2.17)

The perturbation Hamiltonian can be written as:

H ' = !q

0

m0

A " p (2.18)

The vector potential A is related to the polarized EM wave E = E0! cos(kr "#t) ( E

0 is

the electrical field amplitude, ! is the polarization vector and k is the wavevector) by

E = !"A / "t and reads:

A =

iE0!

2"ei(kr #"t)

+ c.c. (2.19)

Theory

42

Since the ! ! L

p (

L

p is the characteristic dimension over which the wavefunction

spreads, which is in the case of the QC laser at maximum the length of one cascade), the

dipole approximation can be applied and the matrix element in (2.17) can be written:

!i,k!

H ' !j ,k!

'

2

=q

0

2 E0

2

4m0

2"

2!

i,k!

# $ p !j ,k!

'

2

(2.20)

Using (2.1), the matrix element in (2.20) can be separated in the following way:

!

i,k!

" # p !f ,k!

'= " # u

vp u

cF

i,k!

(z) Fj ,k!

'(z) +" # u

vu

cF(z)

i,k!

p Fj ,k!

'(z)

(2.21)

where c and v are the band indices. Since our transitions are within the same band, the

Bloch functions have same parity and therefore, the first term in (2.21) vanishes (in

contrast to interband transitions where there is a change in parity because u

v(r) ! u

c(r) ).

In the second term, the overlap integral of Bloch functions becomes unity and it remains

the dipole matrix element of envelope functions, which reads with (2.2):

F(z)i,k!

! " p Fj ,k!

'(z) =

1

Sact

eik!r!#

i(z) !

xp

x+!

yp

y+!

zp

z

1

Sact

eik!

' r!#

j(z)

(2.22)

Only the z-component remains since the contributions in x and y direction vanish. As a

result, the polarization of the electromagnetic field has to be in z direction (growth

direction, TM polarization) in order to couple to the electronic system. Exactly this is

the polarization selection rule for intersubband transitions. Liu et al. validated this result

in a photocurrent experiment where they found that the absorption of TE polarized light

was only 0.2 % of the TM one [132]. Furthermore, initial and final states must share the

same momentum k!= k

!

' , which is nothing else than the momentum conservation,

depicted schematically in Fig. 2.2b. Inserting the remaining matrix element into (2.20)

and substituting the momentum matrix element with the position matrix element results

in:

!

i,k!

H ' !j ,k!

'

2

=

q0

2 E0

2 Eij

2

4"2"

2z

ij

2

#k!k!

'

(2.23)

Fundamentals

43

Now we can insert our result into (2.17) together with the average intensity

I =

1

2E

0

2n

eff!

0c ( n

eff is the refractive index, c is the speed of light) and the absorption

coefficient reads:

!ISB!"( ) =

2# 2q0

2

$0n

eff%

0L

pS

act

zij

2

& Ej(k"

' ) ' Ei(k") ' !"( ) f

dist,i' f

dist, j( )k"

(ij

( (2.24)

Taking into account the in-plane symmetry, one can replace the sum with an integral

over all k!-states:

1

Sact

=1

(2! )2k!dk!

0

"

#k!

$ . Including the double spin occupation by a

factor of two, the absorption coefficient can be written:

!ISB!"( ) =

q0

2

#0n

eff$

0L

p

zij

2

% Ej& E

i& !"( ) f

dist,i& f

dist, j( )k" dk0

'

(ij

) (2.25)

Solving this equation for the case of parabolic bands would result in an infinite value. In

reality, scattering processes result in broadening which can be usually described by

replacing the delta-function with the Lorentzian function with a half-width at half

maximum (HWHM) of !

ij:

L !!( ) ="

ij/ #

!! $ Eij( )

2

+ "ij

2

(2.26)

Integrating over the Fermi-Dirac distributions, an analytical solution can be

derived [133]:

!ISB!"( ) =

q0

2kT

2#0cneff!L

p

fijln1+ exp [! $ E

i] / kT( )

1+ exp [! $ Ej] / kT( )

%

&

''

(

)

**ij

+ ,L !"( ) (2.27)

where µ is the chemical potential and the oscillator strength has been introduced which

reads:

fij= 2m0Eij

!2zij

2

=2

m0Eij

!ipz!j

2

(2.28)

Theory

44

As can be shown for transitions between the first two states in a QW, the oscillator

strength is proportional to the inverse effective mass f21!1 / (m* / m

0) and is therefore

very helpful in comparing different materials. For example in an infinite QW with an

energy spacing of !E

21= (22

"12 )!2#

2 / (2m*L

w

2 ) for the first two states and the

corresponding matrix element of z21= 16L

w/ (9! 2 ) , the resulting oscillator strength

f21= 0.96 / (m* / m

0) . An interesting property of the oscillator strength is that it obeys the

sum rule j

fij= m

0/ m*

! where downward transitions have negative sign. As a

consequence, upwards transitions have an oscillator strength that increases with the

initial state index i and therefore, transitions between excited states naturally yield larger

intersubband absorptions.

Gain between subbands is defined simply as negative absorption g(!! ) = "#(!! ) .

Assuming parabolic subbands and a Lorentzian lineshape for the optical emission

(which includes the Fermi-distributions in the states i and j), the material gain [in cm-1]

between states | i! and | j! can be written as:

G !!( ) =2" 2q

0

2 zij

2

#0n

eff$

0L

p

% nj& n

i( ) %L (E & Eij,'

ij)

(2.29)

where the difference in carrier sheet density

nj! n

i( ) in subbands i and j replaces the

term ( f

dist,i! f

dist, j) / S

act in (2.24). The peak material gain reads:

Gp=

4!q0

2 zij

2

"0n

eff#

0L

p

1

2$ij

% nj& n

i( )

(2.30)

Note, that the peak material gain is inversely proportional to the linewidth. This

equation shows that the gain theoretically can be arbitrarily large depending on the

ability to efficiently inject current in the upper laser state. Replacing the carrier density

by the pumping current J = q

0n / ! (and assuming that the lower laser level is depleted)

leads to the value of differential gain [in cm/kA]:

Fundamentals

45

gd=

Gp

J= !

up

4"q0

zij

2

#0n

eff$

0L

p

1

2%ij

(2.31)

where !

upis the effective upper state lifetime.

As we have seen, one needs an overlap of the (TM polarized) optical mode and the gain

region. As a consequence, only the part of the optical mode overlapping with the gain

medium contributes to the modal gain. The modal gain reads G

M!!( ) = G

P!!( )" ,

where ! is the overlap factor. Another important quantity is the gain cross section

gc= G

M/ !n [in cm], which will later be used in the rate equation approach.

2.1.3. Inter- and intrasubband scattering processes

A proper understanding of inter- and intrasubband scattering between energy states in

QC lasers is essential for the engineering of population inversion and gain. Electrons in

excited subbands can scatter to lower subbands by various ways: Radiatively by

spontaneous emission of a photon, or non-radiatively by longitudinal optical (LO) and

acoustic (LA) phonons, electron-electron interactions, impurities and interface defects.

Fig. 2.3: Schematics of a) intersubband scattering between states | i! and | j!

spaced by more than the LO phonon energy: shown are the stimulated emission of

a photon with E21 and the dominant non-radiative scattering induced by LO

phonons, and b) intrasubband scattering of a LO phonon.

Theory

46

For subband spacings larger than the optical phonon energy !!

LO, the most efficient

scattering process is the emission of LO phonons [134, 135] (see Fig. 2.3a).

Intrasubband scattering of LO phonon can also happen when the thermal energy

exceeds the phonon energy (Fig. 2.3b). Although elastic scattering (allow disorder and

interface roughness) adds to the scattering rate [136], this contribution to the

intersubband scattering is small compared to inelastic LO phonon scattering and is

neglected in our model. However, as will be shown later, interface roughness will be

considered in the linewidth broadening.

Spontaneous emission

Spontaneous emission between an initial | i! and a final | j! state is possible when the

matrix element is non-zero. The spontaneous emission rate can also be derived from

Fermi’s golden rule and reads for a single polarization mode [137]:

Rij

sp=

1

!sp,ij

=

q0

2neff

zij

2

Eij

3

3"c3#

0!

4

(2.32)

Fig. 2.4: Radiative spontaneous lifetime versus transition energy E

21 in an infinite

QW with an oscillator strength f

21= 22 .

Fundamentals

47

Equation (2.32) gives the impression that the spontaneous carrier lifetime is inversely

proportional to the cubic of the energy; however, this is not the case: using the oscillator

strength (2.28), formula (2.32) can be rewritten:

Rij

sp=

1

!sp,ij

=

q0

2neff

fijE

ij

2

6"m0c3#

0!

2

(2.33)

which shows that !sp

is inversely depending on the square of Eij

(see Fig. 2.4). For a

typical mid-IR wavelength of 8 µm, !sp

is in the order of 40 ns which is very long

compared to the non-radiative lifetime !

non, which is in the ps range. This results in a

fairly poor radiative efficiency !rad

= (1+ "sp/ "

non)#1 $ 10#5 and therefore, an intersubband

light emitting diode (LED) is not very efficient.

LO phonon scattering

Since the dominant non-radiative scattering mechanism in our devices is the emission of

LO phonons, we are only considering this scattering mechanism in our calculations.

Since the density of electrons in the subband of the upper laser state is very low

(!1011 cm-1), we assume the electrons to be at k!=0 in this subband. Following the

approach of Ferreira and Bastard for dispersion-less bulk phonons, which neglects any

heterostructure effects on the phonon dispersion [134], the scattering rate for the

spontaneous emission of LO phonons at a temperature of 0 K reads:

Rij

LO=

1

!LO,ij

="m*q

0

2#LO

!2$

pQ

ij

dz dz '%i(z)%

f(z)e

&Qij

z& z '%

i(z ')%

f(z ')''

(2.34)

where !

p

"1= !

#

"1" !

s

"1 and Q

ijis the in-plane momentum defined as

Q

ij= 2m

*(Ei! E

j! !"

LO) ! (2.35)

As one quickly sees from (2.34), the smaller the in-plane momentum Q, the shorter the

LO scattering time; or the closer the transition energy to the energy of the optical

phonon !!

LO(InGaAs: 34 meV), the faster the non-radiative depopulation. The

resulting scattering times are in the ps range. Setting Q=0 results in lifetimes in the

order of !

LO,ij=0.25 ps. Note however, that (2.34) is based on Fermi’s golden rule and is

Theory

48

not able to compute an exact value at resonance. Interesting to note is the inverse

dependence of the effective mass on the scattering time: !LO

"1 / m* , resulting in

larger lifetimes for small-gap materials.

In the end, we are interested in the non-radiative lifetime !

non,ij(T ) at temperature T.

Therefore, we need to include absorption and stimulated emission of LO phonons in our

calculations. For intersubband transitions, the LO phonon scattering rate reads then:

1

!non,ij

(T )=

1

!LO,ij

nLO

(T ) +1

!LO,ij

1+ nLO

(T )( ) (2.36)

where the first term on the right hand side stands for the absorption and the second part

accounts for the emission (including spontaneous events) of LO phonons. The phonon

population n

LO is given by the Bose-Einstein factor:

nLO

(T ) =1

exp(!!LO

/ kT ) "1

(2.37)

The Bose-Einstein factor is the origin for the weak temperature dependence in QC

lasers (see Fig. 2.5). Nevertheless, this quantity is one of the dominating factors that

reduce differential gain with increasing temperature.

Fig. 2.5: Ratio of lifetimes !

non,ij(T ) / !

non,ij(0K) for a phonon energy of

!!LO

=34 meV.

Fundamentals

49

Finally, we can calculate the lifetime of a state | i! by simply summing over all possible

final states j:

1

!i

=1

!ijj

" (2.38)

LO phonon scattering can also happen within the same subband. Intrasubband

scattering happens on a much faster scale since the in-plane momentum Q is much

smaller. The spontaneous emission lifetime !

LO,ii is computed by taking the same initial

and final state in (2.34). However, the number of photons which have sufficient energy

above the optical phonon is reduced. Consequently, the probability to emit an optical

phonon decreases exponentially with the optical phonon energy (Bolzmann

distribution). Considering this in (2.36) results in the intrasubband lifetime of state | i! :

1

!non,ii

(T )=

1

!LO,ii

nLO

(T ) +1

!LO,ii

1+ nLO

(T )( )exp"!#

LO

kT

$

%&'

()

(2.39)

The intrasubband lifetime is a quantity that will be utilized in the computation of the

linewidth of intersubband transitions.

2.1.4. Intersubband linewidths

The finite upper state lifetime and inhomogeneities transform the linewidth from a delta

function to a linewidth with a finite energy width, normally assumed to be Lorentzian.

The standard procedure for calculating gain (see (2.29)) relies on the empirical fit of

experimental data of electroluminescence linewidth 2!

ij, which are not known for new

active region designs.

In this thesis, a model will be presented to a priori calculate the temperature and field

dependent intersubband linewidth of the optical transition in QC laser design. In our

model, we consider lifetime broadening due to LO phonon and interface roughness

scattering. Since the electron densities in our QC lasers are fairly low ( n

s! 10

!11 cm-2)

and the relatively wide band-gap E

g of InGaAs compared with the intersubband

Theory

50

transition energy E

ij, the broadening of the linewidth due to non-parabolicity

!

non-parab" E

F# E

ij/ E

g, where E

F is the fermi level, is small [138]. Furthermore, impurity

scattering is also insignificant since the doped region is separated from the optical

transition.

Lifetime broadening is due to ultrafast intra- and intersubband relaxations. Only inter-

and intrasubband scattering of LO phonons are taken into account since this is the

dominant scattering mechanism in mid-IR QC lasers (seen in previous sections). The

total lifetime broadening reads [133]:*

2!opt

= ! "inter

#1+ 2"

intra

#1( ) (2.40)

where !inter

equals the lifetime of the upper laser state and !intra

is the intrasubband

scattering of the same. Essential is that lifetime broadening contributes half as much to

the broadening as does pure dephasing. Furthermore, note that intrasubband scattering

contributes much stronger to the total broadening since !inter

> !intra

.

Campman et al. observed in an intersubband absorption experiment that by narrowing

the QW width, the linewidth increases, which in case of lifetime broadening should

decrease (from (2.34) follows that a larger energy spacing results in a larger lifetime).

They attributed this to interface roughness scattering, arising from monolayer

fluctuations of QW interfaces [139]. Unuma et al. showed theoretically and

experimentally that interface roughness is the dominant scattering mechanism in QWs

[140, 141]. Their model is based on a statistical description of the interface roughness

assuming that the roughness height !(r) at the in-plane position r = (x, y) along the

interface has a correlation function:

!(r)!(r') = !2 exp" r " r'

2

#2

$

%&&

'

())

(2.41)

*Following the literature, although this is only correct for an infinite lower laser state lifetime. In our structures,

the finite lower laser lifetime would add to the linewidth broadening but this does not change the general

interpretation of the data.

Fundamentals

51

where ! is the mean height of the roughness and ! is the correlation length. We first

consider a single quantum well with energy states | 0! and |1! . The difference of the

intrasubband scattering matrix elements results in roughness broadening [140]:

! IFR=

m*"2#2

!2

F00$ F

11( )

2

d%e$q2#2/ 4

0

&

' (2.42)

where F

mn= (!E

m/ !L

w) " (!E

n/ !L

w) expresses the influence of the interfaces on the

energy levels and Lw

is the quantum well width. The interface parameter product !" is

fixed for a given set of epitaxial growth parameters. The two-dimensional scattering

vector q = k ! k ' is defined as

q2= 4m

*E / !2

! (1" cos#) and ! is the scattering angle. It

is interesting to note that, apart from the additional angular dependence, transport

broadening !

tr= ! / "#

tr$ = !q

0/ µm

*( ) differs from (2.42), mainly by the term F

00 which

replaces F00! F

11( ) for the optical transition, where F

11> F

00 (in the infinite barrier

approximation, F11

is four times larger than F00

). Although the intersubband

scattering element F01

(which replaces F00! F

11( ) in (2.42)) formally adds to the

interface roughness broadening, its contribution is much smaller (due to a much larger

q2 , that differs from the above one) and is neglected. Note that the interface roughness

is proportional to the effective mass and scales quadratically with the band offset.

When the wavefunctions extend over several interfaces k, one has to take into account

all those interfaces. Substituting F

nn

k= !U "

c(z

k)

2

(where !U is the conduction band

offset and !

c is the wavefunction), considering that the integral approaches ! for

typical values of ! and assuming further that the interfaces are uncorrelated to each

other, the roughness broadening can be written [142]:

!ij

IFR="m*

!2#2$2%U 2 &

i

2 (zk) ' &

j

2 (zk)(

)*+

k

,2

(2.43)

Theory

52

In this model, interface roughness broadening is treated as lifetime broadening due to

elastic scattering of conduction electrons (homogeneous broadening) following the

theory of Ando for transport properties [143]. Khurgin presented an inhomogneous

model for interface roughness broadening in which the momentum selection rule is

relaxed by the interface roughness allowing for non-vertical intersubband transitions

[144]. His formula deviates by a factor of 1.6 from (2.43), which is attributed to the

Gaussian rather Lorentzian lineshape.

The linewidth of the optical transition between states | i! and | j! reads then:

2!

ij= 2 !

opt+ !

ij

IFR( ) (2.44)

In our structures, not only the wavefunctions extend over several interfaces but also

several optical transition needs to be considered. In order to calculate the lineshape of

the multi-optical transition power spectrum L

spon(E) , each optical transition with its

specific Lorenzian lineshape, has to be weighted by the oscillator strength and the cubic

energy:

Lspon

(E) ! Rij

sp " Eij"L (E # E

ij,$

ij) !

j

% fij" E

ij

3 "L (E # Eij,$

ij)

j

% (2.45)

As will be shown later, the correct linewidth for different active region designs could be

calculated [102]. However, one has to be aware that gain (2.29) has a different lineshape

for multi-optical transitons:

Lgain

(E) ! fij" n

i# n

j( ) "L (E # Eij,$

ij)

j

% (2.46)

For the active region designs considered here, one can neglect the lower state

population (strong inversion) and the gain spectrum can be extrapolated from the

spontaneous emission power spectrum:

L

gain(E) !

Lspon

(E)

E3

(2.47)

Fundamentals

53

2.1.5. Rate equation approach

The macroscopically accessible quantities such as threshold current density and slope

efficiency of the QC laser can be derived in a very simple way using a rate equation

approach, which considers the time evolution of populations (carrier sheet density per

cascade [in cm-2]) in the upper and lower laser state coupled to the photon flux S

(defined per cascade and active region width [in cm-1s-1]). Fig. 2.6 depicts a schematic

illustration of the rate equation approach, where the upper and lower state lifetimes

read |!3" and

|!

2" and the lifetime between those states is

|!

32" .

Fig. 2.6: Schematic illustration of energy states and lifetimes in the rate equation

approach.

The rate equations for one cascade read as follows [145]:

dn3

dt=

J

q0

!n

3

"3

! Sgc(n

3! n

2)

(2.48)

dn2

dt=

n3

!32

+ Sgc(n

3" n

2) "

n2" n

2

therm

!2

(2.49)

dS

dt=

c

neff

gc

n3! n

2( ) !" tot

non-res( )S + #n

3

$sp

%

&''

(

)**

(2.50)

where ! is the fraction of spontaneous emission coupled into the lasing mode, !

sp is the

spontaneous emission lifetime, !

tot

non-res are the non-resonant total losses and

n

2

therm= n

gexp(!"

inj/ kT

el) represents an approximation for the thermal population

Theory

54

(backfilling) of the lower laser level. In the last equation, n

g is the sheet doping density

of the injector, T

el is the electronic temperature and

!

inj the energy difference between

the lower laser state and the Fermi level of the injector’s ground state | g! . Note that the

lifetime due to stimulated emission is !stim

= (Sgc)"1 .

Below threshold, S is zero (the contribution of the spontaneous emission can be

neglected since !sp! !

3), and from (2.48) an expression which relates the upper state

population and the pumping current is derived:

n

3= J!

3/ q

0 (2.51)

The population inversion as function of pumping current is obtained from (2.49) using

(2.51) and n

2= n

3! "n :

!n =J"

3

q0

1#"2

"32

$

%&'

()# n

2

therm=J"

eff

q0

# n2

therm

(2.52)

where the effective upper state lifetime !

eff= !

3(1" !

2/ !

32) relates the population

inversion to the pumping current. !

eff converges to the upper state lifetime

!

3 when

!

32! !

2, and then !n converges to

n

3 when backfilling is negligible.

The threshold condition is derived from (2.50) by setting the derivative to zero and

neglecting the contribution of the spontaneous emission. The population inversion at

threshold reads:

!n

th= n

3" n

2( ) = #

tot

non-res/ g

c (2.53)

with the non-resonant losses defined as:

!

tot

non-res= "!

ISB

non-res+!

wg

empty+!

m,f+!

m,b (2.54)

where !

wg

empty are the free carrier losses in the waveguide (excluding any doping in the

active region) and !

m,i are the mirror losses of front and back facet. The finite linewidth

of the (off resonance) intersubband absorptions in the active regions results in

absorption at the lasing wavelength that is taken into account by !"ISB

non-res . In a similar

Fundamentals

55

way, one can replace the thermal population of the lower laser level with an equivalent

(resonant) loss term: n

2

therm= !"

ISB

res/ g

c, where

!

ISB

res

c are the intersubband losses at

resonance. Since the carrier populations of all the energy levels are known, calculating

the intersubband absorption using (2.27) is much more precise than assuming a two level

system and all the carriers in the ground state. The threshold current density can be

attained by replacing the population inversion in (2.52) with the threshold condition

(2.53):

Jth=q0

!effgc

"tot

non-res+ #"

ISB

res( ) =q0"tot

!effgc

="tot

#gd

(2.55)

where the gain cross section is replaced with the differential gain using (2.31) and (2.52).

!

tot= !

tot

non-res+ "!

ISB

res indicates that the threshold current density also has to compensate

the resonant losses.

Now, we consider the situation above threshold. The photon flux is obtained from (2.49)

by setting the derivative to zero. Since the gain is clamped above threshold one can

substitute the population inversion by the threshold condition (2.53). One is tempted to

use (2.51) to replace n

3, however this equation is only valid below threshold. Instead of

that one has to derive n

3 from (2.48) which results in

n

3= !

3J / q

0" S#

tot

non-res( ) . The

photon flux can then be written as:

S =J !"

totq

0/ (g

c#

eff)( )# eff

q0"

tot

non-res (#eff+ #

2)

=J ! J

th( )# eff

q0"

tot

non-res (#eff+ #

2)

(2.56)

Note, that the photon flux is independent of the resonant losses. So far, all the quantities

are related to a single cascade. The total power within the laser cavity, which takes into

account N

p cascades, is

P

in= N

p!!" ! S ! w

act (

w

act is the active region width). The

emitting power from the front facet reads: P

out= P

in(1! R

m, f) (assuming that the back

facet is high-reflection coated). A very important quantity is the slope efficiency

dP

dI,

Theory

56

which is proportional to the number of cascades and also to the internal ( !

int) and

external ( !

ext) quantum efficiencies:

dP

dI= N

p!! "#

m,f

dS

dI= N

p

!!

q0

#m,f

#tot

non-res

$eff

$eff+ $

2

= Np

!!

q0

%ext%int

(2.57)

2.2. Design Parameters

In this section, the relevant electrical, optical and thermal design parameters in QC

lasers will be presented, giving the background for understanding the difficulties that

need to be overcome for achieving the goals of this work.

2.2.1. Electrical point of view

From equations (2.55) and (2.57) it is clear that an active region design for a low-

threshold and high-efficient QC laser should have the following properties:

• Large oscillator strength f

32

• Large upper state lifetime !

3

• Large ratio between !

32/ !

2

• Low intersubband losses !

ISB

• Narrow transition linewidth !

32

Furthermore, the following issues need attention:

• Thermionic emission of carriers from the upper state into the continuum

• Efficient injection in the upper laser states and quenching of scattering into the

lower laser state

• The escape time !

esc from the lower states into the injector

To date, the most promising active region designs for high performance are the two-

phonon resonance and bound-to-continuum design, invented in 2001 [65, 66]. Based on

the band diagram of the two-phonon resonance design, depicted in Fig. 2.7, the relevant

parameters will be discussed.

Design Parameters

57

Fig. 2.7: Band diagram of the two-phonon resonance design. The radiative

transition takes place between the states | 3! and | 2! . The states | 2! , |1! and |1'!

are spaced by the optical phonon energy !!

LO. !

inj is the energy seperation

between the ground state | g! and the lower laser state | 2! . The crosses indicate

scattering events that are strongly suppressed in this design.

Injection efficiency

Injection in the upper laser state is achieved by resonant tunneling through an injection

barrier from the ground state | g! into the upper laser state | 3! . Special care has to be

taken to ensure a good injection efficiency while quenching injection into the lower laser

state | 2! . If !

3 significantly deviates from unity, the population inversion in (2.52) needs

to be modified: !n = J / q0" #

3$31% #

2/ #

32( ) % #

2$2

&' () . This problem has been successfully

solved in the two-phonon resonance and bound-to-continuum designs by introducing a

thin well close to the injection barrier. This approach not only results in a deeper

penetration of the wavefunction of | 3! into the injector barrier, and therefore ensures a

good injection efficiency, it also ensures a strong spatial separation of the injector

ground state and the lower laser level, avoiding leakage into the latter.

Theory

58

Oscillator strength and upper state lifetime

The upper state lifetime !

3 cannot be engineered independently from the oscillator

strength since both are coupled: a vertical transition results in a good overlap of

wavefunctions, compared to a diagonal transition, and therefore in a large oscillator

strength f32

, while the lifetime will be approximately half the value of the diagonal

transition. In general a more diagonal transition results in a higher product f

32!

3.

However, a diagonal transition broadens the linewidth due to more interface roughness

scattering. Since the product f

32!

3" (m*)#3 2 , a large product can be attained by choosing

a material system with a low effective mass. Therefore, the InGaAs/InAlAs/InP material

system is a good choice. The matrix element can be further increased by use of excited

states for the laser transition. !

3 can be extended by suppressing leakage into the

continuum. The simplest way would be to increase the thickness of the downstream

barrier. However, this would also reduce the escape time !esc

from the lower states of

the gain region into the injector and therefore this approach is not advised. In a very

efficient way leakage can be suppressed by designing the injector as a Bragg mirror for

the upper state, which has a large minigap around the upper laser state and a miniband

where the lower states of the gain region are situated, ensuring a high escape rate into

the injector (see Fig. 2.7). When the energy of the upper laser state is close to the band

edge, electrons can be thermally activated to continuum states. In order to avoid this,

one can increase the barrier by using strained structures (necessary for QC lasers

emitting in the 5-6 µm range in the InGaAs/InAlAs/InP material system) or move to

material systems with larger band discontinuity.

Lower laser state lifetime and depopulation

An ultra-short lifetime !

2 results by designing the spacing between the states | 2! and |1!

resonant to the optical phonon energy. However, one should not forget that the

extraction barrier of the gain section (see Fig. 2.7) poses an obstacle for fast extraction

of carriers out of the gain region since the escape time !

esc> !

2. Thus, thermal

population can result in backfilling of scattered electrons into the lower laser level. A

Design Parameters

59

very efficient solution has been found, which gave the two-phonon resonance design its

name, where a ladder of three states (instead of just two) spaced by the energy of the

optical phonon are used which significantly reduced the population of the lower laser

state. The bound-to-continuum design uses another approach: Instead of three discrete

levels, it uses a miniband that spans the full length of the cascade. The lifetime !2 of the

upper state in the lower miniband is very short since the large phase space allows for

scattering to any point in the miniband. The upper state is created within the first

minigap by inserting a narrow QW at the beginning of the cascade.

Resonant and non-resonant intersubband losses

The active region has to be doped to ensure global charge neutrality in each cascade in

order to avoid the formation of space charge domains. The doping in QC lasers defines

the maximum injectable current density J

max= q

0n

s/ (!

trans+ !

tunnel) , where

n

s is the

doping sheet density and !

trans is the transit time for traversing one cascade.

!

tunnel= (1+ "

2!!

2+ 4 #

2

!3!!) / (2 #

2

!!) is the resonant tunneling time between the

injector ground state | g! and the upper lasing level | 3! [38, 39, 146], where 2!! is the

energy splitting at resonance between | g! and | 3! (which should be designed to be less

than the broadening, 2! ! " ! / "

#), !! is the energy detuning from resonance, and

!!

is the dephasing time. Since scattering by ionized impurities result in a dramatic

broadening of the electroluminescence spectrum, the doping is placed in the injector

region. However, not only J

max increases linearly with the doping [96] but also the non-

resonant intersubband losses !

ISB

non-res= g

ISB" n

s, where

n

s is the sheet doping density and

g

ISB is the gain cross section for intersubband losses. Therefore, the doping has to be

kept to a minimum in order to realize a low threshold current density J

th but sufficiently

high that the laser has some dynamic range (J

max! J

th) / J

th. An optimum in the doping

concentration has to be found which depends strongly on the wavelength, the particular

active region structure and the intended application (e.g. low power consumption or

high output power).

Theory

60

Thermal backfilling of carriers in the lower laser level increases linearly with doping and

results in resonant losses !

ISB

res . This can be sufficiently suppressed by designing a large

energy difference !

inj between the lower laser level and the chemical potential of the

injector. However, since the operation bias U ! N

p(!" / q

0+ #

inj) increases with

!

inj, a

good compromise is a value of 120-150 meV [147].

Intersubband linewidth

The ultra-short lower state lifetime (!0.2 ps) in the two-phonon resonance and bound-

to-continuum design allows to keep the ratio !

32/ !

2 sufficiently high, although both

designs use a vertical transition. The vertical transition will result in a narrower

linewidth for an optical transition. However, the use of a lower laser miniband in the

bound-to-continuum results in several strong optical transitions and therefore a broader

gain spectrum. While this is a nice feature for broadband tuning, this should result in an

overall weaker laser performance since the threshold current density is inversely

proportional to the gain width. Nevertheless, a pulse operation temperature up to 150 °C

has been shown with this design [103].

The two-phonon resonance and the bound-to-continuum designs show a T0 of 180-200 K

and seem to be promising for realizing high performance devices for either low-

threshold current CW lasers or broadly tunable CW sources. Both designs will be

compared in the experimental part of this thesis.

2.2.2. Optical point of view

Lasers are composed of two components: a gain element (active region) and a resonator

(waveguide and mirrors). A resonator with low losses and a large overlap factor ! is

crucial for achieving laser action at very low threshold current density. Both overlap

factor and (empty) waveguide losses depend on the waveguide design. Vertical

confinement in QC lasers is achieved by sandwiching the active region within cladding

Design Parameters

61

layers, which normally have a refractive index lower than in the active region. The lateral

waveguide is conventionally realized by fabricating ridge waveguides.

Overlap factor

One of the main problems in realizing a laser in the MIR is to confine a large optical

mode into the small active region, where the length of one cascade is only ~50-75 nm

resulting in a small overlap factor !p. The total overlap factor between the mode and

Np cascades is:

! = !p

p=1

Np

" (2.58)

When the individual overlap factors !

p are similar (e.g. in the center of the mode), this

expression can be simplified to ! = N

p!

p. In this case, the threshold current density

(2.55) can be written as Jth= !

tot/ (g

dNp"p) # N

p

$1 , showing that the threshold current is

inversely proportional to the number of states. However, adding more cascades

increases the necessary bias voltage U ! N

p(!" / q

0+ #

inj) and the injected electrical

power at threshold Pth=U

th! J

th" N

p! (!# / q

0+ $

inj) ! N

p

-1" (!# / q

0+ $

inj) is constant.

Nevertheless, the reduction of the threshold current density is beneficial because it also

reduces the population inversion in each cascade, and consequently one can reduce the

active region doping level which further causes less intersubband absorption. A decrease

in threshold current density reduces also joule heating ! (R " I )2 . In addition, the slope

efficiency is directly proportional to N

p. However, adding more and more cascades will

decrease !

p. In the wavelength range of 7-9 µm, a good compromise is a number of

N

p=35 [148], which we use in most of the designs presented in this thesis.

Theory

62

Losses in QC lasers

There are three reasons for losses that have to be considered:

• Mirror losses at the end facets of the laser

• Intersubband losses in the active region (already treated in the previous section)

• Free carrier losses in doped semiconductor layers and metals

Mirror losses

The mirror losses of one facet are !

m,i= " ln(R

i) / (2L) , where L is the resonator length,

R

i is the facet reflectivity and the index i stands for the front (f) or back (b) facet.

R

m,i=0.27 is used for a cleaved facet and

R

m,b=0.97 for the high reflecting (HR) coated

(Al2O3/Au) back facet. For anti-reflection (AR) coatings, we use a bi-stack of quarter-

wave layers of YF3/ZnSe resulting in Rm,i

< 10!3 . Using a dispersive feedback element

(either a distributed feedback grating or an external cavity grating) will selectively

influence the cavity losses, which will be discussed in the next section.

Free carrier losses in doped semiconductor layers

The semiconductor layers of the waveguide have to be doped in order to enable current

flow and avoid joule heating. However, doping will change the refractive index and

results in losses due to free carrier effects. The Drude theory for conductivity is used to

obtain the contribution to the complex refractive index [149]:

!n2= !" 1#

$P

2

$ 2 (1+1 / ($%tr)2 )

1+i

$%tr

&

'()

*+,

-..

/

011

(2.59)

where the plasma frequency reads:

!P

2=

neq

0

2

m*"#"

0

(2.60)

where !"

is the high frequency dielectric constant, and n

e the carrier concentration,

which is equal to the doping concentration at 300 K. The scattering time

Design Parameters

63

!

tr(n

e) = µ(n

e) "m# / q

0 is calculated from mobility µ(n

e) measurements. From (2.59), the

loss part can be written as [150]:

! = "2k0#( !n) =

q0

3$

0

2

4% 2c3neff&

0(m*)2µ

'$

0

2ne

m*

(2.61)

where it becomes clear that the losses in a semiconductor layer scale linearly with the

doping level (neglecting the rise of the effective mass with increasing carrier

concentration) and quadratically with the wavelength. Furthermore, for better

waveguiding, the refractive index can be markedly decreased by increasing the doping

level until the plasma frequency is close to the laser frequency while the losses are still

relatively low (Fig. 2.8). Such a layer is then used in plasmon-enhanced waveguides

[151].

Fig. 2.8: Calculated refractive index and absorption vs doping for InGaAs at 300 K

for 6, 8 and 10 µm wavelength using experimental mobility data. The circles

indicate the doping level at which !

p equals frequency of the emitted light.

Calculation of (empty) waveguide losses and overlap factor

Each layer i has a thickness d

i and a complex refractive index

!n

i. The layers are assumed

to be homogeneous, isotropic, non-magnetic and non-conducting. One has to solve the

wave equation which reads for layer i [152]:

Theory

64

!2

!x2+

!2

!y2

"

#$%

&'E(x, y) ( ) 2 ( k

0

2!n

i

2( )E(x, y) = 0 (2.62)

where x is along the growth direction, y is the in-plane coordinate perpendicular to the

ridge, ! is the propagation constant along z direction, k

0 is the free-space propagation

constant and E(x, y) is the electrical field amplitude. Note that the used coordinate

system is standard for EM waves, and differs from that used in previous sections where z

is the growth direction. Since in the majority of cases, the layers are absorbing and/or the

waveguide is leaky, for each mode, a solver needs to find the complex root in order to

compute the propagation constant ! .

As long as w

act! ! one can treat the vertical structure as a one-dimensional multi-layer

slab waveguide, where the layers range from minus to plus infinity in the y- and z-

direction and therefore, the propagation in z-direction can be assumed to be

independent of y and ! / !y = 0 . Based on the polarization selection rule for

intersubband transitions (2.22), the transversal modes are TM polarized and only the

component in x direction has to be considered (see Fig. 2.9). Consequently, the solution

of (2.62) reads:

E

x ,i(x) = E

R,i!exp(ik

s,i! x) + E

L,i!exp("ik

s,i! x)( ) ! # / k

0!n

i( ) (2.63)

where E

R,i and

E

L,i are the complex field amplitudes of layer i for the right and left

propagating wave and ks,i= k

0

2!ni

2 ! " 2 . The boundary conditions at each interface read:

ER,i(x) + E

L,i(x)( ) ! !ni = E

R,i+1(x) + E

L,i+1(x)( ) ! !ni+1 (2.64)

!ER,i(x) + E

L,i(x)( ) " # i = !E

R,i+1(x) + E

L,i+1(x)( ) " # i+1 (2.65)

where !

i= 1" # 2 / (k

0!n

i)2 . In contrast to the TE modes, the TM modes show a

discontinuity at each interface when there is a change in the refractive index. Once the

field solutions are known, one can obtain the overlap factor from:

! =

Ex

2

act" dx

E2

dx

#$

$

"

(2.66)

Design Parameters

65

Fig. 2.9: Slab waveguide, showing the electrical and magnetic field vector, the

propagation constant ! and the free-space propagation constant k

0.

Fig. 2.10: TM mode intensity and refractive index of the vertical waveguide for a

wavelength of 8.4 µm.

Although the surface plasmon mode at the semiconductor-metal would result in a tight

confinement, this is not advised in the MIR (up to !"12 µm) since this would also

introduce large waveguide losses. To separate the metal contact from the TM field

would require a thick dielectric waveguide, which is impractical. However, since the

plasma frequency of semiconductor layers is close to the emitting wavelength, one can

Theory

66

make use of plasmon-enhanced layers to decouple the mode from the lossy metal. Fig.

2.10 shows the field distribution of the TM mode in a typical waveguide structure, where

the overlap of the TM mode with the active region is 70 %. All waveguides presented

below will use a plasmon-enhanced layer.

So far, we have only considered the TM mode in planar waveguides. However, the mode

is also confined laterally, conventionally by forming a ridge waveguide. The ridge

sidewalls are normally passivated (e.g. Si3N4 or SiO2) following the contact layers. Such

layers however interfere optical mode resulting in additional absorptions. In order to

calculate the field distribution and the propagation constant, the two-dimensional wave

equation (2.62) needs to be solved for which the finite-elements software package

"COMSOL Multiphysics" was used which can compute the field distribution and the

complex propagation constant. Fig. 2.11a shows the electrical field distribution of a ridge

waveguide for an emission wavelength of 8.4 µm. The waveguide is surrounded by a thin

Si3N4 passivation and gold contact layer.

Fig. 2.11: Simulation of the electrical field distribution of a) a 14 µm-wide

conventional ridge waveguide design and b) a 10 µm-wide buried heterostucture

waveguide design (using re-grown InP) for an emission wavelength of 8.4 µm.

From the field distribution, one can calculate the overlap factor, integrating now over x

any y:

! =

Ex

2

act" dxdy

E2

dx dy#$

$

"

(2.67)

Design Parameters

67

The complex propagation constant and the free-space propagation constant are linked

by the complex effective index: ! = !neffk0

, from which one can derive the (real) effective

index n

eff= !( !n

eff) and the waveguide losses

!

WG

empty= "2k

0#( !n

eff) . In Fig. 2.12, the

computed waveguide losses and the overlap factor as function of the ridge width are

shown for an emission wavelength of 8.4 µm. For ridge widths below 15 µm, the

waveguide losses strongly increase while the overlap factor decreases. For low power

consumption devices, a narrow ridge width is crucial in order to keep the total injected

power to a minimum. One possibility to still keep low the waveguide losses is to bury the

waveguide in a low absorbing (semiconductor) material with a lower refractive index

compared with the active region (see Fig. 2.11b). Fig. 2.12 shows that the waveguide

losses increase only marginally which is beneficially, although the overlap factor

decreases faster than in the conventional design. However, this waveguide design is

technological very demanding since it requires the re-growth of epitaxial material.

Fig. 2.12: Calculation of waveguide losses and overlap factor for an emission

wavelength of 8.4 µm for two different waveguide designs.

Theory

68

2.2.3. Thermal point of view

Since CW operation is required to reach the goals of this thesis, the thermal point of

view is the most critical and demanding. This is because a huge amount of electrical

power in the order of 20-50 kW/cm2 within the device must be dissipated, which results

in self-heating.

Impact of self-heating

The self-heating of the QC laser dramatically degrades the laser operation as shown

schematically in Fig. 2.13. The temperature affects inter- and intrasubband lifetimes by

the Bose-Einstein factor (see Fig. 2.5). Although this is fortunately a weak coupling, the

effective upper state lifetime decreases with increasing temperature affecting inversely

the threshold current density. The atomic-like joint density of states (neglecting non-

parabolicity) is beneficially since this will avoid direct temperature broadening of the

linewidth. However, the linewitdh is collision broadened by the ultra-short inter- and

intrasubband lifetimes. As already discussed, linewidth broadening has a detrimental

effect on the gain cross section and increases the non-resonant intersubband losses, both

reduce the threshold current density. Furthermore, the temperature increases the

backfilling and consequently the larger non-resonant losses will increase the threshold

current density.

Fig. 2.13: Schematic illustration of the positive feedback loop in QC lasers due to

self-heating.

This self-heating results in an active region temperature Tact

which is in a simple model

related to the submount temperature Tsub

by a single thermal resistance Rth

[in K/W]:

Design Parameters

69

Tact

= Tsub

+ RthJopSact!U

op (2.68)

where U

op is the operation bias,

J

op is the operation current density and

S

act is the active

region area which is the product of laser length L and width w

act. As in interband lasers,

QC lasers follow the empirical formula for the temperature dependence of the threshold

current density: Jth= J

0exp(T

act/ T

0) . The maximum active region temperature can be

derived expressing the current density by the empirical threshold current density

formula and by setting dT

sub/ dT

act= 0 :

Tsub,max

= T0

lnT

0

RthU

thJ

0S

act

!

"#$

%&'1

(

)**

+

,--= T

0ln

GthT

0

Uth

J0

!

"#$

%&'1

(

)**

+

,--

(2.69)

where Gth

is the specific thermal conductance [in W/( m2K)].

There are obvious four possibilities to keep T

act close to

T

sub:

• An active region with a low (pulsed) threshold current density J

th

• Using an active region design with a large T

0

• Reducing the width of the active region w

act

• Reducing of the thermal resistance R

th

The first two items have already been discussed in the previous section: The two-phonon

resonance and the bound-to-continuum design are well suited as an active region since

both work up to high pulsed operation temperature. For CW operation, the doping has

to be kept minimal in order to avoid intersubband losses and self-heating. The bias is

defined by the number of cascades, which should be as high as possible (as long as the

overlap factor increases linearly with the number of cascades), enabling to reduce the

doping. The last two items concern the thermal waveguide design. The total injected

power (and the dissipated heat) can be minimized by reducing the waveguide width.

This in turn has a positive effect on the thermal conductance (as will be shown later).

Finally, the thermal resistance can be reduced by optimization of the waveguide for

better heat removal.

Theory

70

Thermal waveguide optimization

In 1999, Gmachl et al. used a finite-element software package to model the two-

dimentional isotropic lattice temperature distribution in the waveguide [153]. For the

same purpose, we use the finite-elemente software package "COMSOL Multiphysics" to

solve Fourier’s law of heat conduction:

!" # kth"T( ) = Q (2.70)

where kth

is the thermal conductivity [in W/(m !K)] and Q is the heat source density [in

W/m3], which is assumed to be none-zero in the active region only. For the computation,

we use the thermal conductivities given in Table 2.1.

Table 2.1: Material thermal conductivities used in the heat dissipation model. The

weighted average of the thermal conductivities of InGaAs and InAlAs was used for

the thermal conductivity of the active region.

Material k

th [W/(m !K)]

InP 74

InGaAs 4.84

Si3N4 15

Au 317

Cu 384

AlN 257

Diamond 1200

In solder 81

SnAu solder 57

Active region 4.72

Fig. 2.14 shows the calculated temperature mappings of the front facet of QC laser

devices having the same core structure (see Fig. 2.10), using Si3N4 as passivation layer,

but different geometries: either conventional ridge waveguide with a gold top contact

(either 0.2 or 4.0 µm thick) or buried heterostructures (BHs) (including a 4 µm thick

gold top contact) which are mounted either epi-up or epi-down. The epi-down mounted

device was soldered on diamond while the others were soldered to copper mounts. In

both cases indium was used as solder. In all four cases, the cavity length is 3 mm, the

Design Parameters

71

heat sink temperature is 300 K and the dissipated electrical power is 8.8 W. Due to the

poor thermal conductivity of InGaAs compared to InP, InGaAs is restricted to the thin

cladding layers surrounding the active region, the plasmon-enhanced layer and the

contact layer. Si3N4, which has one order of magnitude higher thermal conductance than

SiO2, was used as passivation material. In the conventional ridge waveguide, the heat is

primarily removed along the growth direction toward the substrate (see Fig. 2.14a). The

lateral heat removal can be improved by surrounding the ridge waveguide with a thick

electroplated gold layer (Fig. 2.14b). Another option is the use of buried

heterostructures, where the waveguide is buried in e.g. re-grown InP (Fig. 2.14c). This

approach has the advantage that devices are planarize allowing for epi-down mounting

(Fig. 2.14d), which further reduces the thermal resistance of the device. Fig. 2.15 shows

the theoretical thermal resistance calculated using (2.68) as function of ridge width

together with experimental data.

Fig. 2.14: Temperature mappings of the front facet of identical QC laser structures

(with 12 µm-wide and 3 mm-long waveguides) and an input electrical power of

8.8 W (24.4 kW/cm2). Conventional ridge waveguide with 0.3 µm Si3N4 passivation

and 0.2 µm (a) and 4.0 µm (b) top gold. Buried waveguide heterostructure (BH)

waveguide design for epi-up (c) and epi-down (d) mounting.

Theory

72

The shown experimental thermal resistances were derived from either spectral

characteristics, using R

th= !T / !P

el= (!" / !P

el) # (!" / !T )$1 , or from comparing of

threshold current data in CW and pulsed operation. However, those two methods probe

different thermal resistances. The threshold method will provide the thermal resistance

of the active region while the spectral characteristic method extracts the thermal

resistance of the active region and the waveguide. Good agreement has been found with

experimental data although only bulk values (no anisotropy) for the thermal conductivity

of the active region have been considered in the model. From Fig. 2.15 is becomes clear

that a narrow ridge and a buried heterostructure design mounted epi-down is the most

efficient way to reduce the thermal resistance of the device. However, the buried

heterostructure designs necessitates additional sophisticated regrowth steps and special

care has to be taken for avoiding parasitic current leakage in the current blocking layers.

Fig. 2.15: Experimental (markers) and theoretical (lines) data of the thermal

resistance for different thermal waveguide designs: (blue) conventional waveguide

with thick electroplated gold, (green) buried waveguide design and (red) buried

waveguide mounted epi-down on diamond. Thermal resistances have been

normalized in order to compare different active regions with area S

act and

thickness dact

(R

th= R

sp! d

act/ S

act) . The experimental data have been deduced

either from the threshold currents (open marker) or spectral characteristics (filled

marker).

Mode control in QC lasers

73

2.3. Mode control in QC lasers

This section is devoted to mode control in QC lasers, since spectroscopic applications

require single-mode sources. First, we consider modes in a Fabry-Pérot cavity. Those

modes are determined by the stationary condition:

rfrbexp(2i!L) = 1 (2.71)

where ri= R

i are the reflectivity coefficients and the complex propagation constant

comprising gain reads:

! = k

0!n

eff= k

0n

eff" i

GM"#

wg

2

(2.72)

The condition on the amplitude of (2.71) gives the threshold modal gain:

GM,th

= !wg+

1

Lln

1

rfr

b

"

#$

%

&'

(2.73)

The phase condition reads:

2k

0n

effL = N !2" (2.74)

which gives the possible modes:

! =2n

effL

N

(2.75)

where N is the mode index. The spacing between two Fabry-Pérot modes N and N-1,

expressed in wavenumbers !" = !(#$1) , is:

!" = (2ngL)#1 (2.76)

where the group index ng= n

eff+! " #n

eff/ #(!) takes into account the dispersion on the

effective refractive index. For a typical cavity length the mode spacing is in the order of

0.5-2.0 cm-1 and therefore much smaller than the gain spectrum (FWHM of 100-

300 cm-1). As a consequence, the laser will emit at an unpredictable wavelength or even

multi-mode. However, spectroscopy applications require a single mode source which is

predictably tunable.

Theory

74

2.3.1. Distributed feedback cavity

This section will briefly introduce the coupled-mode theory helpful in understanding the

relevance of the coupling coefficient, which has to be properly designed in order to avoid

under- and overcoupling. Then, the formalism for computing gratings is presented

(including reflections and phase shifts introduced by the end facets), which allows to

correlate the grating profile parameters to the coupling strength and finally to compute

the cavity losses.

Coupled-mode theory

Kogelnik and Shank have derived the coupled-wave analysis of distributed feedback

lasers [154], which will be presented here with slightly different notations. The

modulation of the effective index and the losses in z-direction (propagation direction)

induced by a sinusoidal grating reads:

n

eff

' (z) = neff+!n

2cos(2"

0z)

(2.77)

! ' (z) = ! +"!

2cos(2#

0z)

(2.78)

where !n and !" are small deviations from the average refractive index and average

losses and !

0 is the Bragg propagation constant defined as:

!0=

N"

#=

2"neff

$B

= k0($

B)n

eff

(2.79)

where N characterizes the grating order and !

B is the Bragg wavelength. From the last

equation, one gets the grating period ! = N"B/ (2n

eff) . One sees immediately, that the

grating period for a first order grating equals half the wavelength in the medium. The

scalar wave equation for the electric field neglecting all transverse and lateral variations

reads:

d2E

dz2+ !! 2 + i2" !! + 4# !! cos(2!

0z)$% &' ( E = 0

(2.80)

where !! = 2"n

eff/ #

0= k(#

0)n

effand the coupling coefficient for the sinusoidal grating

reads:


75

! ="#n

2$0

+ i#%

4

(2.81)

which is a measure of the amount of reflection by unit length. Considering only

wavelengths ! close to the Bragg wavelength !

B (

!! = !

0+ "! where

!" ! "

0), the

electric field can be composed of two counterrunning electric fields with the complex

amplitudes R(z) and S(z) :

E(z) = R(z)exp(!i"

0z) + S(z)exp(i"

0z) (2.82)

Inserting (2.82) into (2.80), neglecting second derivatives of R(z) and S(z) and collecting

terms with identical phase factors ( exp(!i"

0z) and

exp(i!

0z) ) results in the coupled-

mode equations:

!dR

dz+ (" ! i#$)R = i%S

(2.83)

dS

dz+ (! " i#$)S = i%R

(2.84)

Note that for a vanishing coupling coefficient (! = 0) , those equations are not any more

coupled and result in the trivial solution R(z) = R(0)exp([! " i#$]z) and

S(z) = S(0)exp(![" ! i#$]z) and the field is nothing else than a pair of independent

plane waves propagating in +z and –z direction:

E(z) = R(0)exp([! " i !#]z) + S(0)exp("[! " i !#]z) .

In the original paper, Kogelnik and Shank derived the solution of the coupled-wave

equations for the case of anti-reflection coated facets, where the corresponding

boundary condition is R(! 1

2L) = S( 1

2L) = 0 , for a devices spanning between

!

1

2L and

1

2L , which results in the transcendental equation ! = ±i" / sinh("L) , where the complex

propagation constant ! follows the dispersion relation !2=" 2

+ (# $ i%&)2 . Finally, the

field amplitudes can be written: R(z) = sinh(![z +

1

2L]) and

S(z) = ± sinh(![z "

1

2L]) .

In general, the coupling coefficient will be complex. However, the gratings used in this

work have a negligible loss coupling and the coupling coefficient is assumed to be real.

Theory

76

Fig. 2.16 shows the calculation of the amplitudes R(z) and S(z) together with the

intensity distribution for a 1.5 mm long cavity and different coupling products ! L .

Knowing the complex propagation constant ! , one can use the dispersion relation to

calculate the cavity losses !

DFB and the detuning !" for the modes at the stopband edge

(see Fig. 2.17).

Fig. 2.16: a) Intensity distribution and b) amplitudes R(z) (solid) and S(z) (dashed)

in a 1.5 mm-long DFB-QC laser for different ! L .

Although the device is symmetric and should emit on both modes at the edge of the

stopband, in reality a small phase shift at the facets and/or process fluctuations will favor

one mode over the other and the device should emit single mode. However, the modes

are undercoupled for ! L!1 and this will most likely result in multimode operation. On

the contrary, overcoupling ( ! L! 1) will lead to gain saturation in the center of the

device allowing the mode on the other stopband side to build up in the cavity and the

laser will most likely emit bi-mode. In this work, the gratings were designed to result in


77

! L " 3 which should not overcouple the device too much but lead to reasonably low

cavity losses !

DFB.

Fig. 2.17: Detuning !" and cavity losses !

DFB of the modes at the stopband edge

for different coupling products.

Coupling coefficient

Loss coupling (e.g. by metal gratings) should be avoided in order to attain a high

performance device. As a consequence, the gratings presented in this work are etched in

the InGaAs cladding layers, surrounding the active region (see Fig. 2.10), followed by an

InP regrowth. The gratings used in this work are rather square gratings (compared with

the sinusoidal ones in Kogelnik and Shanks work) and the grating coefficient can be

derived in a simple manner (schematically depicted in Fig. 2.18). At the first interface

(from high to low index) the reflectance coefficient follows from the Fresnel equation

and reads r = !n / 2neff

. At the next interface (from low to high index) the Fresnel

equation results in !r and so on. When the wavelength is equal to the Bragg

wavelength, the phase shift !0" = # after one roundtrip and the resulting reflections add

up in phase. There are two reflections per grating period and the coupling coefficient

reads:

! =2r

"=1

"

#n

neff

PF (2.85)

Theory

78

where the profile factor PF is the ratio of the first-order Fourier AC components of the

ideal square grating, with 50 % duty cycle, and the real profile:

PF =!

h"Profile(z)cos(2! z / ") dx

#" / 2

" / 2

$ (2.86)

where h is the grating etching depth. Note, assuming Profile = h / 2 !cos(2" z / #) results

in a profile factor PF = ! / 4 and a coupling product equivalent to the one in equation

(2.81).

Fig. 2.18: Periodic modulation of the effective index in a square grating with 50 %

duty cycle.

Computing DFB gratings

So far only anti-reflection coated devices have been considered. In order to introduce a

facet reflectivity and phase-shift, the simplest way is to treat the square grating as stack

of alternating layers with different (effective) refractive indices, derived for the etched

and unetched waveguide, and using the matrix method with the boundary conditions

(2.64) and (2.65) at each interface to plot the transmission (with normal incidence).

Facet coatings and phase shifts can be introduced by putting extra layers at the

beginning and/or end of the stack. As an example, the transmission spectrum for a

1.5 mm-long device is plotted in Fig. 2.19, which was coated with a high reflectivity

coating on one facet and left uncoated on the other side. The spectrum reveals the

stopband and the cavity mode spectra around the Bragg resonance. In the next step, one

derives the threshold gain for each mode. This can be done by adding gain to the

imaginary part of the refractive index of each layer. The threshold gain (which equals


79

the cavity losses) can be found by successively increasing the gain until the transmission

goes to infinity. Fig. 2.19 also shows the cavity losses for each of the cavity modes. While

the cavity losses equal the mirror losses (4.46 cm-1) for modes far detuned from the

Bragg condition, the losses decrease to 0.6 cm-1 on the right side of the stopband edge,

leading to a strong mode discrimination !" between the Bragg mode and the Fabry-

Pérot modes.

Fig. 2.19: Transmission spectrum of a 1.5 mm-thick stack of alternating layers with

!=1.3, n

eff=3.19 and !n=0.01 and a phase shift introduced by reducing the

thickness of the high index layer, before the HR coating (gold layer), by 30 %.

Tuning of DFB lasers

A good device lases single-mode at the Bragg wavelength !

B(T ) = 2n

eff(T )"(T ) and the

wavelength can be shifted by temperature. The direct temperature tuning coefficient

reads:

! =1

"B

d"B

dT=

1

neff

dneff

dT+

1

#

d#

dT

(2.87)

However, the thermal expansion of InP (4.60 x 10-6 K-1) is one order of magnitude

smaller than the tuning of the refractive index (~8 x 10-5 K-1), and the second part in

(2.87) can be neglected. Indirect temperature tuning can be attained by the injected

electrical power which results, due to the large thermal resistance of the device, in

heating of the active region:

Theory

80

1

!B

d!B

dPel

=1

!B

d!B

dT

dT

dPel

= "Rth

(2.88)

One drawback of a good thermal management is that the indirect temperature tuning

coefficient decreases. However, a low thermal resistance allows higher CW operation

temperatures and therefore a larger direct temperature range.

The mode discrimination !" = "

FP#"

DFB allows in principle a large tuning range, as

long as !" > !g . However, detuning from the gain peak will result in an increase of the

threshold current density Jth(!) = J

th(!

P) " g

d(!

P) / g

d(!) , which requires some dynamic

range (J

max! J

th) / J

th for tuning. Therefore, the gain spectrum should be designed to

peak closely to the Bragg resonance.

Fig. 2.20: Schematic illustration of gain g(!) and cavity losses !(") in a DFB

laser.

2.3.2. External cavity feedback

The Littrow and the Littman-Metcalf configurations are the most common external

cavity configurations [118]. In order to achieve the broadest possible coarse tuning

range, the Littrow configuration is selected, where the light is reflected only once by the

grating providing a stronger feedback. The schematic configuration is shown in Fig. 2.21

where the zeroth order is extracted and the first-order diffracted beam is fed back into

the QC laser cavity.

Similar to (2.71), the stationary condition for the EC modes reads:


81

rEC(!g,") # r

bexp(2i$L) = 1 (2.89)

where the reflectance coefficient of the external cavity (assuming zero reflectivity of the

front facet) [155] reads:

rEC

(!g,") = T

LR

Gexp #

f 2 (" # "g)2

2Wx

2$2 cos2!g

%

&

''

(

)

**

(2.90)

where !

g is the grating selected wavelength, T

L is the transmission of the lens, R

G is the

reflectivity of the grating, f is the distance between the laser and the grating, W

x is the

width of the nearfield (calculated from the farfield angle

tan!1

2

" 0.187 # $ / Wx). Note,

that the last equation is derived for an ideal (diffraction limited) lens (otherwise, the

spot size of the reflected beam is larger and the reflectance coefficient is reduced).

Fig. 2.21: Schematic illustration of an external cavity in Littrow configuration.

The condition on the amplitude results in the threshold modal gain:

GM,th

= !wg+

1

Lln

1

rEC

("g,#) $ r

b

%

&'

(

)*

(2.91)

The phase condition takes into account the phase of the reflectance coefficient:

2k0neffL + arg r

EC(!g,")#

$%& = N '2( (2.92)

Theory

82

For wavelengths far from !

g, the reflectance coefficient of the external cavity

r

EC

vanishes compared to the one of the (residual) front facet r

f and results in the threshold

modal gain (2.73) and mode spacing (2.74) of the Fabry-Pérot case. However, for

wavelengths close to !

g,

r

EC does not vanish and results in the threshold modal gain:

GM= !

wg+

1

2Lln

1

REC

ARR

b

"

#$

%

&'

(2.93)

The phase arg r

EC(!

g,")#

$%& ' 2ik

0L

EC results in the mode spacing of the external cavity:

!" =1

2(Lneff+ L

EC)

(2.94)

Tuning of an EC laser

Tuning in an external cavity setup is achieved by rotating the grating. The reflectance

angles in respect to the incidence angle for various grating orders N are related as

follows:

sin!

i+ sin!

r ,N=

N"

#

(2.95)

where ! is the grating period. The feedback in the Littrow configuration is maximal

when incident and reflected beam are collinear resulting in the grating selected

wavelength:

!g= 2"sin#

g (2.96)

The tuning range is limited by the mode discrimination between Fabry-Pérot modes and

the EC modes. Therefore, single mode tuning will be possible as long as the ratio of

differential gain g

d(!) / g

d(!

p) " # , where

! = "

EC

AR/"

FP

AR (see Fig. 2.20) represents the

ratio of the total losses

!

EC

AR= !

wg

tot"

1

2Lln R

EC

ARR

b

HR( ) (2.97)

with, and


83

!

FP

AR= !

wg

tot"

1

2Lln R

FP

ARR

b

HR( ) (2.98)

without the feedback of the EC of the anti-reflection (AR) coated laser. A high !

requires both, a good anti-reflection broadband coating on the front facet and a large

R

EC

AR . Even more important is to use an active region design with a relatively wide gain

media which is at the same time flat on the top of the spectrum.

Chapter 3

3. Technology

3.1. Introduction

The achievements of this work are largely based on mastering the technology. In this

chapter, the technology for device fabrication will be presented, carried out in ETH’s

FIRST Center for Micro- and Nanoscience laboratory. MBE growth initially was done at

the University of Neuchâtel and later at ETH. In this section, a brief overview will be

given on epitaxial growth, standard processing and assembly of QC lasers. In the

following section, the fabrication of buried (multi-wavelength) distributed feedback

gratings is discussed. In advanced waveguide etching I, a procedure for etching of narrow

waveguides is presented. In the following section, different blocking materials for lateral

current confinement in buried heterostructures are investigated. The technology for

burying waveguides in semi-insulating InP:Fe is shown, followed by a description on how

such buried heterostructures can be mounted epi-down. Finally, in advanced waveguide

etching II the waveguide etching procedure was further developed to end up with

groove-free and mostly defect-free buried heterostructures.

3.1.1. Epitaxial growth

The active region, composed of several hundred of layers of alternating InGaAs/InAlAs

layers (each a few Angstroms thick), and the surrounding InGaAs cladding layers were

grown by a VG V80H (Oxford Instruments) MBE system on low doped 2-inch InP

substrates. The tool is equipped with As, Ga, Al, In and Si sources. Si was used as

dopant of the active region. For homogeneous heat distribution, the wafer (or a quarter

of a wafer) was mounted with In on the sample holder. The growth temperature of

Introduction

85

~530 °C ensured a sticking coefficient of nearly unity of the group-III component. The

growth rate in the ultra-high vacuum (base pressure of 10-10-10-11 mbar), determined by

the group-III flux, was normally ~1 µm/h. The MBE growth was carried out by Dr.

Mattias Beck, Dr. Marcella Giovannini, Nicolas Hoyler and Milan Fischer.

The much thicker planar waveguiding and contact layers (InP, InGaAs and InGaAsP)

were grown by low pressure MOVPE (AIXTRON AIX 200/4). The metal organics

Trimethylgallium Ga(CH3)3 and Trimethylindium In(CH

3)3 are used as group-III

element sources, which are transported into the horizontal reactor at 160 mbar using H

2

as carrier gas. The hydrides AsH

33 and

PH

33 are used as group-V element sources and

SiH

4 is utilized as source for the n-type Si doping. The growth rate at a temperature of

630 °C was ~1.5-2.0 µm/h. Two 15 nm thick InGaAsP layers whose band-gaps

correspond to photoluminescence maxima of 1.1 and 1.28 µm, respectively, were used

for smoothing the conduction band offset between InP and InGaAs. The MOVPE

growth was carried out by Martin Ebnöther and Dr. Emilio Gini.

It is worth mentioning that any p-doping is highly unwanted in the unipolar QC laser

since based on experience [156], it strongly reduces the efficiency of the laser, which

might be due to impurity scattering. An analysis of MOVPE-grown undoped InP, using

low temperature photoluminescence, revealed peaks that have been assigned to the

incorporation of Zn (green curve in Fig. 3.1), which acts as p-doping. This was confirmed

by a SuperSIMS measurement, carried out by Dr. Döbeli at the Institute of Particle

Physics, ETH Zurich, which revealed an average Zn concentration of 4 x 1014 cm-3. As

the quartz liner is by default cleaned before each run, using aqua regia, the origin for Zn

was suspected in the susceptor and disk, which are also used by other groups in the

FIRST laboratory. The red curve in Fig. 3.1 was measured from an undoped InP sample

that was grown using a new disk and susceptor. Not only the peaks corresponding to Zn

have disappeared but also a much stronger intensity of the exciton is observed. Since Zn

has a very long memory effect, a new disk and susceptor unit, which were dedicated to

the growth of n-doped material, were used for the samples shown in this thesis.

Technology

86

Fig. 3.1: Low temperature photoluminescence of intentionally non-doped InP

grown by MOVPE on a common (P723) or dedicated (P771) susceptor and disk.

Peaks have been assigned to reference values from [157].

3.1.2. Processing and assembly

The conventional QC laser processing is sketched in Fig. 3.2. When no gratings are

required, the processing starts after the MOVPE growth of the waveguide and contact

layers. The ridge mask is defined using positive resist and a contact printing mask aligner

(Karl Süss MA6). Afterward, the ridges are etched using

HBr(38 %):HNO3(65 %):H2O(100 %) (1:1:10). The waveguides are passivated with

Si3N4 in a PECVD (plasma enhanced chemical vapor deposition) tool (Oxford

Instruments 80+). Opening of the contact window was done using positive resist and

etching with CHF3/O2 in a RIE (reactive ion etching) tool (Oxford Instruments RIE

80+). In the next step, the contact was evaporated in two runs using negative resist and

an e-gun evaporator (Leybold Univex 500). First, the top contact (see Fig. 3.2e)

consisting of Ti/Pt/Au (30/40/100 nm) was evaporated and in a second run, the extended

contact (interconnected with each other) using Ti/Au (40/150 nm). The last gold

evaporation serves as seed layer for a 4 µm-thick electroplated Au layer. After etching of

the interconnections between different lasers the substrate was lapped down to 150 µm

(Logitec PM5). Finally, either a Ti/Pt/Au (30/40/100 nm) contact or a Ge/Au/Ni/Au

Introduction

87

(18/48/15/150 nm) alloyed contact was evaporated on the backside. Cleaved lasers were

soldered with a precision die bonder (Cammax EDB80-P) to copper mounts using In

and then wire bonded (Westbond 747677E). HR coatings (Al2O3/Au) were evaporated

in an e-gun evaporator (Leybold Univex 450). Fig. 3.3 shows the front facet of a finished

QC laser.

Fig. 3.2: Schematic illustration of the conventional QC laser fabrication process.

Fig. 3.3: Scanning electron microscope (SEM) picture of the waveguide profile of a

conventional processed QC laser showing a large tail of the active region.

Technology

88

3.2. Buried distributed feedback gratings

The DFB gratings were etched into the InGaAs cladding layers surrounding the active

region, which were then overgrown with InP. In contrast to previously holographically

fabricated gratings, standard photolithography was used. This allows for placing several

fields with different gratings on the same piece of epi-material. However, special care

has to be taken for the cleanliness of sample, resist and mask.

Gratings were fabricated using a thin positive resist (AZ 1505) and a contact printing

mask aligner (Karl Süss MA6) applying low vacuum between mask and sample. The

gratings were transferred into the semiconductor by etching with

H3PO4(85 %)H2O:H2O2(30 %) (1:5:1) at a temperature of 0 °C. The photolithography

was slightly underdeveloped in order to compensate the underetching of the mask and

to end up with a duty cycle as close to 50 % as possible. Fig. 3.4 shows an AFM picture

of a grating (with period !=1.270 µm) that was etched 168 nm into the InGaAs layer.

After removal of the resist and proper cleaning, the samples were immediately loaded

into the MOVPE system and the top waveguide was grown. Fig. 3.5 is an optical

microscopy picture that shows an excellent regrowth topography and low defect density.

Fig. 3.4: Atomic force microscope (AFM) picture of a distributed feedback grating.

Advanced waveguide etching I

89

Fig. 3.5: Optical microscope picture of a distributed feedback grating that was

overgrown with 2.6 µm InP and 300 nm InGaAs.

3.3. Advanced waveguide etching I

As seen in Fig. 3.3, the active region (marked with a dashed line) shows a large

difference between the top and bottom width. This results in inhomogeneities in the

inversion density of different cascades, which might degrade the laser performance.

Furthermore, the large tail defines the minimal ridge width. However, narrow ridge

waveguides would strongly reduce the injected power and result in less self-heating of

the device. In order to improve the ridge profile, a new procedure for waveguide etching

has been developed during this work, schematically shown in Fig. 3.6.

Fig. 3.6: Schematic illustration of advanced waveguide etching I.

Technology

90

In this procedure, the waveguide layers InGaAs(P) and InP are etched selectively. For

this purpose, a SiO2 mask is preferred over photoresist, since underetching is strongly

reduced, resulting in much smoother ridge profiles. After deposition of 300 nm SiO2 in

the PECVD tool, the waveguide structure, oriented in the [011]-direction, is defined

onto the oxide using positive resist, and transferred to the oxide using CHF3/Ar in the

RIE system. In the first step, the InGaAs(P) layers are etched selectively using

H3PO4(85 %):H2O:H2O2(30 %) (1:1:1) at a temperature of 0 °C, with InP acting as etch

stop layer (see Fig. 3.6d). In the next step, InP is etched selectively using

CH3COOH:HCl(32 %) (3:1) at room temperature, with InGaAs acting as mask. The

SEM picture in Fig. 3.7 shows that the etching procedure results in steep ridge sidewalls

with a slightly negative angle and stops onto the InGaAs cladding layers surrounding the

active region.

Fig. 3.7: SEM picture of the waveguide after selective wet etching of

InGaAs/InGaAsP and InP.

The etching of the active region is performed using the non-selective etching

CH3COOH:HCl(32 %):H2O2 (30 %) (5:5:1) at a temperature of 0 °C. Further device

processing and assembly is identical to the one descripted in section 3.1.2. Fig. 3.8 shows

the SEM picture of such a device. The tail of the active region could be significantly

reduced compared to conventional waveguide etching (shown in Fig. 3.3). Using this

waveguide etching procedure in combination with a 4 µm-thick electroplated gold on top

Buried heterostructures

91

of the ridge resulted in very low thermal resistances (see Fig. 2.15). Devices processed

this way are presented in a subsequent chapter.

Fig. 3.8: SEM picture of a device that was fabricated using the advanced waveguide

etching I procedure, with thick electroplated Au on top.

3.4. Buried heterostructures

The buried heterostructure design requires the selective growth of epitaxial material

without creating leakage channels. Fig. 3.9 shows a schematic illustration of the device

where the arrows indicate the unwanted current paths.

Fig. 3.9: Schematic illustration of the buried heterostructure design. The arrows indicate

possible leakage through the blocking layers that must be suppressed.

Technology

92

However, if one is able to master the buried heterostructure technology, the advantages

are:

• a low thermal resistance of the device

• low waveguide losses

• possibility of epi-down mounting which further reduces the thermal resistance

• better uniformity for optical coatings on the facets

3.4.1. Investigation of epitaxial blocking layers

In the first buried QC laser, the waveguide was buried in undoped InP (i-InP) [158]. The

parasitic current path, indicated by the arrows in Fig. 3.9, presents an n-i-n structure in

which space-charge-limited current is the main conduction mechanism. The essential

difference between a metal-semiconductor contact and an n-i-n structure is that in the

former case, the barrier is fixed in space, whereas in the latter the barrier (mainly

formed by a mobile charge injected into the i-region) moves toward the emitter contact

with increasing current. Grinberg and Luryi presented a parametric model for

calculating the IV characteristic of symmetric n-i-n structures [159]. The main

assumption in their model is a constant value of the quasi-Fermi level in the n-regions

and that the entire charge in the i-region is due to mobile carriers, injected from the

doped n-regions. That means that they are neglecting both the fixed charge due to

background doping and the mobile charge thermally generated across the forbidden gap.

For high current densities and a large width w of the i-region (high current limit), their

model goes over into the Mott-Gurney law (which simply ignores the field distribution in

the i-region and the diffusion of injected carriers) and the current density reads:

J

high= 9µ!!

0U

2 / (32"w3) where µ is the mobility in the i-region. For the low current

limit, they derived an equation which describes the linear IV regime:

J

low= 2! 2µ""

0kTU / (qw3[1+ #]) where

! = 2

23 w"1 (#

0#kT ) / (4$q2 N

D) exp(0.5) , where

N

D

is the doping of the n-regions. Fig. 3.10 shows the computation of an n-i-n structure as

function of applied bias for different i-region widths, where the n-regions are doped

1 x 1017 cm-3. For a 2 µm-wide i-region at a bias of 9 V (the typical operation bias of a QC


93

laser), this results in a current density of ~4 kA/cm2, which is 3-4 times higher than the

typical pulsed threshold current density of a QC laser.

Fig. 3.10: Experimental data of the n-i-n structure with a 2 µm-wide i-region and

theoretical approximations of the parametric IV for different widths of the intrinsic

region.

In order to prove their theory, a test structure, consisting of a simple n-i-n structure, has

been processed into mesas. The nominal layer thicknesses and doping levels are given in

the figure caption of Fig. 3.11. The IV of the structure is shown in Fig. 3.10 (solid line).

Within the uncertainty of the exact layer thickness of the i-region and considering the

assumptions made in the model, reasonable agreement is found between model and

experiment.

Fig. 3.11: Schematic illustration of the n-i-n teststructure. The growth started on a

~350 µm-thick InP substrate (~1-2 x 1017 cm-3), followed by the 2 µm-thick i-InP.

The top contact consists of 100 nm InP (2 x 1018 cm-3) and 50 nm InGaAs

(2 x 1019 cm-3). Ti/Pt/Au contacts were evaporated on the top and bottom.

Technology

94

As demonstrated, i-InP is inappropriate for proper current confinement in buried

heterostructures. In the framework of this thesis, two approaches have been investigated

to reduce this parasitic current path. Since the space-charge-limited current is

proportional to the mobility, which is actually relatively high in undoped materials (i-

InP: 3000 cm2V-1s-1 at room temperature), one strategy targets on reducing the mobility

by inserting InAlAs barriers within the i-InP. Another possibility that we investigated is

to use Iron-doped InP where the Iron acts as deep level defect (which pins the Fermi

level near the middle of the band-gap) that cancels the net charge. The use of p-n-p-n

blocking layers would have been another option but as already discussed, p-doping is not

welcome in QC lasers and furthermore, a lower capacitance is expected in InP:Fe buried

heterostructures that would enable higher modulation bandwidths.

In order to evaluate the Fe-doping level in InP, a Si-doped compensation structure was

grown, consisting of three sections, where two sections (each 300 nm thick) were doped

with different Fe concentrations. Fig. 3.12 shows the effective doping profile of the

structure, measured with a CV-profiler (Dage CVP 21). The derived Fe-doping levels

are indicated.

Fig. 3.12: Effective doping level in a compensation structure that was grown on a

doped InP wafer. All sections are doped with the same amount of Si. In addition,

sections A and B are doped with two different amounts of Fe-doping.


95

Fig. 3.13 shows schematically the test structures that have been fabricated for evaluating

the blocking characteristics. The detailed layer sequences are given in the figure caption.

Fig. 3.13: Schematic illustration of the blocking layer test structures. The growth

started on a ~350 µm-thick InP substrate (doped ~1-2 x 1017 cm-3), followed by the

blocking layer. The top contact consists of 100 nm-thick InP (Si, 2 x 1018 cm-3) and

50 nm-thick InGaAs (Si, 2 x 1019 cm-3). Ti/Pt/Au contacts were evaporated on the

top and bottom. The blocking layer consists of a) 2 µm-thick InP (Fe, 3 x 1016 cm-3)

and b) 8 stacks of 200 nm i-InP and 20 nm i-InAlAs followed by a layer of 200 nm i-

InP.

As seen in Fig. 3.14, introducing of InAlAs blocking layers has significantly reduced the

leakage current density, compared with i-InP without blocking layers. The space-charge-

limited current could be further reduced by using semi-insulating InP:Fe. The

temperature dependence of the space-charge-limited current is shown in the Arrhenius

plot depicted in Fig. 3.15. The examined temperature range is typical for the core

temperature of a CW operated QC laser. Although the space-charge-limited current

increases in InP:Fe over approximately two orders of magnitude more compared to i-

InP with InAlAs barriers, its absolute values at high temperature are still two orders of

magnitude lower.

Although one could have inserted more InAlAs blocking layers in i-InP, we decided to

use semi-insulating InP:Fe since it would show a lower capacitance, and less problems in

the regrowth on non-planar structures are expected (current channels along the ridge).

Furthermore, the trapping of carriers should also result in less free-carrier absorption.

Technology

96

Fig. 3.14: IV of the test structures using i-InP, InP:Fe and i-InP with 8 InAlAs

barriers as blocking layers.

Fig. 3.15: Arrhenius plot of i-InP with 8 InAlAs barriers and InP:Fe. An activation

energy of 588 meV and 289 meV was extracted for Fe and AlInAs, respectively.

3.4.2. Selective growth on non-planar structures

Selective growth means the restriction of the growth to semiconductor surfaces that are

confined with a mask on which no growth is possible. Fortunately, the MOVPE growth

characteristics for selective epitaxy are very similar to those on planar surfaces.

However, the shape and orientation of mask and waveguide profile will strongly


97

influence the shape of the regrowth, which depends not only on the growth conditions

(III/V-ratio, partial pressures and temperature) but also on the exposed crystallographic

orientation that exhibit different growth rates and the possibility of surface migration.

The requirement on the mask material is that no growth should happen at typical

epitaxial growth temperatures. Furthermore, a good temperature stability and good

adhesion on the semiconductor is required. Commonly, amorphous materials like Si3N4

and SiO2 are used as mask material. The growth conditions need to be chosen in such a

way that desorption of precursors happens before the formation of nucleuses. In order

to avoid the latter, a proper cleaning of the mask prior to the selective regrowth is very

important. The masked area will influence the vertical growth rate which will increase,

because the masking reduces the effective semiconductor surface. Since the growth

proceeds not only vertically but also laterally, an important parameter is the overhang of

the mask. Too small an overhang will favor lateral overgrowth of the mask but too much

overhang will lead to an orifice between mask and regrown material, because the

diffusion of precursors is limited resulting in a reduced growth rate, and as a

consequence, in the formation of void. This would be undesirable for epi-down

mounting.

Fig. 3.16: Schematics for the preparation of the sample for selective regrowth.

The fabrication of the SiO2 mask and the waveguide etching procedure is similar to the

procedure described in the section 3.3, however, the thickness of the mask was increased

to 400 nm which allows deeper underetching of the mask. The waveguide etching is

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98

tuned to end up with an overhang of 5-6 µm on each side of the ridge by increasing the

selective underetching of InGaAs. The structure prior to the regrowth with InP:Fe is

schematically shown in Fig. 3.16. Regrowth of InP:Fe was performed at a total pressure

of 160 mbar, a V/III ratio of 66 and a temperature of 630 °C. Ferrocence (CP2Fe) was

used as precursor for Fe doping (6 x 1016 cm-3). After regrowth, the device was passivated

with Si3N4 in order to avoid possible leakage paths through defects, and a small window

was opened on top of the ridge. An SEM picture of the finalized device is shown in Fig.

3.17. The thermal resistances of such buried structures are shown in the Fig. 2.15.

Fig. 3.17: SEM picture of a QC laser facet in buried heterostructure fashion. The

dashed lines indicate the active region and the regrown blocking regions.

3.5. Epi-side down mounting

As already pointed out, one of the advantages of the buried heterostructure design is its

possibility to end up with planarized waveguides that are suited for epi-down mounting.

Special care has to be taken to avoid shortening the device with the solder. For this

reason, a 3-4 µm thick Au layer is electroplated on top of the device; its function is not

only to spread the heat but also to act as spacer. In the first step, devices were soldered

to submounts which were in a subsequent step mounted to copper mounts. Furthermore,

the solder was deposited on the submount prior to mounting. Evaporated In is used as

solder for mounting devices on diamond since it relaxes the requirement of having

similar thermal expansion coefficients. SnAu eutectic solder is used for mounting on

Advanced waveguide etching II

99

AlN. Fig. 3.18 depicts the thermal resistance versus temperature of a 9.5 µm-wide and

3 mm-long epi-down on diamond mounted QC laser. At 303 K, the device shows a

thermal resistance (extracted from CW and pulsed threshold current values) of

4.28 K/W that equals a thermal conductivity of 820 W/(Kcm2). Surprisingly good

agreement with theoretical values are achieved (see Fig. 2.15).

Fig. 3.18: Experimental data of the thermal resistance versus temperature of a

9.5 µm-wide and 3 mm-long epi-down on diamond mounted QC laser. Shown are

the values for the uncoated and HR-coated device.

3.6. Advanced waveguide etching II

The discussed waveguide etching procedure is well suited for conventional (non-buried)

device fabrication. However, combining this etching procedure with the buried

heterostructure design will result in non-planarized devices, showing a groove on both

sides of the waveguide (see Fig. 3.17). Such a regrowth behavior was never observed in

conventionally etched waveguides. These grooves may not only accumulate residuals of

resist or other processing chemicals, possibly degrading the lifetime of the device, but

can also reduce the heat flow out of the active region.

The origins of the grooves were studied in a separate experiment in which a step (in

[110] direction) was etched into InP pior to the regrowth (dashed line in Fig. 3.19). The

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100

regrowth consisted of InP:Fe (6 x 1016 cm-3) with 2 nm thick InAsP markers to study the

growth behavior, which were spaced by 600 nm. In fact, the grooves, seen after the

overgrowth of the QC laser structure, are also present after the regrowth of this simple

geometry in InP. We believe that the slightly negative angle of the sidewalls in InP

(caused by the selective etching) is responsible for the growth behavior since different

crystallographic orientations exhibit different growth rates. Unfortunately, the exact

growth behavior is not clear since the markers are not seen in the [111] direction, which

might be due to a reduced sticking coefficient of the marker material along this growth

direction.

Fig. 3.19: SEM picture showing the regrowth behavior on a step in InP (dashed

line), oriented in [110] direction. The second groove on the very left side is the

result of another etching step which is not shown.

Obviously, the etching of the active region with the non-selective etching

CH3COOH:HCl:H2O2 (used to etch the active region after selective InP etching) is not

sufficient enough to remove the negative angle in InP. A more isotropic etching is the

HBr:HNO3:H2O etchant solution which removes all negative angles at the waveguide

sidewalls when used for etching the active region. Regrowing InP:Fe on top of this

resulted in a groove-free buried heterostructure (see Fig. 3.20).


101

Fig. 3.20: SEM picture of the buried QC laser structure shows no grooves.

However, lots of defects appeared after the regrowth (see Fig. 3.20 and Fig. 3.21). Since

these defects are mainly located on and along the mask (which purpose is to prevent the

growth), it is assumed that residual Bromine complexes contaminate the mask,

preventing desorption and resulting in the formation of clusters (defects). As a

consequence, further processing is almost impossible and devices will most likely suffer

from high waveguide losses. In order to drastically reduce the defect density, an

experiment with different cleaning procedures has been conducted. A full wafer, on

which an active region and a waveguide have been grown, was cleaved in four quarters.

After masking with SiO2, InGaAs(P) and InP was etched selectively followed by a mask

cleaning according to Table 2.1. Subsequent, all samples were regrown in the same

MOVPE run using InP:Fe.

Fig. 3.21: Microscope images revealing a large number of defects on and along the

alignment figures and ridges.

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102

Table 3.1: List of active region etching and mask clean solutions (RT=room

temperature). In all experiments InGaAs(P) and InP were etched selectively.

Experiment: Active region etching: Cleaning solution:

A CH3COOH:HCl:H2O2 (5:5:1), RT -

B HBr:HNO3:H2O (1:1:10), RT H2SO4 (95 %), RT, 1 min

C HBr:HNO3:H2O (1:1:10), RT HCl:H2O (1:2), RT, 5 min

D HBr:HNO3:H2O (1:1:10), RT CH3COOH:HCl:H2O2 (5:5:1), 0 °C, 1 min

In experiment A, CH3COOH:HCl:H2O2 was used for etching the active region but now

at room temperature, which should result in a more isotropic etching resulting in a

positve angle in InP. In the experiments B, C and D, different acids were tried for

cleaning the mask after etching the active region with the Bromine etchant. While

H2SO4 and HCl:H2O (1:2) should not cause any additional etching of the waveguide,

CH3COOH:HCl:H2O2 at 0 °C will etch ~0.5 µm, however, the positive angle of the

sidewalls should be retained. Fig. 3.22 illustrates the defect density on the ridges after

regrowth. Using CH3COOH:HCl:H2O2 at room temperature for etching the active

region resulted in inhomogeneous underetching of the mask leading to rough sidewalls

and a large number of defects (mainly beside the mask). This might be the result of the

extremely high activity of the etchant at room temperature. Experiment B shows an even

higher defect density on the ridges than without cleaning, disqualifying this cleaning

procedure. In contrast, experiments C and D reveal defect-free masks demonstrating the

efficiency of the cleaning. Fig. 3.23 reveals that using CH3COOH:HCl:H2O2 at room

temperature still results in grooves after the regrowth (experiment A). The SEM picture

for experiment B shows that most of the regrowth material was deposited on top of the

mask resulting in a very low growth rate around the ridge. Astonishingly, experiment C

resulted again in grooves which leads to the assumption that diluted HCl still etches InP

(reshaping the negative angle in InP). Fortunately, experiment D resulted in the desired

regrowth behavior.


103

Fig. 3.22: Microscope pictures show the defect density on the regrown waveguides.

Fig. 3.23: SEM pictures of the front facet of buried QC laser structure after

different cleaning attempts. The arrows indicate grooves.

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104

In summary, selective etching of InGaAs(P) and InP combined with the Bromine

containing acid for etching the active region and CH3COOH:HCl:H2O2 for the mask

cleaning results in groove-free and almost defect-free buried heterostructure QC lasers.

Fig. 3.24 shows the front facet of a QC laser where the ridge width is as narrow as

3.5 µm.

Fig. 3.24: SEM picture of a QC laser front facet showing a width of the active

region of 3.5 µm.

Chapter 4

4. Two-phonon resonance versus bound-to-

continuum design

4.1. Introduction

As already discussed, the two-phonon resonance and the bound-to-continuum design

are the most promising active region designs for high performance. In this chapter, their

performances will be compared utilizing otherwise identical devices. One goal of this

work was to investigate the gain spectrum of those two designs. Therefore, the

intersubband linewidth was measured at different bias voltages and temperatures.

Differential gain, waveguide losses, threshold current densities and slope efficiencies of

lasing devices are compared. Furthermore, since both designs show completely different

linewidths, these experimental data are used to validate the model for the intersubband

linewidth, presented in section 2.1.4.

4.2. Design and experiment

The active region band structures are depicted in Fig. 4.1, both tailored for emission at

8.4 µm. The active regions (consisting of 35 cascades) were grown on low doped

substrates (1-2 x 1017 cm-3) in subsequent runs in the MBE system, sandwiched between a

lower 220 nm and an upper 310 nm thick InGaAs layer (6 x 1016 cm-3). The exact layer

sequences and the doping profiles are given in the figure caption of Fig. 4.1. X-ray

measurement revealed 5.9 % thicker layers than designed for the bound-to-continuum

type, which was considered in following calculations. Subsequently, the samples were

overgrown in the MOVPE system. The waveguide consists of a 4 µm thick InP layer (Si,

Two-phonon resonance versus bound-to-continuum design

106

1 x 1017 cm-3), two 15 nm thick quaternary InGaAsP layers (Si, 1 x 1018 cm-3), with band

gaps corresponding to photoluminescence maxima of 1.1 and 1.28 µm, respectively, and

a 300 nm thick plasmon-enhanced layer (Si, 9 x 1018 cm-3). The growth was terminated by

a 50 nm thick contact layer (Si, 2 x 1019 cm-3).

Ridges 8.5 to 11.5 µm wide were then wet-etched and subsequently buried with InP:Fe.

After passivation with Si3N4, a window was etched on top of the ridge. After contact

evaporation, a 3 µm thick layer of gold was electroplated on the top. Finally, devices

were cleaved, soldered with In to copper mounts, and wire bonded.

Fig. 4.1: Bandstructure and the moduli squared of the relevant wave functions for

one out of Np=35 cascades under an applied electric field of 33 kV/cm. The layer

sequence of one active cell, given in nanometers and starting from the injector

barrier of a) the two-phonon resonance design is 4.3/ 1.7/ 0.9/ 5.4/ 1.1/ 5.3/ 1.2/ 4.7/

2.2*/ 4.3/ 1.5/ 3.8/ 1.6/ 3.4/ 1.8/ 3.0/ 2.1/2.8/ 2.5/ 2.7/ 3.2/ 2.7/ 3.6/ 2.5 and b) the

bound-to-continuum design is 4.4/ 1.7/ 0.9/ 5.3/ 1.1/ 5.2/ 1.2/ 4.7/ 1.3*/ 4.2/ 1.5/ 3.9/

1.6/ 3.4/ 1.8/ 3.1/ 2.1/2.8/ 2.5/ 2.7/ 3.2/ 2.7/ 3.6/ 2.5, where InAlAs barriers are in bold

face, InGaAs wells are shown in normal face, numbers underlined correspond to

the n-doped layers (Si, 1.5 x 1017 cm!3), and the asterisk denotes the extraction

barrier.


107

4.3. Intersubband linewidth

Electroluminescence was measured using a fourier-transform infrared spectrometer

(Nicolet 860) together with a LN2 cooled MCT detector (EG&G J15D16-M208-S250U-

06) in step-scan mode and a lock-in amplifier (EG & G Instruments 7265). In order to

avoid superluminescence, very short lasers (~170-230 nm) were cleaved, and the

spontaneous emission was measured perpendicular to the waveguide. The FWHM of

the linewidths for both designs are shown in Fig. 4.2. The linewidths broaden with

increasing temperature. The bound-to-continuum design shows wider gain spectra;

however, there is a marked narrowing of the linewidth with increasing bias, leading to

widths comparable to the two-phonon resonance design at high bias.

Fig. 4.2: Theoretical and experimental linewidths vs bias voltage at different

temperatures of a) the two-phonon resonance and b) the bound-to-continuum

design.

Fig. 4.3a shows the measured spectra of the two-phonon resonance design at 303 K. The

broad peak centered around 220 meV indicates injection from the ground state |g! into

the second upper state |13!. This peak is also present in the bound-to-continuum design

since both structures have an almost identical injector design. Applying equations (2.43)-


108

(2.47) to the experimental data at 8 V of the two-phonon resonance design, an interface

roughness parameter product !" =0.973 nm2 for the growth of InGaAs/InAlAs layers in

our MBE system is found, which is close to the one extracted in an earlier experiment

(1.01 nm2) [142]. Using this parameter, the theoretical luminescence spectra were

computed, which are shown in Fig. 4.3b. Comparison of theoretical and experimental

curves indicates reduced injection efficiency at biases below 7 V.

Fig. 4.3: a) Experimental and b) theoretical lineshape at different bias voltages of

the two-phonon resonance design.

The model was also applied to the bound-to-continuum data (using the interface

roughness parameter product derived for the two-phonon resonance design). The

calculated linewidths for both designs are shown in Fig. 4.2. In Fig. 4.4, the different

contributions to the bias dependent linewidth are shown for a temperature of 303 K.

Intra- and intersubband linewidth broadening is shown in Fig. 4.4a, which contributes

~5.3-5.8 meV to the linewidth and is dominated by intrasubband broadening. Interface

roughness broadening of the different transitions (see Fig. 4.4b) shows a strong bias

dependence. The different contributions to the linewidth are weighted by the oscillator

strength depicted in Fig. 4.4c. The marked narrowing of the linewidth with increasing

bias voltage in the bound-to-continuum design is explained by the number of states (with


109

different transition energies Eij) over which the oscillator strength spreads (|11!, |10!,

|9! and |8!), which decreases with increasing bias and finally is concentrated on the |11!

state. In the two-phonon resonance design, the oscillator strength is mainly distributed

over two transitions and we observe a narrowing with increasing bias because the active

region is still coupled to the injector region. Since the temperature dependence of the

interface roughness scattering is very weak, the dominating temperature broadening

mechanism in MIR QC lasers is intrasubband lifetime broadening (Fig. 4.2).

Fig. 4.4: Theoretical calculation of a) lifetime broadening, b) interface roughness

broadening and c) oscillator strength vs bias voltage for different transitions of the

two-phonon resonance (left side) and bound-to-continuum design (right side) at

303 K.


110

4.4. Laser performance

For a fair comparison, two 3 mm-long lasers with identical ridge width (10.1 µm) were

selected. In order to derive the resonant and non-resonant waveguide losses, the devices

were measured before and after HR coating of the back facet.

4.4.1. Pulsed and CW laser characteristics

Using a pulse generator (Agilent 8114A), the devices were first measured with 200 ns

wide pulses and a repetition frequency of 99 kHz. Fig. 4.5 shows Light-Current-Voltage

(LIV)-curves of both (HR coated) devices at different temperature, measured with a

calibrated thermopile detector (Ophir Optronics 3A-SH).

Fig. 4.5: LIV-curves of the two-phonon resonance (solid line) and the bound-to-

continuum (dashed) QC laser measured in pulsed operation (200 ns, 99 kHz) for

different temperatures. The setups’ collection efficiency of 74 % is not corrected in

this plot.

Astonishingly, the laser characteristics of the two designs are very comparable.

Although, based on the linewidth measurement, one would expect much higher

threshold current densities, the bound-to-continuum designs shows only marginally

larger values compared to the two-phonon resonance design. Fig. 4.6 shows the LIV-

curves in CW operation measured with a dc laser driver (ILX Lightwave LDX-3232).

Laser performance

111

These devices are lasing CW up to a temperature of 70 °C (bound-to-continuum) and

80 °C (two-phonon resonance), respectively. From CW and pulsed threshold current

data, a thermal resistance of 8.8 and 9.0 K/W, which equals a thermal conductivity of 375

and 376 W/(Kcm2), was extracted for the bound-to-continuum and two-phonon

resonance device, respectively.

Fig. 4.6: LIV-curves of the two-phonon resonance (solid line) and the bound-to-

continuum (dashed) QC laser measured in CW for different temperatures.

4.4.2. Transport

The two active region designs differ mainly by a slightly thicker extraction barrier in the

two-phonon design (marked with an asterisk in the figure caption of Fig. 4.1), which

partly decouples the active region from the injector. An interesting question is whether

the thicker extraction barrier significantly limits the transport. For an accurate

estimation of the transport time !

trans, we consider the reduction of the upper state

lifetime by the optical field (which affects the tunneling time !

tunnel). For this reason,

J

max= q

0n

s/ (!

trans+ !

tunnel) is taken from the luminescence measurement at the bias equal

to the laser’s roll over voltage. This is shown in Fig. 4.7 for the bound-to-continuum

sample.


112

Fig. 4.7: LIV-curve of the lasing and luminescence device (bound-to-continuum

design) measured in pulsed mode (200 ns, 99 kHz). The arrow indicates the

maximum injectable current (without the influence of the phonon field).

The lower J

max in the bound-to-continuum design in respect to the two-phonon

resonance design is explained by the longer tunneling time ( !

tunnel,BTC=2.06 ps and

!

tunnel,2Ph=1.23 ps at 303 K) through the 5.9 % thicker injection barrier (resulting from

the higher growth rate). Since the measured doping level equals in both designs, we find

that the slightly thicker extraction barrier in the two-phonon design is not significantly

limiting the transport time ( !

transit,BTC=2.0 ps and

!

transit,2Ph=2.1 ps at 303 K).

4.4.3. Waveguide losses

Fig. 4.8 shows the experimental total waveguide losses extracted from the ratio of

threshold currents of uncoated (CL) and coated device (HR):

!wg

= (!m,HR

"!m,CL

# Jth,HR

/ Jth,CL) / ([J

th,HR/ J

th,CL]"1) . In addition, the ratio of slope

efficiencies are used for the extraction of the non-resonant losses (excluding resonant

losses, see section 2.1.5). As we assume a sub-linear dependence of gain on the injection

current, we extract the non-resonant losses from the slope efficiencies at 243 K and

extrapolate the temperature dependence from the derivative of the slope efficiency

itself.

Laser performance

113

Fig. 4.8: Theoretical and experimental total and non-resonant waveguide losses for

the bound-to-continuum (BTC) and two-phonon resonance (2Ph) design.

As seen from Fig. 4.8, the total waveguide losses of the two designs are very similar. This

is actually not too surprising, since both designs have an almost identical injector design.

The fact that the total waveguide losses increase faster with temperature than the non-

resonant losses is a clear indication of increased backfilling (resonant losses). Fig. 4.8

also shows the theoretical waveguide losses comprising the empty waveguide losses

(assumed temperature independent) and the intersubband losses. The intersubband

losses are split in resonant losses, arising from thermal backfilling, and the non-resonant

losses, due to the tail of the absorption in the injector. In this calculation, we assume a

fixed line-broadening for the intersubband losses, taken from the theoretical linewidth

calculations at high bias (only one optical transition involved). Although it is a very

crude approach to use a single linewidth value for all the different transitions,

reasonable agreement between experiment and theory was achieved. It could be

improved by calculating the individual linewidth for each transition.


114

4.4.4. Differential gain

Differential gain was derived from the experimental threshold current densities and

total waveguide losses shown in Fig. 4.9. Within errors, differential gain is very similar in

both designs. The theoretical differential gain, as discussed in section 2.1.2, is also

shown. Excellent agreement between theory and experiment was attained for the two-

phonon resonance design. The model results in a lower differential gain for the bound-

to-continuum design because the calculated linewidths are wider than in reality (see Fig.

3.1).

Fig. 4.9: Theoretical and experimental differential gain versus temperature for the

two-phonon resonance (2Ph) and bound-to-continuum (BTC) design.

4.4.5. Threshold current density and slope efficiency

Experimental threshold current densities do not show a significant difference between

the two designs (Fig. 4.10a). This is explained by the larger matrix element in the bound-

to-continuum design ( z

BTC=2.72 nm and

z

2Ph=2.5 nm at 300 K), which largely

compensates for the broader gain spectrum. Theoretical threshold current calculations

show a difference between the two designs, which is due to the difference between

theoretical and experimental linewidths for the bound-to-continuum type. The

theoretical slope efficiency (calculated using the non-resonant waveguide losses)

deviates at low temperature from the measured values, indicating that the losses are not

Conclusion

115

correctly predicted (Fig. 4.10b). In fact, applying the experimental non-resonant losses

for the slope efficiency calculation improves correlation with the measurement (black

curves).

Fig. 4.10: Theoretical and experimental values of a) threshold current density and

b) slope efficiency of the bound-to-continuum (BTC) and two-phonon resonance

(2Ph) design. The setups’ collection efficiency was taken into account.

4.5. Conclusion

Key parameters of the bound-to-continuum and two-phonon resonance active region

design were experimentally and theoretically compared.

The two-phonon resonance design shows very narrow linewidths and seems most

promising for performance in terms of low threshold current densities and therefore low

power consumption. However, the bound-to-continuum design shows wider gain spectra

and is therefore interesting for broad gain applications. Fortunately, the stronger matrix


116

element in the bound-to-continuum compensates to a large extent for the larger

linewidths.

Furthermore, the model for the calculation of the temperature and field dependent

intersubband linewidth in mid-IR quantum cascade laser designs was verified. Excellent

agreement with the experiment was found for the two-phonon resonance design.

Linewidths are slightly overestimated in the bound-to-continuum design. Differential

gain and threshold current density are in excellent agreement for the two-phonon

resonance design. Although the slope efficiency is somewhat underestimated at low

temperatures, there is still reasonable agreement with the experiment. In conclusion,

this simple model constitutes a useful evaluation tool for quantum cascade laser designs

to a priori predict their linewidths.

Chapter 5

5. Low power consumption laser sources

5.1. Introduction

The focus in this chapter is the realization of single mode devices with very low

threshold current densities but enough dynamic range for large thermal tuning in CW

operation. This will permit fabrication of hand-held or remotely deployed, battery-

operated systems using infrared sources with very low electrical power consumption but

high tunability and output power.


As seen in the previous section, the two-phonon resonance design shows the best

performance in terms of low threshold current densities. Therefore, this design was

selected for the realization of a low power consumption device. In this experiment, the

active region design is tailored for an emission at !!9 µm; it was already used for the

first demonstration of CW operation at room temperature in 2002 [92]. However, the

doping levels of injector and top and bottom waveguide were strongly reduced in order

to reduce intersubband and empty waveguide losses. Furthermore, the devices were

designed in a narrow–ridge buried heterostructure fashion and mounted epi-down. This

allows to significantly reduce the CW threshold current. In addition, a strongly coupled

grating was used to further reduce the DFB cavity losses.

The fabrication of these lasers started with a 200 nm InGaAs lower confinement layer

(Si, 4x1016 cm!3) by molecular beam epitaxy, followed by the active region, and a 300 nm

InGaAs upper confinement layer (Si, 4x1016 cm!3). The layer sequence of one active cell,

Low power consumption laser sources

118

out of NP=35 cascades, given in nanometers and starting from the injector barrier is 4.0/

1.9/ 0.7/ 5.8/ 0.9/ 5.7/ 0.9/ 5.0/ 2.2/ 3.4/ 1.4/ 3.3/ 1.3/ 3.2/ 1.5/ 3.1/ 1.9/3.0/ 2.3/ 2.9/ 2.5/ 2.9,

where InAlAs barriers are in bold face, InGaAs wells are shown in normal face, and

numbers underlined correspond to the n-doped layers (Si, 7x1016 cm!3). All these layers

were lattice matched to the low doped InP substrate (Si, 1–2 x 1016 cm!3). The DFB

gratings were etched 0.17 µm deep into the top confinement layer and overgrown by the

MOVPE with a 4.4 µm InP cladding layer (Si, 5 x 1016 cm!3) and two 15 nm quaternary

InGaAsP layers (Si, 2 x 1016 cm!3), for smoothing the conduction band offset. The growth

was terminated by a 330 nm plasmon layer (Si, 7 x 1018 cm!3) and a 50 nm, highly doped

contact layer (Si, 2 x 1019 cm!3). The advanced waveguide etching procedure II was used to

etch ridges 11 to 14 µm wide and the waveguides were re-introduced into the MOVPE

system and buried in InP:Fe. Further processing was identical to that described in

chapter 4. Finally, the lasers were mounted either epi-up on copper mounts using

indium solder, or epi-down on AlN submounts which were then soldered to copper

mounts using tin-gold solder for both steps.

5.3. Laser performance of moderately coupled devices

Mounted lasers were placed on a high-temperature Peltier element and the temperature

was monitored on the submount with a thermistor. Optical power was measured using a

calibrated thermopile detector. The collection efficiency of our setup of 62 % was taken

into account. Spectra were recorded using a FTIR spectrometer Nicolet 860 together

with a deuterated triglycine sulphate (DTGS) detector.

5.3.1. CW laser characteristic

First, two HR coated devices, mounted epi-up and epi-down, were compared, having

identical length (1.5 mm) and only slightly differing ridge width of 12.0 µm (epi-up) and

12.7 µm (epi-down) and grating period !=1.419 µm (epi-up) and !=1.426 µm (epi-

down). The epi-up mounted device lased in CW up to a temperature of 353 K (80 °C),

while the one mounted epi-down showed a maximum CW temperature of 406 K

(133 °C), proving the importance of good thermal management. Fig. 5.1 shows the LIV-

curves of the epi-down mounted device.

Laser performance of moderately coupled devices

119

Fig. 5.1: LIV-curves of a 12.7 µm-wide and 1.5 mm-long epi-down mounted HR

coated device in CW operation.

Fig. 5.2: High resolution spectra of the 1.5 mm-long epi-down on AlN mounted

device at various temperatures and currents, showing a SMSR >25 dB (limited by

the spectrometer resolution).

At 303 K, the epi-down mounted device shows a threshold current density of

1.14 kA/cm2 which increases to 2.2 kA/cm2 at 406 K. The consumed electrical power of

1.6 W for an optical output power of 16 mW is comparable to results recently obtained

for QC lasers emitting at !!5.2 µm [160]. For an optical output power of 100 mW, an


120

electrical power of 3.8 W is consumed. This corresponds to wallplug efficiencies of 1.0

and 2.6 %. At room temperature, an electrical power of 1.7 W is consumed for an

optical output power of 1 mW, which is comparable with very short QC lasers emitting

at !!5.3 µm, where 1 mW was the maximum optical power achieved at room

temperature [161]. Fig. 5.2 shows the spectra of the epi-down mounted device. A total

tuning range of 12.1 cm-1 (13.6 cm-1) for the epi-up (epi-down) mounted device on a

Peltier element was achieved.

5.3.2. Thermal resistance and temperature tuning

In order to determine the thermal resistance, the two devices were measured also in

pulsed operation (200 ns, 99 kHz). The threshold current density values are plotted

together with the CW data in Fig. 5.3. The two devices are comparable in terms of active

region performance and waveguide losses, as shown by the extracted pulsed operation

values T0 and J0 (see Table 5.1) from the empirical equation Jth=J0exp(T/T0). For fitting

the CW data, the increase in temperature of the active region was taken into account by

using the implicit equation for the threshold current density,

Jth=J0exp([T+RthJthUthSact]/T0), where S

act is the area of active region and Uth the bias at

threshold. As one sees from Table 5.1, T0 and J0 are in good agreement with those from

our pulsed measurements and the published pulsed value for Fabry-Pérot devices [92].

A direct temperature tuning (1/")(#"/#T) of -7.9 x 10-5 K-1 (-6.6 x 10-5 K-1) and electrical

power tuning (1/")(#"/#P) of -1.0 x 10-3 W-1 (-5.2 x 10-4 W-1) was extracted for the epi-up

(epi-down) mounted device. As expected, the difference of direct temperature tuning

coefficients is small due to the only weak temperature dependence of the tuning

coefficient, but the !50 % lower electrical power tuning in the epi-down mounted

device is a clear result of the better thermal management. The thermal resistance

derived from the spectral characteristics is also shown in Table 5.1. The epi-up mounted

device shows a larger Rth for the active region compared with the one deduced from the

spectral characteristics, indicating that its active region is hotter than the area seen by

the optical mode.


121

Fig. 5.3: Threshold current density versus temperature for pulsed and CW

operation. The pulsed data were fitted using the empirical formula Jth=J0exp(T/T0).

The dotted lines serve as guide to the eye for the CW data. For calculation of T0

and Rth, see text.

Table 5.1: Values T0 and J0 of the epi-up and epi-down mounted devices, derived

from pulsed and CW data. Thermal resistance Rth for the active region (act) and

active region plus waveguide.

Epi-up Epi-down

Pulsed 171±1 187±3 [K] T0

CW 174±9 182±9 [K]

Pulsed 183±3 217±5 [A/cm2]

J0 CW 187±9 204±11 [A/cm

2]

Active region 17.5±3.5 5.6±2.0 [K/W] Rth

act+waveguide 12.7±0.7 7.9±0.6 [K/W]

5.3.3. Cavity losses

The very low doping of injector, waveguide and substrate leads to computed empty

waveguide losses !wg

empty of 1.8 cm-1 and intersubband losses !

ISB of 8 cm-1. Using the

calculated overlap factor !=0.62, total waveguide losses !

wg= !

wg

empty+ "!

ISB of 6.7 cm-1

are computed. This value is in very good agreement with the experimental value of

!

wg=6.6 cm-1, which was extracted from a 3 mm-long Fabry-Pérot device, using the

threshold current values at 303 K of the uncoated and HR coated device. Using the


122

threshold current density of the same device, we calculated a differential gain

g

d=10.25 cm/kA. From these data, we can derive the DFB cavity losses

!DFB

= Jth"g

d#!

wg!0.7 cm-1 from the threshold current density at 303 K of the epi-down

mounted DFB device.

5.3.4. Longitudinal and lateral mode discrimination

Fig. 5.4 shows the subthreshold emission spectra of the epi-up mounted device,

measured with the Nicolet 860 and a LN2 cooled MCT detector (EG&G J15D16-M208-

S250U-06), with the stopbands of the fundamental and first-order mode.

Fig. 5.4: Sub-threshold dc current spectrum of the epi-up mounted device,

measured at 220 mA and 303 K. Also shown is the laser spectrum just above

threshold.

However, the laser spectrum just above threshold (also shown in Fig. 5.4) indicates that

the device operates on the fundamental mode. From the stopband width !" =2.049 cm-1

and the effective index n

eff= 1 / (2!") =3.167, a coupling coefficient

! = "#$n

eff=20.4 cm-1 was calculated, resulting for our 1.5 mm-long devices in a

coupling product ! L of 3.1, which is three times larger than the critical coupling product

! L!1 [154]. Stable single mode CW operation with a side-mode suppression ratio >25


123

dB (limited by the spectrometer resolution) was observed within the entire examined

frequency, power and temperature range for both devices.

Spectroscopic applications require not only longitudinal single mode operation, but also

lasing on the fundamental lateral mode is highly desired. This is more difficult to achieve

in QC lasers in buried heterostructure fashion since the higher lateral modes are not as

efficiently damped as in the case of conventional waveguides, where the overlap with the

passivation and Au layer induces high optical losses. Fig. 5.5 shows the calculated modal

gain difference (using the software package "COMSOL Multiphysics" to solve the two-

dimentional wave equation) between the fundamental and two higher order modes for

DFB cavity losses between 0.2 and 1.3 cm-1. A modal gain difference !g

m=0.2–0.4 cm-1

between the fundamental and first-order lateral mode was calculated. In fact, stable

single mode operation on the fundamental lateral mode was observed in the evaluated

devices. Moreover, we found that even 14 µm-wide devices with a !g

m of only 0.1–0.2

cm-1 lase on the fundamental lateral mode.

Fig. 5.5: Calculated modal gain difference versus ridge width between the

fundamental and first and second order mode for different DFB cavity losses.


124

5.4. Laser performance of strongly coupled devices

Increasing the coupling product should allow to further reduce the DFB cavity losses.

Therefore, a 2.25 mm long and 11 µm wide device was epi-down mounted on AlN

(!=1.419 µm). The threshold current density reduced to 1.07 kA/cm2 at 303 K,

indicating DFB cavity losses of only 0.3 cm-1. Fig. 5.6 depicts LIV-curves of this chip,

which lased in CW up to a temperature of 423 K (150 °C) with the threshold current

density increasing to only 2.4 kA/cm2. To our knowledge, this is the highest reported CW

operation temperature for an intersubband laser. Fitting of the implicit equation for the

threshold current density results in a T0 of 189±11 K, a J0 of 195±16 A/cm2 and a Rth of

7.6±2.8 K/W. Fig. 5.7 shows the single-mode spectra of this device. The total tuning

range achieved on a Peltier element is 14.2 cm-1 or 1.3 % of center frequency, which is

the largest value reported for CW DFB QC lasers. However, for temperatures below

373 K, the device emits bi-mode for currents higher than 1.25! I

th, which is due to the

strong distributed feedback coupling ( ! L!4.6).

Fig. 5.6: LI-curves of a 2.25 mm-long device mounted epi-down on AlN submounts.

Inset: Threshold current density vs temperature for CW operation. The dotted line

serves as guide to the eye. For calculation of T0 and Rth, see text.

Conclusion

125

Fig. 5.7: High resolution spectra (taken at about 1.1 x Ith) of the 2.25 mm-long epi-

down on AlN mounted device, showing a SMSR>25 dB (limited by the

spectrometer resolution).

5.5. Conclusion

In conclusion, reducing the waveguide losses using a low doping level and strong DFB

coupling in combination with a narrow-gain active region and a good thermal

management allowed to fabricate low-threshold current density and low power

consumption single-mode devices with high CW operation temperature. The doping of

the active region was sufficient to have some dynamic range that allows large thermal

tuning in CW. Tuning of 10 cm-1 or 0.9 % of center frequency was achieved by heating

the device. The threshold current density varies from 1.07 kA/cm2 at 303 K to 2.4 kA/cm2

at 423 K. Low electrical power consumption of 1.6 W and 3.8 W for an optical output

power of 16 mW and 100 mW have been demonstrated. The width of the waveguides is

sufficiently narrow to favor the fundamental lateral mode. Stable single mode operation

was observed in the entire frequency, power and temperature range with a SMSR

>25 dB.

Chapter 6

6. Quantum cascade lasers with widely spaced

operation frequencies

6.1. Introduction

In the previous chapter, low power consumption DFB QC lasers showing a tuning range

of approximately 1 % of the wavelength have been demonstrated. However, this tuning

range may be too small to scan complex mixtures with multiple absorption lines or

mixtures with very broad lines. In order to scan over a wider frequency range, it would

be more appropriate to build a device integrating several DFB lasers on one chip. The

spacing of the different DFB lasers has to be selected in such a way as to cause the single

tuning ranges to overlap in order to access a continuum of frequencies. Such a device

would hereby constitute a multi-channel laser spectrometer. In this chapter, the results

of monolithically integrated DFB lasers with widely spaced operation frequencies are

presented.


In order to integrate several DFB lasers with widely spaced operation frequencies and

reasonable high operation temperatures and powers on one chip, a gain medium with a

broad spectral width is required. Therefore, the bound-to-continuum design was

selected for this type of application. Furthermore, to reach single-mode operation, the

coupling strength of the DFB gratings must be large enough to ensure that the mode

discrimination is larger than the threshold gain difference, even in off-gain peak

Design and experiment

127

operation. At the same time, the coupling strength should not be too high, in order to

avoid overcoupling.

The growth of the laser structure starts with the waveguide core (lower confinement

layer, active region and upper confinement layer), which is grown by MBE. After this,

the gratings are defined into the upper confinement. Then the following layers are

grown by MOVPE. All layers are lattice-matched to the InP substrate. The

InGaAs/InAlAs based active region, which is designed for a center emission at 7.9 µm

(1270 cm-1), consists of 35 periods. The layer sequence of one active cell of the bound-to-

continuum design, given in nanometers and starting from the injector barrier, is 4.2/ 1.7/

0.9/ 5.3/ 1.1/ 5.2/ 1.2/ 4.7/ 1.3/ 3.9/ 1.5/ 3.5/ 1.6/ 3.3/ 1.8/ 3.1/ 2.1/ 2.8/ 2.5/ 2.7/ 2.9/ 2.6/ 3.3/

2.4, where InAlAs barriers are in bold, InGaAs wells in roman, and the numbers

underlined correspond to the n-doped layers (Si, 8 x 1016 cm-3). The lower 220 nm and

the upper 310 nm-thick confinement layers consist of low n-doped InGaAs (Si,

4 x 1016 cm-3) and are grown on an n-doped InP wafer (Si, 1–2 x 1017 cm-3). The DFB

gratings were defined in a single optical lithography step using a mask integrating 25

different grating fields. The first-order DFB grating periods range from 1.185 to

1.305 µm with a constant duty cycle of 50 %. Having defined the grating masks, 0.17 µm-

deep gratings were etched into the upper confinement layer (see photograph in Fig. 6.1).

Fig. 6.1: Photograph of a quarter of a two inch wafer after etching of the gratings.

The growth proceeded with a 4 µm-thick InP cladding layer (Si, 1 x 1017 cm-3) and two

15 nm thick quaternary InGaAsP layers (Si, 1 x 1018 cm-3) with band gap energies of 1.127

and 0.969 eV, respectively. Finally, the structure was terminated with a 300 nm-thick

Plasmon-enhanced layer (Si, 9 x 1018 cm-3) and a 50 nm-thick, highly doped contact layer

Quantum cascade lasers with widely spaced operation frequencies

128

(Si, 2 x 1019 cm-3), both layers consisting of InGaAs. In the next step, ridge waveguides

were formed by using the advanced waveguide etching procedure I and passivated by

deposition of a Si3N4 layer (the buried heterostructure technology was not developed at

that time). After opening the nitride on top of the waveguides, contacts were evaporated

and finally a 3 µm-thick layer of gold was electroplated on top in order to improve the

heat removal capacity of the device. A high-reflection coating was applied to the back of

1.5 mm-long laser bars. Finally, the lasers were epi-side up mounted onto copper

heatsinks with indium.

6.3. Laser performance

For the discussion of the optical and spectral characterization, three samples with three

different grating periods (A: 1.3 µm, B: 1.25 µm, and C: 1.2 µm, out of the 25 fabricated)

were chosen. The Bragg resonance of sample B lies close to center of the gain curve

whereas samples A and C are located towards the lower/upper limits of the available

wavelength range. Mounted lasers were placed on a high-temperature Peltier element.

The laser power was measured using a calibrated thermopile detector. The collection

efficiency of our setup of 74 % was not taken into account. Spectra were recorded using

a Bruker Vertex 70 FTIR spectrometer equipped with a DTGS detector.

6.3.1. CW laser characteristic

Fig. 6.2 shows a series of LIV-curves for all three lasers. At a temperature of +30 °C,

maximum output powers and slope efficiencies of 35 mW and 245 mW/A were observed

for laser B, whereas A and C show lower powers and slope efficiencies. In addition,

sample B reaches a maximum operation temperature of 60 °C while samples A and C

stop lasing CW at 35 and 45 °C, respectively. Fig. 6.3 is a scatter graph of the threshold

current density values of all investigated lasers at +30 °C. Although the plot contains

data for different ridge widths as well as intermediate grating periods (not belonging to

class A, B, or C), one can clearly see the overall trends. The threshold current densities

increase from the 1.87 kA/cm2 (sample B) to 2.62 kA/cm2 (sample A) and 2.45 kA/cm2

(sample C).

Laser performance

129

Fig. 6.2: Optical power and voltage versus current of samples A, B, and C at

different heatsink temperatures. Sample B is close to the center of the gain curve,

sample A and C are located towards the lower/upper limits of available frequency

range (corresponding spectra in Fig. 6.4).

An increasing specific thermal conductivity with decreasing ridge width was observed.

This effect should also decrease the threshold current density of continuous wave lasers,

as was reported for very wide and heavily doped lasers [162]. Nevertheless, narrower

ridges also tend to suffer from larger waveguide losses due to the stronger interaction


130

between the optical mode and the gold metallization. By comparing low doped and

relatively narrow devices, it is not expected to see a clear trend of threshold current

density with ridge width, as already discussed in section 2.2.2. Furthermore, the

threshold current of our DFB devices also depends on the relative phase of the grating

reflectivity and that of the facet. This explains the scattering of the data in Fig. 6.3 for

different ridge widths.

Fig. 6.3: Threshold current density in CW operation at +30 °C versus

wavenumbers for devices with different ridge widths. The threshold current

densities increase from 1.87 kA/cm2 (sample B) to 2.62 kA/cm2 (sample A) and

2.45 kA/cm2 (sample C).

6.3.2. Thermal resistance and tuning properties

Fig. 6.4 shows CW emission spectra of the three devices at different heatsink

temperatures. Emission energies (wavelengths) of 1206 cm-1 (8.3 µm), 1256 cm-1

(8.0 µm) and 1302 cm-1 (7.7 µm), respectively, were observed at +30 °C. Taking into

account the temperature tuning range of samples A and C leads to a total wavelength

coverage of more than 100 cm-1 (i.e. 8 % of the center frequency). Stable single-mode

CW operation with a side-mode suppression ratio > 25 dB was observed within the

entire examined frequency and temperature range.

Laser performance

131

Fig. 6.4: High resolution single mode CW spectra of samples A, B, and C showing

operation with a side-mode suppression ratio >25 dB. Depicted are the spectra at

1.1 x threshold and 30 °C and at the extremes of single laser tuning range achieved

by the variation of temperature. The corresponding single tuning ranges for

samples A, B, and C are 10, 15 and 12 cm-1, respectively.

Thermal resistances Rth and thermal tuning coefficients ! = (1/!)("!/"T) for samples A,

B, and C were extracted from the spectral characteristics. An average thermal tuning

coefficient ! =-8.88 x 10-5 K-1 and an average thermal resistance Rth of 12.4 K/W were

computed, which corresponds to an average specific conductance of 455 W/(Kcm2).

Excellent agreement with theoretical values are found (see Fig. 2.15). The electrical

power tuning (1 / !)("! / "P) = R

th# $ of -1.1 x 10-3 W-1 is two times larger than the one of

the epi-down mounted device in the previous chapter. The thermal resistance of sample

B was also calculated from the comparison of threshold currents in CW and pulsed

operation. A thermal resistance of 18.1 K/W was found. The higher value obtained with

this method compared to the spectral analysis is due to the non-unity ‘thermal overlap’

factor of the active region, already discussed in section 2.2.3.


132

6.3.3. Coupling strength and mode discrimination

The theoretical coupling coefficient ! of the DFB laser is derived by optical mode

calculations. From the SEM picture in Fig. 6.5, one finds that the grating was indeed

etched 170 nm deep into the 310 nm-thick InGaAs confinement layer. Using these

figures, a modulation of the effective index of !n

eff=0.01 was calculated. Assuming a

perfectly rectangular grating with a duty cycle of 50 % yields

! = 1 / " # $n

eff/ n

eff=25.5 cm-1. In this case, a coupling product of ! L=3.8 is computed.

Fig. 6.5: SEM picture of the 170 nm-deep DFB grating, etched into the top 310

nm-thick InGaAs cladding layer (period "=1.245 µm).

Experimentally, ! can be estimated from the stopband measurement of the

subthreshold emission spectrum. Fig. 6.6 shows the subthreshold emission spectra of

sample C, measured at 350 mA and +30 °C in CW operation with a Bruker FTIR IFS

66/S and an LN2 cooled MCT detector. The FP mode spacing, measured sufficiently far

away from the stopband, is 0.979 cm-1 and the stopband width is 2.17 cm-1. This yields a

coupling coefficient ! = "# $% $ n

eff=21.8 cm-1 and a coupling product ! L =3.25. The

discrepancy between the theoretical and the experimental calculations can easily be

explained by examining the profile of the real grating profile (see Fig. 6.5), which reveals

that the profile is not rectangular and the duty cycle is not exactly 50 %. The real shape

of the profile can be taken into account by weighting the theoretically calculated value

by the ratio of the first-order Fourier components of the exact profile and the real

Laser performance

133

profile. This yields !=21.6 cm-1, which corresponds perfectly to the result obtained in the

experiment. Although our coupling product is three times larger than the critical

coupling product (!"L!1), our DFB lasers yield stable single mode operation over the

total investigated spectral range.

Fig. 6.6: Subthreshold high-resolution emission spectra of sample C, measured at

350 mA and 30 °C in CW operation. The FP mode spacing is 0.979 cm-1 and the

stopband is 2.17 cm-1 wide.

6.3.4. Extrapolated gain spectrum and differential gain

In Fig. 6.7, the extrapolated gain spectrum, derived from the electroluminescence

measurement using (2.47), is shown together with the normalized inverse threshold

current densities of the three samples A, B, and C. The electroluminescence was

measured under an applied bias voltage of 9.6 V, a duty cycle of 4 % and a temperature

of 300 K. It exhibits a large FWHM value of 33.9 meV (274 cm-1), which corresponds to

a relative width of #$/$0= 21 %. In order to get a fair comparison between the threshold

values and the electroluminescence, samples A, B, and C were measured in pulsed mode

as well. Their inverse threshold current densities at 2% duty cycle are normalized to

sample B. Good agreement is found with the extrapolated gain spectrum. The overall

behavior leads to the conclusion that the gain must have its maximum close to the Bragg

resonance of sample B.


134

Fig. 6.7: Dashed line: Normalized electroluminescence spectrum at 300 K

measured under an applied bias voltage of 9.6 V. Solid line: Extrapolated gain

spectrum. Crosses: Normalized inverse threshold current density of the three

samples A, B, and C measured in pulse mode.

An interesting question is obviously, how far away from the gain center such a DFB laser

could still yield single mode operation. In order to estimate the gain margin between the

mode discrimination !" and the threshold gain difference !g , the difference between

samples A and B, which are separated by approximately 50 cm-1, was calculated. Since

the gain margin is dependent upon the thermal heat sinking of the device, this study is

only valid for pulsed operation. For two DFB lasers fabricated from the same piece of

material, the threshold gain g

th(!, J

th) = J

thg

d(!) is the same. However, sample B, which

has its Bragg reflectance close to the gain maximum, exhibits a lower threshold current

density compared with sample A, due to a higher differential gain. The ratio of the

differential gain can be expressed in terms of threshold current density

g

d(!

A) / g

d(!

B) = J

th,B/ J

th,A. From the values measured for samples A and B, this ratio is

g

d(!

A) / g

d(!

B) = 0.82. In other words, as one moves away from the gain maximum

(sample B), the 20 % higher threshold current density of sample A goes along with an

approximate 20 % reduction on the gain curve. Consequently, the threshold gain

difference between samples A and B can be written as !g = g

th,B(1" J

th,B/ J

th,A) . For

Evaluation of reliability for NASA Mars mission project

135

modes that have been sufficiently separated, !" is the difference between the threshold

gain of the Fabry-Pérot g

th,FP= !

wg

empty+ "!

ISB+!

m,FP and the DFB cavity

g

th,DFB= !

wg

empty+ "!

ISB+!

m,DFB. Empty waveguide losses

!

wg

empty of 3.4 cm-1, intersubband

losses !

ISB of 9.8 cm-1, cavity losses !

m,DFB of 0.7 cm-1, mirror losses "FP of 4.47 cm-1 and

an overlap factor ! of 74 % were computed. Since !" is as large as 3.8 cm-1, whereas !g

accounts for only about 2.0 cm-1, single mode operation is guaranteed, and could

potentially be extended over an even wider frequency range.

6.4. Evaluation of reliability for NASA Mars mission project

Some of these lasers have been selected for the NASA Mars Science Laboratory Mission

project. Based on an isotopic measurement at 7.79 µm (1283.6 cm-1) for CO2 and H2O2,

the goal is to evaluate whether Mars was ever inhabitable. To prove the robustness of

the lasers, an aging test at constant DC current of 360 mA was performed at Alpes

Lasers SA, using an 11 µm-wide and 1.5 mm-long DFB device (grating period 1.22 µm),

which was HR coated on the back facet. This laser was mounted epi-layer up on an AlN

submount with Indium solder and finally packaged in a module (see Fig. 6.8), which was

then sealed with 90 % N2 and 10 % He. With a thermoelectric cooler, the heatsink

temperature was maintained at 10 °C, corresponding to an active region aging

temperature of approximately 70 °C (estimated by using the calculated thermal

resistance).

Fig. 6.8: Photograph of a hermetical sealed module dedicated for the NASA Mars

Science Laboratory Mission [Courtesy of Alpes Lasers].


136

Optical power was measured using a calibrated thermopile detector placed directly in

front of the laser. Output powers and voltages of the device were recorded for more

than 11000 h at constant DC current. No significant long-term degradation of the

measured bias was observed within the recorded period. The power fluctuations are

mainly attributed to the alignment of the power meter with respect to the laser facet

since the power meter was also used for other measurement purposes. Fluctuations in

the temperature of the environment (laboratory was not tempered) also added to the

scattering of power and voltage data.

Fig. 6.9: Output power and voltage versus operation time of a hermetically sealed

QC laser at !=7.79 µm [Courtesy of Alpes Lasers].

6.5. Conclusion

Single-mode devices emitting CW at room temperature based on the bound-to-

continuum active region have been developed. The broad gain spectrum of this design

allows the fabrication of high-performance devices over a large wavelength range. By

using DFB gratings with 25 different periods, single-mode CW operation between 7.7

and 8.3 µm at a temperature of +30 °C was demonstrated from devices fabricated in a

single processing run, i.e. from one piece of material. This frequency span corresponds

to 8 % of the center frequency. This experiment demonstrated the usability of the

bound-to-continuum design for monolithic integration of high-performance DFB lasers

Conclusion

137

emitting at different wavelengths. Furthermore, an aging test was performed to prove

the reliability of such devices for real-life applications, such as in multi-channel laser

spectrometers.

Chapter 7

7. Broadly tunable heterogeneous quantum cascade

laser sources

7.1. Introduction

Some applications would strongly benefit from an even broader tuning range than

attained in the previous chapter. Broadening of the tuning range by simply increasing

the number of integrated DFB QC lasers is not very feasible because this will reduce the

fabrication yield of fully functional chip arrays and further complicate the optical

alignment of the different beams. An external cavity (EC) configuration is very

promising for this type of application [163], where the tuning range is mainly limited by

the shape of the gain spectrum of the QC laser architecture. EC systems designed for

QC laser have been undergoing constant improvement: the development of mode-hop

free tuning, CW operation at room-temperature, and recently the emergence of hand-

held, battery-operated modules, also suitable for field-deployment [124], [123], [164].

While significant progress has been made in the development of EC setups over the past

few years, the accessible range of frequencies is presently limited by the lack of suitable

gain chips, which are not only optimized for high-power and high-temperature

operation, but also for ultra-broad gain operation in CW, in order to achieve narrow

linewidths. Furthermore, operation at room temperature is most advantageous as it

eliminates the need for complicated and bulky setups. In this chapter, a broadly tunable

high performance QC laser source for broadband applications is presented.

Furthermore, the usability for broadband tuning at room temperature in an EC setup is

demonstrated.


139


Since differential gain is inversely proportional to the gain width, realizing both a broad

gain spectrum and at the same time a low threshold current value are two mutually

exclusive optimization parameters for CW operation at room temperature. Therefore, in

order to realize a high-performance broad gain chip, a careful selection of design

parameters is crucial.

7.2.1. Active region design

The tuning range is limited by the mode discrimination between Fabry-Pérot (FP)

modes and the EC mode. Therefore, single mode tuning will be possible as long as the

ratio of differential gain g

d(!) / g

max" # , where

! = "

EC

AR/"

FP

AR represents the ratio of the

total losses with and without the feedback of the EC of the anti-reflection (AR) coated

laser. In this experiment, two bound-to-continuum active regions with different center

wavelengths are combined within the same waveguide (see Fig. 7.1) and should allow a

broad gain spectrum. However, this can only be achieved as long as the spectral overlap

is strong enough to ensure gain clamping since it presents an inhomogeneous gain

medium. Such a heterogeneous QC laser based on two bound-to-continuum active

region designs was first demonstrated by Maulini et al. [105]. The same layer sequence

was chosen for our experiment: one region is centered at 8.2 µm (1220 cm-1, design A)

and the other at 9.3 µm (1075 cm-1, design B).

Fig. 7.1: Schematic illustration of the heterogeneous QC laser in buried

heterostructure fashion.

Broadly tunable heterogeneous quantum cascade laser sources

140

In order to avoid resonant losses at the lasing wavelength and therefore an increase of

the threshold current density, significant backfilling from the ground state into the lower

laser level must be avoided. Therefore, the energy difference !inj

between the lower

laser state and the chemical potential of the injector should be as large as possible. As

already discussed in section 2.2.1, since the operation bias of the device

U ! N

p(!" / q

0+ #

inj) increases with !

inj, a good compromise is a !

inj of 120-150 meV

[147]. Our injector design should result in a !inj

of 142 and 127 meV, applying a field of

48 and 40 kV/cm and defining the optical transition with the largest matrix element

(E12!E10) as the center transition, 151 meV (8.2 µm) and 133.5 meV (9.28 µm), for

designs A and B respectively. This energy separation should be sufficient to avoid

backfilling and should result in an operation voltage of 11 V. The layer sequence of the

active region, given in nanometer and starting from the injection barrier, is for design A

(8.2 µm): 4.3/ 1.8/ 0.7/ 5.5/ 0.9/ 5.3/ 1.1/ 4.8/1.4/ 3.7/ 1.5/ 3.5/ 1.6/ 3.3/ 1.8/ 3.1/ 2.0/ 2.9/ 2.4/

2.9/2.6/2.7/3.0/2.7, and for design B (9.3 µm): 3.9/2.2/0.8/6/0.9/5.9/1.0/5.2/1.3/4.3/1.4/3.8/

1.5/3.6/1.6/3.4/1.9/3.3/2.3/3.2/2.5/3.2/2.9/3.1, where InAlAs barriers are in bold print,

InGaAs wells are shown in roman numerals, and underlined values correspond to the n-

doped layers.

Another key design parameter is the doping of the injector. Doping leads to non-

resonant losses arising from the injector, as well as resonant losses resulting from

thermal backfilling. In order to realize low threshold currents, the doping should be as

low as possible but sufficient to ensure that tuning is limited by the mode discrimination

!" between Fabry-Pérot modes and external cavity modes and not by the gain.

Therefore, enough current needs to be supplied so that at least the threshold condition

can be reached: g(!) / g

max= J

th,EC

AR (gmax

) / Jth,EC

AR (!) . In order to have some dynamic range

(J

max! J

th,EC

AR ) / Jth,EC

AR to attain an output power level enabling high performance, the

lower bound of the Si doping can be estimated by: n

s= J

max!

tunnel+ !

trans( ) / q

0. A sheet-

density of 1.0 x 1011 cm-2 was chosen, resulting in a calculated maximum injectable


141

current J

max of 5.35 kA/cm2, which should be sufficient to allow some dynamic range. In

this calculation, we assumed a transit time !

trans of the electron across a period of the

active region at resonance of 1.4 ps (derived by multiplying the number of LO phonon

energy steps after the first intersubband scattering event N = (!! + "inj) / !!

LO#1 with

the LO phonon time of 0.2 ps [96]) and a injection barrier tunneling time

!

tunnel= (1+ 4 "

2

!3!!) / (2 "

2

!!) of 1.59 ps (using a dephasing time

!! of 40 fs, an upper

state lifetime !

3 of 0.56 ps and an energy splitting at resonance 2! ! of 6.78 meV).

7.2.2. Waveguide and thermal design

Doping of the waveguide layers was kept to a minimum since it affects the total

waveguide losses by free-carrier absorption. The growth started with MBE. The active

region was sandwiched between a lower 220 nm and an upper 300 nm-thick InGaAs (Si,

4 x 1016 cm-3) layer. Subsequently, the sample was introduced into the MOVPE. The

layer sequence and doping levels of the MOVPE grown layers was identical to that

described in chapter 5.

Fig. 7.2: SEM picture of an epi-side down on diamond mounted QC laser chip.

Inset: Close-up view of buried active region and Au heat spreader soldered to the

diamond.


142

Choosing 20 stages for each active region design resulted in an overlap factor of 74 %.

Empty waveguide losses !

wg

empty of 2.1 and 2.5 cm-1 for designs A and B were calculated.

Since the difference between the waveguide losses is minimal, no compensation of the

losses by the number of stages has been considered. After wet-etching 10 to 13 µm-wide

ridges, the waveguides were re-introduced into the MOPVE and buried with InP:Fe.

Further processing was identical to that described in chapter 4. After cleaving in 3 mm-

long devices, the lasers were Indium-mounted epi-side down on diamond submounts,

which had previously been soldered on copper heatsinks. Fig. 6.1 shows an SEM picture

of such a mounted device.

7.2.3. Single mode control in external cavity setup

A strong mode discrimination !" between FP and EC modes is realized by a

broadband multi-layer anti-reflection coating for the chip and a strong EC feedback.

The EC setup (shown in Fig. 7.3) is realized in Littrow configuration, where the first-

order diffracted beam from a 4 by 4 cm Au-coated grating (150 grooves/mm, blazed for

9.3 µm) is directly fed back into the laser cavity through an AR coated (3-24 µm)

Germanium aspheric lens (f/0.8).

Fig. 7.3: Photograph of the external cavity setup for continuous wave operation.

The ZnSe window of the laser housing (Alpes Lasers LLH-100) was removed.

Condensation is suppressed by operating the laser close to room temperature and

purging of the laser housing with N2.

Device characterization

143

The buried heterostructure design is very effective, since the planar facet allows the

deposition of uniform coatings and a more symmetric farfield pattern compared to ridge

waveguides. Since the light was extraced from the zeroth order of the grating (front

extraction), a HR coating could be evaporated on the back facet.

7.3. Device characterization

7.3.1. Gain chip performance

For characterization in terms of light output in CW and pulsed operation, the laser

power was measured using a calibrated thermopile detector. Spectra were recorded

using a Nicolet 860 FTIR spectrometer, together with a DTGS detector. Mounted lasers

were placed on a high-temperature thermoelectric cooler/heater and the temperature

was monitored on the submount with a thermistor. Fig. 7.4 depicts a series of LIV-curves

of an 11.8 µm-wide device at different temperatures.

Fig. 7.4: Optical power and voltage versus DC current of an 11.8 µm-wide and

3 mm-long HR coated device. Measurement was terminated at 4.9 kA/cm2 in order

to avoid damage of the device.

In order to avoid damage of the device, the maximum current density was limited to

4.9 kA/cm2. At 30 °C, a threshold current density of 3.97 kA/cm2 and a slope efficiency of


144

363 mW/A were observed. An output power of 100 mW was attained at a current density

of 4.9 kA/cm2. Despite the broad gain design, a maximum CW operation temperature of

50 °C with still 10 mW output power was achieved. Fig. 7.5 shows the spectrum of this

device measured in pulse operation indicating laser action over 180 cm-1, which takes

place mainly between the center wavelengths of designs A and B.

Fig. 7.5: High-resolution spectra taken at 1665 mA at 303 K in pulsed operation

(50 ns, 380 kHz) spanning over approximately 181 cm-1. The arrows indicate the

center frequency of the two active region designs. Inset: LI-curve, measured in

pulsed mode (100 ns, 99 kHz), exhibits a peak power of 1 W at 298 K at the

electrical roll-over at 3 A.

In order to investigate the thermal behavior, the device was also measured in pulsed

operation at different temperatures. At 30 °C, a current density of 2.97 kA/cm2 and a

slope efficiency of 698 mW/A were measured. The threshold current densities for

different temperatures are plotted in Fig. 7.6, together with the CW data. A

characteristic temperature T

0 of 117 and 206 K for CW and pulsed operation is

extracted, respectively. The extracted thermal resistance of 4.8 K/W accounts for the

buried heterostructure design and epi-down mounting on diamond. Although this is a

very low value, at a current density of 4.9 kA/cm2, the active region reaches a


145

temperature of 110 °C in CW (heatsink temperature of 30 °C), thus demonstrating the

paramount importance of a good active region design and heatsinking.

Fig. 7.6: Threshold current density versus submount temperature in CW and pulse

operation (200 ns, 99 kHz). The experimental data were fitted with the empirical

formula J

th= J

0exp(T / T

0) , resulting in a

T

0 of 117 and 206 K for CW and

pulsed operation, respectively.

Fig. 7.7: Solid line: CV-profile of the MBE-grown layers normalized by the

measured thickness using selective etching. Dashed line: The measured doping

profile reveals a 54±5 % higher active region doping level compared to the nominal

values.


146

The inset of Fig. 7.5 shows the LI-curve taken in pulsed operation at room temperature

with a peak power of 1 W. The device has a large dynamic range with the roll-over at a

current density of 8.47 kA/cm2. This value is higher than the one estimated in section

7.2.1. In order to clarify this point, the doping levels of the active regions were

measured. It turned out that the average doping level over one period is 54±5 % higher

than the nominal one (see Fig. 7.7), resulting in a carrier sheet density of 1.54 x 1011 cm-2

and a Jmax

of 8.24 kA/cm2. This is in good agreement with the measurement.

The total waveguide losses (resonant and non-resonant losses) were extracted from the

ratio of the threshold current densities of the coated and uncoated device, resulting in

!

wg

tot =10 cm-1. The non-resonant waveguide losses comprising losses from the empty

waveguide and non-resonant intersubband (ISB) losses !

wg

non-res= !

wg

empty+ "!

ISB

non-res are

derived from the slope efficiencies of the coated and uncoated device, resulting in

4.8 cm-1. This leads to resonant losses from backfilling !wg

res= "!

ISB

res of 5.2 cm-1. However,

since there might be a sub-linear dependence of the gain on the injection current, this

value has to be considered as an upper bound for the resonant losses. One possible

explanation for those rather high resonant losses is found from the low threshold voltage

of 8.2 V which indicates that the threshold fields are only 33 and 28 kV/cm for designs A

and B. In fact, only a !

inj of 85 and 78 meV for designs A and B corresponds to the

threshold fields (defining the center transition energies (E12!E9) at 145.8 meV for

design A and 129.74 meV for design B). These values are approximately 40 % less than

those calculated in section 7.2.1 and may explain the rather strong backfilling at the

threshold voltage. Higher !

inj should result for CW operation since the device operates

between 9 and 10 V. Using the pulsed threshold current densities at 30 °C, a gain-

gamma product g!

of 4.1 cm/kA was calculated.


147

7.3.2. Extrapolated gain spectrum

The spontaneous emission of our device was measured at 303 K and 9 V in pulsed

operation with an FTIR in step-scan mode and an LN2-cooled MCT detector. In order

to avoid super-luminescence, a short laser (212 µm-long) was prepared and the light was

extracted perpendicular to the waveguide. Fig. 7.8 depicts the extrapolated gain

spectrum, which was corrected by the approximate 1/energy dependence of the detector

sensitivity, showing a width of 350 cm-1 (FWHM). The shoulder at 156 meV reveals

transitions from a higher state above the upper laser level. The data can be well fitted by

a sum of two Gaussian functions centered at 8.1 µm (1226 cm-1) and 9.4 µm (1065 cm-1),

which is in good agreement with our simulation.

Fig. 7.8: Solid line: Extrapolated gain spectrum shows a width of 350 cm-1

(FWHM). Dashed line: Fitting by a sum of two Gaussians centered at 8.1 and

9.4 µm. Crosses: Normalized inverse threshold current density measured in pulsed

mode with EC feedback at 303 K. The dotted line indicates the limit of the tuning

range ! =0.61, given by the mode discrimination.

7.3.3. Broadband tuning in external cavity setup

From the threshold current densities of the uncoated and AR coated front facet of the

laser, a residual reflectivity of 0.245 % was calculated. The laser was mounted in a

standard laboratory housing (Alpes Lasers LLH-100), where the ZnSe window was


148

removed, and purged with nitrogen during operation to avoid condensation on the laser

and Peltier element. Spectra were measured with a Nicolet 800 FTIR spectrometer.

First, the device was tested in pulsed operation (400 ns, 99 kHz) at 30 °C and 1.6 A. The

device could be tuned from 1013 cm-1 (9.87 µm) to 1305 cm-1 (7.66 µm). The operation

spanning over 292 cm-1 (2.2 µm) equals 25 % of center frequency (see Fig. 7.9). From

earlier experiments, it is known that the Fabry-Pérot modes, centered at 1080 cm-1, are

just present within the first 12-15 ns of the pulse [105] until mode competition has built

up.

Fig. 7.9: High-resolution spectra at the extremes of the tuning range, accessible

with our EC configuration at 30 °C in pulsed operation (400 ns, 99 kHz) and

spanning over 292 cm-1.

At the gain maximum (!1200 cm-1), a peak power of 800 mW and a threshold current

density of 2.97 kA/cm2 were observed, which is very close to the threshold current value

of the uncoated front facet without EC feedback. Since

J

th,FP

CLg

max( ) / Jth,EC

ARg

max( ) = !FP

CL/!

EC

AR , one can conclude that the effective feedback of the

external cavity results in a reflectivity of R

EC=27 %. With the calculated waveguide

losses and mirror losses of 2.23 cm-1 for the uncoated laser chip, this result in a mode

discrimination !" of 7.8 cm-1 and a ! = "

EC

AR/"

FP

AR of 0.61.


149

In Fig. 7.8, the inverse threshold current densities normalized to the threshold current at

the gain maximum are plotted. There is good agreement with the extrapolated gain

spectrum. Taking the ratio of the differential gain to the gain maximum from the

threshold current densities results in g !( ) / g

max= J

th,max/ J

th!( )=0.67, which is very

close to the calculated value of ! and demonstrates that the tuning is not gain limited.

In the next step, our device was tested in CW. In this operation mode, it could be tuned

from 1045 cm-1 (9.6 µm) to 1246 cm-1 (8.0 µm) while operating the device between 13

and 18 °C (see Fig. 7.10). This covers a tuning range of 201 cm-1, which equals 18 % of

the center frequency. The side-mode suppression ratio was more than 35 dB over the

full tuning range.

Fig. 7.10: High-resolution CW spectra at the extremes of the tuning range.

Fig. 7.11 shows the CW output power of the external cavity as function of frequency.

The output power was in excess of 20 mW over 162 cm-1 at 23 °C and over 172 cm-1 at

18 °C. At gain maximum at 15 °C, a CW output power of 135 mW was measured.


150

Fig. 7.11: CW output power of external cavity as function of frequency for three

different sets of operation conditions.

7.4. Conclusion

A heterogeneous high performance quantum cascade laser gain chip comprising two

bound-to-continuum active region designs emitting at 8.2 and 9.3 µm was realized, with

an extrapolated gain spectrum FWHM of 350 cm-1. Though a broad gain bandwidth

invariably results in a reduced gain cross section, devices with a high-reflection coated

back facet still lased CW up to a temperature of 50 °C and showed output powers in

excess of 100 mW at 30 °C.

To prove the usability for broadband tuning, this chip was used in our EC setup

operated at room temperature. In pulsed mode, the gain chip could be tuned over

292 cm-1, which is 25 % of center frequency. In CW, a coarse tuning range of 201 cm-1

(18 %) and an output power in excess of 135 mW at the gain maximum at 15 °C was

reached. This gain chip represents a very promising solution for laser photoacoustic

spectroscopy (L-PAS) needs since it can be tuned over 172 cm-1 with output powers in

excess of 20 mW in a room-temperature operated EC setup.

Chapter 8

8. Conclusion and Outlook

This work on high performance quantum cascade lasers for spectroscopic applications

demonstrates the maturity of this type of mid-IR laser source for the realization of

compact, reliable and lightweight, ultra-sensitive and selective sensors for real-world

applications requiring high spectral resolution.

The success of this work was largely based on mastering the technology. In the first

buried QC laser in 2001, the waveguide was embedded in non-intentional doped InP (i-

InP), where the parasitic structure presented an n-i-n structure. We demonstrated

experimentally that space charge limited current in such blocking structures gives rise to

a large leakage current, as predicted in the paper of Grinberg and Luryi for n-i-n

structures. Since these leakage current densities are 3-4 times higher than typical pulsed

threshold current densities of QC lasers, undoped InP is inappropriate for proper

current confinement in buried heterostructures. In the framework of this thesis, two

approaches that could significantly reduce this parasitic current path have been

investigated. One strategy targets on reducing the mobility by inserting InAlAs barriers

within the i-InP. Another possibility is to use Iron-doped InP, where the Iron acts as a

deep level defect that cancels the net charge. We decided to use semi-insulating InP:Fe

as blocking material, since less problems in the regrowth on non-planar structures are

expected, and trapping of carriers should result in less free-carrier absorption.

Furthermore, a new procedure for the etching of narrow waveguides was presented,

which allows the fabrication of ridge widths as narrow as 3.5 µm.

Conclusion and Outlook

152

We experimentally and theoretically compared the key parameters of the most

promising active region designs for high performance using quantum cascade lasers

otherwise identical. The two-phonon resonance design shows the lowest threshold

current densities, which is due to narrow linewidths in this design. Therefore, this design

is most promising for the realization of low power-consumption single-mode devices.

However, the wider gain spectra in the bound-to-continuum design makes this design

very interesting for broad gain applications. Fortunately, the stronger matrix element in

the bound-to-continuum compensates to a large extent for the wider linewidths.

Furthermore, since the two active region designs show different linewidths, the

experimental data were used to verify a model to calculate a priori the temperature and

field dependent intersubband linewidth in quantum cascade laser designs. We conclude

that this model constitutes a useful tool for the development of novel narrow-gain and

high wallplug efficiency active region designs or designs for broad gain applications.

Our results on low power consumption DFB-based single-mode devices in the 9 µm

wavelength range demonstrate the feasibility of realizing portable applications. Low

electrical power consumption of 1.6 W and 3.8 W for an optical output power of 16 mW

and 100 mW has been demonstrated. While attaining room temperature was a challenge

a few years ago, devices operating up to 150 °C in continuous wave were presented. Such

devices are tunable by 1.3 % of its center wavelength.

We demonstrated that the tuning range of an individual DFB laser of about 1 % could

be increased to 8 % of center wavelength by using a broad gain active region design and

monolithic integration of different DFB gratings. We achieved high-performance

devices with single-mode emission between 7.7 and 8.3 µm at a temperature of +30 °C.

Furthermore, an aging test over 11,000 hours revealed no significant long-term

degradation and proved the reliability of such devices for real-life applications, such as

in multi-channel laser spectrometers for the detection of complex mixtures with multiple

absorption lines.

Conclusion and Outlook

153

Even broader tuning was attained by using a heterogeneous high-performance quantum

cascade laser gain chip comprising two bound-to-continuum active region designs

emitting at 8.2 and 9.3 µm. Though a broad gain bandwidth invariably results in a

reduced gain cross section, devices with a high-reflection coated back facet still lased

CW up to a temperature of 50 °C and showed output powers in excess of 100 mW at

30 °C. This chip was used in our external cavity (EC) setup, operated at room

temperature. We demonstrated single-mode tuning of the center wavelength at room

temperature of 25 % in pulsed mode and 18 % in CW operation, which is the widest

reported tuning range in literature. This gain chip represents a very promising tool for

laser photoacoustic spectroscopy (L-PAS) since it can be tuned over 172 cm-1 with

output powers in excess of 20 mW in a room-temperature operated EC setup. An output

power in excess of 135 mW was reached at the gain maximum in CW mode.

Extrapolating from our results at 7-10 µm, devices emitting at 5 µm which consume less

than 1 W of electrical power should be feasible, since the waveguide width scales down

with the wavelength. This should allow for uncooled applications. A larger frequency

coverage can be attained by using heterogeneous quantum cascade lasers with several

active regions. However, CW operation will become more and more challenging,

requiring more efficient active region designs. An alternative way to engineer a

broadband source might be self-assembled quantum dots embedded in quantum cascade

structures. This should allow for reducing the non-radiative relaxation rate of the upper

laser level by the suppression of LO phonon scattering since the electron motion is

quantized in three dimensions [165]. Since these quantum dots result naturally in a non-

uniform growth, a broad-gain spectrum is to be expected. Recently, room temperature

mid-IR electroluminescence was observed from InAs quantum dots [166].

List of abbreviations

2Ph Two-phonon resonance

AFM Atomic force microscope

AO Acoustic optical

AR Anti reflection

BH Buried heterostructure

BTC Bound-to-continuum

CL As cleaved, uncoated

COMD Catastrophic optical mirror damage

CW Continuous wave

DBR Distributed Bragg reflector

DFB Distributed feedback

DFG Difference frequency generation

DTGS Deuterated triglycine sulphate

EC External cavity

EDFA Erbium-doped fiber amplifier

EM electromagnetic

FP Fabry-Pérôt

FTIR Fourier transform infrared

FWHM Full-width at half maximum

HR High reflection

HWHM Half-width half maximum

IC Interband cascade

ISB Intersubband

L-PAS Laser photoacoustic spectroscopy

LED Light emitting diode

LIV Light-current-voltage

LO Longitudinal optical

LPE Liquid phase epitaxy

List of abbreviations

155

MBE Molecular beam epitaxy

MCT Mercury cadmium telluride

MIR Mid-infrared

MOVPE Metal organic vapor phase epitaxy

NIR Near-infrared

OP-GaAs Orientation-patterned GaAs

OPO Optical parametric oscillator

PE-SRO Plasma-enhanced singly resonant oscillator

ppb Parts-per-billion

PPLN Periodically-poled LiNbO3

ppt Parts-per-trillion

QC Quantum cascade

QPM Quasi-phase-matched

QW Quantum well

RT Room temperature

SEM Scanning electron microscope

SEM Scanning electron microscope

SIMS Secondary ion mass spectroscopy

SL Superlattice

SMSR Side-mode suppression ratio

SRO Singly resonant oscillator

TIR Total internal reflection

TM Transversal magnetic

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Acknowledgement

I would like to express my gratitude to many people for this fruitful time as a PhD

student. First and foremost, I wish to thank Prof. Dr. Jérôme Faist for giving me the

opportunity to work in his group. He gave me the chance to do research on quantum

cascade lasers and semiconductor processing technology. He supported me during the

sometimes very challenging 4 12

years of my PhD, and was always available to discuss the

physics of our devices and offer me advice and direction concerning the progression of

my work.

I would also like to express my gratitude to several others:

Prof. Dr. M. W. Sigrist and Prof. Dr. J. Wagner for their willingness to be my co-

examiners.

Dr. Yargo Bonetti for proofreading this work. It was a pleasure sharing the office and

most of my lunch breaks with you.

The MBE/MOVPE team: Dr. Mattias Beck, Martin Ebnöther, Milan Fischer, Dr.

Emilio Gini, Dr. Marcella Giovannini and Nicolas Hoyler for the epitaxial growth and

regrowth of my samples.

Res Neiger for the high-precision lapping of my samples. There was just one accident in

four years when the sample was thinned down to 90 µm instead of 150 µm, which saved

me a lot of measurement time.

Andreas Hugi for his staying power until late at night when we explored our devices in

the external cavity setup while enjoying pizza. When we left the Institute at around

3.00 AM, we had beaten all world records in broadband tuning.

Dr. Max Döbeli for the Super-SIMS measurement.

Hansruedi Scherrer and his trainees for the evaporation of Indium on our diamond

mounts.

Acknowledgement

173

Hansjakob Rusterholz for keeping a cool head while replacing the hard drive of my

iBook.

Furthermore, I would like to thank all the people I met while working in ETH’s FIRST

laboratory for sharing their technological tricks and support, especially Andreas Alt, Dr.

Peter Cristea, Yuriy Fedoryshyn, Dr. Matthias Golling, Peter Kaspar, Dr. Hans-Jörg

Lohe, Dr. Frank Robin, Dr. Andreas Rutz, Dr. Patric Strasser, Dr. Heiko Unold, Dr.

Werner Vogt and Dr. Yohan Barbarin.

Likewise, I am very grateful to the FIRST team: Dominique Aeschbacher, Sandro

Bellini, Petra Burkard, Martin Ebnöther, Christian Fausch, Dr. Emilio Gini, Dr. Otte

Homan, Maria Leibinger, Hansjakob Rusterholz, Dr. Silke Schön for keeping the

cleanroom running and for giving me their constant support.

I would like to thank Walter Bachmann, Marcel Baer, Harald Hediger, Andreas Stuker

and the workshop team for their excellent work.

Special thanks to all the current and former QOE members not previously mentioned:

Dr. Thiery Aellen, Dr. Lassad Ajili, Maria Amanti-Bismuto, Alfredo Bismuto, Kemal

Celebi, Dr. Laurent Diehl, Milan Fischer, Dr. Marcella Giovannini, Tobias Gresch,

Nicolas Hoyler, Erna Hug, Dr. James Lloyd-Hughes, Dr. Valeria Liverini, Dr. Richard

Maulini, Dr. Laurent Nevou, Dr. Giacomo Scalari, Dr. Maxi Scheinert, Dr. Lorenzo

Sirigu, Romain Terazzi, Christoph Walther, Samuel Wiesendanger, Dr. Dmitri Yarekha.

It was a great pleasure working with you.

I am also grateful to the staff members of our Industrial Partners, Alpes Lasers SA

(Neuchâtel, Switzerland) and AL Technology GmbH (Darmstadt, Germany), to which

we sucessfully transferred the developed high-yield fabrication process: Dr. Andreas

Bächle, Dr. Stéphane Blaser, Sophie Brunner, Steffen Bunzel, Emmanuel

Gentilhomme, Stéphane Goeckeler, Dr. Stefan Hansmann, Sandra Hofmann, Dr.

Martin Honsberg, Sandrine Huin, Dr. Lubos Hvozdara, Dr. Stephan Jochum, Dr.

Antoine Müller, Lim-Vitou Nam, Vanessa Piot and Guillaume Vandeputte.

Acknowledgement

174

Many thanks to all our friends, especially Dr. Ernst-Eberhard Latta, René, Esther and

Cornelia Lips, Penelope and Werner Pfleger, Daniel und Maja Suter for their support,

encouragement, counsel, advice and the enjoyable times we spent together.

Finally, I would like to express my gratitude to the members of my family: my parents,

Günther and Hildegund Wittmann, my parents-in-law, Boris and Gudrun Soucek, my

sister, Christine and my brother, Wolfgang and his wife Suzan, as well as my brother and

sister-in-law, Sinja and Alex Matter. Last but not least, I would like to thank my wife,

Nadia, for her love and great support during my Master and PhD studies. I would not

have been able to do this without you!

This project was financially supported by the Swiss Commission for Technology and

Innovation (CTI) and the Swiss National Science Foundation (NCCR-Quantum

Photonics).

Zurich, April 27, 2009

Andreas Wittmann

Curriculum vitae

Personal data

Name Andreas Wittmann

Date of birth 2nd January 1974 (Neuburg an der Donau, Germany)

Nationality German, Swiss (dual nationality)

Marital status Married, 1 daughter

Education

2009 PhD degree in Physics from the Swiss Federal Institute of Technology

Zurich (ETH Zurich), Switzerland

2007 – 2009 PhD studies in Physics at Swiss Federal Institute of Technology Zurich

(ETH Zurich), Switzerland

2004 – 2007 PhD studies in Physics at the University of Neuchâtel, Switzerland

2004 Master’s degree in Electrical Engineering from Technical University of

Munich (TUM), Germany

2002 – 2004 Master studies in Electrical Engineering at Technical University of

Munich (TUM), Germany

1997 Diploma degree in Precision and Micro Engineering, University of

Applied Sciences Nuremberg, Germany

1992 – 1997 Bachelor studies in Precision and Micro Engineering, University of

Applied Sciences Nuremberg, Germany

Professional experience

Nortel Networks Optical Components AG, Zurich Switzerland

(former JDS Uniphase, Laser Enterprise, spin-off of IBM Research

Laboratory Zurich)

2001 – 2002 Group leader of the mirror-coating & electro-optical testing division

2000 – 2001 Project leader for the realization of a new production line

1998 – 2002 Process engineer for semiconductor laser mirror coatings

Publications

Journal papers

1. A. Wittmann, Y. Bonetti, M. Fischer, J. Faist, S. Blaser, E. Gini, Distributed

Feedback Quantum Cascade Lasers at 9 µm Operating in Continuous Wave up to

423 K, Photon. Techn. Lett., accepted for publication.

2. B. G. Lee, H. A. Zhang, C. Pflügl, L. Diehl, M. A. Belkin, M. Fischer,

A. Wittmann, J. Faist, F. Capasso, Broadband distributed feedback quantum

cascade laser array operating from 8.0 to 9.8 microns, Photon. Techn. Lett.,

accepted for publication.

3. A. Wittmann, A. Hugi, E. Gini, N. Hoyler, J. Faist, Heterogeneous high-

performance quantum cascade laser sources for broadband tuning, IEEE J.

Quantum Electron. 44, 1083 (2008).

4. R. Terazzi, T. Gresch, A. Wittmann, J. Faist, Sequential resonant tunneling in

quantum cascade lasers, Phys. Rev. B 78, 155328 (2008).

5. C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer,

A. Wittmann, J. Faist and F. Capasso, Surface-emitting THz quantum cascade laser

source based on intracavity difference-frequency generation, Appl. Phys. Lett. 93,

161110 (2008).

6. A. Wittmann, Y. Bonetti, J. Faist, E. Gini, M. Giovannini, Intersubband linewidths

in quantum cascade laser designs, Appl. Phys. Lett. 93, 141103 (2008).

7. M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, J. Faist,

Room temperature terahertz quantum cascade laser source based on intracavity

difference-frequency generation, Appl. Phys. Lett. 92, 201101 (2008).

8. A. Wittmann, T. Gresch, E. Gini, L. Hvozdara, N. Hoyler, M. Giovannini, J.

Faist, High-Performance Bound-to-Continuum Quantum-Cascade Lasers for

Broad-Gain Applications, IEEE J. Quantum Electron. 44, 36 (2008).

Publications

177

9. A. Mohan, A. Wittmann, A. Hugi, S. Blaser, M. Giovannini, J. Faist, Room

temperature continuous-wave operation of an external-cavity quantum cascade laser,

Opt. Lett. 32, 2792 (2007).

10. A. Wittmann, M. Giovannini, J. Faist, L. Hvozdara, S. Blaser, D. Hofstetter, E.

Gini, Room temperature, continuous-wave operation of distributed feedback

quantum cascade lasers with widely spaced operation frequencies, Appl. Phys. Lett.

89, 201115 (2006).

Patent

11. A. Wittmann, M. Gotza, M. Solar, E.-E. Latta, T. Kellner, M. Krejci, Anti-

reflection coatings for semi-conductor lasers, US 2004/0151226 (2004).

Invited Talk

12. A. Wittmann, A. Hugi, Y. Bonetti, M. Fischer, M. Beck, J. Faist, L. Hvozdara, S.

Blaser, E. Gini, Single-mode quantum cascade lasers for spectroscopy, Laser

seminar ETH Zurich, Zurich (Switzerland), October 20 (2008).

Talks and conference proceedings

13. S. Blaser, L. Hvozdara, P. Horodysky, S. Brunner, G. Vandeputte, A. Muller, A.

Bächle, S. Jochum, M. Honsberg, A. Wittmann, Y. Bonetti, M. Beck, E. Gini and

J. Faist, MOVPE grown single-mode quantum-cascade lasers, International

Quantum Cascade Lasers School & Workshop, Monte Verita (Switzerland),

September 14-19 (2008).

14. A. Hugi, A. Wittmann, R. Terazzi, E. Gini, S. Blaser, M. Beck, J. Faist,

Broadband external-cavity quantum cascade laser, International Quantum Cascade

Lasers School & Workshop, Monte Verita (Switzerland), September 14-19

(2008).

15. A. Wittmann, A. Hugi, Y. Bonetti, M. Fischer, M. Beck, J. Faist, M. Giovannini,

N. Hoyler, D. Hofstetter, L. Hvozdara, and S. Blaser, High-performance single-

mode and broadly tunable quantum cascade laser sources, Mid-Infrared

Publications

178

Optoelectronics: Materials and Devices (MIOMD-IX), Freiburg (Germany),

September 7-11 (2008).

16. L. Hvozdara, S. Blaser, S. Brunner, G. Vandeputte, A. Muller, A. Bächle, S.

Jochum, M. Honsberg, A. Wittmann, M. Beck, J. Faist and E. Gini, Prospects of

the quantum cascade lasers in spectroscopic applications, 3rd International

Workshop on Infrared Plasma Spectroscopy (IPS2008), Greifswald (Germany),

July 23-25 (2008).

17. A. Hugi, A. Wittmann, A. Mohan, S. Blaser, M. Giovannini, J. Faist, Broadband

external-cavity quantum cascade laser, Annual Meeting of Swiss Physical Society,

Geneva (Switzerland), March 26-27 (2008).

18. A. Muller, S. Blaser, L. Hvozdara, S. Brunner, G. Vandeputte, A. Bächle, S.

Jochum, M. Honsberg, S. Hansmann, A. Wittmann and J. Faist, Continuous-wave

quantum cascade lasers, Field Laser Applications in Industry and Research

(FLAIR 2007), Florence (Italy), September 2-7 (2007).

19. A. Wittmann, L. Hvozdara, S. Blaser, M. Giovannini, J. Faist, D. Hofstetter, M.

Beck, E. Gini, High-performamce continuous wave quantum cascade lasers with

widely spaced operation frequencies, Proc. SPIE 6485, 64850P (2007).

20. A. Wittmann, L. Hvozdara, S. Blaser, M. Giovannini, J. Faist, D. Hofstetter, M.

Beck, E. Gini, High-performamce continuous wave quantum cascade lasers with

widely spaced operation frequencies, Novel In-Plane Semiconductor Lasers VI,

Photonics West 2007, San Jose (USA), January 20-25 (2007).

21. A. Muller, S. Blaser, L. Hvozdara, A. Wittmann, N. Hoyler, M. Giovannini, J.

Faist, W. Vogt and E. Gini, Room-temperature continuous-wave single-mode

quantum cascade lasers, The 2nd International Workshop on Quantum Cascade

Lasers, Marina di Ostuni, Brindisi (Italy), September 6-9 (2006).

22. B. Schmidt, S. Pawlik, N. Matuschek, J. Muller, T. Pliska, J. Troger, N.

Lichtenstein, A. Wittmann, S. Mohrdiek, B. Sverdlov, C. Harder, 980 nm single

mode modules yielding 700 mW fiber coupled pump power, OFC 2002, 702 (2002).

[wittmann, andreas] high-performance quantum casca

Documents

single mode qc lasers

spectroscopic applications

semiconductor lasers

low power

center wavelength

singlemode tuning

pulse operated lasers

single dfb device