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1

Basics of Optical Emission and Absorption

Optical emission and absorption are fundamental processes which areexploited when electrical energy is converted into optical energy and viceversa. Optoelectronics is based on these energy conversion processes. Lightemitters such as light-emitting diodes (LEDs) and diode lasers convert elec-trical energy into optical energy. Photodetectors convert optical energy intoelectrical energy. In this chapter, the most important factors needed for thecomprehension of light emitters and photodetectors will be summarized ina compact form. For a detailed description of the basics of optical emissionand absorption, the book [1] can be recommended. Here, emphasis will, ofcourse, be placed on silicon devices. First we will introduce photons andthe properties of light. Then, the consequences of the band structure foroptical emission and absorption will be dealt with. Photogeneration will be

defined. Furthermore, optical reflection and its consequences on the efficiencyof photodetectors will be described.

1.1 Properties of Light

Due to the work of Max Planck and Albert Einstein it is possible to describelight not only by a wave formalism, but also by a quantum-mechanical par-ticle formalism. The smallest unit of light intensity is a quantum-mechanicalparticle called a photon. The photon, consequently, is the smallest unit ofoptical signals. Photons are used to characterize electromagnetic radiation inthe optical range from the far infrared to the extreme ultraviolet spectrum.

The velocity of photons c in a medium with an optical index of refraction nis

c= c0

n, (1.1)

wherec0is the velocity of light in vacuum. Photons do not possess a quiescentmass and, unfortunately for the construction of purely optical computers,

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2 1 Basics of Optical Emission and Absorption

cannot be stored. Photons can be characterized by their frequency and bytheir wavelength:

= c

. (1.2)

The frequency of a photon is the same in vacuum and in a medium withindex of refraction n. The wavelengthin a medium, therefore, is shorter thanthe vacuum wavelength 0 (= 0/n). As a consequence, the vacuum wave-length is used to characterize light sources like light-emitting diodes (LEDs)or semiconductor lasers, because it is independent of the medium in whichthe light propagates.

Photons can also be characterized by their energy E (h is Plancksconstant):

E= h= hc

= hc00

. (1.3)

A useful relation is given next which allows a quick calculation of theenergy for a certain wavelength and vice versa:

E= 1,240

0(1.4)

whereEis in eV and 0in nm. Let us define the flux density as the numberof photons incident per time interval on an area A. The optical power Poptincident on a detector with a light sensitive area A, then, is determined bythe photon energy and by the flux density:

Popt= EA= hA. (1.5)

The magnitude of the momentum of a photonpin a medium is determinedby its wavelength in this medium:

p=h

. (1.6)

The wave number k is the magnitude of the wave vector k , which definesthe direction of the motion of the photon:

k= 2

. (1.7)

The momentum of a photon p is proportional to the wave vector

p= k, (1.8)

where = h/(2).

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1.2 Energy Bands of Semiconductor Materials 3

1.2 Energy Bands of Semiconductor Materials

The energy-band structure of a semiconductor determines not only itselectrical properties but also its optical properties such as the absorptionof photons and the probability of radiative transitions of electrons from theconduction band to the valence band. The absorption of photons, which isimportant for photodetectors, will be dealt with in the next section. Here, wewill just point out the consequences of the kind of energy-band structure forthe applicability of a semiconductor material when we want to obtain efficientlight emitters.

There are two requirements for transitions of electrons between the valenceand the conduction band and vice versa: (a) the energy has to be conservedand (b) the momentum has to be conserved. The conservation of energy usu-ally is not a problem in direct and in indirect semiconductors. For an electron

transition between the maximum of the valence band and the minimum ofthe conduction band, or vice versa, the conservation of momentum, however,cannot be fulfilled with the absorption or emission of a photon alone in anindirect semiconductor, because the magnitude of the momentum of a photonis several orders of magnitude smaller than that of an electron in a semicon-ductor. The same large difference holds between the wave vectors of a photonand an electron in a crystal. It is, therefore, possible to compare the mo-mentums or the wave vectors. The energy bands in dependence on the wavevector are calculated from the Schrodinger equation with a periodic poten-tial that is characteristic for a certain semiconductor. The wave vector of anelectron in a crystal is between approximately 0 and 2/a, i.e., between thek values at the boundaries of the first Brillouin zone, where a is the lattice

constant. The minimum of the conduction band in the first Brillouin zonein silicon, for instance, is at 0.85 2/a [1]. The momentum of an electronin the minimum of the conduction band of Si with a =0.543nm, therefore,can reach 0.852h/a= 21024 Js m1, whereas the momentum of a photonwith E =1eV is only 5.3 1028 Js/m. In addition to a photon, a phononhas to be absorbed or emitted in order to conserve the momentum. Phononsare quantized lattice vibrations. They possess small energies (up to approx-imately 100 meV) and a momentum of the order of that of an electron in asemiconductor. Many phonons are present in crystals like semiconductors atroom temperature.

Let us first consider GaAs, which has a direct bandgap (Fig. 1.1), where theminimum of the conduction band (CB) is above the maximum of the valenceband (VB). No phonon is needed for the conservation of the momentum when

an electron makes a transition from the minimum of the conduction bandto the maximum of the valence band (recombining with a hole) and when aphoton with the energy of the bandgap is emitted.

Silicon is known to have an indirect bandgap. A phonon is needed for theconservation of the momentum in order to enable the radiative transition ofan electron from the minimum of the conduction band to the maximum of the

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4 1 Basics of Optical Emission and Absorption

E CB

VB

0

k

e

Eg

h

Direct semiconductor

EgEp

Eg+Ep

ECB

VB

kk0

e

h2h1

Eg

Indirect semiconductor

0

Fig. 1.1. Electron transitions in direct (left) and indirect (right) semiconductors

as, for instance, GaAs and Si, respectively

valence band. A phonon has to be consumed or created when a photon withan energy of approximatelyEg is emitted (see Fig. 1.1). The photon energy isexactly (Ep is the phonon energy)

E= h= hc

=Eg Ep. (1.9)

The generation of a phonon possesses a larger probability than the con-sumption of a phonon in connection with an electron transition in an indirectsemiconductor. Therefore, more photons will have the energy EgEp thanEg+ Ep. From quantum mechanics it is, however, known that the probabilityof all electron transitions combined with phonon transitions is very small. Theprobability of radiative transitions in indirect semiconductors in fact is fourto six orders of magnitude lower than that in direct semiconductors. Silicondevices, therefore, are usually very poor light emitters. This work will sum-marize the attempts to obtain more efficient silicon light emitters and it will,of course, focus on silicon photodectors.

1.3 Optical Absorption of Semiconductor Materials

The energy of a photon can be transferred to an electron in the valence bandof a semiconductor, which is brought to the conduction band, when the pho-

ton energy is larger than the bandgap energy Eg. The photon is absorbedduring this process and an electronhole pair is generated. Photons with anenergy smaller than Eg, however, cannot be absorbed and the semiconductoris transparent for light with wavelengths longer than c=hc0/Eg.

The optical absorption coefficientis the most important optical constantfor photodetectors. The absorption of photons in a photodetector to produce

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1.3 Optical Absorption of Semiconductor Materials 5

0.001

0.01

0.1

1

10

100

1000

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Absorptioncoefficient(m1)

Wavelength (m)

Si

GeGaAs

InP6H-SiC

In0.53Ga0.47As

Fig. 1.2.Absorption coefficients of important semiconductor materials versus wave-length

carrier pairs and thus a photocurrent, depends on the absorption coefficient for the light in the semiconductor used to fabricate the detector. The ab-sorption coefficient determines the penetration depth 1/ of the light in thesemiconductor material according to LambertBeers law:

I(y) =I0exp(y). (1.10)

The optical absorption coefficients for the most important semiconduc-tor materials are compared in Fig. 1.2. The absorption coefficients stronglydepend on the wavelength of the light. For wavelengths shorter than c,which corresponds to the bandgap energy (c = hc0/Eg), the absorptioncoefficients increase rapidly according to the so-called fundamental absorp-tion. The steepness of the onset of absorption depends on the kind of bandband transition. This steepness is large for direct bandband transitions asin GaAs (Edirg =1.42eV at 300K), in InP (E

dirg =1.35eV at 300K), in Ge

(Edirg =0.81eV at 300K), and in In0.53Ga0.47As (Edirg =0.75eV at 300K).

For Si (Eindg = 1.12eV at 300 K), for Ge (Eindg = 0.67 eV at 300K), and for the

wide bandgap material 6HSiC (Eindg = 3.03 eV at 300K) the steepness of theonset of absorption is small.

In0.53Ga0.47As and Ge cover the widest wavelength range including thewavelengths 1.3 and 1.54 m which are used for long distance optical datatransmission via optical fibers. The absorption coefficients of GaAs and InPare high in the visible spectrum (400700nm). Silicon detectors are alsoappropriate for the visible and near infrared spectral range. The absorptioncoefficient of Si, however, is one to two orders of magnitude lower than that of

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6 1 Basics of Optical Emission and Absorption

Table 1.1. Absorption coefficients of silicon and intensity factors I0 (ehp cm3

means electronhole pairs per cm3) for several important wavelengths for a constantphoton flux density of = I0/= 1.58 1018 photons/cm2

Wavelength I0(nm) (m1) (ehp cm3)

980 0.0065 1.03 1020

850 0.06 9.50 1020

780 0.12 1.89 1021

680 0.24 3.79 1021

635 0.38 6.00 1021

565 0.73 1.16 1022

465 3.6 5.72 1022

430 5.7 9.00 1022

the direct semiconductors in this spectral range. For Si detectors, therefore, amuch thicker absorption zone is needed than for the direct semiconductors. Wewill, however, see in this work that with silicon photodiodes GHz operationis nevertheless possible. Silicon is the economically most important semicon-ductor and it is worthwhile to investigate silicon optoelectronic devices andintegrated circuits in spite of the nonoptimum optical absorption of silicon.

The absorption coefficients of silicon for wavelengths which are the mostimportant ones in practice are listed in Table 1.1[2, 3]. In order to comparethe quantum efficiencies of photodetectors for different wavelengths, it is ad-vantageous to use the same photon flux for the different wavelengths. Thephotocurrents of photodetectors are equal for the same fluxes of photons with

different energy, i.e., for different light wavelengths, when the quantum effi-ciency of the photodetector is the same for the different photon energies orwavelengths, respectively. According to the LambertBeer law, different in-tensity factors I0 result for a constant photon flux. As an example, intensityfactors are listed for the most important wavelengths in Table 1.1for a certainarbitrary photon flux density.

1.4 Photogeneration

The LambertBeer law can be formulated for the optical power P analogouslyto (1.10):

P(y) =P0exp(y). (1.11)

The optical power at the surface of the semiconductor P(y = 0) i sP0 = (1 R) (see Fig. 1.3). The optical power of the light penetrating intoa medium decreases exponentially with the penetration coordinate y in themedium (compare Fig. 2.1).

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1.5 External Quantum Efficiency and Responsivity 7

nS Popt

R.

Popt

Semiconductor

nSC

y

PoptP0

P0 exp(y)

P

Fig. 1.3. Reflection at a semiconductor surface and decay of the optical power inthe semiconductor (P0= (1 R)Popt)

The absorbed light generates electronhole pairs in a semiconductor dueto the internal photoeffect provided thath > Eg. Therefore, we can expressthe generation rate per volumeG(y) as:

G(y) =P(y) P(y+ y)

y1

Ah. (1.12)

In this equation,Ais the area of the cross section for the light incidence andhis the photon energy. For y 0, we can write (P(y) P(y +y))/y=dP(y)/dy. From(1.11), dP(y)/dy= P(y) then follows and the generationrate is

G(y) = P0

Ah

exp(

y). (1.13)

1.5 External Quantum Efficiency and Responsivity

The external or overall quantum efficiency is defined as the number of photo-generated electronhole pairs, which contribute to the photocurrent, dividedby the number of the incident photons. The external quantum efficiency canbe determined, when the photocurrent of a photodetector is measured for aknown incident optical power.

A fraction of the incident optical power is reflected (see Fig. 1.3) due tothe difference in the index of refraction between the surroundings ns (air:

ns = 1.00) and the semiconductor nsc (e.g., Si, nsc 3.5). The reflectivity Rdepends on the index of refraction nscand on the extinction coefficient of anabsorbing medium, for which the dielectric function = 1+ i2 = (nsc+ i)2

is valid (ns = 1) [2].

R= (1 nsc)2 + 2(1 + nsc)2 + 2

. (1.14)

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8 1 Basics of Optical Emission and Absorption

.

nS Popt

nARC

nSCSemiconductor

dARC

R Popt

Fig. 1.4. Semiconductor with an antireflection coating

The extinction coefficient is sufficient for the description of the absorption.The absorption coefficient can be expressed as:

=4

0. (1.15)

The optical quantum efficiency o can be defined in order to consider thepartial reflection:

o = 1 R. (1.16)

The reflected fraction of the optical power can be minimized by introducingan antireflection coating (ARC) with thickness dARC (see Fig. 1.4):

dARC= 04nARC

. (1.17)

The index of refraction of the ARC-layer can be calculated:

nARC=

nsnsc. (1.18)

The optimum index of refraction of the ARC-layer is determined by therefractive index ns of the surroundings and by the refractive index nsc of thesemiconductor. A complete suppression of the partial reflection, however, isnot possible in practice. For silicon photodetectors, SiO2 (nsc = 1.45) andSi3N4 (nsc = 2.0), ARC-layers are most appropriate.

Because of the partial reflection, it is useful to define the internal quan-

tum efficiencyi

as the number of photogenerated electronhole pairs, whichcontribute to the photocurrent, divided by the number of photons which pen-etrate into the semiconductor.

The external quantum efficiency is the product of the optical quantumefficiencyo and of the internal quantum efficiency i:

= oi. (1.19)

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1.5 External Quantum Efficiency and Responsivity 9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.21.3

1.4

1.5

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Responsivity(A/W)

Wavelength (m)

Fig. 1.5.Responsivity of an ideal photodetector with a quantum efficiency = 1 ver-sus wavelength (c = 1.8 m). The responsivity of real detectors possesses smallervalues

The internal quantum efficiency i will be discussed in Sect. 2.2.3 aftercarrier diffusion and drift have been introduced.

For the development of photoreceiver circuits, and especially of tran-simpedance amplifiers, it is interesting to know how large the photocurrentis for a specified power of the incident light with a certain wavelength. TheresponsivityR is a useful quantity for such a purpose:

R= IphPopt

= q0

hc=

0

1.243

A

W, (1.20)

where 0 is in micrometers. The responsivity is defined as the photocurrentIph divided by the incident optical power. R depends on the wavelength;therefore, wavelength has to be mentioned if a responsivity value is given.The dependence of the responsivity R on wavelength 0 is shown in Fig. 1.5for a quantum efficiency = 1.

The line shown in Fig. 1.5represents the maximum responsivity of an idealphotodetector with = 1. The responsivity of real detectors is always lowerdue to partial reflection of the light at the semiconductor surface and due topartial recombination of photogenerated carriers in the semiconductor or atits surface.

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