*Corresponding author. Tel.: #39-06-72597372; fax: #39-06-2020519 .

E-mail address: lugli@uniroma2.it (P. Lugli)

Physica B 272 (1999) 513}517

Study of the steady state and dynamical behavior ofsemiconductor optical ampli"ers

Andrea Reale, Aldo Di Carlo, Paolo Lugli*

INFM and Dept. Electronic Eng., University of Roma **Tor Vergata++, I-00133 Roma, Italy

Abstract

We clarify the physical limitations of time-dependent dynamical characteristics of multi-quantum well semiconductoroptical ampli"ers (SOA), using a phenomenological model based on a `rate equationsa approach, in gain compressionexperiments. Then we perform a calculation of the optical gain using a tight-binding model for di!erent multiplequantum well structures used as the active region of the SOA. We explain how to introduce strain in a multiple quantumwell active region in order to achieve polarization-insensitive optical ampli"cation. ( 1999 Published by ElsevierScience B.V. All rights reserved.

PACS: 42.60.Da; 42.79.Lh; 42.25.Ja; 71.15.Fv

Keywords: Semiconductor optical ampli"er; Tight binding; Strain

1. Carrier dynamics: rate equation model and pulsepropagation

It is possible to describe the carrier dynamics asa function of the mean electron density N

iof each

layer i, where i can refer to one of the separatecon"nement heterolayers (SCH) or the QW layers.Fig. 1 illustrates the transport processes in theheterostructure. For the two SCHs (labeled 1 and2 for left and right regions, respectively) one canwrite explicitly:

dN4#)1

dt"

g*/+

I

q¸4#)

!

N4#)1q4

!

N4#)1

q/(N

4#)1)

#

N1

q%

¸8%--

¸4#)

#mN

4#)2q4

, (1)

dN4#)2

dt"!

N4#)2q4

!

N4#)2

q/(N

4#)2)

#

NM

q%

¸8%--

¸4#)

#mN

4#)1q4

, (2)

where I is the injected current, g*/+

is the injectione$ciency, and ¸ is the thickness of the layer. Thevarious terms in Eqs. (1) and (2) account for thelosses due to di!usive transport and subsequentcapture in the adjacent QW (N

4#)/q

4, where

q4"q

$*&&#q

#!1), losses due to non-radiative or

spontaneous recombination (N4#)

/q/, where the re-

combination time q/

depends on carrier density),carrier accumulation due to thermionic emissionfrom the adjacent QW (the total numberN

28)¸

8%--/q

%is normalized with respect to SCH

0921-4526/99/$ - see front matter ( 1999 Published by Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 3 3 2 - 4

Fig. 1. Transport processes in an MQW-SOA.

layer width ¸4#)

) and exchange contribution be-tween the two SCHs due to leakage current(mN

4#)/q

4, where m is the coupling factor, between

0 and 1). In MQW systems, one must distinguishbetween the lateral wells adjacent to the SCH, andthe inner ones. The density of the central QWs isdescribed by

dNi

dt"

N*~1

!Ni

q#

!

Ni!N

*`1q#

!

Ni

q/(N

i)

!MCwvgg(N

i)S. (3)

For the two external QWs similar equations hold,which also account for the carrier exchange withthe SCH layers [1]. All parameters coupling thevarious equations are shown in Table 1. The gain-carrier density relationship is described in Ref. [2].

In the experiment performed at CSELT (Turin)described in Ref. [1] a CW probe beam (j"1565nm) was injected into the structure, together withpump pulses (j"1521 nm) of short duration (8 ps),

emitted by F-color center laser, with an energy ofa few pJ per pulse. The bias currents considered inthe experiment range between 30 and 150 mAcovering low bias (I(45 mA) CW conditionswhere the device exhibits net absorption up toa higher current bias (I*45 mA) where one ob-serves a net gain. A non-equilibrium carrier distri-bution induced by the pump pulses changes theSOA gain either through stimulated emission orthrough absorption, depending on the bias value.Furthermore, for driving currents of 90 mA ormore, the device response is nearly exponentialwith respect to the pumping power. The gain com-pression mechanism at high current bias is due tothe pump ampli"cation, that causes carrier de-pletion and, through g(N)"g(t), a negative spike inthe probe output. Figs. 2(a) and (b) show these twodi!erent conditions of gain compression at highbias and gain enhancement at low bias, respect-ively. The theoretical results (dashed lines) agreewell with the experimental ones. By comparison of

514 A. Reale et al. / Physica B 272 (1999) 513}517

Fig. 2. Gain modulation at high (a) and low (b) current regimes.

Table 1Parameters of rate equation model

inj. e!. g*/+

0.95SCH width ¸

4#)130 nm

QW width ¸8

4.8 nmBarrier width ¸

"6 nm

Barrier height EB

110 meVTherm. em. q

%20 ps

Capture time q#

1 psTunnel. time q

51 ps

El mob. (SCH) kSCH/

0.8]104 cm2 V~1 s~1

Holes mob. (SCH) kSCH1

0.005]104 cm2 V~1 s~1

El mob. (QW) kSCH/

1.1]104 cm2 V~1 s~1

Holes mob. (QW) kQW1

0.02]104 cm2 V~1 s~1

Temperature T 300 KOptical conf. C

80.02

Group vel. v'

8.5]107 m s~1

Threshold dens. N5)

1.87]1018 cm~3

Traps coe!. A 109 s~1

Spont. coe!. B 2]10~10 cm3 s~1

Auger coe!. C 2]10~29 cm6 s~1

Leakage factor m 0.2

the time constant obtained from an exponential"tting of the data, it is possible to understand whichprocesses determine the gain compression behav-ior. By considering one process at once in the

simulation, we have reached the conclusion thatAuger recombination is the most important one inthe high current injection regime [1].

2. Calculation of optical gain in presence of strain

In order to achieve the desired polarization in-sensitivity for the gain, several SOA structures withstrain between the di!erent layers have been pro-posed [3,4]. TM and TE contributions can be bal-anced since strain allows alignment between HHand LH levels. We studied an MQW-SOA basedon the concept of the d-strain [3]. The referencestructure for our study consists of 153 As wide (52monolayers (ML)) In

0.533Ga

0.467As quantum well

surrounded by In0.74

Ga0.26

As0.56

P0.44

barriers,lattice matched to an InP substrate. We investigatethe di!erences in optical matrix elements and gaincoe$cients between the reference structure and onewhere three monolayers of InGaAs in the middle ofthe well are replaced by strained GaAs, to achievepolarization-insensitive optical ampli"cation. De-tails of the tight-binding calculation can be foundin [3]. Figs. 3(a) and (b) show the valence band

A. Reale et al. / Physica B 272 (1999) 513}517 515

Fig. 3. Comparison of valence band dispersions and gain coe$cient between unstrained reference structure ((a) and (c)) with d-strainedSOA structure ((b) and (d)).

dispersions for the structure without and withGaAs d-strain, respectively. For the unstrainedQW, the "rst two valence bands have heavy-holecharacter (close to k

@@"0), while the third one

has a light-hole character. With d-strain, the "rstlight-hole level lifts up in energy, while the "rstheavy-hole level shifts down, leading to a banddegeneration at k

@@"0. It can be deduced by look-

ing at the squared optical matrix elements [3] thatthe "rst valence band has a light-hole character("rst LH level), while the second valence band hasa heavy-hole character ("rst HH level).

The gain coe$cient can be calculated witha proper choice of the quasi-Fermi levels. We fol-low a simpli"ed approach where we assume thecharge density in the well to be approximately2]1012 cm~2, corresponding to a quasi-Fermilevel 150 meV from the conduction band edge.

The calculated gain coe$cient without and withGaAs d-strain is shown in Figs. 3(c) and (d), respec-tively. The sharp structure in the gain coe$cient isdue to the negative mass of the "rst valence state.Such a mass is similar to the conduction band mass.For this reason, vertical transitions can occur atequal energy even for kO0, since the two para-boloids remain equally distanced.

3. Conclusions

The role of the recombination processes has beenclari"ed with a rate equation model, showing thatgain compression (exploited in cross gain modula-tion for WDM applications) is controlled bythe Auger process. The in#uence of a delta-strainon the modal absorption/gain characteristic of a

516 A. Reale et al. / Physica B 272 (1999) 513}517

semi-conductor optical ampli"er has been studiedby means of a tight-binding calculation. The rela-tion between level alignment, valence band mixing,TE and TM optical gain has been evidenced.

Acknowledgements

For helpful discussions and for providing theexperimental results the authors wish to thankD. Campi of CSELT, Turin. This work is partially

supported by CNR under Progetto FinalizzatoMADESS.

References

[1] A. Reale et al., IEEE J. Quantum Electron. 35 (1999) 1697.[2] T.A. De Temple et al., IEEE J. Quantum Electron. 29 (1993)

1246.[3] A. Di Carlo et al., IEEE J. Quantum Electron. 34 (1998)

1730.[4] K. Magari et al., IEEE J. Quantum Electron. 30 (1994) 695.

A. Reale et al. / Physica B 272 (1999) 513}517 517