Modulation doped InGaAsP quantum well laser emitting at 1.55 μmN. Choudhury and N. K. Dutta Citation: Journal of Applied Physics 90, 38 (2001); doi: 10.1063/1.1376403 View online: http://dx.doi.org/10.1063/1.1376403 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/90/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Reliability and low-frequency noise measurements of InGaAsP multiple quantum well buried-heterostructurelasers J. Vac. Sci. Technol. A 20, 1061 (2002); 10.1116/1.1464839 InGaAsNSb/GaAs quantum wells for 1.55 μm lasers grown by molecular-beam epitaxy Appl. Phys. Lett. 78, 4068 (2001); 10.1063/1.1379787 Strain optimization for high differential gain and low current operation in 1.55 μm InGaAs/InGaAsP quantum welllasers J. Appl. Phys. 86, 6425 (1999); 10.1063/1.371706 Maximum operating temperature of the 1.3 μm strained layer multiple quantum well InGaAsP lasers J. Appl. Phys. 84, 4076 (1998); 10.1063/1.368621 Low threshold 1.55 μm wavelength InAsP/InGaAsP strained multiquantum well laser diode grown by chemicalbeam epitaxy Appl. Phys. Lett. 71, 13 (1997); 10.1063/1.119453

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09

Modulation doped InGaAsP quantum well laser emitting at 1.55 mmN. Choudhury and N. K. Duttaa)

Department of Physics, University of Connecticut, Storrs, Connecticut 06269

~Received 23 May 2000; accepted for publication 6 April 2001!

A number of parameters, such as gain, modulation response, linewidth enhancement factor andrelative intensity noise, in a modulation-doped InGaAsP quantum well~QW! laser emitting at 1.55mm have been theoretically investigated. The results indicate that the relaxation oscillationfrequency for ap-type modulation doped QW laser is enhanced by a factor of more than 2 comparedto that for undoped MQW lasers, the linewidth enhancement factor of ap-type modulation dopedQW laser is reduced to 1/2 that of an undoped MQW laser and the relative intensity noise is reducedby a factor of.10 dB compared to that for undoped MQW lasers. ©2001 American Institute ofPhysics. @DOI: 10.1063/1.1376403#

I. INTRODUCTION

Modulation doping is a widely used technique for thefabrication of high electron mobility transistors~HEMTs!.GaAs/AlGaAs based modulation doped lasers have been pre-viously investigated.1 The band diagram of a modulationdoped multiquantum well~MQW! ~MD-MQW! structurewith p- andn-type doping is shown in Fig. 1. The MD-MQWstructure is composed of a periodic structure with highlydoped well layers. The band edge of the conduction andvalence band are bent by the space charge caused by ionizedimpurities in the barrier layers. The majority carriers fromimpurity atoms, that is, majority holes from acceptors forp-type cases or majority electrons from donors forn-typecases are relaxed and localized only in well layers. In thisstructure the localized carriers in well layers are spatiallyseparated from the ionized impurities in barrier layers. Ifimpurities were incorporated everywhere in MQW layers,the band tail states and nonradiative recombination centerscreated by ionized impurities would reduce the optical gain.

Multiquantum well lasers have been extensively studiedboth theoretically and experimentally over the last decade.1

Kakimoto and Watanabe2 have studied the gain and relax-ation frequency in MQWs and bulk distributed feedback la-sers. Ryuet al.3 have theoretically and experimentally stud-ied the performance of tensile strained MQW lasers andBelenky et al.4 have studied MQW lasers emitting near 1.3mm. Shimizu et al.5 fabricated InAsP modulation dopedMQW lasers emitting near 1.3mm. In this article we showthat the relaxation oscillation frequencyf r in MD-MQW la-sers can be enhanced by more than a factor of 2 over that ofundoped MQW lasers usingp-type modulation doping. Also,the a factor can be reduced to 1/2 the value for an undopedMQW laser byp-type modulation doping and the relativeintensity noise is reduced by a factor of.10 dB compared tothat for undoped MQW lasers. The improvement in thesevalues in modulation doped MQW lasers is due to asymme-try in the occupation of the conduction band and valenceband states.

The high value off r ~relaxation oscillation frequency!and small value ofa ~linewidth enhancement factor! in regu-lar QW lasers are essentially attributed to large differentialgain (dg/dn),1 wheren is the injected carrier density andgis the optical gain coefficient which is given by the followingwell-known expression:6

g}uMbu2D red~ f c2 f v!. ~1!

Here, uMbu2 is the matrix element for the transition,D red isthe reduced density of states, andf c( f v) are the Fermi–Diracdistribution function for the electrons~holes! in the conduc-tion ~valence! band. It is also known that the differential gainincreases with increasedp-type doping.7 The MD-MQWstructure enables the utilization of both of these effects, i.e.,higher differential gain due to doping of the active region,and higher differential gain due to the quantum size effect8 inthe same material.

The charge neutrality over the MD-MQW structure isgiven by

p01pi1ND15n01ni1NA

2 , ~2!

where,ND1 is the ionized donor concentration,n0 is the ma-

jority electron density from the ionized donors (n05ND1),

NA2 is the ionized acceptor concentration,p0 is the majority

hole density from the ionized acceptors (p05NA2), and ni

andpi are the injected hole and electron densities (ni5pi),respectively.

The quasi-Fermi levels for electronsEf c and for holesEf v are determined by the electron and hole densities.Ef v isdetermined by the density of the majority holes, that is, bythe concentration of the ionized acceptors due to the intro-duction of thep-type MD-MQW structure. Similarly,Ef c isdetermined by the majority electrons due to the introductionof the n-type MD-MQW structure. Therefore, the Fermi–Dirac term (f c2 f v) in Eq. ~1! is determined by the impuritydoping in the barrier layers. As a result, the gain and differ-ential gain are enhanced or suppressed by the concentrationand the type of impurities in the barrier.a!Electronic mail: niloy@engr.uconn.edu

JOURNAL OF APPLIED PHYSICS VOLUME 90, NUMBER 1 1 JULY 2001

380021-8979/2001/90(1)/38/5/$18.00 © 2001 American Institute of Physics

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09

II. GAIN

This analysis treats the case when band-to-band recom-bination is dominant underK-selection rules considering thepolarization dependence of gain. Transition broadening isneglected~i.e., intraband relaxation timet in5`) to avoidunderestimation in the gain calculation.9 Under these as-sumptions, the optical linear gaing(E) of the transverseelectric ~TE! mode in the MD-MQW laser is given by

g~E!52ph2e2

nrm02c«0E

F (j 5h,l

(i 51

`

uMbj ~u!u2D red,i

j

3$ f c~E!2 f v~E!%G , ~3!

whereh is the Plank constant divided by 2p, e is the elec-tronic charge,nr is the refractive index of the material,m0 isthe free electron mass,c is the velocity of light,e0 is thedielectric constant in vacuum,E is the photon energy, anduMb(u)u2 is the polarization dependent squared momentummatrix element for the quantum well structure, whereu is theangle of wave vectork to the quantum well plane,7,8 D red isthe reduced density of states,j designates either heavy hole~h! or light holes ~l!, and i representsith subband of thequantum well.

Figure 2 shows the calculated peak gaingp as a functionof injected electron densityni at various doping concentra-tions in the barrier layers forp- and n-type InGaAsP MD-MQW lasers at a temperature of 300 K. In Fig. 2 two re-markable points are illustrated.

~1! The injected electron densityn0 needed for transpar-ency decreases with an increase in the doping concentration.n0 is especially reduced more forn-type doping than forp-type doping at the same dopant concentration.

~2! The differential gain (dg/dp), that is, the slope ofthe gain curve inp-type doping, increases with an increase in

the acceptor concentration. On the other hand,dg/dn forn-type doping decreases with an increase in the donor con-centration.

The physical explanation is as follows. The condition forstimulated emission in a semiconductor may be written asFc1Fv.hn2Eg wherehn denotes the photon energy,Eg isthe band gap, andFc and Fv are electron and hole quasi-Fermi levels in the conduction and valence bands measuredfrom the respective band edges. Increased doping increasesFc andFv and hence fewer carriers are needed to satisfy thecondition for gain. The temperature plays a role through theFermi factors and affects the distribution of electrons andholes in the conduction and valence bands, respectively.Since the effective mass of the conduction band is smallerthan that of the valence band, the electrons are distributedover a wider energy range than holes for an equal number ofelectrons and holes. Also,Fc.Fv for n5p wheren, andpare electron and hole densities, respectively. Thus a changein gain due to additional electrons is smaller than the changein gain due to additional holes, i.e.,dg/dn,dg/dp for n;p. This qualitatively explains why the effect of doping isdifferent in n- andp-type materials.

III. RELAXATION OSCILLATION FREQUENCY

It is well known that the light output of a semiconductorlaser driven by fast current pulses exhibits relaxation oscil-lations resulting from the interaction of the optical field and

FIG. 1. Band diagram of a modulation doped multiquantum well. CB andVB are the conduction band and the valence band, respectively.

FIG. 2. Gain as a function of injected carrier concentration for differentdoping concentrations.

39J. Appl. Phys., Vol. 90, No. 1, 1 July 2001 N. Choudhury and N. K. Dutta

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09

the inverted carrier population. The direct modulation band-width of a laser is limited by the relaxation oscillation fre-quencyf r , which is given by10

f r51

2pA c

nr

P0

tpS dg

dnD , ~4!

whereP0 is the internal photon density andtp is the photonlifetime of the laser mode, which is given by

tp215

c

nr$am1a i%, ~5!

wheream is the mirror loss anda i is the internal mode loss.a i depends on doping.f r can be calculated using the valuesof linear gain and differential gain (dg/dn) as discussedabove. From Fig. 2, it is seen that the differential gain islarger for p-type modulation doped material than that forundoped material which results in larger resonance fre-quency and hence a larger bandwidth forp-type modulationdoped lasers. For simplicity, the dependencies ofP0 andtp

on laser structure are ignored. We consider here a laser withcleaved facets. In Fig. 3, the calculatedf r of p-type andn-type MD-MQW lasers normalized by that of the DH laserare plotted versus various dopant concentrations in the bar-rier layers. The solid line assumes the optical loss is inde-pendent of carrier concentration. The dashed line is for thecase where the optical loss depends on the carrier concentra-tion. For n doping the loss is assumed to be given by7,8

a loss553n/1018 cm21, and for p-type doping the loss isassumed to be given by7,8 a loss5103p/1018 cm21. It mustbe noted that the modulation doping effect onf r is mostremarkable when the doping concentration is larger than 1018

cm23. The f r of a p-type modulation doped laser is furtherenhanced with an increase in the doping concentration due tothe increase indg/dn shown in Fig. 2~a!. In particular it is

enhanced by a factor of 4 compared to that of DH lasers at aconcentration of about 1019 cm23. On the other hand, thef r

of n-type MD-MQW lasers decreases with an increase indonor concentration due to the decrease indg/dn. The lowdoping concentration (0.0131018 cm23 in Fig. 3! representsthe case for undoped MQW lasers. From Fig. 3 it followsthat for undoped MQW lasers the relaxation oscillation fre-quency (f r) is about 1.6 times that for a regular DH lasers.This is primarily due to a higher gain coefficient (dg/dn) inMQW lasers compared to that of a regular DH laser. Figure4 shows the dependence off r on the QW structure~QWthickness,Lw) of p-type MD-MQW lasers. It follows fromFig. 4 thatp-type doping is capable of enhancing the value off r to four times that of DH laser irrespective of the laserstructure.

IV. LINEWIDTH ENHANCEMENT FACTOR

The linewidth enhancement factor~a factor! is a keyparameter which determines the spectral width under bothhigh speed direct modulation and under continuous wave~cw! operation. It is essential to reduce thea factor to reducethe spectral width. Thea factor is defined by the ratio be-tween the derivatives of the refractive indexnr and gaingwith respect to carrier densityn as11,12

a52~4p/l!~dnr /dn!/~dg/dn!, ~6!

wherel is the lasing wavelength. From Eq.~6! we see that ifthe differential gain (dg/dn) is increased thea factor isdecreased. The calculated values of thea factor for p-typeMD-MQW lasers for well thicknesses of 5 and 10 nm nor-malized by that for undoped MQW lasers are shown as afunction of acceptor concentration in Fig. 5. In the calcula-tion, the real part of the index is calculated using theKramers–Kronig relation. Therefore, the acceptor concentra-

FIG. 3. Relaxation oscillation frequencyf r in p-type andn-type MD-MQWlasers normalized to the value of the DH laser as a function of dopingconcentration (1018 cm23). The solid line is for the case where the loss isassumed to be independent of the carrier concentration. The dashed line isfor the case where the loss depends on the carrier concentration. Forndoping the loss is assumed to be given bya loss553n/1018 cm21, and forp-type doping the loss is assumed to be given bya loss5103p/1018 cm21.

FIG. 4. Ratio of the relaxation frequency of a modulation doped MQW to aDH InGaAsP laser plotted as a function ofp-doping concentration. Thedashed lines are for the case where absorption changes with doping (a loss

5103p/1018 cm21) and the solid lines are for the case where the absorptionis independent of the doping. The calculation is done for well thicknesses of5 and 10 nm, respectively, as indicated.

40 J. Appl. Phys., Vol. 90, No. 1, 1 July 2001 N. Choudhury and N. K. Dutta

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09

tion dependence of thea factor comes from that ofdg/dn.As seen from Fig. 5, thea factor is strongly influenced bythe acceptor doping when the concentration is larger than1018 cm23. It is found that thea factor is reduced to.1/2 ofthe undoped value for QW thickness of 10 nm and acceptorconcentration of 1019 cm23. This theoretical calculation for aMD-MQW InGaAsP laser is confirmed by the experimentalresults obtained by Kanoet al.13 Their measured value of thea factor for a MD-MQW InGaAsP laser operating at 1.55mm at a p-type modulation doping concentration of 1.531018 cm23 is ;0.5 that of an undoped laser which agreeswell with the calculated result shown in Fig. 5.

V. RELATIVE INTENSITY NOISE

The power emitted by a semiconductor laser fluctuatesaround its steady state value. The spectrum of these fluctua-tions can be measured by detecting the laser output using awide-bandwidth detector and a spectrum analyzer. Such ameasurement yields the noise spectrum associated with thetotal power. The intensity noise at a given frequencyv ischaracterized by the relative intensity noise~RIN! definedas9

RIN

52Rsp@~GN

2 1v2!1GN2 P2~11geN/RspP!22GNGNP#

P@~VR2v!21GR2 #@~VR1v!21GR

2 #,

~7!

whereRsp is the spontaneous emission rate,GN is the smallsignal carrier decay rate,GR is the relaxation oscillation de-cay rate,GN is the differential gain (dg/dn), P is the num-ber of photons in the cavity,N is the number of carriers inthe cavity, andVR is 2p times the relaxation frequency. InFig. 6 the ratio of the RIN of the MD-MQW laser to that ofan undoped MQW laser is plotted. We see that for ap-typeMD-MQW laser the RIN value is almost 13 dB/Hz less than

that of the undoped case for acceptor concentration of 131019 cm23. We also see that the changes in RIN valuesbecome significant for acceptor concentrations of more than1018 cm23.

The RIN of ap-type MD-MQW laser normalized to thatfor a regular MQW laser as a function of frequency is plottedin Fig. 7 for different values of acceptor concentration. Asmall variation of the RIN with frequency is observed in thefrequency range of interest~plotted!. The resonant frequencyused in the calculation is 25 GHz.

In this article we describe a calculation of measurableparameters such as resonance frequency, linewidth enhance-ment factor, and relative intensity noise of MD-MQW lasers.The calculation is based on the assumption that modulationdoping does not introduce any nonradiative loss mechanismsdue to defects. It is also assumed that the band structureparameters such as effective masses and carrier injection ef-ficiency are not altered by modulation doping. In experimen-

FIG. 5. Ratio of thea factor of a modulation doped MQW and an undopedMQW InGaAsP laser.

FIG. 6. RIN for bothp-type andn-type MD-MQW lasers normalized to theRIN value of an undoped MQW laser plotted as a function of doping con-centration (31018 cm23). The dashed line gives the values for then-typeMD-MQW laser and corresponds to the scale on the left.

FIG. 7. RIN for ap-type MD-MQW laser normalized to the value of anundoped MQW laser plotted as a function of frequency for different dopingconcentrations. The broken line gives the values for doping concentration of4.031018 cm23 and the thicker solid line corresponds to a doping concen-tration of 1.031018 cm23; the thinner solid line refers to a doping concen-tration of 131019 cm23.

41J. Appl. Phys., Vol. 90, No. 1, 1 July 2001 N. Choudhury and N. K. Dutta

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09

tal verification of these results it is important to fabricatelasers with no parasitic elements such as high capacitance orresistance or too large a leakage current. These are generalfactors that must be addressed for the fabrication of laserswith high bandwidth and relatively low intensity noise.

VI. SUMMARY

In this work, the properties of InGaAsP modulationdoped multiquantum well lasers, such as gain, modulationresponse, and RIN, have been theoretically studied. The cal-culated results show that the relaxation oscillation frequencyf r in MD-MQW lasers can be enhanced by more than afactor of 2 over that of undoped MQW lasers usingp-typemodulation doping. Also, thea factor can be reduced to 1/2of the value for undoped MQW laser byp-type modulationdoping and the relative intensity noise is reduced by a factorof .10 dB compared to that for undoped MQW lasers. Theimprovement in these values in modulation doped MQW la-sers is due to asymmetry in the occupation of conductionband and valence band states.

ACKNOWLEDGMENTS

The authors acknowledge the support of Connecticut In-novation, Inc.

1Quantum Well Lasers, edited by P. Zory~Academic, New York, 1993!.2S. Kakimoto and H. Watanabe, IEEE J. Quantum Electron.34, 921~1998!.

3S. Ryu, I. Kim, W. G. Jeong, and B. Choe, IEEE J. Quantum Electron15,711 ~1997!.

4G. Belenky, C. L. Reynolds, L. Shterengas, M. Hybertsen, D. Donetsky,G. Shtengel, and S. Luryi, IEEE Photonics Technol. Lett.12, 969 ~2000!.

5H. Shimizu, K. Kumada, N. Yamanaka, N. Iwai, T. Mukaihara, and A.Kasukawa, IEEE J. Quantum Electron.36, 728 ~2000!.

6K. Uomi, Jpn. J. Appl. Phys., Part 129, 81 ~1990!.7G. P. Agarwal and N. K. Dutta,Semiconductor Lasers, 2nd ed.~VanNostrand Reinhold, New York, 1993!, Chap. 3.

8M. Asada, A. Kameyama, and Y. Suematsu, IEEE J. Quantum Electron.QE20, 745 ~1984!.

9M. Yamanishi and Y. Lee, IEEE J. Quantum Electron.QE23, 367~1987!.10K. Y. Lau, N. Bar-Chaim, I. Ury, Ch. Harder, and A. Yariv, Appl. Phys.

Lett. 43, 1 ~1993!.11C. H. Henry, IEEE J. Quantum Electron.QE18, 259 ~1982!.12K. Vahala and A. Yariv, IEEE J. Quantum Electron.QE19, 1096~1983!.13F. Kano, T. Yamanaka, N. Yamamoto, Y. Yoshikuni, H. Mawatari, Y.

Tohomori, M. Yamanato, and K. Yokoyama, IEEE J. Quantum Electron.29, 1553~1993!.

14Kano et al. Ref. 2, Chap. 6.

42 J. Appl. Phys., Vol. 90, No. 1, 1 July 2001 N. Choudhury and N. K. Dutta

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

141.210.2.78 On: Tue, 25 Nov 2014 13:30:09