exciton saturation in gaas multiple quantum wells at room ...a. miller,a) p. riblet, m. mazilu, s....

Exciton saturation in GaAs multiple quantum wells at room temperatureA. Miller, P. Riblet, M. Mazilu, S. White, T. M. Holden et al. Citation: J. Appl. Phys. 86, 3734 (1999); doi: 10.1063/1.371244 View online: http://dx.doi.org/10.1063/1.371244 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v86/i7 Published by the American Institute of Physics. Related ArticlesElectronic and optical properties of ZnO/(Mg,Zn)O quantum wells with and without a distinct quantum-confinedStark effect J. Appl. Phys. 111, 063701 (2012) Formation of fullerene superlattices by interlayer bonding in twisted bilayer graphene J. Appl. Phys. 111, 043513 (2012) Mapping the electronic properties of individual graphene grain boundaries Appl. Phys. Lett. 100, 053114 (2012) Aharonov-Bohm oscillations in the local density of topological surface states Appl. Phys. Lett. 99, 243110 (2011) Charge transfer complex states in diketopyrrolopyrrole polymers and fullerene blends: Implications for organicsolar cell efficiency APL: Org. Electron. Photonics 4, 269 (2011) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 7 1 OCTOBER 1999

Exciton saturation in GaAs multiple quantum wells at room temperatureA. Miller,a) P. Riblet, M. Mazilu, S. White, T. M. Holden, A. R. Cameron, and P. PerozzoSchool of Physics and Astronomy, University of St Andrews, Fife, KY16 9SS, Scotland, United Kingdom

~Received 16 March 1999; accepted for publication 30 June 1999!

Pump-probe experiments in GaAs/AlGaAs multiple quantum well samples are described using bothpicosecond and femtosecond laser pulses in different polarization configurations. The excitonic andfree carrier components of exciton absorption saturation were analyzed as a function of well width.The relative importance of phase space filling, Coulomb screening and broadening contributionswas determined from polarization and laser bandwidth dependencies via spin-dependent andspin-independent components. A five-level model was used to fit the data and nonlinear coefficientsfor the individual contributions were determined for each well width. The Coulomb contributionsarising from screening and broadening of the excitons was found to dominate the absorptionbleaching using picosecond pulses, whereas phase space filling was largest in the femtosecondregime. Exciton phase space filling was found to be four times larger than free carrier phase spacefilling at narrower well widths. A sublinear dependence of exciton broadening with carrier densitywas observed. ©1999 American Institute of Physics.@S0021-8979~99!06919-4#

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I. INTRODUCTION

Excitons in multiple quantum well~MQW! semiconduc-tors exhibit large resonant optical nonlinearities1,2 which of-fer a number of useful functions for optoelectronic device3

These include laser mode-locking elements,4 saturable ele-ments for controlling the propagation of optical solitonsfiber transmission systems,5 all-optical bistable etalons,6 all-optical directional coupler switches,7 and self-electro-opticdevices8 for high speed communications, signal processand computing.9 The operation and optimization of these dvices rely on an understanding of the mechanisms that ctribute to bleaching of the exciton absorption feature at rotemperature. Previous work has shown that the relative ctributions of the various mechanisms which cause bleachcan be distinguished by the use of circularly polarizlight10,11 and different laser pulse widths12 in pump-probemeasurements. This article describes pump-probe meaments in GaAs/AlGaAs MQWs using both picosecond afemtosecond duration pulses, as a function of wavelenpolarization, bandwidth, carrier density, and well widthorder to quantify the individual contributions to excitonoptical nonlinearities. Three MQW samples with differewell widths have been compared in these studies.

II. BACKGROUND

Excitonic absorption features are clearly resolvedroom temperature in quantum wells compared to bulk seconductors because confinement leads to larger bindingergies and enhanced oscillator strengths. The loss of deeracy of light hole~lh! and heavy hole~hh! valence bandsleads to an exciton doublet in MQWs. Bleaching of the ecitonic features is observed in GaAs/AlGaAs MQWs at blow 1 mW average power, for laser spot sizes on the orde

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10–100mm. This saturation occurs due to the optical geeration of excitons or free carriers at two-dimensional~2D!densities in excess of 1010cm22.

Resonant excitation initially creates bound electron-hpairs, i.e., excitons. When the density of excitons approacthat required to fill space (;1017cm23 based on an excitondiameter of 30 nm for bulk GaAs!, then the number of additional excitons which can be created is reduced by Pexclusion, thus decreasing the level of absorption. Knet al.13 measured a room-temperature ionization time forcitons into free electron-hole pairs of 300 fs. Therefore,time scales less than 300 fs, bleaching results primarily frthe excess exciton density, while on picosecond and lontime scales, it can be assumed that the exciton saturaresults from free carriers.

In order to describe the different nonlinearities resposible for exciton saturation, the generalized Wannier eqtion can be used. This is deduced from the screened Hatonian for a two-band, quasi-two-dimensionsemiconductor:11,14,15

@\v2Ee,k2Eh,k1 i ~G01G!1Sk,s#xk,s

5~12 f e,s,k2 f h,s,k!Fdk1(k8

Vs~k2k8!xk8,sG ~1!

for the polarizabilityx(\v)5(kdkxk,s(\v) whose imagi-

nary part is proportional to the absorption coefficieEe,k ,Eh,k correspond to the single-particle energies of eltron and hole, respectively.Vs(k) is the Fourier transformedquasi-two-dimensional screened Coulomb potential,dk thedipole moment~proportional to the modulus of the interbanmomentum matrix element! and f i ,s,k ( i 5$e,h%) are theFermi functions describing the distribution of electro~holes! in their energy bands with spins. Sk,s , the real partof the self-energy is given by

4 © 1999 American Institute of Physics

license or copyright; see http://jap.aip.org/about/rights_and_permissions

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3735J. Appl. Phys., Vol. 86, No. 7, 1 October 1999 Miller et al.

Sk,s5(k8

~ f e,s,k1 f h,s,k!Vs~k2k8!

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whereV(k) is the Fourier transformed unscreened potentThe first term of these summations is the ‘‘exchan

hole’’ energy and results from the Pauli exclusion principwhich implies that each fermion is surrounded by a regwhere the probability of the existence of another identifermion is very small. This repulsive energy occurs for pticles with equal spin and charge.

The second term is the ‘‘Coulomb hole’’ energy whicinvolves equally charged fermions avoiding each othercause of Coulomb repulsion. This term is independent ofspin of the particles. A finite homogeneous linewidthG0 , isintroduced to account for dephasing collisions~electron-phonon interactions! and is accompanied with the termGwhich corresponds to the imaginary part of the self-enerepresenting the carrier-carrier scattering rate.

Finally, the term (12 f e,s,k2 f h,s,k) is the filling factorrepresenting a blockade of transitions by Pauli exclusiwhere a state occupied by a fermion is no longer availabla final state in an optical absorption process.

We can therefore distinguish three different mechanisinducing exciton saturation:

Phase space filling~PSF! is the mechanism resulting drectly from the Pauli exclusion principle and will reduce texcitonic oscillator strength through the filling factor and texchange hole energy.

Screening is the mechanism resulting from the Coulointeraction and will reduce the excitonic oscillator strengthrough the screened potentialVs and the Coulomb hole energy.

Broadening is the mechanism resulting from carricarrier scattering and will increase the homogeneous lwidth of the exciton with the same overall oscillator strengthrough the imaginary part of the self-energy.

PSF depends on the spin of the electron since the filfactor and the exchange hole energy are both spin-depenquantities, in contrast to screening and broadening~in thelow density regime!. This difference has already been eploited in pump-probe experiments in MQWs at rootemperature11,12where it was possible to separate experimtally the effect of PSF from the combined effects of screing and broadening. This is made possible only in MQsemiconductors because of the lifting of the degeneracytween the light and heavy hole bands due to confinemallowing access to polarization sensitive optical selectrules, as shown in Fig. 1.

Circularly polarized light resonant with the heavy hoexciton generates 100% spin-polarized electron-hole paThe initial spin orientation of the optically generated extons is maintained by the electrons for tens of picosecoafter exciton ionization.16 Spin relaxation is not a coherenphenomenon. The physics of electron spin relaxationbeen analyzed theoretically in bulk17 and MQW18 semicon-ductors at room temperature and is most likely due to


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D’Yakonov and Perel~DP! process.16,17 The DP spin relax-ation mechanism results from spin-orbit splitting of the coduction band. Spin splitting is equivalent to the existencea magnetic field acting on the electron spins. Between cosions the spin precesses about the direction of the psofield, defined by the momentum direction. During colsions, changes in momentum cause a rotation ofprecession axis, allowing the spins to flip.

Hole spin relaxation is much faster~subpicosecond timescale at room temperature! because of valence band mixinand the mixed spin character of the light hole states.19,20

Therefore, because PSF is spin dependent, it is possibseparate out electron PSF and to deduce the spin relaxtime for free electrons by studying the change in transmsion of the probe as a function of time delay under differepolarization combinations of pump and probe. In additionstudy of the change in transmission of the probe as a funcof carrier density and excitation wavelength will show trelative importance of broadening as compared to screenThe density dependence of the broadening is complexnot well established theoretically.

III. EXPERIMENT

Pump-probe experiments were carried out using a smode-locked Ti:sapphire laser~Spectra-Physics, Tsunam!producing either 100 fs or 1 ps pulses at 82 MHz. The bewas split to form pump and probe pulses, and the timearrival of the probe pulses at the sample could be varied wa variable optical delay. The pump beam was choppedsubsequent phase sensitive detection. Each of these bwas passed through a linear polarizer followed by a quarwave plate or a half-wave plate to produce either left or righanded circularly polarized or linearly polarized light. A sof three samples, S51, KLB, and FK141 were studied.

Sample S51 consists of 60 periods of 4.4 nm Gaquantum wells surrounded by 17.5 nm Al0.33Ga0.66As barri-ers with no doping background. KLB contains 120 periods6.5 nm GaAs quantum wells surrounded by 21.2 nAl0.4Ga0.6As barrier with an intentionalp-type doping back-ground of;1016cm23. FK141 incorporates 15 periods ofnm GaAs quantum wells surrounded by 10 nm Al0.2Ga0.8Asbarrier with no doping background.

FIG. 1. Selection rules for the transitions from the heavy hole and light hvalence bands to the conduction band in MQWs. The (j , mj ) refer to thequantum numbers for angular momentum and its component along onrection. Thes1 and s2 refer to the transitions excited by each sensecircularly polarized light and correspond toDmj561, respectively, wherethe propagation direction is used to definemj .


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3736 J. Appl. Phys., Vol. 86, No. 7, 1 October 1999 Miller et al.

The GaAs substrate was etched off to allow transmissmeasurements and an antireflection coating applied to esurface for all three samples. Figure 2 shows the hh-lh eton doublet in the linear absorption spectrum for sample S

A pump power of 1 mW resonant with a hh excitoabsorption peak creates an estimated carrier density of;531016cm23 for each sample~within a factor 2, taking intoaccount the different absorption coefficients, thicknessand well widths!. This corresponds to a two-dimensiondensity of;1010cm22. ~Although there will be some nonuniformity of carrier density across the wells, particularlyS51 and KLB, within the low density~linear! regime, thisdoes not affect the results.! We measure the change in tranmission DT of the probe beam and deduce the changeabsorptionDa from the relation:

Dad52 lnS dT

T011D'2

DT

T0, ~3!

whered is the effective thickness of the sample andT0 itslinear transmission. For sufficiently small change in tramission, the two quantities are proportional.

IV. WAVELENGTH DEPENDENCE

Bleaching of exciton absorption produces both absotive and refractive optical nonlinearities at moderate optipowers.21 There is no observed shift in wavelength of tpeak of the exciton during saturation. Any reduction of tbinding energy caused by Coulomb screening to yield a bshift of the exciton is balanced by a redshift resulting froband-gap renormalization.22 This may not be entirely coincidental, since band-gap renormalization arises from a comnation of exchange and correlation effects between carrwhich is a Coulomb interaction, plus the fact that the exciis a neutral particle.23 Above about 3 mW, the absorptiobecomes progressively more difficult to saturate beca

FIG. 2. Optical density,ad, as a function of wavelength for sample S51room temperature (hh5heavy hole, lh5light hole)


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band-gap renormalization causes a redshift of the fundamtal band-gap energy and thus a progressively larger denof states needs to be blocked. At high optical powers,thus very high carrier densities, band filling will cause tremaining absorption to saturate, but this is normally accopanied by a redshift of the band gap due to local heatingthe lattice.

Figure 3 compares differential transmission spectrathe three GaAs/AlGaAs MQW structures with different wewidths under conditions of moderate excitation level. Thespectra were recorded in a pump-probe configuration uslinearly polarized 1 ps duration pulses. There was a fixdelay of a few picoseconds between the pump and prpulses. The negative signals are caused by broadening oexciton features. It may be noted that the magnitude ofnegative signal is largest in the sample with the narrowquantum wells and clearly occurs on both sides of theexciton feature in this case.

V. POLARIZATION DEPENDENCE

Figure 4 shows the results of time-resolved saturatmeasurements carried out at the peak of the hh exciton

FIG. 3. Change in transmission as a function of the laser wavelength ulinear polarization for the three samples FK141, KLB, and S51.


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sorption in sample KLB at room temperature using 1pulses with the three polarization configurations of pump aprobe beams,~a! opposite linear polarization~OLP!, ~b!same circular polarization~SCP!, and ~c! opposite circularpolarization~OCP!. One picosecond pulses have a specbandwidth much less than the hh exciton spectral linewidThe transmission change is due to the combined effectPSF, screening and broadening on exciton saturation wall reduce the absorption at the center of the line. The Oconfiguration shows a rapid rise in transmission of the prat zero delay followed by a recovery due to carrier recomnation on nanosecond time scales. The signal is thereobserved as an almost flat plateau on the picosecondscales recorded here.~Note that there is no difference usinthe same and opposite linear polarizations.!

When the pump is circularly polarized, all of the carriegenerated will initially have the same spin orientation. Tprobe can be chosen to have either the same sense of cirpolarization as the pump, SCP, or the opposite circularlarization, OCP. The SCP result in Fig. 4 shows an initiaenhanced saturation, compared to the OLP case, and a reery to the plateau level within a time on the order of 100This enhancement arises from spin-dependent PSF.probe interacts with electron spin states that are twice asas those in the OLP case~for the same total number of excited carriers!. For the OCP condition, the initial bleachingless than for OLP. In this case, immediately after excitatall of the electrons are in the opposite spin state to that beprobed, so there is no PSF. This results in less bleacinitially, but as the electron spins randomize, the OCP sigrises to the OLP level. The initial level in the OCP signclose to zero delay is due to the combined spin-indepenCoulomb effects of screening and broadening. The recovtime of the enhanced~SCP! and reduced~OCP! bleaching

FIG. 4. Dependence of probe transmission change on optical time delpump-probe measurements for three polarization configuratiOLP5opposite linear polarization, SCP5same circular polarization,OCP5opposite circular polarization for sample KLB.


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gives a characteristic electron spin relaxation timetspin of 50ps.

For the OCP configuration, the combined influencePFS, screening, and broadening sets the transmission chat the plateau level, whereas the initial change in transmsion before any spin relaxation occurs, is due to screenand broadening alone. Again for the SCP configuration,difference between the plateau level and the initial signasolely due to PSF. We note that the influence of PSF inSCP configuration, is roughly double that in the OLP cofiguration. This is because there is only one electron avable per state~all of the electrons have the same spin in tSCP configuration! compared to the OLP configuration iwhich both spin states are excited. As a result, for the sagenerated electron population, there will be twice as maoccupied states in the probed spin band in the SCP cascompared to the OLP case, doubling the influence of PAlthough the general equation@Eq. ~1!# relates the differentmechanisms in a complex manner, calculations have bperformed,11 that well describe the results obtained for tthree different polarization configurations in pump-promeasurements in a low density regime (,1010cm22).

We have been able to separate PSF due to electronthis experiment only because the hole spin randomiwithin 1 ps at room temperature. It is possible that PSF dto the holes occurs even in the OCP configuration. Howethe average in-plane effective mass for holes is much lathan for electrons, which means that PSF should be donated by the electron contribution. Furthermore, calculatishow only a small difference when PSF induced by the hois taken into account.

VI. SPECTRAL BANDWIDTH DEPENDENCE

The broad bandwidth of ultrashort pulses can be useidentify the broadening contribution to the exciton absotion nonlinearity as described by Holdenet al.12 Figures 5~a!and 5~b! compare results of pump-probe measurements~asdescribed in Sec. V! using 1 ps and 100 fs pulses for sampS51. One picosecond pulses have a spectral bandwidth;2 meV, so that the observed transmission change centerethe peak of the hh exciton of spectral linewidth 6.4 meV~seeFig 2!, is due to the combined effects of PSF, screeningbroadening. On the other hand, for 100 fs pulses, the msured bandwidth is; 10 nm~20 meV!, which is greater thanthe hh exciton absorption linewidth. Consequently, 100duration probe pulses effectively measure the integratedsorption change rather than the change at the line center.striking difference between the two sets of results in Fi5~a! and 5~b! follows from the absence of any sensitivity tbroadening of the exciton when using the shorter duratpulses. Collisional broadening lowers the absorption at lcenter while it increases it in the wings leaving the integraabsorption unchanged. A comparison of the initial step sifor the OCP configuration for picosecond results, Fig. 5~a!,and femtosecond results, Fig. 5~b!, demonstrates that broadening is the dominant contribution to the peak exciton asorption quenching in this sample for picosecond or londuration pulses.

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VII. CARRIER DENSITY DEPENDENCE

So far, we have identified broadening to be the mosignificant contribution to exciton bleaching in the sampwith the narrowest wells~S51! using longer duration pulsesfrom the wavelength dependence and from the laser bawidth dependence in polarization sensitive pump-probe sties. Broadening can also be identified in measurementsried out as a function of pump power when the polarizatiselection rules are again used to extract the magnitude ofspin-independent contribution to exciton saturation.

Results such as those shown in Fig. 4 using 1 ps puwere used to quantify the relative magnitudes of the electPSF and Coulomb contributions to exciton saturation at lexcitation from the initial changes in transmission in ththree polarization configurations. We now extend thisstudy the variation as a function of generated excess cardensity. Figure 6 plots the spin-dependent~PSF! and spin-independent~Coulomb! components of the initial transmission change of 1 ps pulses as a function of the average pu

FIG. 5. Probe transmission changes as a function of delay time for the tpolarizations, SCP, LP, and OCP using~a! 1 ps and~b! 100 fs pulses forsample S51.


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power from results similar to those shown in Fig. 4 for tthree MQW samples.

First, we note that the Coulomb contribution is alwalarger than the PSF contribution for all three well widthSecond, the power dependence is observed to be linear icases except for the Coulomb contribution in sample S5

In all three samples, the spin-independent componDTPSF, increases linearly with the carrier density. This implies that the excitonic oscillator strength decreases linewith carrier density~up to 1010cm22) as expected for a thirdorder nonlinearity. The experiment remains in a low densregime because the excitonic absorption is not complesaturated.

For samples KLB and FK141, the spin-independecomponent,DTOCP, follows the same linear dependencePSF. This similar behavior is expected for the screenmechanism and has been calculated previously.12 This com-ponent is significantly larger than PSF and is found tomore dominant in FK141 than in KLB in comparison wit

eeFIG. 6. Coulomb~screening and/or broadening! and PFS contributions tothe transmission changes as a function of the pump power at the peak oheavy hole exciton in the three samples FK141, KLB, and S51.


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PSF. One possible explanation would be the influenceconfinement. In fact, the quantum wells in sample KLB haa well width of 6.5 nm with an electron confinement enerof 63 meV, whereas the wells in FK141 are 9 nm wide wan electron confinement energy of 37 meV. Previous thretical studies12 predicted that PSF should increase its inflence with confinement and become the dominant mecnism. This evolution is consistent with our measuremewith the exception that the spin-independent componentmains larger than PSF although its influence decreasesconfinement.

The carrier density dependence of the spin-independCoulomb contribution is strongly sublinear in the narroquantum well sample, S51. We propose that the domincontribution is broadening whereas screening dominatethe other two samples. This is supported by the negachanges in transmission as a function of wavelengthshown in Fig. 2 in which the broadening mechanism cleaappears in sample S51 at the hh exciton but is not as imtant in KLB or FK141. This observation indicates that fsamples KLB and FK141 the two principal mechanismssaturation using picosecond pulses are screening andwhereas broadening plays a more important role for S51

For sample S51,DTOCP shows a clear nonlinear behaior. The change in transmission varies linearly up to a pupower of; 0.2 mW which corresponds to a carrier densof ;33109 cm22 and is followed by a saturation effect.we assume an exciton resonance centered at the wavelelmax to have a Gaussian shape, the absorption will be

ad5a0d expS 2~l2lmax!

2

G82 D , ~4!

whereG8 is the linewidth of the resonance. If we considbroadening to be the only mechanism, we have the relatiol5lmax:

G85G0a0d

a0d2 ln~DT/T011!, ~5!

where G0 and a0 are the initial linewidth and absorptiocoefficient before the pump excitation. For relatively smchanges in transmission and with a coefficienta0d close tounity, relation Eq.~5! becomes

G

G05

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a0dT0. ~6!

As a result,DTOCP gives a measure of the change of texciton linewidth.G corresponds to the same collision ratedefined in Eq.~1!. In general, scattering of the excitoncaused by exciton-exciton and exciton-free carrier intertions. A direct measurement of collisional broadening of ecitons in GaAs quantum wells has been reported attemperatures,24 showing separately the scattering inducedfree carriers and excitons. The free carrier-exciton scatte


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rate has been observed to increase linearly up to a cadensity of 53109 cm22 as predicted by many-body theorylow density.25 At room temperature, excitons ionize withi300 fs which implies that the dominant scattering mechancontributing to the increased exciton linewidth will bexciton-free carrier collisions. Our measurements are content with the low temperature measurements of Ref. 24,as the carrier density increases above;53109 cm22, thecollision rate begins to saturate. Many-body theory is nwell established for a correct description of the scatterrates and phenomenological dependencies are usually iduced if this effect has to be taken into account.11 We can,however, understand this behavior qualitatively. As the dsity of carriers becomes more significant, the number of stering events per unit volume increases in proportion tocarrier density; but simultaneously the carrier-carrier intertion, which is nothing but the Coulomb interaction,screened, thereby reducing the impact of any collision aba critical density. From this point of view, the screeninmechanism, as it has been defined in this paper, andbroadening mechanism have the same physical origin,the Coulomb interaction. Screening corresponds to the efof Coulomb interaction on the oscillator strength, wherebroadening corresponds to the effect of Coulomb interacon the resonance linewidth.

In this analysis for sample S51, we have assumedthe only mechanism that contributes toDTOCP is broadening.However, the screening mechanism should also be incluas indicated by the spectral bandwidth results discusseSec. VI. From Fig. 5~b!, the contribution due to screeningabout two thirds of the PSF contribution, so that the broening can be estimated from Fig. 5~a! at around five timesthat of screening at low excitation levels. The quantum wein sample S51 are 4.4 nm wide, with an electron confinemenergy of 93 meV. From the analysis of KLB and FK141, wexpect the screening mechanism to be linearly dependencarrier density and to have a maximum value of the saorder of magnitude as PSF. However, such a correctionto screening would have the effect of reinforcing the satution characteristic of the curve. Besides, we have measuin single beam experiments that the maximum changetransmission for S51 reaches 15% compared with onlyfor KLB, indicating that the effect of screening onDT is notas strong as the effect of broadening in S51.

As illustrated in Fig. 2, S51 is of high optical qualitwith a sharp well-resolved heavy hole exciton at room teperature (G056.4 meV). This is partly due to good materiquality and partly because the well width of 4.4 nm givclose to the maximum exciton binding energy. Thereforesmall change of the linewidth can induce a rather lachange in transmission at the maximum of the resonancethe other hand, the excitonic absorption features in KLB aFK141 are not as well resolved which make the broadenmechanism less sensitive for these two samples. Moreothe broadening effect may become more important wmore confinement but there is no theory available for sucprediction.


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tion


VIII. TIME DEPENDENCE

Higher time resolution pump-probe measurements us100 fs pulses allow a comparison of exciton absorption sration before and after exciton ionization.12,13 In this section,we will describe an analysis of pump-probe results, whgives the relative magnitudes of exciton and free carrier ctributions to spin-dependent and spin-independent hh excbleaching. Using 100 fs pulses, broadening is averagedand the contributions from free carrier phase space fill~spin dependent! and free carrier Coloumb screening~spinindependent! can be isolated and compared. Circular polizations were again employed in order to create and prthese spin-dependent and spin-independent mechanism

An example of a set of higher time resolution pumprobe scans using 100 fs pulses and recorded within 2 pzero delay are shown in Fig. 7. In his case, a probe besteering mirror was vibrated to eliminate any coherencetifacts. Resonant excitation with a 100 fs pulse initially prduces a population of cold (k50) bound electron-hole pair~excitons!. Further creation of excitons is inhibited by exctonic PSF and thus the absorption becomes bleachedroom temperature, excitons strongly ionize via collisiowith LO phonons within about 300 fs.13 A fast transient fea-ture is seen in SCP and LP configurations in Fig. 7, asexcitons are rapidly generated and then ionize, creatingfree carriers. Within the first 1 ps after excitation, excitcontributions have passed and free carrier contributionexciton saturation dominate. The enhanced transmischange at small delays results from the fact that the presof excitons is more efficient in saturating the hh exciton asorption feature than the presence of the same density ofcarriers. This transmission enhancement is observed tolarger for the SCP configuration than LP, confirming that

FIG. 7. Probe transmission changes at the hh exciton absorption peakfunction of delay using 100 fs pulses for SCP~same circular polarizations!,LP ~same linear polarizations!, and OCP~opposite circular polarizations! asa function of time for sample S51.


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spin-dependent PSF component is larger for excitons tfor free carriers.

On inspection of the OCP trace in Fig. 7, the initial rishows a step followed by a slow increase in transmisstowards the LP curve at the spin reorientation rate. Perhsurprisingly, there is no signature of exciton ionization.PSF does not contribute to the initial OCP condition, thobservation may indicate that screening due to excitonsfree carriers is equal.12 However, an alternative interpretatiois that the exciton contribution is minimal because the crelated opposite charge carriers cancel each other out.26 Inthis latter case, the initial rise in the OCP transmission is donly to the free carrier population build up after exciton ioization. The theoretical fits for the OCP data described laare highly sensitive to the pulse duration and the zero deposition. Further experiments are needed to determineprecise relative magnitude of the exciton screening.

The schematic in Fig. 8 shows a five-level model cotaining two coupled three-level systems, one for spin-up aone for spin-down carriers with a common ground state. TcoefficientsG1 andG2 correspond to the recombination ratof the free carriers and excitons andG3 gives the rate ofexciton ionization. The inverses of these coefficients givecharacteristic ionization or relaxation times. Another facchanging the carrier populations is the pump excitation. Texcitation is represented by intensity profiles of the pudecomposed into the two opposite circular polarizatG1(t) and G2(t). The selection rules, Fig. 1, imply thaG1(t) andG2(t) correspond to the rate of excitation of thcarriers from the ground level into the spin-up and spdown exciton levels, respectively. Further, we take intocount the spin relaxation ratesGs1 and Gs2 , which imply ahomogenization of the spin after the selective excitationonly one spin state. Finally, the probe pulse is represenhere to be resonant with the spin-up exciton level.

The evolution of the population of such a five-level sytem is given by a system of four coupled first-order diffeential equations

s a

FIG. 8. Diagram of the five-level system. The arrows represent the direcof flow of population.


e

meenfo

ity

nv

tr

a

th

y

ithted

and

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la-o at

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theions

thein-

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hehent.


dnex1

dt52~G21G31Gs1!nex

11Gs1nex21G1~ t !,

dnex2

dt51Gs1nex

12~G21G31Gs1!nex21G2~ t !,

~7!dnFC

1

dt51G3nex

12~G11Gs2!nFC1 1Gs1nFC

2 ,

dnFC2

dt51G3nex

21Gs2nFC1 2~G11Gs2!nFC

2 ,

wherenex1 , nex

2 , nFC1 , andnFC

2 represent the exciton and frecarrier populations in the spin-up and spin-down states.

In order to find a simple analytic solution to this systeof equations, we assume that the intensity profile of thecitation is Gaussian. We can distinguish three differmodes of excitation, which can be summarized into thelowing expressions:

G1~ t !5g01 expS 2

t2

Dt02D ,

~8!

G2~ t !5g02 expS 2

t2

Dt02D ,

whereg06 andDt0 corresponds, respectively, to the intens

coefficient and duration of the pump pulses. In the caselinear polarized light, we have

g025g0

151/2. ~9!

For circular polarized light, either the spin-up or spin-dowexciton level is excited. For the spin-up excitation, we ha

g0151, g0

250, ~10!

and for the spin-down case,

g0150, g0

251. ~11!

To solve Eq.~7! we transform it into two uncoupledsystems each corresponding to a three-level system. Inducing the sum and difference of populations

sex5nex11nex

2 , sFC5nFC1 1nFC

2 ,~12!~12!

dex5nex12nex

2 , dFC5nFC1 2nFC

2 ,

the evolution equations of the two three-level systems re

d

dtsex52~G21G3!sex1G1~ t !1G2~ t !,

~13!d

dtsFC51G3sex2G1sFC,

and

d

dtdex52~G21G312Gs1!dex1G1~ t !2G2~ t !,

~14!d

dtdFC51G3dex2~G112Gs2!dFC.

By analyzing these two systems of equations, we seethey correspond indeed to simple three-level systems.


x-t

l-

of

e

o-

d

at

In the s system, Eq.~13!, the excitation is given by thesum of G1(t) and G2(t) and is further characterized bexciton recombination and ionization rates,G2 andG3 . Thefree carrier recombination rate isG1 . We remark that allthree excitation configurations@Eqs.~9!–~11!# have the sameeffect on thes system and thus this system is invariant wrespect to the polarization. Indeed, this is to be expecbecause of the symmetry of switching between spin-upspin-down states.

Similarly, in the d system, Eq.~14!, the exciton term,dex, has recombination and ionization rates given by (G2

12Gs1) and G3 . The ‘‘free carrier’’ recombination rate is(G112Gs2). Its excitation corresponds to the difference btweenG1(t) andG2(t). In this case, the system is not ecited at all by the linear polarization excitation, Eq.~9!,whereas the circular polarization excitation correspondsther to a ‘‘positive,’’ Eq.~10!, or ‘‘negative,’’ Eq. ~11!, ex-citation.

To determine the solution of Eqs.~13! and~14!, we needto assume the initial conditions, i.e., the state of the poputions before the excitation pulse. We take them to be zert52`. The exact solutions read

sex~ t !5~g011g0

2!KG21G3~ t !,

sFC~ t !5~g011g0

2!@KG1~ t !2KG21G3

~ t !#,

~15!dex5~g0

12g02!KG21G312Gs1

~ t !,

dFC5~g012g0

2!@KG112Gs2~ t !2KG21G312Gs1

~ t !#,

where

KG~ t !5Ap

2Dt0 expS 2Gt1

G2Dt02

4 D3F11erfS 2t2GDt0

2

2Dt0D G . ~16!

Using the population evolution of Eqs.~15! and~12!, wecan define the induced transmission change of the prbeam due to the saturation effects. Indeed the densityexcitons, and subsequently free carrier pairs, created bypump pulse under the conditions described in earlier sectwas estimated to be 1010cm22. At this density, Boltzmannstatistics apply and we can assume that the strength ofsaturation and transmission change is proportional to thestantaneous particle density. Thus, using the variable deltbetween the pump and probe pulses, one can scan the plation evolution after an excitation. The transmission chanof the probe pulse is given by the integration of the satution effects over the duration of the pulse and is proportioto

DT~t!}E2`

1`

G1~ t2t!@pexnex1~ t !1~sFC1pFC!nFC

1 ~ t !

1sFCnFC2 ~ t !#dt, ~17!

where the coefficients in front of the populations give tamount of interaction with the probe pulse. Further, in tcase of free carriers, we take two contributions into accou


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SFente

. Infs

ustfor

100ns asi-to

exci-n-up


One is due to the screening effect,sFC, and is present forboth spin-up and spin-down populations of free carriers. Tother part corresponds to the magnitude of the PSF,pFC, andthus is only present on the spin-up side if the circularly plarized probe pulses are probing this transition. In the casexciton populations, we include only a PSF contributiopex, because the screening effects are negligible.

Another benefit of using Gaussian intensity profilesthe excitation pulse is that it is possible to evaluate the ingral given by Eq.~17! exactly. To simplify the solution weconsidered the recombination ratesG1 and G2 and the spinrelaxation ratesGs1 andGs2 to be negligible in comparisonwith the ionization rateG3 . This has no effect on the calculated transmission change because of the large differencetween these rates.

After simplification, the transmission change is propotional to

DT~t!}pexg01KG3

l ~t!1sFC~g011g0

2!@KG1

l ~t!2KG3

l ~t!#

1pFC@ 12~g0

11g02!KG1

l ~t!2g01KG3

l ~t!

1~g012g0

2!K2Gs2

l ~t!# ~18!

with

KGl ~t!5exp~2Gt!F11erfS t2GDt0

2

&Dt0D G . ~19!

Both short scan pump-probe measurements with a prdelay of a few picoseconds, Fig. 9, and long scans of up120 ps, Fig. 10, were carried out for the three samples u100 fs pulses. In this way, both the exciton ionization trasient and spin relaxation were time resolved. The experimtal data from scans on both time scales were then fittedmultaneously using the three pump configurations for eaThis greatly improved the parameter confidence, as therelaxation times derived from the opposite and same circpolarization must be the same for each sample. Furthersimultaneous fit of the three polarization configurations mpossible the determination of the relative contributionsscreening and PSF to exciton saturation. In Fig. 9, whshows the short time scale scans for sample S51, we hplotted the individual contributions from spin-up and spdown excitons and free carriers, as well as the resultingtals. Figure 9~a! and 9~b! show that it takes almost 1 ps fothe free carrier concentration to become established.times less than 1 ps, both exciton and free carrier densmust be taken into account. An exciton ionization timearound 250 fs was determined from the decays in the inpeaks for SCP and LP results. The decays in the longerscale results in Fig. 10 are determined by spin relaxation,clearly show the well width dependence of the spin reoritation time by a comparison of the three samples.

We summarize the results of the fits for the thrsamples using 100 fs pulses in Table I. The magnitudethe contributions have been normalized to the free carscreening component in order to illustrate trends in the sration components as a function of well width. We stress tit is important to carry out this fitting procedure rather th


e

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be-

-

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arheefhve

o-

oresfled-

ofr

u-t

estimate the step sizes in the pump-probe data, in ordeaccurately determine the relative importance of the differcomponents. Note that the parameters,sFC, pFC, and pex

were defined above@Eq. ~17!# as nonlinear coefficients peexcess electron-hole pair. This definition gives values ofpFC

andpex which are twice as large as the nonlinear coefficiedefined with respect to the polarization dependence in Fi~see Holdenet al.12!.

We first note that both the exciton and free carrier Pcontributions are always larger than the spin-independfree carrier Coulomb contribution. This is contrary to thresults shown in Fig. 6 obtained with picosecond pulsesthis case, broadening has been eliminated using 100pulses. These results therefore imply that broadening mprovide some contribution to the Coulomb componentFK141 and KLB in Figs. 6~a! and 6~b!, but the linear density

FIG. 9. Change of probe transmission as a function of delay time usingfs pulses for sample S51 using the same three polarization configuratioFig. 7~a! SCP,~b! LP, and~c! OCP. The solid lines are fits to the expermental data~dots!. Also shown are the components of the contributionsthe transmission change from spin-up and spin-down free carriers andtons deduced from the fits assuming the probe is coupled to the spistates~Fig. 8!.


oe

t

ith-

eos-

toron-hhis

ertiontedd

on-eeim-

ofas

siblem-beeneondnc-emi-ex-on-ier

m-di-lvetedesthatSF

nicrier

ulones.

tim

hinno


dependencies point to the dominance of the screening cponent. From Table I, it can be observed that when broading is eliminated, the ratio of free carrier PSF to screeninggreater than unity for all three samples, ranging from 1.53.6 as the confinement increases.

FIG. 10. Change of probe transmission using 100 fs pulses at longdelays for samples FK141, KLB, and S51 together with numerical fits~solidlines! for the three polarization configurations as defined in Fig. 7.

TABLE I. Results of fitting pump-probe data using 100 fs pulses.pFC andpex are the relative magnitudes of the PSF contributions to exciton bleacper electron-hole pair due to free carriers and excitons, respectively,malized to the free carrier screening contribution per electron-hole pair,sFC .tspin is the fitted spin relaxation.

SampleWell width

~nm! sFC pFC pex pex /pFC

tspin

~ps!

FK141 9.0 160.05 1.560.1 11.160.5 7.4 180615KLB 6.5 160.05 3.260.1 13.260.3 4.1 90610S51 4.4 160.03 3.660.1 14.060.2 3.9 5065


m-n-iso

Second, the results in Table I show that, consistent wtheory,26 both pFC andpex increase with confinement. Exciton PSF is larger than free carrier PSF~for equal excitationdensities! for all three well widths, but the ratio of thescontributions decreases with increasing confinement. A psible explanation may be found by referring again to Eq.~1!.We stated in Sec. II that PSF comprises both a filling facand an exchange term. We may expect the free carrier ctribution to be primarily via the filling factor whereas botterms will contribute in the presence of excess excitons. Tfollows from the fact that cold excitons will have a highrepulsive potential because they are more highly localizathan free carriers. Additionally, whereas optically generaexcitons are created close tok50, the free carriers createby thermal ionization of excitons will occupy a range ofkstates thus reducing the filling factor. Greater quantum cfinement will serve to increase the localization of the frcarriers thus making the exchange part relatively moreportant.

Finally, we observe that the well width dependencethe spin relaxation time is consistent with the DP modelreported by Brittonet al.16

IX. CONCLUSION

In these studies, the three main mechanisms responfor the heavy hole exciton saturation in MQWs at room teperature, i.e., PSF, screening, and broadening, havestudied in samples with different well widths using thpump-probe technique. Both picosecond and femtosecpulses were employed in experiments carried out as a fution of wavelength, polarization, and excitation level. Whave shown that the broadening mechanism plays a donant role for picosecond and longer pulses when the hhciton absorption resonance is narrow, and we have demstrated for the first time a saturation of the carrier-carrcollision rate at low density (;53109 cm22). This is ofimportance for any optoelectronic device using room teperature excitonic nonlinearities in quantum wells. In adtion, measurements such as four-wave mixing which invoresonant excitonic optical nonlinearities must be interpreappropriately in the light of this observation. In samplwhere broadening is less important, we have shownscreening remains an important contribution although Pbecomes increasingly dominant in narrower wells. ExcitoPSF is approximately four times larger than the free carcomponent in narrower wells.

ACKNOWLEDGMENTS

The authors would like to thank Ian Galbraith for usefdiscussions and Karl Woodbridge, Geoff Duggan, and DMcDaniels for the MQW samples used in these studiEPSRC is acknowledged for financial support.

1Optical Nonlinearities and Instabilities in Semiconductors, edited by H.Haug ~Academic, San Diego, 1988!.

2S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Adv. Phys.38, 89~1989!.

e

gr-


-v

nd

-L

ta

.

er,

r,

.

c

R.

t,

g-


3A. Miller, in Fabrication, Properties and Applications of Lowdimensional Semiconductors, edited by M. Balkanski and I. Yanche~Kluwer, Dordrecht, 1995!, pp. 383–413.

4U. Keller, W. H. Knox, and G. W. ‘tHooft, IEEE J. Quantum Electron.28,2123 ~1992!.

5D. Atkinson, W. H. Loh, V. V. Afansjev, A. B. Grudinin, S. J. Seeds, aD. N. Payne, Opt. Lett.19, 1514~1994!.

6T. Rivera, F. R. Ladan, A. Izrael, R. Azoulay, R. Kuszelewicz, and J.Oudar, Appl. Phys. Lett.64, 869 ~1994!.

7S. Shi, P. LiKamWa, A. Miller, J. Pamulapati, P. Cooke, and M. DutAppl. Phys. Lett.66, 79 ~1995!.

8D. A. B. Miller, Opt. Quantum Electron.22, S61~1990!.9A. L. Lentine, L. M. F. Chirovsky, L. A. D‘Asaro, C. W. Tu, and D. A. BMiller, IEEE Photonics Technol. Lett.1, 129 ~1989!.

10A. Takeuchi, S. Muto, T. Inata, and T. Fujii, Appl. Phys. Lett.56, 2213~1990!.

11M. J. Snelling, P. Perozzo, D. C. Hutchings, I. Galbraith, and A. MillPhys. Rev. B49, 17160~1994!.

12T. M. Holden, G. T. Kennedy, A. R. Cameron, P. Riblet, and A. MilleAppl. Phys. Lett.71, 936 ~1997!.

13W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, CV. Shank, A. C. Gossard, and W. Weigmann, Phys. Rev. Lett.54, 1306~1985!.


.

,

14H. Haug and S. W. Koch,Quantum Theory of the Optical and ElectroniProperties of Semiconductors~World Scientific, London, 1993!.

15M. Lindberg and S. W. Koch, Phys. Rev. B38, 3342~1988!.16R. S. Britton, T. Grevatt, A. Malinowski, R. T. Harley, P. Perozzo, A.

Cameron, and A. Miller, Appl. Phys. Lett.73, 2140~1998!.17M. I. D’Yakonov and V. I. Perel, Zh. Eksp. Teor. Fiz.60, 1954 ~1971!

@Sov. Phys. JETP33, 1053~1971!#.18M. I. D’Yakonov and V. Yu. Kachorovskii, Sov. Phys. Semicond.20, 110

~1986!.19R. Ferreira and G. Bastard, Phys. Rev. B43, 9687~1991!.20A. Tkeuchi, Y. Nishikawa, and O. Wada, Appl. Phys. Lett.68, 797

~1996!.21A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crus

and K. Woodbridge, J. Opt. Soc. Am. B6, 567 ~1989!.22C. Weber, C. Klingshirn, D. S. Chemla, D. A. B. Miller, J. E. Cunnin

ham, and C. Ell, Phys. Rev. B38, 12748~1988!.23S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Adv. Phys.38, 89

~1989!.24A. Honold, L. Schultheis, J. Kuhl, and C. W. Tu, Phys. Rev. B40, 6442

~1989!.25G. Manzke, K. Henneberger, and V. May, Phys. Status Solidi B130, 233

~1987!.26S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Phys. Rev. B32,

6601 ~1985!.


exciton saturation in gaas multiple quantum wells at room ...a. miller,a) p. riblet, m. mazilu, s....

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