Pump-probe investigations of biexcitons in GaAs quantum wells

~ Pergamon

Solid State Communications, Vol. 92, No. 4, pp. 325-329, 1994 Elsevier Science Ltd Printed in Great Britain 0038-1098(94)0{i)572,9 0038-1098(94)$7.00 + .00

PUMP-PROBE INVESTIGATIONS OF BIEXCITONS IN GaAs QUANTUM WELLS G.O. Smith, E.J. M a y e r , J. Kuhl, and K. Ploog* Max-Planck-Institut ~ r FestkOrperforschung Heisenbergstr. 1, D-70569 Stuttgart, Federal Republic of Germany (Received 10 July 1994, by M. Cardona)

The observation ofbiexcitonic contributions to time-resolved pump-probe measurements of a 25 run multiple quantum well are reported. Results from wavelength and polarization dependent studies of the differential transmission in the vicinity of the heavy hole exciton transition demonstrate the strong influence of the biexciton state on the nonlinear response. Intensity dependent measurements are consistent with biexciton formation, The previously predicted angle dependence of the beating between light and heavy hole excitons is also observed.

Keywords: A. quantum wells A. semiconductors D. optical properties

the apparent dephasing rate, 10 a phase shift ofthe QBs and a shift in the DFWM signal emission time of an inhomogeneously broadened exciton transition from t = 2 r • to t = r (where t is the real time and x is the time delay between the excitation pulses) if the excitation geometry is changed from parallel polarized (PP) to linearly crosspolarized (CP) optical excitation fields. Additionally, contributions of the biexciton state to the differential absorption of the 21:) exciton in C_ntAshave been postulated earlier in Ref. 4.

Excitonic resonances dominate the linear and nonlinear optical properties at the band edge of GaAs/AIGaAs Quantum Well (QW) structures. Until recently, two independent degenerate three-level systems, each consisting of a ground, light-hole and heavy-hole state excited by either o+ or o- polarized light, have been considered as the proper theoretical model to describe the corresponding optical dipole transitions between the J = 1/2 and J = 3/2 valence and the J = 1/2 conduction band states for light propagating perpendicular to the layers. This theoretical model has been used to successfully explain the 180* phase shift between quantum beats (QB) excited with parallel and perpendicular polarized beams in two-pulse degenerate-four-wave-mixing (DFWM) experiments. 1 Systematic polarization dependent studies of DFWM, however, have recently revealed substantial discrepancies when compared to the theoretical model I of Schmitt-Rink et al. These observations include: remarkable changes of the peak intensity as well as the polarization of the time-integrated (TI) DFWM signal in dependence on the polarization of the excitation beams at various excitation densities,2 the appearance of a DFWM signal at negative delays between the incident pulses,3 and indications for the formation of biexcitons.4,5,6,7,s,9 Further experimental results, in contradiction to the model of two independent 3-level systems, include an increase of *present address: Paul-Drude-Institut fiir Festktrperelektronik D-10177 Berlin, Federal Republic of Germany.

In a recent publication, we have shown that the two independent 2-level systems, usually applied to describe the hh exciton transitions in a QW, are equivalent to a 4-level system consisting of a ground state [g) two single exciton states ]e+) and le.) representing an exciton excited either by or+ or o- light and a two exciton state 12e) = le+)le.> (both the le+) and the [e.) are excited).8 These two systems are equivalent representations of the exciton states in two single-particle Hilbert spaces and one two-particle Hilbert space, respectively. In these 4-level systems, exeiton/exeiton interaction can be phenomenologieally included by breaking the symmetry between the lower and upper transitions. This renormalization can be accomplished through the variation of the matrix elements Ix and v and dephasing rates ¥~t and Yv for the lower and upper transitions, and/or renormalization of the transition frequencies so that the energy of the two-exeiton state is different from twice that of the single-exciton state. In

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PUMP-PROBE INVESTIGATIONS

particular, the interaction of the o+ and o- excitons may result in the formation ofa biexciton state which is lowered by the biexciton binding energy (A) with respect to the corresponding two-exeiton scattering state. Calculations based on the resulting 5-level system (10-level if light hole excitons are included) have been used successfully to describe TI-DFWM and time-resolved (TR) DFWM experiments, s Further expansion to include field renormaiization effects fiRE), and fifth order contributions has provided a remarkably accurate phenomenoiogical model capable of describing subtle characteristics of 3pulse TI-DFWM and TR-DFWM measurements. 9

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The pump-probe measurements were performed in the transmission geometry using a mode-locked Ti:Sapphire laser providing tunable pulses of 120 fs duration and 10 meV bandwidth at a repetition rate of 76 MHz. For spectrally resolved studies, the bandwidth was reduced to 2.2 meV (1.8 ps pulse duration) by external spectral filtering. The laser output was split into a pump and a probe beam which were sent through a variable optical delay line, focused to a spot size of 220 t~m in diameter and then superimposed on the sample surface. Half-wave and quarter-wave plates were used to achieve perpendicular and circular polarization, respectively, with a polarization definition of better than 100:1. The signal was detected using a photodiode and standard lock-in techniques. The sample was maintained at 9 K in a variable-temperature, continuous-flow He cryostat. The luminescence measurements were made at 5 K using a cw tunable dye laser. The sample was illuminated with light intensities ranging from 1.6 - 500 ~tW with a spot size of 160 ~tm diameter. The luminescence was detected with a doublemonochromator and photomultiplier using standard photon-counting. Figure la shows the change in transmission with probe delay for three different angles (0 °, 45 °, 90 °) between the incident linear polarizations of the pump and probe pulses. The MQW was excited slightly below the lh-exciton line using laser pulses of 120 fs duration and 10 meV bandwidth. ARer the first high transmission peak during the temporal overlap of both pulses, an enhanced transmission of the MQW due to phase-space filling is observed which decays with the recombination time of the excitons. During the first 10 ps, this decay is modulated by a beat frequency which corresponds to the binding energy difference of 1.85 meV between the lh- and hh-excitons. A phase shift of 180° in the beating is observed between the PP and CP signals. In contrast to TI-DFWM experiments, where lightheavy hole beating vanishes only for polarization angles

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In this communication, we present time-resolved differential transmission experiments in the vicinity of the lowest hh-and Ih-exeiton transition of a 10 period, 25 nm CraAs/Alo.3Gao.TAs etched MQW. Spectrally dependent measurements which take advantage of the excitation selection rules in the two-exciton picture allow for direct observation of induced absorption from the single-exciton hh state to the bound two-exciton (biexciton) state.

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Probe Delay (ps) Fig. 1 (a) The change in transmission as a function of probe delay for different angles between the polarization of the pump and probe pulse. (b) Comparison of the pumpprobe and the DFWM signals.

near 700,10 beating is observed to vanish at an angle of 45° in accordance with predictions based on calculations in Ref. 1. In order to compare the pump-probe decay with the corresponding DFWM experiment, we plot both results in Fig. lb for parallel polarizations of the pulses. For this comparison, we subtract the recombination decay time of the pump-probe signal. Both signals beat in-phase to each other, however the DFWM signal decays with T 2 ffi 4.4 ps, twice as fast as the modulation of the pump-probe signal. This difference is explained by the fact that the coherent part of the pump/probe signal in the direction (krkl)+k 2 is proportional to the product of the third order polarization P(3)(m,t) with the electric field Ez(co, t ) of the probe pulse Ik, oCpC3)(co,t).E2(co, t), whereas the DFWM signal in the direction 2k2-k I is proportional to (P(~)(co,t ))2. One indication of biexcitonic contributions to the optical properties of our sample can be observed through photoluminescenee (PL) experiments. The presence of a two-exciton state is indicated by a second PL line at an energy below that of the hh-exciton corresponding to the binding energy of the two-particle state. The relaxation converts the two-exciton state into a single exeiton and a photon with an energy equivalent to the transition from the two-exciton to the single-exciton state. 5 Figure 2 displays the PL spectra of the MQW at the heavy-hole luminescence for various excitation intensities. Two contributions to the luminescence are observed. The luminescence at 1.5233 eV corresponds to the hh-exciton luminescence line, whereas the luminescence at 1.5221 eV is due to biexciton decay. The lower energy luminescence corresponds to a two-particle binding energy of 1.2 meV. The dependence of the biexciton peak luminescence intensity on the exciton peak intensity is plotted in the insert of Fig. 2. The luminescence strength of the biexciton line is seen to increase superlinearly with respect to the heavy-hole line.

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PUMP-PROBE INVESTIGATIONS

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At excitation energies slightly above the lh-exciton maximum (closed triangles: 1.5258 eV), an increase in transmission is observed for both polarizations which is consistent with the reduction of available states after excitation between two levels, followed by a long-term relaxation of the light-hole excitons. For PP polarization, the signal reveals the same qualitative features for all studied frequencies: (i) photoinduced transmission at longer delays varying only in magnitude and being strongest at the position of the hh-exciton transition. (ii) a still higher transmission peak in the coherent interaction regime decaying with the phase relaxation time. However,

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Time-dependent differential transmission measurements performed across the lh- and hh-exciton lines indicate the presence of an additional polarizable dipole transition in the sample below the peak of the hhexciton line which is attributed to the transition between the single exciton and biexciton states. Figure 3 displays the change in transmission with probe delay at four different energies spread over the spectral range from below the hh-exciton to above the Ih-exciton (see insert in Fig. 3 which depicts the energy positions of the lh-, Ida- and biexciton transition in our sample). The upper and lower parts of the graph display traces recorded for PP and CP polarization of the pump and probe, respectively. The curves show two different regimes. At short times ( r < 5 ps), in the coherent regime, the pump and probe fields interact coherently. For delays large compared to the excitonie dephasing time, the probe pulse detects population changes of the excitonic levels induced by absorption of the pump pulse.

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Fig. 2 The PL spectra for various excitation intensities. The curves are normalized to each other at the hh peak and offset for clarity. Insert: the ratio of the area under the biexciton luminescence to that of the heavy-hole exciton versus the excitation density. The areas were calculated using a double Gaussian fit to the luminescence data. The line is a linear fit to the data and yields a slope of 1.6.

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in the case of CP polarization, we observe the appearance of a negative signal in the coherent regime as the laser frequency is tuned to the low energy side of the hh-exciton transition. The negative signal becomes the dominant effect as the frequency approaches the position of the single exciton/biexciton transition. In the lower part of Fig. 3, the curve at 1.5244 eV (open triangles) shows a small absorption dip and slightly increasing transmission following the initial pumping of the system. This additional absorption is seen to increase for excitation slightly below the hh-exeiton maximum (closed circles: 1.5230 eV), where an increase in transmission is followed by a rapid decrease and then slower relaxation towards higher transmission. After approximately 30 ps, the transmission decreases again towards the equilibrium level. At 1.5212 eV (open circles), only absorption is observed during pumping, followed by a similar increase in transmission past the equilibrium point and to positive transmission values. Since the induced absorption occurs between the single-exciton and biexciton levels, as the laser is tuned to the biexciton energy, the weight of the transition to the biexciton level is expected to be higher due to the better overlap with the laser spectrum and the broader width of the absorption spectrum caused by the faster dephasing rate of the upper transition. Independent of the sign of the signal in the coherent regime, photoindueed transmission appears at all frequencies at longer delays.

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PUMP-PROBE INVESTIGATIONS

The problem of exciting both single and two exciton states, which causes both transmissive and absorptive processes to be present in the CP case, can be avoided by taking advantage of the selection rules for circular polarization. The insert of Fig. 4 illustrates the excitation of single and two exciton states in the 5-level representation for both o+o+ and o+o- polarization configurations, s In the coherent regime, the signal which results from the third order polarization of the system is indicated by the curved line. The solid lines represent the k I and -k I contribution of the pump pulse and the dashed line is the k 2 contribution of the probe. Based on the excitation selection rules, the o+ pump pulse populates the single-exciton hh state. When followed by a o'+ polarized probe pulse, no transition to the biexciton state is allowed and thus an increase in transmission is expected in the coherent regime from the third order signal as well as in the incoherent regime due to phase space filling. However, a o- probe will provide a third order polarization signal only through the excitation of hh-excitons excited by the pump from the single-exciton to the biexciton state. Spectrally resolved pump-probe measurements using circular polarization show the same behavior as linear polarization in Fig. 3 except near the biexciton energy. This difference can be seen in Fig. 4 which compares the differential transmission versus the probe delay for all

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Fig. 4 Comparison of the differential transmission as a function of the probe delay at 1.5212 eV for parallel (closed squares), perpendicular (closed circles), o+o+ (open squares), and o+o- (open circles) polarization. Insert: Excitation diagram based on the 5-level model for o+o+ (left side) and o+o- (right side) pump-probe polarization configurations. The 5-level system consists of: ground state Ig), single exciton states le+) and [e.), two exciton scattering state 12e), and biexciton state Ib). Excitation by the pump pulse (solid arrows), probe pulse (dashed arrow) and resulting emission (curved arrow) is indicated on the diagram for each configuration.

Vol. 92, No. 4

possible polarizations at an excitation energy slightly below the biexciton energy. In the coherent regime, we observe photoinduced transmission for o+o+ and parallel polarized pulses. Contrary to this, only induced absorption is observed in the case of o'+o- polarization. At first glance, the change of the signal's sign with polarization configuration seems to represent a highly puzzling result since, independent of polarization of the interacting fields, the third order coherent polarization created within the 5-level scheme of Fig. 4 is always positive. This apparent contradiction is easily resolved, however, if the absorption of the probe field, which is mixed with the third order polarization to create the signal, is taken into account. In our experiment, the laser is tuned to the low energy side of the hh-exciton line and thus, the coherent population of the single exciton state created by the o+ pump pulse causes a significant attenuation of the o- polarized probe due to the giant oscillator strength of the single exciton to biexciton transition, whereas the o+ polarized probe sees a much smaller bleaching of the transition from the ground state to the singie exciton state. It should be noted, however, that in the coherent regime, the decrease of the probe field in the presence of the pump beam corresponds principally to contributions from a fifth order optical nonlinearity. In the incoherent regime, the o+o- geometry exhibits photoinduced absorption whereas the other three configurations show transmission. This result seems to be reasonable since contrary to the situation for linearly polarized pulses which interact with both spin states of the valence hand electrons, the ability to detect the ground state depopulation due to the a+ pump pulse by a o- probe pulse implies a preceding spin flip of the hole in the valence band. This process is expected to occur on a time scale of several 10 ps. 4 Thus the induced transmission on the [g)/le.) transition will be considerably smaller than the photoinduced absorption on the [e+)/lb) transition during the first 20-30 ps. Figure 5a displays the change in transmission with probe delay time for various intensities of the pump and probe beams having the same circular polarization (o+o+). An increase in transmission is observed with increasing pump power as expected. Figure 5b displays measurements which were made using beams with opposite circular polarization (o+o-) and show an increase in absorption with increasing intensity. The insert of Fig. 5a shows the change in the ratio of peak transmission for o ~ + polarization and peak absorption for o+o- polarization with the incident intensity. A linear fit to the data gives a slope of 1.4. This compares well with the value of 1.6 obtained in the insert of Fig. 2. If the formation time and decay time of the biexciton are fast in comparison to the decay time of the single exciton, then the induced absorption for o+o- polarization is expected to increase superlinearly with respect to the induced transmission for o+o+ polarization and with approximately the same rate as the photoluminescence peaks (insert Fig. 2) since excitation of biexcitons for the two-step o+o- process is equivalent to excitation via parallel polarization.

Vol. 92, No. 4

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The lifetime of the induced absorption for o+oconfiguration is 11 ps, whereas the measured exciton lifetime with o+o+ polarization is 160 ps. We attribute the shorter lifetime to the aforementioned spin relaxation of the single exeiton state since the single-exeiton hh population created by the pump pulse will have the same lifetime independent of the polarization of the probe pulse. The relaxation of o+ to o- excitons decreases the induced absorption due to the reduction of available o+ excitons for the formation of biexcitons and introduces an induced transmission for the Ig) to [e.) transition. Based on earlier calculations, assuming v =- tt = 1, this time would indicate a spin relaxation time o f - 2 2 ps which is in qualitative agreement with earlier measurements. 4 Under this assumption, the spin relaxation time, Tspin would provide only a small contribution to the dephasing time T 2.

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In summary, we have presented polarization dependent measurements of the differential transmission in the vicinity of the hh-exciton in a 25 run GaAs multiple quantum well. We observe contributions to the differential absorption that are in qualitative agreement with a previously presented 5-level system which includes field renormalization effects, excitation induced dephasing, and biexeiton formation. The observed absorption for o+o- polarization is consistent with the formation of biexcitons and is attributed to induced absorption from the le+) to the Ib) exeiton. Previously predicted angle dependence of ih-hh exeiton beating is also observed.

The authors would like thank D. Bennhardt, K. Bott, S. Cundiff, and P. Thomas for their helpful discussions as well as W.W. g0hle for careful reading of the manuscript.

REFERENCES 1. S. Schmitt-Rink, D. Bennhardt, V. Heukeroth, P. Thomas, G. Maidorn, H. Bakker, K. Leo, D.-S. Kim, J. Shah, and K. K6hler, Phys. Rev. B 46,7248 (1992). 2. R. Eccleston, J. Kuhl, D. Bennhardt, and P. Thomas, Sol. Stat. Comm. 86, 93 (1993). 3. B. Feuerbacher, J. Kuhi, and K. PIoog, Phys. Rev. B 43, 2439 (1991). 4. S. Bar-Ad and I. Bar-Joseph, Phys. Rev. Lett. 68, 349 (1992). 5. R.T. Phillips, D.J. Lovering, G.J. Denton, and GW. Smith, Phys. Rev. B 45, 4308 (1992). 6. D.J. Lovering, R.T. Phillips, G.J. Denton, and G.W. Smith, Phys. Rev. Lett. 68, 1880 (1992).

7. K.-H. Pantke, D. Oberhauser, V.G. Lyssenko, and J.M. Hvam, Phys. RevB 47, 2413 (1993). 8. K. Bott, O. Heller, D. Bennhardt, S.T. Cundiff, P. Thomas, E.J. Mayer, G.O. Smith, R. Eecleston, and J. Kuhl, Phys. Rev. B 48, 17418 (1993). 9. E.J. Mayer, G.O. Smith, V. Heuckeroth, J. Kuhl, K Bott, A. Schulze, D. Bennhardt, S.W. Koch, P. Thomas, R. Hey, and K. Ploo8, paper submitted to Phys. Rev. B. 10. D. Bennhardt, P. Thomas, R. Eccleston, E.J. Mayer, and J. Kuhl, Phys. Rev. B 47, 13485 (1993).