GaAlAs quantum well structures

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Surface Science 196 (1988) 584-589 North.Holland, Amsterdam

OPTICAL INVESTIGATION OF 2D MOTT TRANSITIONS IN GaAs/GaAIAs QUANTUM WELL STRUCTURES G. TRANKLE, E. LACH, M. WALTHER, A. FORCHEL 4. Physikalisches lnstitut, Universit~itStuttgart, D- 7000 Stuttgart-80, Fed. Rep. of Germany

and G. WEIMANN Forschungsinstitut der Deutschen Bundepost, D-6100 Darmstadt, Fed. Rep. of Germany Received 19 June 1987; accepted for publication 16 October 1987

In transmission experiments performed under quasi-equilibrium conditions at low lattice temperalures we investigated the bleaching of the quasi-2D excitons in GaAs/GaAIAs MQW structures with special emphasis on the behaviour of the excitons at the different subband edges. The I hh excitons are found to be much more sensitive to bleaching than the or.her excitons. We attribute this to phase space filling effects which should reduce the I hh excitonic structures additionally to the usual screening due to the long-range Coulomb interaction, which screens the excitons related to transitions be-tween higher subbands only. We determined the 2D Molt density of the 2hh exciton performing a lineshape analysis of the luminescence of the electron-hole pairs measured simultaneously.

Intrinsic semiconductors display in absorption spectra excitonic peaks belonging to transitions between the bands. Three-dimensional (3D) structures show a single exciton at the fundamental band edge, in contrast to two-dimensional (2D) structures which display different excitons related to the different transitions between the 2D subbands [ 1 ]. Each exciton is characterized by its binding energy and Bohr radius, which vary for the different excitons significantly due to the confinement of the carriers and due to nonparabolicities in the valence band as well as in the conduction band. With increasing carrier density in the semiconductors the excitonic peaks in the ~s~,~i~,~ of ~r~ st,-,,ot,,~ ~t )ow t ~ m ~ t , , , - , ~ are reduced ~ncl hrr~rl~nort [~], mainly by the screening due to the long-range Coulomb interactions of free electron-hole pairs. At the Molt density a transition of the excilon gas to an electron-hole plasma (EHP) takes place [ 3 ]. In 2D structures the additional mechanisms of phase space filling and shortrange exchange interaction have beer~ reported to reduce adtitionally the l hh exciton peaks in transmission measurements done at room temperature and on short 0039-6028/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )

G. Triinkle et aL/2D Mott tran.vitions in GaAs/GaAIAs Q W structures

585

time scales [ 4,5 ]. In order to clearly separate the different bleaching mechanisms we study the behaviour of the excitonic transitions at the higher subbands which are affected only by the Coulomb-type screening and compare the results with the variation: of the I hh exciton. The higher excitons should show the "classical" Mott transitions like in 3D structures. The appropriate 2D Mort densities are expected to be larger than in the bulk due to the reduced efficiency of screening in 2D stru~:tu,res. In this paper we report results of transmission experiments performed under quasi-equilibrium conditions at low temperatures. We investigated high-quality GaAs/GaAIAs MQW structures grown by MBE with well widths between 4.1 and 24.7 nm, barrier widths of typically 18 nm and AI conterts between 19% and 43%. For the measurements the GaAs substrates were removed in ~mall spots (200 /zm × 200/~m) using dry etching techniques. The high excitation experiments have been performed in an excite and probe arrangement. A frequency-doubled Q-switched Nd:YAG laser (7.= 532 nm; repetition rate: 1 kHz) was used to excite electron-hole pairs in the barrier layers. The fluorescence light of a laser dye (Styryl 9) pumped "w ~ part of the Nd:YAG laser beam was used to probe the absorption of the quantu,a well structures as a function of the excitation intensity. 1"he intensity of the probe light was small enough to excite only a negligible part of the total carrier density. The intensity ofth" exciting beam could be increased up to 100 kW/cm 2 close to the damage threshold of the samples. The pulse duration of the laser of about 70 ns was much larger than typical relaxation times in GaAs/GaA1As QW structures and provided quasi-equilibrium conditions in the exciton gas and the EHP, in contrast to the transmission experiments in QW structures performed on a fs-time scale [ 6 ]. We used modulation techniques to separate the strong luminescence due to the recombination of the electron-hole pairs from the transmitted light. In fig. 1 we show a series of typical transmission spectra measured in a sample with a well width of 18 nm at a lattice temperature of 2 K. Without any additional excitation the transm~ssien spectra show the well-known allowed and forbiddenbut-parity-allowed excitonic transitions between electron and hole subbands. With increasing excitation intensity the excitonic structures become weaker. Especially the 1hh exciton is strongly reduced at low laser powers already. The linewidths of the 1hh and the 1lh excitons are nearly independent of the laser power in contrast to the 2hh and the 3hh excitons which show a significant broadening. At higher intensities the 1hh and the 1lh excitons vanish and a step-like absorption due to band-band transitions in the quantum we!! st~acture remains. The higher excitons a:'e still clearly vis;.ble. Under the quasi-stationary excitation conditions the excitonic peaks show no blue-shift in contrast to the results of the excite and probe experiments performed on the fs-time scale [ 6 ]. Within the experimental uncertainties on the other hand there is also no red-shift of the ex,:itons with increasing excitation intensity: like in 3D structures there seems to be nearly a complete balance of the band renormali-

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zation and reduction of the exciton binding ener~.y with increasing carrier density and the energy of the excitonic transition is therefore unchanged [ 2 ]. The reduction of the excitonic peaks in the transmission spectra is quite different for the different excitons. Fig. 2 depicts for a sample with L _ - 18 nm the relative change of the peak intensities of the first four allowed excitonic transitions with increasing laser power. Obviously the 1hh exciton shows a strong bleaching even at relatively low exci-

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tation intensities. At a laser power of 0.3 kW/cm 2 its peak value reduces already to 50% of its strength without additional excitation. The other excitons show a much smaller bleaching. The 2hh exciton reduces to 50% of its maximum value at a laser power of 0.6 kW/cm2; the 3hh exciton at a laser power of nearly 2.5 kW/cm 2. The 1lh exciton shows an intermediate behaviour. Especially at low excitation intensities it is only slightly affected and it decreases less than the 2hh exciton. At intensities larger than 0.5 kW/cm 2 on the contrary its [;,leaching becomes even stronger than that of the 2hh exciton. The broadening of the excitonic peaks is also quite different for the different excitons. In fig. 3 we show this for the first four allowed transitions of the sample with L: = 18 ran. The 1hh and 1lh excitons broaden only very slightly with increasing laser power in contrast to the 2hh and especially the 3hh exeitons which broaden strongly (compare fig. 1 ). These data cannot be explained by considering only the screening due to longrange Coulomb interaction. In this case the bleaching of the excitons would correlate with their appropriate binding energies, i.e. the stronger bound electron-hole pairs would be too,e, stable against screening than the weaker bound ones at the same carrier densities. The binding energy of a 2D exciton increases with its reduced mass and correlates to its "2D character" (an ideal 2D exciton has a binding energy about a factor of 4 larger than that in the 3D limit [ 7]). Clearly the l hh exciton has the strongest "2D character" because it is built ofwavefunct]on~ closely confined to the potential wells. Additionally its reduced mass is relatively ~arge. From this the 1hh exciton is bound strongly compared to the 2hh and 3hh excitons and should be more stable against screening. There must be another mechanism for the experimentally observed strong reduction of this exciton. This mechanism is the bleaching of the excitons due to the Pauli exclusion principle analogous to that found in experiments performed on the fs-time scale [4,5 ].

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G. Triinkle et al./2D Mott transitions in GaAs/GaAIAs Q W structures

According to that the excitonic absorption is reduced if the states which form the excitons are populated with carders. Obviously under our experimental conditions mainly the I hh excitons are populated and affected by the phase space filling effects in contrast to the higher excitons. This interpretation i:~ supported by the peculiar bleaching of the 1lh exciton, which in this particular sample is only slightly separated in energy from the 1hh exciton. At low excitation intensities it exhibits only the screening due to the Coulomb interaction and shows a very weak decrease. In contrast, at higher excitation intensities its states are also occupied partially and it decreases steeply due to the onset of phase space filling effects. This interpretation is confirmed by the broadening of the different excitons. The 1hh and 1lh excitons w~ich are bleached mainly due to the phase space filling show no broadening in contrast to the strong broadening of the 2hh and 3hh excitons which are screened only by the Coulomb interaction. A "classical" Mott transition is therefore to be expected only for the 2hh exciton and higher ones. To determine the appropriate 2D Mort density we measured in our experiments the luminescence due to the recombination of the elec,tron-hole pairs simultaneously with the transmitted light. The criterion tbr the Mort transition is taken analogous to experimental and theoretical investigations in 3D structures, which showed that at the Mott transitions the exciton peak is reduced to about one half of its initial value [ 2 ]. The dotted line in fig. i depicts the plasma emission for the Mort transition of the 2hh exciton in the sample with a well width of 18 nm. We evaluated the carrier density and temperature performing a lineshape analysis in a well-established model [8] for band-band transitions in 2D structures under quasi-equilibrium conditions. The comparison of the theoretical spectra with the experimental luminescence spectrum measured at the Mott transition for t~e 2hh exciton of the sample with L_ = 18 nm yields a Mott density of about 1 X 10~ ~ c m - 2 and a plasma temperature of about 150 K. The Mott density of bulk structures of GaAs at this carrier temperature is about one order of magnitude smaller. In summary, we have evaluated the bleaching of the excitons belonging to the different transitions in quasi-2D structures. For the excitons at the fundamental band edge it is not only due to the screening by the long-range Coulomb interaction but also duc ~o phase space filling. The 2D Mott density of the 2hh exciton is about one order of magnitude large than that in buik structures due to the reduced efficiency of screening in structures with lower dimensionality.

We acknowledge the collaboration of R. Gcrmann and G. H6rcher who did the sample preparation, D.A. Broido and T.L. Reinecke who calculated dispersion relations of the hole subbands and thank M. Pilkuhn for encouraging discussions. We are grateful for the financial support by the Deutsche Forschungsgemeinschaft (contract Pi7t/20) and the Stiftung Volkswagenwerk.

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References [1] R. Dingle, in: Advances in Solid State Physics, Vol. 15, Ed. H.J. Queisser (Vieweg, Braunsckweig, 1975) p. 21. [2] H. Schweizer, A. Forchel, A. Hangleiter, S. Schmitt-Rink, J.P. L6wenau and H. Haug, Phys. Rev. Letters 51 (1983) 698. [ 3 ] N.F. Mort, Metal-lnsulator Transitions ( Barnes and Noble, New York, 1974). [4] S. Schmitt-Rink, D.S. Chemla and D.A.B. Miller, Phys. Rev. B32 (1985) 6601. [5] W.H. Knox, R.L. Fork, M.C. Downer, D.A.B. Miller, D.S. Chemla and C.V. Shank, Phys. Rev. Letters 54 (1986) 1191. [ 6 ] N. Peyghambarian, H.M. Gibbs, J.L. Jewell, A. Antonetti, A. Migus, D. Hulin and A. Mysyrowicz, Phys. Rev. Letters 53 (1984) 2433. [7] L.V. Keldysh, JETP Letters 29 (1979) 658. [8] G. Tr~inkle, E. Lach, F. Scholz, A. Forchel, hLH. Pilkahn, G. Weimann, H. Kroemer, S. Subbanna, G. Griffiths and M. Razeghi, Inst. Phys. Conf. Set. 83 (Institute of Physics, Bristol, 1987) p. 221.