M. KOCH et al.: Exciton Scattering with Bare Electrons 48 5

phys. stat. sol. (b) 188, 485 (1995)

Subject classification: 71.35 and 73.40; 78.47; S7.12

Fachbereich Physik und Zentrum fur Materialwissenschaften der Philipps- Universitat, Marburg') (a) and Department of Pure and Applied Physics, UMIST , Manchester2) (b)

Exciton Scattering with Bare Electrons

BY M. KOCH (a), G. BASTIAN (a), R. HELLMANN (a), J . FELDMANN (a), E. 0. GOBEL (a), and P. DAWSON (b)

It is shown that exciton-electron scattering is twice as efficient as exciton-exciton scattering by performing transient four-wave-mixing experiments on a mixed type-I- type-I1 GaAs/AIAs double quantum well structure. In addition it is found that the presence of bare electrons in the wide well leads to a quenching of the high-energetic part of the photoluminescence spectrum. Scattering with electrons releases excitons localized at shallow states and leads to a more: complete relaxation of excitons into the energetically lowest quantum well states.

1. Introduction The knowledge of scattering processes of carriers in semiconductor structures is an absolute prerequisite to understand the transport properties in modern electronic devices as well as the thermalization and relaxation scenario of optically excited or electrically injected carriers in modern optoelectronic devices such as semiconductor lasers. Experimentally, a variety of transport measurement techniques [ l to 51 and various ultrafast optical techniques using very short laser pulses [6 to 121 have been applied to determine the rates for scattering of carriers due to phonons, other carriers, impurities, interface roughness, alloy potential fluctuations, and so on. In particular, coherent optical experiments such as transient four-wave-mixing (FWM) experiments have proven to be a powerful tool to study ultrafast scattering events in semiconductors [12].

Carrier-carrier scattering is one of the most complicated scattering phenomena, since it represents a many-body problem, where exchange, screening, collective plasma, and plasmon-phonon coupling effects play a crucial role [13], for a recent review on coherent techniques, see [12]. In this context of carrier-carrier Co'ulomb interaction the scattering of bound electron-hole states, i.e., excitons, with other cntrriers is particularly interesting. Schultheis et al. [14] have determined the rates for exciton-exciton (X-X) scattering and for scattering of excitons with unbound electron-hole pairs (X-eh) by performing transient FWM experiments with a frequency-tunable prepulse. As schematically depicted in Fig. 1, the authors find that X-eh scattering is approximately ten times more efficient than X-X scattering. In addition, both scattering processes are more efficient in 2D as compared to 3D, since screening of the Coulomb interaction is weaker in 2D. The scattering of excitons with unbound electron-hole pairs is a complicated process, since holes screen the exciton-electron interaction and electrons screen the exciton-hole interaction. Accordingly, it is desirable to investigate a system, where, e.g., electr'ons scatter with excitons in the absence ofany unbound holes (X-e scattering) as shown on the right-hand side of Fig. 1.

') Renthof 5, D-35032 Marburg, Federal Republic of Germany. ') Manchester M60 lQD, U.K.

486

n

M. KOCH et al.

ELECTRONS EXCITONS

Fig. 1. Schematic illustration of X-X, X-eh, and X-e scattering

4 ELECTRON-HOLE PAIRS

One possibility would be to perform transient FWM experiments on n-modulation-doped quantum well structures, where the electron density can be controlled by a gate voltage [2 ] . To the best of our knowledge, only Kim et al. [15] have performed time-resolved FWM experiments on n-modulation-doped quantum wells. However, in their experiments the electron density was fixed to two very high values of 2 x 10" and 6 x 1011 cm-2 leading to degenerate electron systems, i.e., to Fermi seas with 7 and 20 meV depth. The authors find a strong inhibition of scattering near the Fermi edge due to Pauli blocking. At these high densities, where the Fermi energy is comparable to or larger than the exciton binding energy, bound exciton states do not exist and thus the concept of exciton-electron scattering makes no sense.

In this paper we report optical experiments on mixed type-I-type-I1 GaAs/AlAs double quantum well structures. Optical excitation of electron-hole pairs in the narrow well (NW)

- NW WW

laser

Ti-sapp. experiment / FWM

prepulse

/ \

I I GaAs AlAs GaAs 2.5 nm 10.3nm 6.8nm

sample

prepulsa

and the successive T-X-T electron transfer to the wide well (WW) offer the unique opportunity to optically control the electron density in the WW. Transient FWM experi- ments show that X-e dipole-monopole scat- tering is twice as efficient as X-X dipole-di- pole scattering. The presence of electrons in the WW drastically changes the WW photo-

Fig. 2. Upper part: schematic band scheme of the mixed type-I-type-I1 GaAs/AlAs double quantum well sample. The FWM experiment is performed at the heavy-hole exciton transition of the WW and is disturbed either by a prepulse from the Ti : sap- phire laser (X-X scattering) or by a cw He-Ne laser (X-e scattering). Lower part: geometrical set-up for the two-beam FWM experiment with an addi- tional prepulse or with an additional He-Ne laser

Exciton Scattering with Bare Electrons 487

lunimescence (PL) spectrum. Energy transfer from a high-energetic quantum well island to a low-energetic quantum well island and an overall partial quenching of the PL are observed. This is a direct consequence of exciton scattering with electrons. In the absence of any additional electrons excitons are localized in shallow states of the quantum well islands, but become mobile due to X-e scattering. Being mobile, excitons on higher-energetic islands diffuse to and are trapped into lower-energetic islands or reach non-radiative recombination centers. This leads to an energetic redistribution and a partial quenching of the luminescence.

2. Experimental

The investigated mixed type-I-type-I1 sample consists of twenty periods of 2.5 nm narrow GaAs wells and 6.8 nm wide GaAs wells separated by a 10.3 nm AlAs barrier [16, 171. As shown in the upper part of Fig. 2, the lowest n = 1 r electron state in the NW is energetically higher than the lowest X-state in the AlAs barrier. The lowest n = 1 r electron state in the WW, however, is lower than the AlAs X-state. This characteristic band scheme of a mixed type-I-type-I1 double quantum well structure leads to an efficient T-X-T transfer of electrons initially photoexcited in the NW [16 to 181. Since the lifetime of the spatially separated electron-hole system lies in the ps regime, optical excitation of electron-hole pairs in the NW at very low density is sufficient to create high densities of cold electrons in the WW and of cold holes in the NW.

As schematically illustrated in the lower and upper parts of Fig. 2, the FWM experiments are performed at T = 5 K on the energetically lowest excitonic n = 1 transition of the WW using 100 fs pulses from a mode-locked Ti: sapphire laser. We use a so-called two-beam geometry, i.e., two laser pulses impinge onto the sample with wave vectors k , and k,. As a result, a FWM signal is emitted into the phase-matched direction 2k2 - k , and can be measured as a function of the time delay between the two laser pulses (for details see, e.g., [12]). We choose the excitation intensity as low as possible to obtain a long dephasing time T2 mainly determined by scattering of excitons with acoustic phonons and disorder potentials. We now perform two kinds of experiments. First, a prepulse from the same Ti : sapphire laser is used to create an incoherent density of excitons in the WW in order to measure the dephasing rate due to exciton-exciton (X--X) scattering as was done in [14]. Second, a cw He-Ne laser is used to photocreate electron-hole pairs in the NW and thus cold electrons in the WW after the T-X-T transfer.

3. Experimental Results and Discussion

3.1 Four-wave-mixing experiments

The inset of Fig. 3 shows the normalized FWM transients for three cases. The solid curve is obtained when neither the Ti : sapphire prepulse nor the He-Ne laser excites the sample. From the decay of the signal we obtain a time constant z = 0.92 ps corresponding to a dephasing time T2 = 4 z = 3.68 ps. 3, The decaying FWM signal shows some moderate beating with a time period of TB = 1.4ps, which corresponds to an energy splitting of AE = 3.0 meV. This splitting is also observed in the photoluminescence spectra (see below)

’) The overall absorption linewidth of the excitonic transition in the WW is 4.1 meV and thus mainly determined by inhomogeneous broadening effects.

488 M. KOCH et al.

Fig. 3. The inset shows the normalized FWM transients without an additional laser (solid curve), with a Ti : sapphire laser prepulse (dashed curve), and with an additional cw He-Ne laser (dotted curve). The main part shows the de- pendence of rho,,, on the exciton density (circles) and on the electron density (triangles)

and is due to exciton transitions associated with different quantum well islands differing in thickness by only one monolayer [19, 201. In the presence of the Ti : sapphire laser pulse (dashed curve) or of the cw He-Ne laser (dotted curve) the FWM decay becomes f a ~ t e r . ~ ) This is a direct consequence of X-X scattering or X-e scattering, respectively. By changing the laser intensities the dependence of the homogeneous linewidth given by rho,,, = h/zT2 on the densities n of excitons or electrons can be measured. Special care is necessary for the experimental determination of n. We carefully measure the optical transmission of the sample, use pinholes to exactly determine the laser spot size. Furthermore, the lifetime of the spatially separated electron-hole systems is obtained from the data reported in [17]. Fig. 3 shows the dependence of Thorn on the exciton density (circles) and on the electron density (triangles) for densities far below the Mott density. In both cases rho,,, increases linearly with density. The slopes directly reflect the interaction strengths of X-X and X-e scattering. We find 6.5 x meV cm2 for X-e scattering. This means that exciton-electron scattering is twice as efficient as exciton-exciton scattering.

For bulk semiconductors, i.e., for three-dimensional electron systems Haug [21] calculated the matrix elements for X-X (dipole-dipole) and X-e (dipole-monopole) interaction. He found that the X-e matrix element is 2.8 times larger than that for X-X interaction, which is in reasonable agreement with our results. However, since the calculations in [21] are performed for the 3D case and consider only matrix elements they might not be directly

meV cm2 for X-X scattering and 13.2 x

") Simultaneously, the FWM signal strength decreases.

Exciton Scattering with Bare Electrons 489

PL excited by 7 ps dye laser (tunable)

Fig. 4. Experimental set-up for the PL experiments using a dye and a He-Ne laser

comparable to our experimental findings. To our knowledge, a comprehensive theory concerning the problem of incoherent X-e scattering in quasi-2D quantum structures has not been developed so far, but should be a topic of further theoretical considerations.

In order to show that our density calculations are correct, we compare our results on X-X scattering with those of Kuhl et al. [22]. The homo- geneous linewidth due to X-X scatter- ing can be written as

~ h o m ( 4 = Yxxa3Bnx, (1) where uB is the exciton Bohr radius (7 nm for our sample), EB is the exciton binding energy (13 meV for obr sample), and nX is the exciton density [14]. From the slope of 6 . 5 ~ 1 0 ~ ~ m e V c m - ~ for X-X scattering we then obtain a yxx value of 1.0 for the 6.8 nm thick GaAs quantum well structure in good agree- ment with [22].

Fig. 5 . PL spectra of the WW without (solid curve)^ and with He-Ne excitation (dashed curve)^. The lower part shows the difference APL between the two PL spectra

490 M. KOCH et al.

3.2 Photoluminescence experiments

We now investigate how the addition of electrons changes the energetic relaxa- tion and recombination of excitons in the wide GaAs well. As an experimental technique we employ low-temperature PL measurements. The experimental set-up is shown in Fig. 4. A synchronously pumped dye laser emitting 7 ps pulses at 1.63 eV is used to optically excite only the wide GaAs well. As in the FWM experiments a He-Ne laser is used to photocreate electron-hole pairs in the NW and thus a cold electron density in the wide GaAs well. Again the electron density is controlled by the intensity of the He-Ne laser. When the He-Ne laser is switched off, the PL spectrum shown as the solid curve in the upper part of Fig. 5 is obtained. The two peaks energetically separated by AE = 3.1 meV correspond to recombination of excitons associated with different quantum well islands as already discussed above in context with the beating of the FWM signal. The dashed curve in Fig. 5 is the PL spectrum when 6 x 10" cm-' electrons photoexcited by the He-Ne laser are present in the WW. The high-energetic peak is completely gone and the low-energetic peak is higher in intensity as compared to the case without any additional electrons. The changes induced by the He-Ne laser can be seen more clearly in the lower part of Fig. 5, where the difference APL between the dashed and the solid curves is shown. In addition to the energy transfer from the high-energetic part of the PL spectrum to its low-energetic part there is an overall decrease in the PL efficiency. Related effects induced by an electron-hole plasma were recently observed by Ashkinadze et al. [23] in a conventional type-I GaAs/ AlGaAs quantum well sample within one spectrally broad PL peak.

The drastic change of the PL induced by the additional electrons can be understood in the following way. It is reasonable to assume that in the absence of any additional electrons excitons on any quantum well island are partially localized due to short-scale potential fluctuations. Otherwise, excitons located on islands with narrower well widths would diffuse to islands with wider well widths within the lifetime and a high-energetic PL peak would not be as pronounced as observed in Fig. 5 (solid curve). As can be inferred from Fig. 3, the presence of 6 x lolo cm-' electrons leads to a high scattering rate of excitons. This

RADIATIVE NON-RADIATIVE RECOMBINATION RECOMBINATION CENTER

Fig. 6. Schematic illustration of the exciton dynamics when they become mobile due to exciton-electron scattering

Exciton Scattering with Bare Electrons 49 1

means that excitons localized in the absence of additional electrons now become mobile (see the schematic drawing in Fig. 6). When they reach a quantum well island with wider well width they relax down to the lowest energetic states of this island (island trapping). Accordingly, with increasing electron density the low-einergetic PL peak associated with islands having a wider well width gains in intensity, whereas the high-energetic peak is more and more quenched. In addition, the higher mobility of excitons in the presence of electrons leads to a higher probability that excitons reach non-radiative recombination centers. This explains the overall quenching of the PL.

4. Summary

In summary, we have used the unique properties of a mixed type-I-type-I1 GaAs/AlAs double quantum well structure to optically create a pure electron density in the wide GaAs well and to investigate the effects of exciton-electron scattering on exciton dephasing and on the exciton relaxation scenario. We find that X-e scattering is twice as efficient as X-X scattering in qualitative agreement with theory. As a consequence of X-e scattering, excitons normally localized in shallow states of the quantum well islands become mobile and migrate to islands with wider well width and to non-radiative recombination centers. This leads to drastic changes in the PL spectrum.

Acknowledgements

We thank S. Haas, H. Haug, S. W. Koch, F. Rossi, and P. Thomas for fruitful discussions and M. Preis for the excellent technical assistance. The work at Marburg University has been financially supported by the “Deutsche Forschungsgemeinschaft” through the Leibniz- and Gerhard-Hess Forderpreise.

References

[13 M. HEIBLUM, D. GALBI, and M. WECKWERTH, Phys. Rev. Letters 62, 1057 (1989). [2] C. WEISBUCH and B. VINTER, Quantum Semiconductor Structures: Fundamentals and Applica-

[3] L. W. MOLENKAMP, M. J. P. BRUGMANS, H. VAN HOUTEN, and C. T. FOXON, Semicond. Sci.

[4] R. A. HOPFEL, J. SHAH, P. A. WOLFF, and A. C. GOSSARD, Phys. Rev. Letters 56, 2736 (1986). [5] H. HILLMER, A. FORCHEL, S. HANSMANN, M. MOROHASHI, 1:. LOPEZ, H. P. MEIER, and K. PLOOG,

[6] J. L. OUDAR, A. MIGUS, D. HULIN, G. GRILLON, J. ETCHEPARE, and A. ANTONETTI, Phys. Rev.

[7] J. SHAH, B. DEVEAUD, T. C. DAMEN, W. T. TSANG, A C. GOSSARD, and P. LUGLI, Phys.

[8] W. KNOX, D. S. CHEMLA, G. LIVESCU, J. E. CUNNINGHAM, and J. E. HENRY, Phys. Rev. Letters

[9] P. C. BECKER, H. L. FRAGNITO, C. H. BRITO CRUZ, R. L. FORK, J. E. CUNNINGHAM, J. E. HENRY,

[lo] J. FELDMANN, R. SATTMANN, E. 0. GOBEL, J. KUHL, J. HEBLING, K. PLOOG, R. MURALIDHARAN,

[I11 G. NOLL, U. SIEGNER, S. G. SHEVEL, and E. 0. GOBEL, Phys. Rev. Letters 64, 792 (1990). [I21 R. T. PHILLIPS (Ed.), NATO AS1 Series No. 330, Plenum Press, New York 1994. [13] F. ROSSI, S. HAAS, and T. KUHN, Phys. Rev. Letters, 72, 152 (1994), and references therein. [14] L. SCHULTHEIS, J. KUHL, A. HONOLD, and C. W. Tu, Phys. Rev. Letters 57, 1635 (1986).

tions, Academic Press, Boston 1991, and references therein.

Technol. 7, B228 (1992).

Phys. Rev. B 39, 10901 (1989).

Letters 53, 384 (1984).

Rev. Letters 59, 2222 (1987).

61, 1290 (1988).

and C. V. SHANK, Phys. Rev. Letters 61, 1647 (1988).

P. DAWSON, and C. T. FOXON, Phys. Rev. Letters 62, 189;! (1989).

492 M. KOCH et al.: Exciton Scattering with Bare Electrons

[15] D. S. KIM, J. SHAH, J. E. CUSSINGHAM, T. C. DAMES, S. SCHMITT-RINK, and W. SCHAFER, Phys.

[I61 P. DAWSOS, I. GALBRAITH, A. I. KUCHARSKA, and C. T. Foxos, Appl. Phys. Letters58,2889 (1991). [I71 I. GALBRAITH, P. DAWSOS, and C. T. Foxos, Phys. Rev. B 45, 13499 (1992). [18] J. FELDMANS, M. PREIS, E. 0. GOBEL, P. DAWSON, C. T. Foxos, and I. GALBRAITH, Solid State

[19] E. 0. GOBEL, K. LEO, T. C. DAMES, J. SHAH, S. SCHMITT-RISK, and W. SCHAFER, Phys. Rev.

[20] M. KOCH, J. FELDMASS, E. 0. GOBEL, P. THOMAS, J. SHAH, and K. KOHLER, Phys. Rev. B 48,

[21] H. HAUG, Z. Phys. B 24, 351 (1976). [22] J. KUHL, E. J. MAYER, G. SMITH, R. ECCLESTON, D. BENNHARDT, P. THOMAS, K. BOTT, and

[23] B. M. ASHKISADZE, E. COHEN, A. RON, and L. PFEIFFER, Semiconductors 27, 1073 (1993).

Rev. Letters 68, 2838 (1992).

Commun. 83, 245 (1992).

Letters 64, 1801 (1990).

11480 (1993).

0. HELLER, see [12] (p. 1).

(Received November 7, 1994)