Optical studies of acceptor centre doped GaAsAlGaAs quantum wells

Solid-Stare ElecrronicsVol. 40, Nos l-8, pp. 89-92. 1996 Copyright G 1996 Elrvier Science Ltd Printed in Great Britain. All rights reserved 0038~1101(%)0021%7

Pergnmon

0038.ItOt/

OPTICAL

STUDIES OF ACCEPTOR GaAs/AlGaAs QUANTUM

A. C. FERREIRA’,

CENTRE WELLS

P. 0. HOLTZ’, B. E. SERNELIUS’, A. BUYANOV’, U. EKENBERG*, 0. MAURITZ’, M. SUNDARAM3, K. CAMPMAN’, A. C. GOSSARD’

615.00i0.00

DOPED B. MONEMAR’, J. L. MERZ3 and

‘Department of Physics and Measurements Technology, Linkbping University, S-581 83 Linkoping, Sweden, 2Department of Physics, Royal Institute of Technology, S-100 44 Stockholm, Sweden and “Center for Quantized Electronic Structures (QUEST), University of California at Santa Barbara, CA 93016. U.S.A. Abstract-We present a theoretical and experimental study of the optical properties of acceptor centre doped quantum wells. We have performed theoretical calculations for the dependence of the band structure with doping level. Steady state photoluminescence and photoluminescence excitation results are compared with theoretical calculations involving exchange and correlation effects for the electron-hole system and the interaction between charge carriers and acceptor ions. We have studied the intensity, energy peak position, and broadening effects for excitons at doping level between 108and IO” cm-?. Theoretical calculations that only consider band filling effects are not sufficient to describe the effect on the band structure due to the doping. A much better agreement is achieved when exchange and correlation effects for the electron-hole system are taken into account. Excitons can still be detected at high hole concentrations, above the degenerated limit. They survive due to the inefficiency of screening in the two-dimensional system.

theoretical study of an acceptor centre doped QW structure has been presented in the literature up to now. This fact is mainly due to the many difficulties associated with the complicated nature of the valence band. The energy region near the bandgap. as observed in photoluminescence for a highly doped QW, is affected by two major counteracting effects: a blue shift due to the band filling up to the Fermi level, the “Burstein-Moss” shift, and on the other hand, a red shift caused by the presence of ionized dopant ions and carriers, the bandgap renormalization. These bandgap shifts depend on, e.g. the semiconductor material, the type of doping and the carrier concentration[4,8]. The Burstein-Moss shift and the shift caused by bandgap renormalization are of different sign, but of comparable magnitude. For x-type bulk GaAs. the former Fermi level shift dominates, which results in a PL blue shift with increasing hole concentrationp-I I], while the reverse situation applies to p-type bulk GaAs[5.6.8]. At a certain hole concentration, the excitons are quenched. The principal mechanism behind the quenching of the excitons is screening. The screening of three-dimensional excitons is strong already at very low doping and carrier densities, while the corresponding screening effect in the two-dimensional case is much weaker. The restriction on the movement of carriers due to the lower dimensionality inhibits their ability for screening. For the case of QWs, excitons are expected to survive all the way up to the degenerate limit due to the inefficient screening

1. INTRODUCTION

The properties of quantum well (QW) structures are strongly influenced by the presence of dopant impurities either in the well or in the barrier. The major part of the basic research has been focused on modulation-doped structures, with their potential for the direct study of many-body (MB) effects, due to the high carrier concentration in combination with the maintained high mobility level. Anti modulationdoped QWs, i.e. QW structures doped within the well, have received significantly less attention. The possible effects of impurities within the well are manifold: they can provide carriers for conduction, act as scattering sites, hence limiting the mobility, or be important as centres for radiative or nonradiative recombination. At a sufficiently high acceptor concentration, the acceptor impurity band will overlap with the free carrier continuum. This level corresponds to the metallic limit, i.e. the electronic phase transition from a semiconducting to a metallic behaviour. The properties of QWs doped with donors in the central part of the QW, up to the metallic limit, have recently been investigated( 1,2]. Richards et a/.[31 have investigated some specific aspects of optical properties for the corresponding acceptor centre doped QWs above the degenerated limit. For the case of p-doped bulk GaAs, Semelius[4] has calculated the bandgap renormalization in the high hole concentration regime including exchange and correlation effects of the electron-hole system together with the interaction with ionized impurities. However, no corresponding 89

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A. C. Ferreira er 01.

[2,12]. Consequently, a major difference between the two-dimensional and three-dimensional system is the relatively stronger exciton recombination in optical spectra for the two-dimensional case even at high carrier concentrations. In this paper we present theoretical and experimental results of a systematic study of optical properties vs the hole concentration for acceptor centre doped QWs. Steady state PL and PLE results are compared with theoretical calculations involving exchange and correlation effects for the electron-hole system and the interaction between charged carriers and acceptor ions. 2. THEORY

We have determined the hole subband dispersions by a self-consistent calculation of the Schrodinger and Poisson equations. The kinetic energy operator is given by the Luttinger-Kohn Hamihonian[l3] which includes the interaction between the heavy holes (HH) and the light holes (LH). We have applied the axial approximation[l4] in which an average dispersion in the xl!-plane is assumed. For the symmetric potential in this problem both matrices give the same subband structure corresponding to a two-fold spin degeneracy. Current-conserving boundary conditions are fulfilled with the use of a modified variational method described elsewhere[ 151. The many-body (MB) effects are obtained in perturbation theory on the states determined beforehand, self-consistently neglecting the MB effects. We use the Rayleigh-Schrodinger perturbation theory, or on-the-mass-shell perturbation theory[ 161. The MB shifts are derived in a two-dimensional approximation in the random phase approximation with Hubbard’s local field correction. 3. EXPERIMENTAL

RESULTS AND DISCUSSION

The samples used in this study were grown by molecular beam epitaxy (MBE) at a temperature of nominally 680°C without interruptions at the QW interfaces. The layers were grown on top of a semiinsulating GaAs (100) substrate with a 0.35pm undoped GaAs buffer layer. The Al,Ga, _,As barriers were 150A wide with a nominal Al composition of x = 0.3. The wells had a width of I50 A and were doped with Be in the central 20% at a concentration varying from IOr up to IO”cm~‘. The link between the acceptor doping level and the hole concentration was estimated via Hall measurements under the same conditions as the optical measurements. For the PL and PLE measurements, an Ar’ ion laser was used to pump a tuneable titanium-doped sapphire solid-state laser. The emitted light from the samples was focused on the slits of a I-m doublegrating monochromator and detected with a dry-ice cooled GaAs photomultiplier. For the polarization dependent measurements, we have employed the

1500

1.510 PHOTON

1,520

1530

ENERGY

1,540

(eVJ

Fig. 1. Photoluminescence (PL) spectra for different hole concentrations. The weak intensity of the FEHH peaks have partly been enlarged for clarity. The feature at the low energy side (z 1.51 eV) corresponds to GaAs luminescence.

photoelastic modulation technique[ 171. All optical measurements presented were performed at I.5 K. We have measured the dependence of the intensity, broadening effects and peak position of bound excitons (BEs), HH and LH states of the FE on the hole concentration in steady state PL and PLE measurements. Figure I displays the development of the PL spectrum with increasing hole concentration. As can be seen in this figure, the exciton peaks are red shifted and broadened as the hole concentration increases. Also, the intensity of the FEHH decreases with increasing doping level, accompanied by an increase in the BE intensity. As can be expected, the reduced FE/BE intensity ratio can be understood as an increase of the FE capture by the impurities. The random potential distribution produced by a high doping density gives rise to a strong localization of the FEs[2]. The r-space localization corresponds to a delocalization in k-space, which in turn results in an increasing inhomogenous linewidth of the excitons. A new feature appears at the low energy side of the BEs, which becomes pronounced at the medium doping level regime. It gains strength with increasing doping level and dominates at approximately 9 x IO” acceptors cm 2 (1.8 x IO9 holes cm-’ ). As seen from Fig. 1, it corresponds to a peak at approximately I .5 meV below the main BE. With increasing doping level the BEs will experience an attractive Coulomb interaction with the neighbouring acceptors, and form interacting acceptor BEs. Figure 2 shows a PL spectrum, for a sample with doping level mentioned above, for two different laser intensities. Increasing the laser intensity, and consequently the FE and the acceptor BE population, leads to a decrease of the

Optical studies of acceptor centre doped GaAs/AIGaAs

91

quantum wells,

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Fig. 2. Photoluminescence spectra for a QW with 9 x lOLoacceptors per cm-? (1.9 x 10q holes cm-‘) for two different laser excitations. BE#2 is the normal acceptor bound exciton (BE) and BE# I is the interacting acceptor BE.

acceptor BE population, since fewer single acceptors are available to form interacting acceptor BEs. This new feature, the interacting acceptor BE, quenches at approximately 15 K due to its weak interaction with neighbour acceptors. We also discard the poss~biiity of the ionized acceptor BE, since the ionized acceptor population relative to the neutral acceptor population is expected to increase with increasing tem~rature. ~x~~menta~~y, we observe the opposite effect. As illustrated in Fig, 3, for a degenerated QW structure (6 x 10” acceptors per cn-‘), not only the FEHH, but also the FELH can be monitored in PL. The relatively high FELH intensity in the PL spectrum implies that there is a considerable LH-population, i.e. the Fermi level. is close to the LH-band. Also the PLE spectrum is depicted in the same figure. The diamagnetic shifts of FEHH and FELL-i have been experimentally estimated to 3.5 x IO-” and 2.0 x lo-‘eV/T’, respectively, a quadratic dependence with magnetic field typical for excitons. The polarization dependent PLE spectrum (insert of Fig. 3) confirms

1.58

1

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interacting

2

I.50

1.51

1.52

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1.53

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1.55

1.56

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Fig. 3. Photoluminescence (PL) of a sample with a hole concentration of 1.2 x lO’“cm-? (above the degenerate limit). A polarized PLE spectrum is depicted in the insert.

1.521 " ...I IOZ4 10"

HoIe

.....I 10'6

IO"

Concentration

10'"

-I 20"

(cm”)

Fig.4.Peak position dependence of the free excitons (FE) on the hole con~ntrat~on in PLE, where (a) and (b) correspond to FE light and heavy hole, respectively. (x ), (0)

and (0) correspond to the experimental. results of theory A and theory B. respectively.

the LH and HH characteristics of the FEs as compared with the unpolarized PLE measurements. In bulk GaAs, excitons are quenched at a hole concentration well below the metallic limit, around 1Oi6cme3, due to a strong screening of the electronhole interaction[f 81. It has earlier been found that excitons survive all the way up to the degenerate limit in n-type QW structures, due to the inefficiency of screening in a two-dimensional system[2]. In our study of p-type QWs, we can confirm the same tendency and state that they can survive even above the degenerate limit. The presence of excitons at such a high hole concentration is due to the inefficiency of screening in a two-dimensional system. In Fig. 4 we show the dependence of the FEs peak positions on the hole concentration. It was found experimentally that there is no equilibrium LH population for all analysed samples. We compare our experimental data with two distinct theories. The so-called theory A includes only the band-filling effect (Bu~tein-Moss shift) and theory B includes Burstein-Moss shift and exchange-correlation effects, as already mentioned in Section 2. Theory A, as expected, deviates from the experimental values when the MB effects start to become important. This effect is quite clear for the FEHH in PLE with (k =k,), where the theory A prescribes an increase of the

A. C. Ferreira 91 al.

92

exciton energy with hole concentration. The agreement with our second theory is excellent. It should be pointed out that the exciton binding energy was assumed to be constant for all hole concentrations, which we expect to have a quite small dependence for the hole concentration range studied here. In conclusion we have studied optical properties in p-type centre doped QWs for hole concentration varying between 10”and 10” cm-‘. Our theory taking into account the exchange-correlation effects gives a good agreement with experimental results. We have verified that excitons are strong also for degenerated samples. Excitons survive at these high hole concentrations due to the inefficiency of the screening in our system. Acknow1edgemetzts-C

Hallin for sample preparations. A.C.F. acknowledges the Brazilian agency RHAE/CNPq for financial support. REFERENCES I. C. I. Harris, H. Kalt, B. Monemar and K. K(ihler, Surf Sci. 263, 462 (1991). 2. C. 1. Harris, B. Monemar, Phys. Rert B 48, 4687 (1993).

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