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Observation of the Fermi-edge singularity in n-doped single asymmetric quantum wells: the influence of residual acceptors
Physica E 9 (2001) 709–715
www.elsevier.nl/locate/physe
Observation of the Fermi-edge singularity in n-doped single asymmetric quantum wells: the in uence of residual acceptors Fanyao Qua , N.O. Dantasa , P.C. Moraisb; ∗ a Laboratà orio
de Novos Materiais Isolantes e Semicondutores, Departamento de Ciˆencias FÃsicas, Universidade Federal de Uberlˆandia, CEP 38400-902 - Uberlˆandia-MG, Brazil b NÃ ucleo de FÃsica Aplicada, Instituto de FÃsica, Universidade de BrasÃlia, C.P. 04455, Campus Universitario, CEP 70919-970 - BrasÃlia-DF, Brazil Received 5 July 2000; accepted 26 September 2000
Abstract The investigation of the evolution of the photoluminescence spectra, in single asymmetric quantum wells (SAQWs), from a typical emission spectrum to a Fermi-edge singularity, is carried out as a function of both the optical excitation intensity and the temperature. The three samples used here are n-doped, low carrier density (below 5 × 1011 cm−2 ), GaAs=Al0:35 Ga0:65 As SAQWs grown by molecular beam epitaxy. The strong collective recombination of electrons with di erent k states up to the Fermi wave vector as well as the optical signature of the Fermi-edge singularity is observed in two samples containing residual acceptors inside the GaAs SAQW. In contrast, a third sample containing no experimental evidence of residual acceptors in the GaAs SAQW shows no optical signature of the Fermi-edge singularity. ? 2001 Elsevier Science B.V. All rights reserved. PACS: 71.10.Ca; 71.35.−y; 71.45.Gm; 78.66.−w Keywords: Fermi-edge singularity; Asymmetric quantum wells; GaAs; Photoluminescence
1. Introduction The Fermi-edge singularity (FES) is a typical many-body e ect [1] with a dramatic in uence on the optical properties of a doped semiconductor system due to the enhanced, multiple electron–hole scattering rate for carriers close to the Fermi energy (EF ). As ∗
Corresponding author. Tel.: +55-61-273-6655; +55-61-272-3151. E-mail address: pcmor@ s.unb.br (P.C. Morais).
fax:
far as the photoluminescence (PL) data are concerned the optical signature of the FES in semiconductors is a strong enhancement of the PL intensity towards EF , as shown in the pioneering work of Skolnick et al. [2]. Since then, experimental evidence of the FES has been reported for semiconductor quantum wires [3], delta-doped semiconductor structures [4], and one-side modulation-doped asymmetric step quantum wells [5]. Despite the maturity of the eld and the intense scienti c research performed in the last two decades, the nature of the FES is still a matter of
1386-9477/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 0 ) 0 0 2 8 0 - 0
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F. Qu et al. / Physica E 9 (2001) 709–715
controversy. The involvement of acceptors, either residual or intentional, has long been used to explain the onset of the FES via localized holes [6], while more recent results support the participation of free holes instead [7]. The role played by the unoccupied subbands above EF has o ered an alternative explanation of the optical feature associated to the observation of the FES as well [8]. Finally, a very recent observation of a trion peak in addition to the exciton peak, and the smooth evolution of the former into the optical feature associated with the FES, strongly suggests that the reduction of the system’s dimensionality needs to be taken into account in the explanation of the FES in low-dimensional semiconductor systems [9]. One-side modulation-doped or single asymmetric quantum wells (SAQWs) [10] have been used as ideal systems to investigate di erent aspects related to many-body e ects in two-dimensional (2D) one-component carrier plasmas. Among the manybody e ects investigated using SAQWs are the FES [2], the band-gap renormalization [11], and the dimensionality crossover [12], all of them strongly dependent upon the carrier density (NS ). A very interesting property of the SAQWs is the possibility of continuously changing the 2D carrier density from its maximum value down to zero, by applying a bias voltage in a eld-e ect transistor con guration [13] or simply by illuminating the sample with increasing optical excitation intensity, either in the absence [14] or in the presence [15] of magnetic elds. The experimental evidence of the correlation between the optical feature associated to the FES and the presence of a PL peak assigned to residual acceptors, in high-quality n-doped GaAs=AlGaAs SAQWs, is the main issue of the present work. Furthermore, the smooth evolution of the usual emission spectrum into a FES-like pro le and its dependence upon the optical excitation intensity and the temperature are reported as well. 2. Experimental details The PL experiments were carried out using three n-doped GaAs=Al0:35 Ga0:65 As SAQW samples (W1506, W1413, and W1504) grown by molecular beam epitaxy. The nominal growth pro le of the W1506 (W1413, W1504) sample consists of a thick GaAs bu er layer grown on top of the semi-insulat-
ing GaAs substrate, a GaAs=Al0:35 Ga0:65 As superlattice (from 7 × 36 + 8 × 100 to 7 × 40 + 8 × (150; 200 A) 100 A), the 152 A GaAs SAQW, the 295 A (300; 250 A) undoped Al0:35 Ga0:65 As (380; 400 A) spacer layer, the 385 A Si-doped (1:8 × 1018 cm−3 ) Al0:35 Ga0:65 As layer, and the GaAs cap layer. The whole structure is nominally undoped except at the Si-doped Al0:35 Ga0:65 As layer. At low temperature, all the samples have electron mobility higher than 105 cm2 =V × s and 2D electron gas (2DEG) density below 5 × 1011 cm−2 . From the Shubnikov–de Haas (SdH) oscillations, a 2DEG density of about 3:1 × 1011 ; 4:4 × 1011 , and 3:4 × 1011 cm−2 were obtained for samples W1506, W1413, and W1504, respectively. Actually, the 2DEG inside the GaAs SAQW is due to the charge transfer from the remote Si-donors intentionally introduced in the doped Al0:35 Ga0:65 As layer [10]. Upon laser illumination, with energy above the band gap of the undoped Al0:35 Ga0:65 As layer, the photocreated electron in the spacer layer initially moves back to the spatially distant donors while the corresponding photocreated hole is drifted into the SAQW by the built-in electric eld, there recombining with electrons from the 2DEG. Later on, the photocreated electron moves from the donor back into the SAQW by tunneling through the Al0:35 Ga0:65 As spacer layer. At a given optical excitation intensity, the steady-state 2DEG density (NS ) is lower than the 2DEG density in dark condition (NS0 ) or near-zero optical excitation. It has been found that increasing the optical excitation leads to the reduction of the 2DEG density [16]. Therefore, very weak optical excitation provides very low density of photocreated electrons and holes, with a consequent negligible reduction of the 2DEG density. In contrast, strong optical excitation may remove all the electrons from the SAQW. In our experiments, the samples were optically excited above the band gap of the undoped Al0:35 Ga0:65 As using the 5145 A argon-ion laser line focused on a spot on the order of 90 m wide, at di erent optical excitation intensities. The PL spectra were recorded at several temperatures using a SPEX-750M monochromator equipped with a Joban-Yvon CCD (2000 × 800 − 3). The PL spectra of samples W1506 and W1413 show a residual p-type doping in the nominally undoped GaAs SAQW. However, no evidence of residual p-type doping from the PL spectra of sample W1504 was found.
F. Qu et al. / Physica E 9 (2001) 709–715
Fig. 1. The photoluminescence spectra of the GaAs SAQW (sample W1506) at 20 K, under di erent optical excitation intensities (2.4, 3.9, 16, and 90 W=cm2 ).
3. Results The low-temperature (20 K) PL spectra of sample W1506 at di erent optical excitation intensities (2.4, 3.9, 16, and 90 W=cm2 ) are shown in Fig. 1. The PL peak A (at 2:4 W=cm2 ) on the high-energy side of the spectra (1.5214 eV) has been associated to the n = 0 optical transition inside the GaAs SAQW. This is the transition between the ground state of the conduction subband and the ground state of the heavy-hole subband. Two striking aspects are related to the PL peak A (see Fig. 1). First, the energy position shows a maximum blue shift of 10.3 meV as the optical excitation intensity increases from 2.4 to 90 W=cm2 . Second, at low optical excitation intensities a high-energy tail develops while a shoulder appears in this high-energy tail, approximately 16.8 meV above the PL peak A. Figs. 2(a) and (b) show the temperature dependence of the PL spectra of sample W1506 at low (0:4 W=cm2 ) and intermediate (7:8 W=cm2 ) optical excitation intensities, respectively. The PL peak B around 1.515 eV (10 –20 K) has been assigned to the thick GaAs bu er layer. The temperature dependence of the PL peak B position is described by ET (T ) = ET (0) − T 2 =(ÿ + T ), where ET (T ) is the interband recombination energy at temperature T; = 5:405 × 10−4 eV=K, and ÿ = 204 K. Note from Fig. 1 that as
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the optical excitation intensity increases the PL peak A tends to separate from the PL peak B, the latter becoming stronger than the former. Finally, PL peaks C and D in Figs. 1 and 2(a) have been assigned to acceptor transitions. While PL peak C (around 1.494 eV) has been assigned to the carbon acceptor transition in the GaAs substrate, the PL peak D (around 1.480 eV) originates from the residual acceptor transition in the nominally undoped GaAs SAQW. Note from Figs. 1 and 2(a) that the intensity of the PL peak D goes in parallel with and in favor of the shoulder that appears at the high-energy tail of PL peak A. Fig. 3(a) illustrates the optical excitation intensity dependence (0.4, 1.6, and 220 W=cm2 ) of the PL spectra of sample W1413, at 10 K. Note the similarity (see arrows) between the optical behavior of samples W1413 (Fig. 3(a)) and W1506 (Fig. 1). In particular, Fig. 3(a) shows the PL peak D associated to the residual acceptors. Fig. 3(b) shows the temperature dependence (10, 40, and 80 K) of the PL spectra of sample W1413, excited at 3.9 W/cm2 . Again, note the similarity (see arrows) between the optical behavior of samples W1413 (Fig. 3(b)) and W1506 (Fig. 2(b)). Similarly to what has been observed before for sample W1506, the PL peak D in sample W1413 goes in parallel with and in favor of the shoulder that appears at the high-energy tail of PL peak A. Further, such a correlation between PL peaks A and D occurs in both the optical excitation intensity dependence experiment (Fig. 3(a)) and in the temperature dependence experiment (Fig. 3(b)) (see arrows). In order to investigate in more detail the shoulder that appears at the high-energy side of PL peak A the third SAQW sample (W1504) was used. Fig. 4 shows the PL spectra of sample W1504, at di erent temperatures (10, 50, and 70 K) and under di erent optical excitation intensities (1.6 and 105 W=cm2 ). In contrast to the data obtained from samples W1506 and W1413 (see Figs. 1 and 3(a)), the PL peaks C and D, respectively, associated with the carbon acceptor (in the GaAs substrate) and to the residual acceptor (in the GaAs SAQW) were not observed in the PL spectra of sample W1504 (data not shown). Further, inspection of Fig. 4 shows that the PL peak A has no indication of a shoulder at the high-energy side of the PL peak A.
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Fig. 2. The photoluminescence spectra of the GaAs SAQW (sample W1506) as a function of temperature, under an optical excitation intensity of (a) 0:4 W=cm2 and (b) 7:8 W=cm2 .
Fig. 3. The photoluminescence spectra of the GaAs SAQW (sample W1413) (a) at 10 K as a function of the optical excitation intensity and (b) at 3:9 W=cm2 as a function of the temperature. At 0:4 W=cm2 the PL peaks C and D are not shown, for the data were taken above 1.51 eV only.
4. Discussion The blue shift observed in the PL peak A (10.3 meV) of sample W1506, as the optical excitation intensity is increased from 2.4 to 90 W=cm2 (see Fig. 1), is due to the reduction of both the band bending and the band-gap renormalization as a consequence of the reduction of the 2DEG density, ac-
cording to the charge-transfer mechanism proposed by Chaves et al. [16]. When the optical excitation intensity is increased above 16 W=cm2 (see Fig. 1), almost all the electrons are removed from the GaAs SAQW. Then, the GaAs SAQW turns into an almost perfect square potential well and the calculated n = 0 transition energy occurs at 1.5387 eV. The calculation was performed using the following
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Fig. 4. The photoluminescence spectra of the GaAs SAQW (sample W1504) at 10, 50, and 70 K, under low (1:6 W=cm2 ) and high (105 W=cm2 ) optical excitation intensity.
parameters: e ective electron mass m∗e = 0:067m0 , e ective heavy-hole mass m∗h = 0:371m0 , the lowfrequency dielectric constant r = 13:10 , the 60% (40%) rule, the Alx Ga1−x As band gap of Eg = 1:247x eV (here x = 0:35), and the GaAs band gap at 1.519 eV. The exciton binding energy associated to the ground state in the GaAs SAQW was also calculated (8.2 meV). Therefore, the PL peak A located at 1.5317 eV (20 K and 90 W=cm2 ) has been identi ed as a free exciton transition in the GaAs SAQW. Self-consistent calculation was used to investigate the shoulder that develops at the high-energy side of the PL peak A (samples W1506 and W1413). The coupled Schrodinger and Poisson equations were numerically solved, in the frame of the nite di erence method [17], to obtain the 2DEG density (3:388 × 1011 cm−2 ), the Fermi energy (12.095 meV), and the rst electron excited state energy relative to the ground state (47.762 meV) of sample W1506 at 20 K. The bound energy associated to the donors in the Si-doped (1:8 × 1018 cm−3 ) Al0:35 Ga0:65 As layer was xed at ED = 45 meV. Furthermore, the e ect of the residual acceptor density (NA = 1 × 1014 cm−3 ) inside the GaAs SAQW was included in the Poisson equation as well. In the case of the W1506 sample, it was found that the electrons only occupy the ground state of the conduction subband. Using the SdH data and the rela-
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tionship between the Fermi energy and the 2DEG density (EF = NS ˜2 =m∗e ), the Fermi level relative to the electron ground state energy is 11.07 meV. Note that the values obtained from the many-body calculations relative to the 2DEG density and the Fermi energy are in very good agreement with the values obtained from the SdH data. On the other hand, the Fermi energy can be roughly deduced from the PL peak A by taking the energy di erence between the low-energy onset and the high-energy cuto , both at half-maximum intensity. The low-temperature PL spectra (see Fig. 1) give the maximum Fermi energy of about 12.51 meV. Therefore, the intensity enhancement observed at the high-energy side of the PL peak A re ects the interband transition involving the electrons in the Fermi sea. In other words, the shoulder in the high-energy side of the PL peak A in samples W1506 (see Fig. 1) and W1413 (see Fig. 2(a)) is the well-known optical signature of the FES. Note that the PL peak A in Figs. 2(a) and (b) exhibit the expected behavior of the FES, i.e., the shoulder appearing at the high-energy tail which is less pronounced under both higher temperatures and higher optical excitation intensities. Fig. 1 shows that as the photoexcitation intensity increases from 2.4 towards 90 W=cm2 , the PL peak A revels a progressive linewidth narrowing and the quenching of the FES optical feature. The narrowing of the energy bandwidth re ects the reduction of the 2DEG density in the quantum well. At a rst glance, this nding may be hard to understand. Actually, it results from the charge-transfer mechanism in the SAQW, from which the increasing of the optical excitation leads to a decreasing of the 2DEG density. In the low optical excitation regime, the photogenerated excess holes collected by the quantum well are less than the number of the ionized acceptors introduced by the residual doping. Since the trapping of the holes by electrons is very ecient, the optical transition remains k-nonconserving. Under high optical excitation regime, however, the photogenerated holes outnumber the ionized acceptors. As a result, free holes are present in the quantum well and band-to-band optical transition may occur. Therefore, the FES optical feature associated with the k-nonconserving optical transition becomes weaker and nally disappears at higher optical excitation intensities. On the other hand, as the optical excitation intensity increases the PL spectrum characterizing the one-component
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plasma, in which the excitons are suppressed due to screening and phase- lling e ects, develops into a spectrum dominated by excitonic e ects. Fig. 2(a) shows that the PL peak C is suppressed as the temperature increases. The extrinsic origin of the PL peak C is supported by the saturation behavior or tendency to saturate at high optical pumping levels. As far as the optical excitation intensity is concerned, the intensity of the PL peaks C and D show similar behavior, i.e., reduces as the optical pumping increases (see Fig. 1). However, as the temperature increases, the intensity and the full-width at half-maximum of the PL peak D increases (see Fig. 2(a)). In fact, the PL peak D originates from the residual acceptor transition in the nominally undoped GaAs SAQW, accompanied by LO-phonon emission. Note from Figs. 1 and 2(a) that the optical transition represented by the PL peak D goes in parallel with and in favor of the FES optical feature (see the arrows), thus indicating a strong correlation between the PL peak D and the FES. This result is consistent with the picture of residual acceptors in the GaAs SAQW region to which the photocreated hole is bound in order to ensure the optical observation of the FES. Further, the observation of the FES in optical spectra requires a strong overlap of electron and hole wave functions to provide effective electron–hole interaction. The strong overlap of electron and hole wave functions is provided by the hole localization, which arises from a hole bound to the ionized acceptor, in the case of high-quality n-doped GaAs=AlGaAs SAQWs. The radius of the Using the localized hole wave function is about 18 A. uncertainty relation this radius corresponds to a hole wave vector of about 3 × 106 cm−1 , which is of the order of the value required (kF = 1:46 × 106 cm−1 ) to give ecient recombination without wave vector restriction, for electrons in all states up to EF . As the temperature increases the width of the PL peak A becomes broader on the high-energy side while the intensity enhancement at EF is reduced, re ecting the change of the electron distribution according to the Fermi statistics. At temperatures above 70 K (see Figs. 2(a) and (b)), the enhancement of the PL peak A towards EF disappears because of the thermal broadening of the Fermi edge. This nding provides additional support for the observation of the FES optical feature in the PL spectra of the investigated sample and excludes the possibility that the high-
energy tail in the PL peak A comes from the recombination of electrons and holes involving higher energy subbands. Inspection of Figs. 2(a) and (b) shows the evolution of the optical feature associated to the FES. As the temperature increases, the FES optical feature becomes weaker and more quickly suppressed at intermediate optical excitation intensity (7:8 W=cm2 ) compared to the lower optical excitation intensity (0:4 W=cm2 ). Indeed, the permanence of the FES optical feature at a relatively high temperature is a characteristic of the sample W1506. This indicates a competition between two distinct radiative recombination mechanisms. At low temperature, the PL spectra are dominated by the k-nonconserving transitions involving the 2DEG and the holes bound to the ionized acceptors. Under low photoexcitation intensity (0:4 W=cm2 ) and at low temperature (10 K) there are few free holes in the valence band and the band-to-band transition is hardly observed. As the temperature increases (see Fig. 2(a)), the bound holes are thermalized to become free holes and thus band-to-band transition (k-conserving) develops. These two competing radiative mechanisms are strongly temperature dependent. Under intermediate photoexcitation intensity (7:8 W=cm2 ), however, a huge amount of photogenerated holes may be collected by the SAQW. Then, the excess holes eciently neutralize the ionized acceptors introduced by the residual doping, thus reducing the k-nonconserving transition. Besides, under intermediate optical excitation intensity, the residual bound holes may be thermalized to become free holes at lower temperatures. Finally, samples W1506 and W1413 exhibit similar optical excitation intensity and temperature dependence as far as the PL signature of the FES is concerned, though sample W1413 presents a slightly higher 2DEG density. In contrast, the PL peak D associated with residual acceptors inside the GaAs SAQW has not been observed in sample W1504 as it has been observed in samples W1506 and W1413. Furthermore, inspection of Fig. 4 shows that the PL peak A has no optical signature of the FES as observed in Figs. 2 and 3. Indeed, the data in Fig. 4 strongly supports the picture of the optical observation of the FES associated with the residual acceptors inside the SAQWs analyzed in this work.
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5. Conclusions In summary, the collective radiative recombination of the 2DEG with photogenerated holes presumably bound to ionized acceptors has been observed in two n-doped GaAs=Al0:35 Ga0:65 As SAQW samples (W1506 and W1413). The data indicate that in samples W1506 and W1413 residual acceptors are uniformly distributed all over the region around the GaAs SAQW. Even at low carrier densities (below 5 × 1011 cm−2 ), the optical signature of the Fermi-edge singularity in the W1506 and W1413 samples is clearly observed. At low temperatures the k-nonconserving process dominates, while at higher temperatures thermalization of the bound holes occurs and the k-conserving process develops. Due to the strong binding energy associated to the acceptor, the FES would be optically observed even at high temperatures. When the photoexcitation density is suciently high, the photogenerated excess holes outnumber the acceptors. Thus, the k-nonconserving channel is saturated, and the PL spectrum presents features of k-conserving electron–hole transitions. As a consequence, the observation of the optical feature associated to the FES is quenched. In striking contrast, no optical signature of the FES is observed in a GaAs SAQW with low density of residual acceptors (sample W1504). Finally, our results demonstrate that if enough acceptors are present in the GaAs SAQW the FES singularity at low carrier density can be successfully investigated using conventional PL spectroscopy. Acknowledgements We wish to thank Professor G. Weimann for providing the samples used in this work. Support from the
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Brazilian agencies FAPEMIG, FAP-DF, and CNPq is gratefully acknowledged. References [1] G.D. Mahan, Phys. Rev. B 21 (1980) 1421. [2] M.S. Skolnick, J.M. Rorison, K.J. Nash, D.J. Mowbray, P.R. Tapster, S.J. Bass, A.D. Pitt, Phys. Rev. Lett. 58 (1987) 2130. [3] J.M. Calleja, A.R. Goni, B.S. Dennis, J.S. Weiner, A. Pinczuk, S. Schmittrink, L.N. Pfei er, K.W. West, J.F. Muller, A.E. Ruckenstein, Solid State Commun. 79 (1991) 911. [4] M. Fritze, A. Kastalsky, J.E. Cunningham, W.H. Knox, R.N. Pathak, I.E. Peradis, Solid State Commun. 100 (1996) 497. [5] H.X. Li, Z.G. Wang, J.B. Liang, B. Xu, C. Jiang, Q. Gong, F.Q. Liu, W. Zhou, Solid State Commun. 106 (1998) 811. [6] Q.X. Zhao, P.O. Holtz, B. Monemar, E. Sorman, W.M. Chen, C. Hallin, M. Sundaram, J.L. Merz, A.C. Gossard, Phys. Rev. B 44 (1991) 3821. [7] S.A. Brown, J.F. Young, Z. Wasilewski, P.T. Coleridge, Phys. Rev. B 56 (1997) 3937. [8] W. Chen, M. Fritze, A.V. Nurmikko, J.M. Hong, L.L. Chang, Phys. Rev. B 43 (1991) 14 738. [9] V. Huard, R.T. Cox, K. Saminadayar, A. Arnoult, S. Tatarenko, Phys. Rev. Lett. 84 (2000) 187. [10] H. Burkhard, W. Schlapp, G. Weimann, Surf. Sci. 174 (1986) 382. [11] C. Delalande, G. Bastard, J. Orgonasi, J.A. Brum, H.W. Liu, M. Voos, Phys. Rev. Lett. 59 (1987) 2690. [12] F. Qu, P.C. Morais, IEEE J. Quantum Electron. QE-34 (1998) 1419. [13] C. Delalande, J. Orgonasi, M.H. Meynadier, J.A. Brum, G. Bastard, G. Weimann, W. Schlapp, Solid State Commun. 59 (1986) 613. [14] A.J.C. Cardoso, P.C. Morais, H.M. Cox, Appl. Phys. Lett. 68 (1996) 1105. [15] A.J.C. Cardoso, F. Qu, P.C. Morais, Phys. Rev. B 60 (1999) 4501. [16] A.S. Chaves, A.F.S. Penna, J.M. Worlock, G. Weimann, W. Schlapp, Surf. Sci. 170 (1986) 618. [17] F. Qu, P.C. Morais, J. Chem. Phys. 111 (1999) 8588.
www.elsevier.nl/locate/physe
Observation of the Fermi-edge singularity in n-doped single asymmetric quantum wells: the in uence of residual acceptors Fanyao Qua , N.O. Dantasa , P.C. Moraisb; ∗ a Laboratà orio
de Novos Materiais Isolantes e Semicondutores, Departamento de Ciˆencias FÃsicas, Universidade Federal de Uberlˆandia, CEP 38400-902 - Uberlˆandia-MG, Brazil b NÃ ucleo de FÃsica Aplicada, Instituto de FÃsica, Universidade de BrasÃlia, C.P. 04455, Campus Universitario, CEP 70919-970 - BrasÃlia-DF, Brazil Received 5 July 2000; accepted 26 September 2000
Abstract The investigation of the evolution of the photoluminescence spectra, in single asymmetric quantum wells (SAQWs), from a typical emission spectrum to a Fermi-edge singularity, is carried out as a function of both the optical excitation intensity and the temperature. The three samples used here are n-doped, low carrier density (below 5 × 1011 cm−2 ), GaAs=Al0:35 Ga0:65 As SAQWs grown by molecular beam epitaxy. The strong collective recombination of electrons with di erent k states up to the Fermi wave vector as well as the optical signature of the Fermi-edge singularity is observed in two samples containing residual acceptors inside the GaAs SAQW. In contrast, a third sample containing no experimental evidence of residual acceptors in the GaAs SAQW shows no optical signature of the Fermi-edge singularity. ? 2001 Elsevier Science B.V. All rights reserved. PACS: 71.10.Ca; 71.35.−y; 71.45.Gm; 78.66.−w Keywords: Fermi-edge singularity; Asymmetric quantum wells; GaAs; Photoluminescence
1. Introduction The Fermi-edge singularity (FES) is a typical many-body e ect [1] with a dramatic in uence on the optical properties of a doped semiconductor system due to the enhanced, multiple electron–hole scattering rate for carriers close to the Fermi energy (EF ). As ∗
Corresponding author. Tel.: +55-61-273-6655; +55-61-272-3151. E-mail address: pcmor@ s.unb.br (P.C. Morais).
fax:
far as the photoluminescence (PL) data are concerned the optical signature of the FES in semiconductors is a strong enhancement of the PL intensity towards EF , as shown in the pioneering work of Skolnick et al. [2]. Since then, experimental evidence of the FES has been reported for semiconductor quantum wires [3], delta-doped semiconductor structures [4], and one-side modulation-doped asymmetric step quantum wells [5]. Despite the maturity of the eld and the intense scienti c research performed in the last two decades, the nature of the FES is still a matter of
1386-9477/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 0 ) 0 0 2 8 0 - 0
710
F. Qu et al. / Physica E 9 (2001) 709–715
controversy. The involvement of acceptors, either residual or intentional, has long been used to explain the onset of the FES via localized holes [6], while more recent results support the participation of free holes instead [7]. The role played by the unoccupied subbands above EF has o ered an alternative explanation of the optical feature associated to the observation of the FES as well [8]. Finally, a very recent observation of a trion peak in addition to the exciton peak, and the smooth evolution of the former into the optical feature associated with the FES, strongly suggests that the reduction of the system’s dimensionality needs to be taken into account in the explanation of the FES in low-dimensional semiconductor systems [9]. One-side modulation-doped or single asymmetric quantum wells (SAQWs) [10] have been used as ideal systems to investigate di erent aspects related to many-body e ects in two-dimensional (2D) one-component carrier plasmas. Among the manybody e ects investigated using SAQWs are the FES [2], the band-gap renormalization [11], and the dimensionality crossover [12], all of them strongly dependent upon the carrier density (NS ). A very interesting property of the SAQWs is the possibility of continuously changing the 2D carrier density from its maximum value down to zero, by applying a bias voltage in a eld-e ect transistor con guration [13] or simply by illuminating the sample with increasing optical excitation intensity, either in the absence [14] or in the presence [15] of magnetic elds. The experimental evidence of the correlation between the optical feature associated to the FES and the presence of a PL peak assigned to residual acceptors, in high-quality n-doped GaAs=AlGaAs SAQWs, is the main issue of the present work. Furthermore, the smooth evolution of the usual emission spectrum into a FES-like pro le and its dependence upon the optical excitation intensity and the temperature are reported as well. 2. Experimental details The PL experiments were carried out using three n-doped GaAs=Al0:35 Ga0:65 As SAQW samples (W1506, W1413, and W1504) grown by molecular beam epitaxy. The nominal growth pro le of the W1506 (W1413, W1504) sample consists of a thick GaAs bu er layer grown on top of the semi-insulat-
ing GaAs substrate, a GaAs=Al0:35 Ga0:65 As superlattice (from 7 × 36 + 8 × 100 to 7 × 40 + 8 × (150; 200 A) 100 A), the 152 A GaAs SAQW, the 295 A (300; 250 A) undoped Al0:35 Ga0:65 As (380; 400 A) spacer layer, the 385 A Si-doped (1:8 × 1018 cm−3 ) Al0:35 Ga0:65 As layer, and the GaAs cap layer. The whole structure is nominally undoped except at the Si-doped Al0:35 Ga0:65 As layer. At low temperature, all the samples have electron mobility higher than 105 cm2 =V × s and 2D electron gas (2DEG) density below 5 × 1011 cm−2 . From the Shubnikov–de Haas (SdH) oscillations, a 2DEG density of about 3:1 × 1011 ; 4:4 × 1011 , and 3:4 × 1011 cm−2 were obtained for samples W1506, W1413, and W1504, respectively. Actually, the 2DEG inside the GaAs SAQW is due to the charge transfer from the remote Si-donors intentionally introduced in the doped Al0:35 Ga0:65 As layer [10]. Upon laser illumination, with energy above the band gap of the undoped Al0:35 Ga0:65 As layer, the photocreated electron in the spacer layer initially moves back to the spatially distant donors while the corresponding photocreated hole is drifted into the SAQW by the built-in electric eld, there recombining with electrons from the 2DEG. Later on, the photocreated electron moves from the donor back into the SAQW by tunneling through the Al0:35 Ga0:65 As spacer layer. At a given optical excitation intensity, the steady-state 2DEG density (NS ) is lower than the 2DEG density in dark condition (NS0 ) or near-zero optical excitation. It has been found that increasing the optical excitation leads to the reduction of the 2DEG density [16]. Therefore, very weak optical excitation provides very low density of photocreated electrons and holes, with a consequent negligible reduction of the 2DEG density. In contrast, strong optical excitation may remove all the electrons from the SAQW. In our experiments, the samples were optically excited above the band gap of the undoped Al0:35 Ga0:65 As using the 5145 A argon-ion laser line focused on a spot on the order of 90 m wide, at di erent optical excitation intensities. The PL spectra were recorded at several temperatures using a SPEX-750M monochromator equipped with a Joban-Yvon CCD (2000 × 800 − 3). The PL spectra of samples W1506 and W1413 show a residual p-type doping in the nominally undoped GaAs SAQW. However, no evidence of residual p-type doping from the PL spectra of sample W1504 was found.
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Fig. 1. The photoluminescence spectra of the GaAs SAQW (sample W1506) at 20 K, under di erent optical excitation intensities (2.4, 3.9, 16, and 90 W=cm2 ).
3. Results The low-temperature (20 K) PL spectra of sample W1506 at di erent optical excitation intensities (2.4, 3.9, 16, and 90 W=cm2 ) are shown in Fig. 1. The PL peak A (at 2:4 W=cm2 ) on the high-energy side of the spectra (1.5214 eV) has been associated to the n = 0 optical transition inside the GaAs SAQW. This is the transition between the ground state of the conduction subband and the ground state of the heavy-hole subband. Two striking aspects are related to the PL peak A (see Fig. 1). First, the energy position shows a maximum blue shift of 10.3 meV as the optical excitation intensity increases from 2.4 to 90 W=cm2 . Second, at low optical excitation intensities a high-energy tail develops while a shoulder appears in this high-energy tail, approximately 16.8 meV above the PL peak A. Figs. 2(a) and (b) show the temperature dependence of the PL spectra of sample W1506 at low (0:4 W=cm2 ) and intermediate (7:8 W=cm2 ) optical excitation intensities, respectively. The PL peak B around 1.515 eV (10 –20 K) has been assigned to the thick GaAs bu er layer. The temperature dependence of the PL peak B position is described by ET (T ) = ET (0) − T 2 =(ÿ + T ), where ET (T ) is the interband recombination energy at temperature T; = 5:405 × 10−4 eV=K, and ÿ = 204 K. Note from Fig. 1 that as
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the optical excitation intensity increases the PL peak A tends to separate from the PL peak B, the latter becoming stronger than the former. Finally, PL peaks C and D in Figs. 1 and 2(a) have been assigned to acceptor transitions. While PL peak C (around 1.494 eV) has been assigned to the carbon acceptor transition in the GaAs substrate, the PL peak D (around 1.480 eV) originates from the residual acceptor transition in the nominally undoped GaAs SAQW. Note from Figs. 1 and 2(a) that the intensity of the PL peak D goes in parallel with and in favor of the shoulder that appears at the high-energy tail of PL peak A. Fig. 3(a) illustrates the optical excitation intensity dependence (0.4, 1.6, and 220 W=cm2 ) of the PL spectra of sample W1413, at 10 K. Note the similarity (see arrows) between the optical behavior of samples W1413 (Fig. 3(a)) and W1506 (Fig. 1). In particular, Fig. 3(a) shows the PL peak D associated to the residual acceptors. Fig. 3(b) shows the temperature dependence (10, 40, and 80 K) of the PL spectra of sample W1413, excited at 3.9 W/cm2 . Again, note the similarity (see arrows) between the optical behavior of samples W1413 (Fig. 3(b)) and W1506 (Fig. 2(b)). Similarly to what has been observed before for sample W1506, the PL peak D in sample W1413 goes in parallel with and in favor of the shoulder that appears at the high-energy tail of PL peak A. Further, such a correlation between PL peaks A and D occurs in both the optical excitation intensity dependence experiment (Fig. 3(a)) and in the temperature dependence experiment (Fig. 3(b)) (see arrows). In order to investigate in more detail the shoulder that appears at the high-energy side of PL peak A the third SAQW sample (W1504) was used. Fig. 4 shows the PL spectra of sample W1504, at di erent temperatures (10, 50, and 70 K) and under di erent optical excitation intensities (1.6 and 105 W=cm2 ). In contrast to the data obtained from samples W1506 and W1413 (see Figs. 1 and 3(a)), the PL peaks C and D, respectively, associated with the carbon acceptor (in the GaAs substrate) and to the residual acceptor (in the GaAs SAQW) were not observed in the PL spectra of sample W1504 (data not shown). Further, inspection of Fig. 4 shows that the PL peak A has no indication of a shoulder at the high-energy side of the PL peak A.
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Fig. 2. The photoluminescence spectra of the GaAs SAQW (sample W1506) as a function of temperature, under an optical excitation intensity of (a) 0:4 W=cm2 and (b) 7:8 W=cm2 .
Fig. 3. The photoluminescence spectra of the GaAs SAQW (sample W1413) (a) at 10 K as a function of the optical excitation intensity and (b) at 3:9 W=cm2 as a function of the temperature. At 0:4 W=cm2 the PL peaks C and D are not shown, for the data were taken above 1.51 eV only.
4. Discussion The blue shift observed in the PL peak A (10.3 meV) of sample W1506, as the optical excitation intensity is increased from 2.4 to 90 W=cm2 (see Fig. 1), is due to the reduction of both the band bending and the band-gap renormalization as a consequence of the reduction of the 2DEG density, ac-
cording to the charge-transfer mechanism proposed by Chaves et al. [16]. When the optical excitation intensity is increased above 16 W=cm2 (see Fig. 1), almost all the electrons are removed from the GaAs SAQW. Then, the GaAs SAQW turns into an almost perfect square potential well and the calculated n = 0 transition energy occurs at 1.5387 eV. The calculation was performed using the following
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Fig. 4. The photoluminescence spectra of the GaAs SAQW (sample W1504) at 10, 50, and 70 K, under low (1:6 W=cm2 ) and high (105 W=cm2 ) optical excitation intensity.
parameters: e ective electron mass m∗e = 0:067m0 , e ective heavy-hole mass m∗h = 0:371m0 , the lowfrequency dielectric constant r = 13:10 , the 60% (40%) rule, the Alx Ga1−x As band gap of Eg = 1:247x eV (here x = 0:35), and the GaAs band gap at 1.519 eV. The exciton binding energy associated to the ground state in the GaAs SAQW was also calculated (8.2 meV). Therefore, the PL peak A located at 1.5317 eV (20 K and 90 W=cm2 ) has been identi ed as a free exciton transition in the GaAs SAQW. Self-consistent calculation was used to investigate the shoulder that develops at the high-energy side of the PL peak A (samples W1506 and W1413). The coupled Schrodinger and Poisson equations were numerically solved, in the frame of the nite di erence method [17], to obtain the 2DEG density (3:388 × 1011 cm−2 ), the Fermi energy (12.095 meV), and the rst electron excited state energy relative to the ground state (47.762 meV) of sample W1506 at 20 K. The bound energy associated to the donors in the Si-doped (1:8 × 1018 cm−3 ) Al0:35 Ga0:65 As layer was xed at ED = 45 meV. Furthermore, the e ect of the residual acceptor density (NA = 1 × 1014 cm−3 ) inside the GaAs SAQW was included in the Poisson equation as well. In the case of the W1506 sample, it was found that the electrons only occupy the ground state of the conduction subband. Using the SdH data and the rela-
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tionship between the Fermi energy and the 2DEG density (EF = NS ˜2 =m∗e ), the Fermi level relative to the electron ground state energy is 11.07 meV. Note that the values obtained from the many-body calculations relative to the 2DEG density and the Fermi energy are in very good agreement with the values obtained from the SdH data. On the other hand, the Fermi energy can be roughly deduced from the PL peak A by taking the energy di erence between the low-energy onset and the high-energy cuto , both at half-maximum intensity. The low-temperature PL spectra (see Fig. 1) give the maximum Fermi energy of about 12.51 meV. Therefore, the intensity enhancement observed at the high-energy side of the PL peak A re ects the interband transition involving the electrons in the Fermi sea. In other words, the shoulder in the high-energy side of the PL peak A in samples W1506 (see Fig. 1) and W1413 (see Fig. 2(a)) is the well-known optical signature of the FES. Note that the PL peak A in Figs. 2(a) and (b) exhibit the expected behavior of the FES, i.e., the shoulder appearing at the high-energy tail which is less pronounced under both higher temperatures and higher optical excitation intensities. Fig. 1 shows that as the photoexcitation intensity increases from 2.4 towards 90 W=cm2 , the PL peak A revels a progressive linewidth narrowing and the quenching of the FES optical feature. The narrowing of the energy bandwidth re ects the reduction of the 2DEG density in the quantum well. At a rst glance, this nding may be hard to understand. Actually, it results from the charge-transfer mechanism in the SAQW, from which the increasing of the optical excitation leads to a decreasing of the 2DEG density. In the low optical excitation regime, the photogenerated excess holes collected by the quantum well are less than the number of the ionized acceptors introduced by the residual doping. Since the trapping of the holes by electrons is very ecient, the optical transition remains k-nonconserving. Under high optical excitation regime, however, the photogenerated holes outnumber the ionized acceptors. As a result, free holes are present in the quantum well and band-to-band optical transition may occur. Therefore, the FES optical feature associated with the k-nonconserving optical transition becomes weaker and nally disappears at higher optical excitation intensities. On the other hand, as the optical excitation intensity increases the PL spectrum characterizing the one-component
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plasma, in which the excitons are suppressed due to screening and phase- lling e ects, develops into a spectrum dominated by excitonic e ects. Fig. 2(a) shows that the PL peak C is suppressed as the temperature increases. The extrinsic origin of the PL peak C is supported by the saturation behavior or tendency to saturate at high optical pumping levels. As far as the optical excitation intensity is concerned, the intensity of the PL peaks C and D show similar behavior, i.e., reduces as the optical pumping increases (see Fig. 1). However, as the temperature increases, the intensity and the full-width at half-maximum of the PL peak D increases (see Fig. 2(a)). In fact, the PL peak D originates from the residual acceptor transition in the nominally undoped GaAs SAQW, accompanied by LO-phonon emission. Note from Figs. 1 and 2(a) that the optical transition represented by the PL peak D goes in parallel with and in favor of the FES optical feature (see the arrows), thus indicating a strong correlation between the PL peak D and the FES. This result is consistent with the picture of residual acceptors in the GaAs SAQW region to which the photocreated hole is bound in order to ensure the optical observation of the FES. Further, the observation of the FES in optical spectra requires a strong overlap of electron and hole wave functions to provide effective electron–hole interaction. The strong overlap of electron and hole wave functions is provided by the hole localization, which arises from a hole bound to the ionized acceptor, in the case of high-quality n-doped GaAs=AlGaAs SAQWs. The radius of the Using the localized hole wave function is about 18 A. uncertainty relation this radius corresponds to a hole wave vector of about 3 × 106 cm−1 , which is of the order of the value required (kF = 1:46 × 106 cm−1 ) to give ecient recombination without wave vector restriction, for electrons in all states up to EF . As the temperature increases the width of the PL peak A becomes broader on the high-energy side while the intensity enhancement at EF is reduced, re ecting the change of the electron distribution according to the Fermi statistics. At temperatures above 70 K (see Figs. 2(a) and (b)), the enhancement of the PL peak A towards EF disappears because of the thermal broadening of the Fermi edge. This nding provides additional support for the observation of the FES optical feature in the PL spectra of the investigated sample and excludes the possibility that the high-
energy tail in the PL peak A comes from the recombination of electrons and holes involving higher energy subbands. Inspection of Figs. 2(a) and (b) shows the evolution of the optical feature associated to the FES. As the temperature increases, the FES optical feature becomes weaker and more quickly suppressed at intermediate optical excitation intensity (7:8 W=cm2 ) compared to the lower optical excitation intensity (0:4 W=cm2 ). Indeed, the permanence of the FES optical feature at a relatively high temperature is a characteristic of the sample W1506. This indicates a competition between two distinct radiative recombination mechanisms. At low temperature, the PL spectra are dominated by the k-nonconserving transitions involving the 2DEG and the holes bound to the ionized acceptors. Under low photoexcitation intensity (0:4 W=cm2 ) and at low temperature (10 K) there are few free holes in the valence band and the band-to-band transition is hardly observed. As the temperature increases (see Fig. 2(a)), the bound holes are thermalized to become free holes and thus band-to-band transition (k-conserving) develops. These two competing radiative mechanisms are strongly temperature dependent. Under intermediate photoexcitation intensity (7:8 W=cm2 ), however, a huge amount of photogenerated holes may be collected by the SAQW. Then, the excess holes eciently neutralize the ionized acceptors introduced by the residual doping, thus reducing the k-nonconserving transition. Besides, under intermediate optical excitation intensity, the residual bound holes may be thermalized to become free holes at lower temperatures. Finally, samples W1506 and W1413 exhibit similar optical excitation intensity and temperature dependence as far as the PL signature of the FES is concerned, though sample W1413 presents a slightly higher 2DEG density. In contrast, the PL peak D associated with residual acceptors inside the GaAs SAQW has not been observed in sample W1504 as it has been observed in samples W1506 and W1413. Furthermore, inspection of Fig. 4 shows that the PL peak A has no optical signature of the FES as observed in Figs. 2 and 3. Indeed, the data in Fig. 4 strongly supports the picture of the optical observation of the FES associated with the residual acceptors inside the SAQWs analyzed in this work.
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5. Conclusions In summary, the collective radiative recombination of the 2DEG with photogenerated holes presumably bound to ionized acceptors has been observed in two n-doped GaAs=Al0:35 Ga0:65 As SAQW samples (W1506 and W1413). The data indicate that in samples W1506 and W1413 residual acceptors are uniformly distributed all over the region around the GaAs SAQW. Even at low carrier densities (below 5 × 1011 cm−2 ), the optical signature of the Fermi-edge singularity in the W1506 and W1413 samples is clearly observed. At low temperatures the k-nonconserving process dominates, while at higher temperatures thermalization of the bound holes occurs and the k-conserving process develops. Due to the strong binding energy associated to the acceptor, the FES would be optically observed even at high temperatures. When the photoexcitation density is suciently high, the photogenerated excess holes outnumber the acceptors. Thus, the k-nonconserving channel is saturated, and the PL spectrum presents features of k-conserving electron–hole transitions. As a consequence, the observation of the optical feature associated to the FES is quenched. In striking contrast, no optical signature of the FES is observed in a GaAs SAQW with low density of residual acceptors (sample W1504). Finally, our results demonstrate that if enough acceptors are present in the GaAs SAQW the FES singularity at low carrier density can be successfully investigated using conventional PL spectroscopy. Acknowledgements We wish to thank Professor G. Weimann for providing the samples used in this work. Support from the
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Brazilian agencies FAPEMIG, FAP-DF, and CNPq is gratefully acknowledged. References [1] G.D. Mahan, Phys. Rev. B 21 (1980) 1421. [2] M.S. Skolnick, J.M. Rorison, K.J. Nash, D.J. Mowbray, P.R. Tapster, S.J. Bass, A.D. Pitt, Phys. Rev. Lett. 58 (1987) 2130. [3] J.M. Calleja, A.R. Goni, B.S. Dennis, J.S. Weiner, A. Pinczuk, S. Schmittrink, L.N. Pfei er, K.W. West, J.F. Muller, A.E. Ruckenstein, Solid State Commun. 79 (1991) 911. [4] M. Fritze, A. Kastalsky, J.E. Cunningham, W.H. Knox, R.N. Pathak, I.E. Peradis, Solid State Commun. 100 (1996) 497. [5] H.X. Li, Z.G. Wang, J.B. Liang, B. Xu, C. Jiang, Q. Gong, F.Q. Liu, W. Zhou, Solid State Commun. 106 (1998) 811. [6] Q.X. Zhao, P.O. Holtz, B. Monemar, E. Sorman, W.M. Chen, C. Hallin, M. Sundaram, J.L. Merz, A.C. Gossard, Phys. Rev. B 44 (1991) 3821. [7] S.A. Brown, J.F. Young, Z. Wasilewski, P.T. Coleridge, Phys. Rev. B 56 (1997) 3937. [8] W. Chen, M. Fritze, A.V. Nurmikko, J.M. Hong, L.L. Chang, Phys. Rev. B 43 (1991) 14 738. [9] V. Huard, R.T. Cox, K. Saminadayar, A. Arnoult, S. Tatarenko, Phys. Rev. Lett. 84 (2000) 187. [10] H. Burkhard, W. Schlapp, G. Weimann, Surf. Sci. 174 (1986) 382. [11] C. Delalande, G. Bastard, J. Orgonasi, J.A. Brum, H.W. Liu, M. Voos, Phys. Rev. Lett. 59 (1987) 2690. [12] F. Qu, P.C. Morais, IEEE J. Quantum Electron. QE-34 (1998) 1419. [13] C. Delalande, J. Orgonasi, M.H. Meynadier, J.A. Brum, G. Bastard, G. Weimann, W. Schlapp, Solid State Commun. 59 (1986) 613. [14] A.J.C. Cardoso, P.C. Morais, H.M. Cox, Appl. Phys. Lett. 68 (1996) 1105. [15] A.J.C. Cardoso, F. Qu, P.C. Morais, Phys. Rev. B 60 (1999) 4501. [16] A.S. Chaves, A.F.S. Penna, J.M. Worlock, G. Weimann, W. Schlapp, Surf. Sci. 170 (1986) 618. [17] F. Qu, P.C. Morais, J. Chem. Phys. 111 (1999) 8588.