- Email: [email protected]
GaAs interface
Microelectronic Engineering 51–52 (2000) 235–240 www.elsevier.nl / locate / mee
Observation of excitons formed by the holes confined at the Al 0.5 Ga 0.5 As / GaAs interface a, a a a a b M. Ciorga *, M. Kubisa , K. Ryczko , L. Bryja , J. Misiewicz , O.P. Hansen a
~ Wyspianskiego ´ 27, 50 -370 Wrocl«aw, Poland Institute of Physics, Wrocl«aw University of Technology, Wybrzeze b Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Abstract The radiative recombination in the Be-doped single heterojunction Al 0.5 Ga 0.5 As / GaAs, so-called H-band, has been studied by photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy. Magnetophotoluminescence measurements were also performed. The H-band was interpreted as the recombination of holes confined on the ground level in the quantum well at the interface and electrons from GaAs conduction band. The carriers involved in the recombination originate from 3D excitons excited in the flat band region of GaAs, which diffuse towards the interface. In the PLE spectra two new lines were observed. We interpret them in means of short life-time excitons composed of a confined 2D hole and a free electron, which are excited near the interface. 2000 Elsevier Science B.V. All rights reserved. Keywords: Exciton; H-band; Two-dimensional hole gas; AlGaAs / GaAs interface
1. Introduction A great deal of effort has recently been focused on the radiative recombination processes associated with the Al x Ga 12x As / GaAs heterojunction interface. The line on the low energy side of the GaAs exciton in PL spectra from single heterojunction, so called H-band, was first observed by Yuan et al. [1]. They attributed the H-band emission to 2D electrons (holes, in p-type samples) that tunnel from the triangular well at the interface and recombine with holes (electrons) in the flat band region. Most later papers concerned n-type samples with 2D electrons recombining with free holes [2–5]. Some papers [2,3,6] have agreed with the Yuan explanation of the H-band peak, but other authors concluded that recombining electrons and holes are bound by Coulomb interaction [5,7]. In this paper we present results of experimental and theoretical studies which shed new light on the origin of the H-band emission phenomenon.
*Corresponding author. Tel.: 1 48-71-320-2358; fax: 1 48-71-328-3696. E-mail address: [email protected] (M. Ciorga) 0167-9317 / 00 / $ – see front matter PII: S0167-9317( 99 )00483-9
2000 Elsevier Science B.V. All rights reserved.
236
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
2. Experiment The studied sample was obtained by the molecular-beam epitaxy growth on a [001] semi-insulating substrate, using the following sequence of layers: 1 mm GaAs, 7 nm undoped Al 0.5 Ga 0.5 As spacer, 50 nm Be-doped 1 3 10 18 cm 23 Al 0.5 Ga 0.5 As and 5 nm Be-doped 2 3 10 18 cm 23 GaAs cap. The wafers were originally grown in order to investigate magnetotransport properties [8]. All measurements were carried out at liquid helium temperatures down to 2 K in magnetic fields up to 5 T, applied both perpendicular (B'z) and parallel (Biz) to the growth axis. In the former case both s 1 and s 2 polarizations of emitted light were analyzed, while in the latter case s and p light polarizations were studied. As an excitation source, we used an Ar 1 -ion laser (PL) and a tunable dye laser with Styryl 9M dye (PL and PLE) pumped by the argon laser. A power density of the excitation beam on the sample was approximately 50 mW/ cm 2 . Luminescence was analyzed by a 2-m double grating monochromator with the photomultiplier as a detector.
3. Results and discussion The PL spectrum of the sample is shown in the inset of Fig. 1. The emission lines with energies close to 1.515 eV were identified as free excitons (X), neutral donor-bound excitons (D 0 X) and neutral acceptor-bound excitons (A0 X) of GaAs. Similarly, the donor-carbon acceptor (D-CAs ) and the free electron-acceptor (e-CAs ) lines with energies close to 1.491 eV originate from the GaAs layer. The peak H at the energy of 1.5033 eV was assigned to the H-band emission. We found that its position depends on temperature and excitation intensity, but not so significantly as reported by other authors [1,3,5]. Fig. 1 also shows the PLE spectra: one measured with the detector-hold position on the low energy slope of the H-band and the second obtained for detector-hold position at 1.4905 eV — close to the D-CAs line. In the former case we observe a single strong peak at the energy of 1.5153 eV of the bulk GaAs exciton, which supports the interpretation that electrons and holes involved in the H-band emission arise mainly from free GaAs excitons. In the PLE spectrum obtained in the latter case, apart from the weak free exciton X line at 1.5153 eV, we observe two stronger peaks with energies of 1.5096 eV (A) and of 1.5123 eV (B). They are located below the lowest GaAs exciton line A0 X (1.5127 eV) and above the H-band position. We attribute lines A and B to the excitation of interface excitons, first proposed by Balslev [9]. Our interpretation of PLE phenomena in the region of H-band emission is based on theoretical results presented in Ref. [10]. We performed detailed calculations of the potential distribution and hole energy levels in a p-doped Ga 12x Al x As / GaAs heterojunction, taking into account exchange–correlation effects. We also showed that holes from excited 2D levels can bind free electrons and create interface excitons. These excitons have, however, a quasi-stationary character: the interface electric field repels electrons from the junction and destroys the electron–hole coupling. For this reason, they can be observed in a PLE (quasi-absorption) experiment, but they do not contribute to a PL emission. Calculated interface exciton energies allowed us to attribute line A of Fig. 1 as the HH2 excitonic transition and line B as the LH1 (or HH3) excitonic transition. An excitonic state with the hole from the ground HH1 level cannot be formed because of the phase space filling effect. On the basis of our theoretical results we also proposed an improved interpretation of the H-band emission [10]. As demonstrated in Refs. [5,7,11], bulk excitons, which are photo-created in the
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
237
Fig. 1. Low temperature PL spectrum from studied sample (inset) and PLE spectra obtained with a detection energy slightly below the energy of H-band emission (Edet1 ) and close to the D-CAs line (Edet2 ). For details, see text.
flat-band region of GaAs layer, drift toward the interface and recombine, giving rise to line H. However, they recombine as free particles, because the excitonic binding is destroyed by the interface electric field. In p-doped heterostructures, free electrons recombine with 2D holes from the ground HH1 level, since the occupation of excited hole levels is substantially smaller even under conditions of light excitation. Comparing the measured H-band position with the calculated potential distribution and the HH1 level energy, we conclude that the recombination occurs at a distance of about 6 nm from the junction. On the other hand, the valence band electrons excited by light from 2D hole levels (with the exception of HH1 electrons) form short-living interface exciton states. Electrons in these states are situated about 35 nm from the interface and after some picoseconds escape towards the flat band region. They are trapped by ionized donors and recombine contributing to the D-CAs emission line of PL spectrum. Because of the interface electric field, these electrons cannot contribute to the H-band emission, which takes place closer to the interface. Consequently, no interface exciton lines are observed in the PLE spectrum with the detector-hold position at the H-band. In a magnetic field perpendicular to the interface the H splits and shows a pronounced shift to
238
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
higher energies. Fig. 2 shows PL spectra of our sample measured for different magnetic fields in the s 2 light polarization. At a field of 4 T a new line appears, located 5 meV above the main H peak. The energies of the peak positions as a function of magnetic field are shown in Fig. 3 (open dots). This figure also presents the energies of H emission measured in the s 1 polarization for Biz (squares) and the results of measurements in B'z configuration (closed dots). In the latter case no splitting is observed in any of the emitted light polarization (s and p ). The energetic shift of the H in the B'z configuration (3.5 meV in B 5 5 T) is comparable to the shift of a free GaAs electron in the first Landau level.This confirms our interpretation of the H-band line as originating from the recombination of free GaAs electrons with 2D holes confined at the interface. We attribute the lower energy line observed in the s 2 polarization and the line observed in the s 1 polarization as originating from transitions to the spin split lowest Landau level of the HH1 hole sub-band. Ekenberg and Altarelli [12]
Fig. 2. PL spectra obtained in different values of magnetic field applied perpendicular to the interface (parallel to the axis growth Biz) in s 2 polarization of emitted light.
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
239
Fig. 3. Energetic shift of the H-band line in the magnetic field. Squares and circles represent experimental points. Solid lines represent the shift of the H-band observed in the B'z added to the shift of the spin–split lowest hole Landau level calculated by Ekenberg and Altarelli [12].
calculated the magnetic field dependence of 2D hole levels in a p-doped Ga 12x Al x As / GaAs heterostructure. We used their results and added the shift of the H-band observed in the B'z configuration to calculated shifts of the spin–split lowest hole Landau level (solid lines shown in Fig. 3). A good agreement with the measured positions of two lower energy components of the H-band confirms our interpretation. The origin of the higher energy line observed in the s 2 polarization is not clear. A similar line was reported by Ossau et al. [6] and attributed to the recombination of a free electron with a 2D hole from an LH1 sub-band. Our calculations [10] show, however, that the energetic distance between the ground HH1 sub-band and excited hole sub-bands at B 5 0 ( $ 18 meV) is too large to confirm this interpretation.
4. Summary In this paper we discuss the observation of excitons in the 2D hole gas in a p-type Al 0.5 Ga 0.5 As / GaAs interface. We showed that the H-band observed in low-temperature PL spectra is the effect of recombination of free GaAs electrons with 2D holes confined on the HH1 level of a triangular quantum well. Recombining carriers arise from bulk excitons photocreated in the flat-band region of GaAs, which drift towards the interface, where they are destroyed by the electric field. However, the holes confined on excited 2D levels can bind free electrons and form so-called interface excitons. Because of the quasi-stationary character of such excitons we observe them only in PLE experiment, with a detection energy slightly below the energy of the D-CAs emission line.
240
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
Acknowledgements The MBE-growth was carried out by C. B. Soerensen at the III–V Nano-Lab in Copenhagen. References [1] Y.R. Yuan, M.A.A. Pudensi, G.A. Vawter, J.L. Merz, New photoluminescence effects of carrier confinement at an AlGaAs / GaAs heterojunction interface, J Appl. Phys. 58 (1985) 397–403. [2] I.V. Kukushkin, K.v. Klitzing, K. Ploog, Optical spectroscopy of two-dimensional electrons in GaAs–Alx Ga 12x Asx single heterojunction, Phys. Rev. B 37 (1988) 8509–8512. [3] D.Y. Kim, T. Kang, T.W. Kim, Electric sub-band studies at an alGaAs / GaAs heterointerface by photoluminescence, Thin Solid Films 261 (1995) 168–172. [4] Q.X. Zhao, J.P. Bergman, P.O. Holtz, B. Monemar, C. Hallin, M. Sundaram, J.L. Merz, A.C. Gossard, Radiative recombination in doped AlGaAs / GaAs heterostructures, Semicond. Sci. Technol. 5 (1990) 884–889. [5] D.C. Reynolds, D.C. Look, B. Jogai, P.W. Yu, K. Evans, C.E. Stutz, L. Radomsky, Radiative recombination at the Al x Ga 12x As–GaAs heterostructures interface by two-dimensional excitons, Phys. Rev. B 50 (1994) 7461–7466. [6] W. Ossau, E. Bangert, G. Weimann, Radiative recombination of a 3D-electron with a 2D-hole in p-type GaAs / (GaAl)As heterojunctions, Solid State Commun. 64 (1987) 711–715. [7] G.D. Gilland, D.J. Wolford, T.F. Kuech, J.A. Bradley, Luminescence kinetics of intrinsic excitonic states quantummechanically bound near high-quality (n-type GaAs) /(p-type Al x Ga 12x As) heterointerfaces, Phys. Rev. B 49 (1994) 8113–8125. [8] O.P. Hansen, J.S. Olsen, W. Kraak, B. Saffian, Minina, A.M. Savin, Effect of uniaxial compression on quantum Hall plateaus and Shubnikow-de Haas oscillations in p-type GaAs /Al x Ga 12x As heterostructures, Phys. Rev. B 54 (1996) 1533–1536. [9] I. Balslev, Recombination via two-dimensional excitons in GaAs–(AlGa)As heterojunctions, Semicond. Sci. Technol. 2 (1987) 437–441. [10] M. Ciorga, K. Ryczko, M. Kubisa, L. Bryja, J. Misiewicz, O.P. Hansen, Observation of quasistationary excitons in p-doped Ga 12x Al x As / GaAs single heterojunctions (submitted). [11] J.X. Shen, Y. Oka, W. Ossau, G. Landwehr, K.-J. Friedland, R. Hey, K. Ploog, G. Weimann, Vertical transport of photo-excited carriers for excitonic recombinations in modulation doped GaAs / Ga 12x Alx As heterojunctions, Solid State Commun. 106 (1998) 495–499. [12] U. Ekenberg, M. Altarelli, Subbands and Landau levels in the two-dimensional hole gas at the GaAs–Alx Ga 12x As interface, Phys. Rev. B 32 (1985) 3712–3722.
Observation of excitons formed by the holes confined at the Al 0.5 Ga 0.5 As / GaAs interface a, a a a a b M. Ciorga *, M. Kubisa , K. Ryczko , L. Bryja , J. Misiewicz , O.P. Hansen a
~ Wyspianskiego ´ 27, 50 -370 Wrocl«aw, Poland Institute of Physics, Wrocl«aw University of Technology, Wybrzeze b Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Abstract The radiative recombination in the Be-doped single heterojunction Al 0.5 Ga 0.5 As / GaAs, so-called H-band, has been studied by photoluminescence (PL) and photoluminescence excitation (PLE) spectroscopy. Magnetophotoluminescence measurements were also performed. The H-band was interpreted as the recombination of holes confined on the ground level in the quantum well at the interface and electrons from GaAs conduction band. The carriers involved in the recombination originate from 3D excitons excited in the flat band region of GaAs, which diffuse towards the interface. In the PLE spectra two new lines were observed. We interpret them in means of short life-time excitons composed of a confined 2D hole and a free electron, which are excited near the interface. 2000 Elsevier Science B.V. All rights reserved. Keywords: Exciton; H-band; Two-dimensional hole gas; AlGaAs / GaAs interface
1. Introduction A great deal of effort has recently been focused on the radiative recombination processes associated with the Al x Ga 12x As / GaAs heterojunction interface. The line on the low energy side of the GaAs exciton in PL spectra from single heterojunction, so called H-band, was first observed by Yuan et al. [1]. They attributed the H-band emission to 2D electrons (holes, in p-type samples) that tunnel from the triangular well at the interface and recombine with holes (electrons) in the flat band region. Most later papers concerned n-type samples with 2D electrons recombining with free holes [2–5]. Some papers [2,3,6] have agreed with the Yuan explanation of the H-band peak, but other authors concluded that recombining electrons and holes are bound by Coulomb interaction [5,7]. In this paper we present results of experimental and theoretical studies which shed new light on the origin of the H-band emission phenomenon.
*Corresponding author. Tel.: 1 48-71-320-2358; fax: 1 48-71-328-3696. E-mail address: [email protected] (M. Ciorga) 0167-9317 / 00 / $ – see front matter PII: S0167-9317( 99 )00483-9
2000 Elsevier Science B.V. All rights reserved.
236
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
2. Experiment The studied sample was obtained by the molecular-beam epitaxy growth on a [001] semi-insulating substrate, using the following sequence of layers: 1 mm GaAs, 7 nm undoped Al 0.5 Ga 0.5 As spacer, 50 nm Be-doped 1 3 10 18 cm 23 Al 0.5 Ga 0.5 As and 5 nm Be-doped 2 3 10 18 cm 23 GaAs cap. The wafers were originally grown in order to investigate magnetotransport properties [8]. All measurements were carried out at liquid helium temperatures down to 2 K in magnetic fields up to 5 T, applied both perpendicular (B'z) and parallel (Biz) to the growth axis. In the former case both s 1 and s 2 polarizations of emitted light were analyzed, while in the latter case s and p light polarizations were studied. As an excitation source, we used an Ar 1 -ion laser (PL) and a tunable dye laser with Styryl 9M dye (PL and PLE) pumped by the argon laser. A power density of the excitation beam on the sample was approximately 50 mW/ cm 2 . Luminescence was analyzed by a 2-m double grating monochromator with the photomultiplier as a detector.
3. Results and discussion The PL spectrum of the sample is shown in the inset of Fig. 1. The emission lines with energies close to 1.515 eV were identified as free excitons (X), neutral donor-bound excitons (D 0 X) and neutral acceptor-bound excitons (A0 X) of GaAs. Similarly, the donor-carbon acceptor (D-CAs ) and the free electron-acceptor (e-CAs ) lines with energies close to 1.491 eV originate from the GaAs layer. The peak H at the energy of 1.5033 eV was assigned to the H-band emission. We found that its position depends on temperature and excitation intensity, but not so significantly as reported by other authors [1,3,5]. Fig. 1 also shows the PLE spectra: one measured with the detector-hold position on the low energy slope of the H-band and the second obtained for detector-hold position at 1.4905 eV — close to the D-CAs line. In the former case we observe a single strong peak at the energy of 1.5153 eV of the bulk GaAs exciton, which supports the interpretation that electrons and holes involved in the H-band emission arise mainly from free GaAs excitons. In the PLE spectrum obtained in the latter case, apart from the weak free exciton X line at 1.5153 eV, we observe two stronger peaks with energies of 1.5096 eV (A) and of 1.5123 eV (B). They are located below the lowest GaAs exciton line A0 X (1.5127 eV) and above the H-band position. We attribute lines A and B to the excitation of interface excitons, first proposed by Balslev [9]. Our interpretation of PLE phenomena in the region of H-band emission is based on theoretical results presented in Ref. [10]. We performed detailed calculations of the potential distribution and hole energy levels in a p-doped Ga 12x Al x As / GaAs heterojunction, taking into account exchange–correlation effects. We also showed that holes from excited 2D levels can bind free electrons and create interface excitons. These excitons have, however, a quasi-stationary character: the interface electric field repels electrons from the junction and destroys the electron–hole coupling. For this reason, they can be observed in a PLE (quasi-absorption) experiment, but they do not contribute to a PL emission. Calculated interface exciton energies allowed us to attribute line A of Fig. 1 as the HH2 excitonic transition and line B as the LH1 (or HH3) excitonic transition. An excitonic state with the hole from the ground HH1 level cannot be formed because of the phase space filling effect. On the basis of our theoretical results we also proposed an improved interpretation of the H-band emission [10]. As demonstrated in Refs. [5,7,11], bulk excitons, which are photo-created in the
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
237
Fig. 1. Low temperature PL spectrum from studied sample (inset) and PLE spectra obtained with a detection energy slightly below the energy of H-band emission (Edet1 ) and close to the D-CAs line (Edet2 ). For details, see text.
flat-band region of GaAs layer, drift toward the interface and recombine, giving rise to line H. However, they recombine as free particles, because the excitonic binding is destroyed by the interface electric field. In p-doped heterostructures, free electrons recombine with 2D holes from the ground HH1 level, since the occupation of excited hole levels is substantially smaller even under conditions of light excitation. Comparing the measured H-band position with the calculated potential distribution and the HH1 level energy, we conclude that the recombination occurs at a distance of about 6 nm from the junction. On the other hand, the valence band electrons excited by light from 2D hole levels (with the exception of HH1 electrons) form short-living interface exciton states. Electrons in these states are situated about 35 nm from the interface and after some picoseconds escape towards the flat band region. They are trapped by ionized donors and recombine contributing to the D-CAs emission line of PL spectrum. Because of the interface electric field, these electrons cannot contribute to the H-band emission, which takes place closer to the interface. Consequently, no interface exciton lines are observed in the PLE spectrum with the detector-hold position at the H-band. In a magnetic field perpendicular to the interface the H splits and shows a pronounced shift to
238
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
higher energies. Fig. 2 shows PL spectra of our sample measured for different magnetic fields in the s 2 light polarization. At a field of 4 T a new line appears, located 5 meV above the main H peak. The energies of the peak positions as a function of magnetic field are shown in Fig. 3 (open dots). This figure also presents the energies of H emission measured in the s 1 polarization for Biz (squares) and the results of measurements in B'z configuration (closed dots). In the latter case no splitting is observed in any of the emitted light polarization (s and p ). The energetic shift of the H in the B'z configuration (3.5 meV in B 5 5 T) is comparable to the shift of a free GaAs electron in the first Landau level.This confirms our interpretation of the H-band line as originating from the recombination of free GaAs electrons with 2D holes confined at the interface. We attribute the lower energy line observed in the s 2 polarization and the line observed in the s 1 polarization as originating from transitions to the spin split lowest Landau level of the HH1 hole sub-band. Ekenberg and Altarelli [12]
Fig. 2. PL spectra obtained in different values of magnetic field applied perpendicular to the interface (parallel to the axis growth Biz) in s 2 polarization of emitted light.
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
239
Fig. 3. Energetic shift of the H-band line in the magnetic field. Squares and circles represent experimental points. Solid lines represent the shift of the H-band observed in the B'z added to the shift of the spin–split lowest hole Landau level calculated by Ekenberg and Altarelli [12].
calculated the magnetic field dependence of 2D hole levels in a p-doped Ga 12x Al x As / GaAs heterostructure. We used their results and added the shift of the H-band observed in the B'z configuration to calculated shifts of the spin–split lowest hole Landau level (solid lines shown in Fig. 3). A good agreement with the measured positions of two lower energy components of the H-band confirms our interpretation. The origin of the higher energy line observed in the s 2 polarization is not clear. A similar line was reported by Ossau et al. [6] and attributed to the recombination of a free electron with a 2D hole from an LH1 sub-band. Our calculations [10] show, however, that the energetic distance between the ground HH1 sub-band and excited hole sub-bands at B 5 0 ( $ 18 meV) is too large to confirm this interpretation.
4. Summary In this paper we discuss the observation of excitons in the 2D hole gas in a p-type Al 0.5 Ga 0.5 As / GaAs interface. We showed that the H-band observed in low-temperature PL spectra is the effect of recombination of free GaAs electrons with 2D holes confined on the HH1 level of a triangular quantum well. Recombining carriers arise from bulk excitons photocreated in the flat-band region of GaAs, which drift towards the interface, where they are destroyed by the electric field. However, the holes confined on excited 2D levels can bind free electrons and form so-called interface excitons. Because of the quasi-stationary character of such excitons we observe them only in PLE experiment, with a detection energy slightly below the energy of the D-CAs emission line.
240
M. Ciorga et al. / Microelectronic Engineering 51 – 52 (2000) 235 – 240
Acknowledgements The MBE-growth was carried out by C. B. Soerensen at the III–V Nano-Lab in Copenhagen. References [1] Y.R. Yuan, M.A.A. Pudensi, G.A. Vawter, J.L. Merz, New photoluminescence effects of carrier confinement at an AlGaAs / GaAs heterojunction interface, J Appl. Phys. 58 (1985) 397–403. [2] I.V. Kukushkin, K.v. Klitzing, K. Ploog, Optical spectroscopy of two-dimensional electrons in GaAs–Alx Ga 12x Asx single heterojunction, Phys. Rev. B 37 (1988) 8509–8512. [3] D.Y. Kim, T. Kang, T.W. Kim, Electric sub-band studies at an alGaAs / GaAs heterointerface by photoluminescence, Thin Solid Films 261 (1995) 168–172. [4] Q.X. Zhao, J.P. Bergman, P.O. Holtz, B. Monemar, C. Hallin, M. Sundaram, J.L. Merz, A.C. Gossard, Radiative recombination in doped AlGaAs / GaAs heterostructures, Semicond. Sci. Technol. 5 (1990) 884–889. [5] D.C. Reynolds, D.C. Look, B. Jogai, P.W. Yu, K. Evans, C.E. Stutz, L. Radomsky, Radiative recombination at the Al x Ga 12x As–GaAs heterostructures interface by two-dimensional excitons, Phys. Rev. B 50 (1994) 7461–7466. [6] W. Ossau, E. Bangert, G. Weimann, Radiative recombination of a 3D-electron with a 2D-hole in p-type GaAs / (GaAl)As heterojunctions, Solid State Commun. 64 (1987) 711–715. [7] G.D. Gilland, D.J. Wolford, T.F. Kuech, J.A. Bradley, Luminescence kinetics of intrinsic excitonic states quantummechanically bound near high-quality (n-type GaAs) /(p-type Al x Ga 12x As) heterointerfaces, Phys. Rev. B 49 (1994) 8113–8125. [8] O.P. Hansen, J.S. Olsen, W. Kraak, B. Saffian, Minina, A.M. Savin, Effect of uniaxial compression on quantum Hall plateaus and Shubnikow-de Haas oscillations in p-type GaAs /Al x Ga 12x As heterostructures, Phys. Rev. B 54 (1996) 1533–1536. [9] I. Balslev, Recombination via two-dimensional excitons in GaAs–(AlGa)As heterojunctions, Semicond. Sci. Technol. 2 (1987) 437–441. [10] M. Ciorga, K. Ryczko, M. Kubisa, L. Bryja, J. Misiewicz, O.P. Hansen, Observation of quasistationary excitons in p-doped Ga 12x Al x As / GaAs single heterojunctions (submitted). [11] J.X. Shen, Y. Oka, W. Ossau, G. Landwehr, K.-J. Friedland, R. Hey, K. Ploog, G. Weimann, Vertical transport of photo-excited carriers for excitonic recombinations in modulation doped GaAs / Ga 12x Alx As heterojunctions, Solid State Commun. 106 (1998) 495–499. [12] U. Ekenberg, M. Altarelli, Subbands and Landau levels in the two-dimensional hole gas at the GaAs–Alx Ga 12x As interface, Phys. Rev. B 32 (1985) 3712–3722.