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AlGaAs asymmetric quantum wells
Superlattices and Microstructures, Vol. 21, No. 4, 1997
Photoreflectance measurements in GaAs/AlGaAs asymmetric quantum wells M. A. G. Soler, J. Depeyrot, P. C. Morais Departamento de F´ısica da Universidade de Bras´ılia, Caixa Postal 04629, 70910-900 Bras´ılia, DF, Brazil
J. A. N. T. Soares, L. M. R. Scolfaro, E. C. F. da Silva, R. Enderlein Instituto de F´ısica da Universidade de S˜ao Paulo, Caixa Postal 66318, 05315-970 S˜ao Paulo, SP, Brazil
G. Weimann, G. Trankle Walter Schottky Institut, Technische Universit¨at, 85748 M¨unchen, Germany
(Received 15 July 1996) In this work we investigated the optical control of the bidimensional electron gas density in a single asymmetric quantum well using, for the first time, photoreflectance. We performed our measurements at 80 and 300 K as a function of the power density of the pump beam. Under strong illumination, the bidimensional electron gas density is washed out of the quantum well and under a dark condition, it reaches its maximum value. The variation of the optical transitions observed in our photoreflectance spectra was related to the induced changes of the band profile in between these two limiting cases. c 1997 Academic Press Limited
1. Introduction Single asymmetric quantum wells (AQWs) have received a great deal of interest in recent years due to their technological applications and as a valuable system to study fundamental properties of a two-dimensional electron gas (2DEG) [1, 2]. In such structures carriers are released from intentionally doped impurities in the wider gap layer diffusing into the narrower gap layer, where the 2DEG is formed. The spacer—an undoped wide gap layer—is grown in between the quantum well and the impurities sites thus offering a barrier through which carriers have to tunnel in their pathway towards the AQW. Optical control of the 2DEG density in modulation-doped GaAs/AlGaAs [3, 4] and InGaAs/InP [5] single AQWs has been reported by several authors using different experimental techniques. According to the authors, under strong illumination the 2DEG is washed out from the quantum well. On the other hand, the 2DEG reaches its maximum value under dark conditions. In between these two limiting conditions the 2DEG density may be controlled by the optical excitation intensity. A blue shift in photoluminescence (PL) measurements under strong illumination has been reported [3, 5] as a signature of the optical control of the 2DEG in single AQWs. This variation of the band-to-band recombination energy has been attributed to both the reduction of the band bending in the AQW and the band gap renormalization which results from carrier exchange and correlation effects. In this work, photoreflectance (PR) measurements, performed at 80 and 300 K, have been used to investigate .
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0749–6036/97/040581 + 05 $25.00/0
sm960206
c 1997 Academic Press Limited
582
Superlattices and Microstructures, Vol. 21, No. 4, 1997
the optical control of the 2DEG density in single AQWs of GaAs/AlGaAs:Si, grown by MBE. However, it is important to note that the PR signal is proportional to the optical absorption in the structure while the PL spectra are strongly dependent on the radiative and non-radiative lifetimes of the carriers. Our attention is focused on the changes of the band profile at the barrier AQW region which goes from a flat condition under strong excitation, to a triangular potential barrier under dark condition.
2. Experiments ˚ thick GaAs quantum The sample used in the present experiments is a one-side-modulation-doped 166 A well clad between Ga0.65 Al0.35 As barriers. The actual structure consists of a semi-insulating GaAs substrate ˚ GaAs quantum wells within covered by a buffer layer of intrinsic GaAs, followed by several narrow (35 A) ˚ ˚ of Ga0.65 Al0.35 As and the 166 A-thick GaAs quantum well, all these layers being nominally a layer (100 A) ˚ ˚ doped. The quantum well was topped by a 350 A-thick Ga0.65 Al0.35 As undoped spacer followed by a 380 A ˚ of the cap layer grown on top of Si-doped (Nd = 1.8 × 1018 cm−3 ) Ga0.65 Al0.35 As layer. In addition, 100 A the overall structure were removed to decrease the optical absorption. At the temperature of 80 K, the carrier density in the quantum well, measured by Shubnikov–de Haas experiments, is about 2.5 × 1011 cm−2 and the carrier mobility is about 7.4 × 104 cm2 Vs−1 . The PR spectra were taken by a conventional PR apparatus using the 488 nm line of an Argon laser with a maximum power output of 26 mW, giving a maximum power density on the sample of about 8 W cm−2 . The chopper frequency was fixed at 340 Hz. The measured quantity was the ratio 1R/R, where 1R is the change in the reflection coefficient associated with the modulation by the laser radiation and R is the reflection coefficient.
3. Results and discussions We have recorded PR spectra for various values of the power density P of the pump beam. Typical spectra recorded at 80 K are displayed in Fig. 1. As it can be seen, at lower power density our spectra exhibit two equally strong structures (indicated by arrows) located at energies about 1.504 eV and 1.508 eV. We assign the lower energy structure (marked a) to the AQW fundamental optical transition which corresponds to the radiative recombination between the first heavy-hole subband and the first electron subband (E1 -HH1 ). The structure b is associated with the optical transition from the first light-hole level to the first electron level (E1 -LH1 ). Let us now consider the intensity of the AQW PR structures of Fig. 1. As the power density P of the pump beam increases, the intensity of the E1 -HH1 transition increases while the intensity of the E1 -LH1 transition decreases. For the maximum value of P used in our experiments, equal to 8 W cm−2 , we only observed the E1 -HH1 transition. It is well known that the M matrix element for an interband optical transition is proportional to the overlap of the electron and hole envelope functions [6]. Moreover, in the case of a symmetric quantum well corresponding to flat-band conditions, the E1 -HH1 transition is approximately three times more intense than the E1 -LH1 . Therefore the variations of the intensities of the observed transitions with the power density can be qualitatively understood from 1R/R ∼ |M|2 [7]. As already mentioned, under dark conditions the band profile at the well region is a triangular potential. At low power density the quantum well remains strongly asymmetric. Thus the band bending in the well, and consequently the electric field existing in the well, induces a spatial shift of the carriers envelope functions, along or opposite to the field direction for the holes or for the electrons, respectively [8]. Furthermore, because of their larger mass the heavy-holes are more strongly affected by the field than the light-holes. As a consequence, the overlap of the envelope functions of electrons and light-holes does become of the same .
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Superlattices and Microstructures, Vol. 21, No. 4, 1997
583
–2
8 W cm 8 × 10–1 W cm–2 8 × 10–2 W cm–2 8 × 10–3 W cm–2
T = 80 K a
∆R/R (a. u.)
a × 10 b
a
× 10 b
a × 10
1.49
1.50
1.51
1.52
Energy (eV) Fig. 1. Photoreflectance spectra recorded at 80 K for selected values of power density of pump beam (arrows indicate the transition energies). .
.
E1
HH1 LH1
Strong excitation
E1
HH1 LH1
Dark condition
Fig. 2. Schematic AQW bands profile in the dark (on the right) and under strong illumination (on the left). .
.
order of magnitude as that of electrons and heavy-holes (see Fig. 2). Then, the E1 -LH1 optical transition starts to compete with the E1 -HH1 transition as can be seen in our spectra. When we illuminate the sample with photons whose energy overcomes the barrier energy gap, the photogenerated carriers are separated by the built-in electric field, the electrons being recaptured by the doped region in the barrier and the holes moving into the AQW where they radiatively recombine with the electrons. Then, as the power density of the pump beam increases, the 2DEG density decreases which leads to a reduced band bending in the AQW. Simultaneously, the spatial shift of the carriers envelope function is also reduced and the ratio of the optical matrix elements (E1 -HH1 )/(E1 -LH1 ) transition increases. The E1 -LH1 transition becomes less intense and, for P = 0.8 W cm−2 , vanishes completely as can be seen in Fig. 1. Moreover, when the power density of the pump beam is increased over four orders of magnitude, the observed transitions are slightly shifted towards higher energies. Indeed as the electron concentration decreases, the recombination energies increase because of both the upwards shifts of electron and hole subband levels
584
Superlattices and Microstructures, Vol. 21, No. 4, 1997 Table 1: Calculated band bending V of the AQW, recombination energy of the AQW fundamental transition Er and energy shift 1 between the light- and heavy-holes for various carrier densities n s . .
.
n s (cm−2 ) 2.5 × 1011 1.9 × 1011 1010 109
V (meV) 36 29 20 1.4
1 (meV)
Er (eV) 1.527 1.527 1.526 1.526
8.7 8.5 7.9 7.9
and the reduction of the band gap renormalization. The measured blue-shift is about 4 meV for the E1 -HH1 transition. This value is in good agreement with the one obtained from PL experiments by Chaves et al. for a similar sample in the same range of power density [3]. Our qualitative interpretations are strongly supported by self-consistent calculations which were carried out to determine the subband structure of our GaAs/AlGaAs:Si AQW. The confined states for the conduction band quantum well was calculated by numerically solving the Schr¨odinger and Poisson equations for the onedimensional motion parallel to the growth direction, in the effective mass approximation [9, 10]. Exchangecorrelation effects were taken into account within the local density approximation. The confined energy subbands for the holes were calculated by using the electrostatic potential obtained in the self-consistent calculations for electrons as an input. The values used for the effective mass of electrons, heavy- and lightholes were 0.067m 0 , 0.4m 0 and 0.087m 0 respectively, m 0 being the free electron mass [11]. The 60–40% rule was adopted for the conduction-to-valence band discontinuities. Table 1 gives the calculated values of the recombination energy Er of the E1 -HH1 transition, using the 1.507 eV value for the GaAs bandgap at 80 K, for various values of the carrier density n s in the quantum well. The transition energy has been calculated assuming that the transition occurs at k⊥ = 0 where k⊥ is the in-plane wave vector of the carrier which is assumed to be conserved. The energy difference between the value obtained for n s = 2.5 × 1011 cm−2 and the measured value at low power density is equal to 23 meV. However, it is important to bear in mind that our calculations do not include the reduction of the recombination energy due to both the bandgap renormalization and excitonic effects. The reduction value induced by the bandgap renormalization has been discussed by Delalande et al. [12] for ˚ various carrier concentrations. In the case of a one-side 150 A-thick modulation doped quantum well, it varies approximately from 10 to 20 meV when the carrier density goes from 1010 to 4 × 1011 cm−2 . Although the excitonic behaviour of optical transitions is characteristic of undoped quantum wells, it has been observed in doped quantum wells [12]. Then, taking into account the heavy-hole exciton binding energy, which in our case can be evaluated to be of the order of 8 meV [13], one can account for the difference between the calculated and measured results. Table 1 also gives the energy shift between the light- and heavy-holes levels. The calculated value for n s = 2.5 × 1011 cm−2 is equal to 8.7 meV which gives a difference of 4.7 meV with the measured one. It is probably due to both the value of the light-hole exciton binding energy, which is about 2 meV larger than the heavy-hole binding energy, and the approximations used in our theoretical approach of the valence subbands. Indeed, we do not take into account the coupling between the light- and heavy-holes states and we assume that the potential drop along the well has the same value as that obtained for the electrons. Moreover, we calculated the recombination energy for k⊥ = 0 which is not exactly true, since the Fermi energy is above the E1 electron level for such a value of carrier density. Therefore the energy shift between the light- and heavy-holes levels should be smaller than the value found in our calculations. Comparing the variation of the calculated and measured values of the recombination energies of the observed transitions, it is clear that the maximum power density of the pump beam used in our experiments .
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Superlattices and Microstructures, Vol. 21, No. 4, 1997
585
is not sufficient to completely wash out the 2DEG existing in the quantum well, which means we do not rise the flat-band conditions. Indeed the expected blue-shift deduced from our calculations between the low excitation intensity case and the flat-band one would be about 15 meV, and the measured one is equal to 4 meV. Moreover, variation of the order 11 meV has been measured in similar samples [3]. Nevertheless this level of excitation intensity is high enough to decrease the optical matrix element of the E1 -LH1 transition until vanishing. .
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4. Conclusion We have recorded PR spectra of GaAs/AlGaAs:Si AQW for various values of the power density of the pump beam. When the power density is increased over four orders of magnitude, we measured a blue shift of the recombination energy associated to the fundamental AQW transition equal to 4 meV, a value which is in good agreement with reported results. For the first time PR experiments provide evidence of the optical control of the 2DEG density in AQW. Our theoretical results of subband calculations are in reasonably good agreement with the measured ones and show that, even in doped structures, the observed transitions can be due to excitonic recombinations rather than band-to-band ones.
References .
[1] }C. Delalande, J. Orgonasi, J. A. Brum, G. Bastard, M. Voos, G. Weimann, and W. Schlapp, Appl. Phys. Lett. 51, 1346 (1987). } Burkbard, W. Schlapp, and G. Weimann, Surf. Sci. 174, 382 (1986). [2] H. } S. Chaves, A. F. S. Penna, J. M. Worlock, G. Weimann, and W. Schlapp, Surf. Sci. 170, 618 (1986). [3] A. } H. Meynadier, J. Orgonasi, C. Delalande, J. A. Brum, G. Bastard, M. Voos, G. Weimann, and [4] M. W. Schlapp, Phys. Rev. B 34, 2482 (1986). } J. C. Carneiro, P. C. Morais, and H. M. Cox, Appl. Phys. Lett. 68, 1105 (1996). [5] A. } Bastard, in Wave Mechanics Applied to Semiconductor Heterostructures, Les Editions de Physique, [6] G. Les Ulis: p. 246 (1988). } J. Glemobcki, B. V. Shanabrook, N. Bottka, W. T. Beard, and J. Comas, Appl. Phys. Lett. 46, 970 [7] O. (1985). } Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, Phys. Rev. B 28, 3241 (1983). [8] G. } M. G. Oliveira, V. M. S. Gomes, A. S. Chaves, J. R. Leite, and J. M. Worlock, Phys. Rev. B 35, 2896 [9] G. (1987). } A. C. Mendon¸ca, L. M. R. Scolfaro, J. B. B. Oliveira, F. Plentz, M. Micovic, J. R. Leite, and E. A. [10] C. Meneses, Superlatt. Microstruct. 12, 257 (1990). } Harber, in Numerical Data and Functional Relationships in Science and Technology, edited by [11] G. O. Madelung, Landoldt-Bornstein, New Series, Group III, Vol. 17, Springer-Verlag, Berlin, (1982). } Delalande, Phys. Script. T 19, 129 (1985). [12] C. } Olegart, M. Proctor, D. Martin, F. Morrier, G. Genaud, F. K. Reinhart, B. Orschel, L. C. Andreani, and [13] G. H. Rhan, Phys. Rev. B 49, 10456 (1994). .
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Photoreflectance measurements in GaAs/AlGaAs asymmetric quantum wells M. A. G. Soler, J. Depeyrot, P. C. Morais Departamento de F´ısica da Universidade de Bras´ılia, Caixa Postal 04629, 70910-900 Bras´ılia, DF, Brazil
J. A. N. T. Soares, L. M. R. Scolfaro, E. C. F. da Silva, R. Enderlein Instituto de F´ısica da Universidade de S˜ao Paulo, Caixa Postal 66318, 05315-970 S˜ao Paulo, SP, Brazil
G. Weimann, G. Trankle Walter Schottky Institut, Technische Universit¨at, 85748 M¨unchen, Germany
(Received 15 July 1996) In this work we investigated the optical control of the bidimensional electron gas density in a single asymmetric quantum well using, for the first time, photoreflectance. We performed our measurements at 80 and 300 K as a function of the power density of the pump beam. Under strong illumination, the bidimensional electron gas density is washed out of the quantum well and under a dark condition, it reaches its maximum value. The variation of the optical transitions observed in our photoreflectance spectra was related to the induced changes of the band profile in between these two limiting cases. c 1997 Academic Press Limited
1. Introduction Single asymmetric quantum wells (AQWs) have received a great deal of interest in recent years due to their technological applications and as a valuable system to study fundamental properties of a two-dimensional electron gas (2DEG) [1, 2]. In such structures carriers are released from intentionally doped impurities in the wider gap layer diffusing into the narrower gap layer, where the 2DEG is formed. The spacer—an undoped wide gap layer—is grown in between the quantum well and the impurities sites thus offering a barrier through which carriers have to tunnel in their pathway towards the AQW. Optical control of the 2DEG density in modulation-doped GaAs/AlGaAs [3, 4] and InGaAs/InP [5] single AQWs has been reported by several authors using different experimental techniques. According to the authors, under strong illumination the 2DEG is washed out from the quantum well. On the other hand, the 2DEG reaches its maximum value under dark conditions. In between these two limiting conditions the 2DEG density may be controlled by the optical excitation intensity. A blue shift in photoluminescence (PL) measurements under strong illumination has been reported [3, 5] as a signature of the optical control of the 2DEG in single AQWs. This variation of the band-to-band recombination energy has been attributed to both the reduction of the band bending in the AQW and the band gap renormalization which results from carrier exchange and correlation effects. In this work, photoreflectance (PR) measurements, performed at 80 and 300 K, have been used to investigate .
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.
.
0749–6036/97/040581 + 05 $25.00/0
sm960206
c 1997 Academic Press Limited
582
Superlattices and Microstructures, Vol. 21, No. 4, 1997
the optical control of the 2DEG density in single AQWs of GaAs/AlGaAs:Si, grown by MBE. However, it is important to note that the PR signal is proportional to the optical absorption in the structure while the PL spectra are strongly dependent on the radiative and non-radiative lifetimes of the carriers. Our attention is focused on the changes of the band profile at the barrier AQW region which goes from a flat condition under strong excitation, to a triangular potential barrier under dark condition.
2. Experiments ˚ thick GaAs quantum The sample used in the present experiments is a one-side-modulation-doped 166 A well clad between Ga0.65 Al0.35 As barriers. The actual structure consists of a semi-insulating GaAs substrate ˚ GaAs quantum wells within covered by a buffer layer of intrinsic GaAs, followed by several narrow (35 A) ˚ ˚ of Ga0.65 Al0.35 As and the 166 A-thick GaAs quantum well, all these layers being nominally a layer (100 A) ˚ ˚ doped. The quantum well was topped by a 350 A-thick Ga0.65 Al0.35 As undoped spacer followed by a 380 A ˚ of the cap layer grown on top of Si-doped (Nd = 1.8 × 1018 cm−3 ) Ga0.65 Al0.35 As layer. In addition, 100 A the overall structure were removed to decrease the optical absorption. At the temperature of 80 K, the carrier density in the quantum well, measured by Shubnikov–de Haas experiments, is about 2.5 × 1011 cm−2 and the carrier mobility is about 7.4 × 104 cm2 Vs−1 . The PR spectra were taken by a conventional PR apparatus using the 488 nm line of an Argon laser with a maximum power output of 26 mW, giving a maximum power density on the sample of about 8 W cm−2 . The chopper frequency was fixed at 340 Hz. The measured quantity was the ratio 1R/R, where 1R is the change in the reflection coefficient associated with the modulation by the laser radiation and R is the reflection coefficient.
3. Results and discussions We have recorded PR spectra for various values of the power density P of the pump beam. Typical spectra recorded at 80 K are displayed in Fig. 1. As it can be seen, at lower power density our spectra exhibit two equally strong structures (indicated by arrows) located at energies about 1.504 eV and 1.508 eV. We assign the lower energy structure (marked a) to the AQW fundamental optical transition which corresponds to the radiative recombination between the first heavy-hole subband and the first electron subband (E1 -HH1 ). The structure b is associated with the optical transition from the first light-hole level to the first electron level (E1 -LH1 ). Let us now consider the intensity of the AQW PR structures of Fig. 1. As the power density P of the pump beam increases, the intensity of the E1 -HH1 transition increases while the intensity of the E1 -LH1 transition decreases. For the maximum value of P used in our experiments, equal to 8 W cm−2 , we only observed the E1 -HH1 transition. It is well known that the M matrix element for an interband optical transition is proportional to the overlap of the electron and hole envelope functions [6]. Moreover, in the case of a symmetric quantum well corresponding to flat-band conditions, the E1 -HH1 transition is approximately three times more intense than the E1 -LH1 . Therefore the variations of the intensities of the observed transitions with the power density can be qualitatively understood from 1R/R ∼ |M|2 [7]. As already mentioned, under dark conditions the band profile at the well region is a triangular potential. At low power density the quantum well remains strongly asymmetric. Thus the band bending in the well, and consequently the electric field existing in the well, induces a spatial shift of the carriers envelope functions, along or opposite to the field direction for the holes or for the electrons, respectively [8]. Furthermore, because of their larger mass the heavy-holes are more strongly affected by the field than the light-holes. As a consequence, the overlap of the envelope functions of electrons and light-holes does become of the same .
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.
.
Superlattices and Microstructures, Vol. 21, No. 4, 1997
583
–2
8 W cm 8 × 10–1 W cm–2 8 × 10–2 W cm–2 8 × 10–3 W cm–2
T = 80 K a
∆R/R (a. u.)
a × 10 b
a
× 10 b
a × 10
1.49
1.50
1.51
1.52
Energy (eV) Fig. 1. Photoreflectance spectra recorded at 80 K for selected values of power density of pump beam (arrows indicate the transition energies). .
.
E1
HH1 LH1
Strong excitation
E1
HH1 LH1
Dark condition
Fig. 2. Schematic AQW bands profile in the dark (on the right) and under strong illumination (on the left). .
.
order of magnitude as that of electrons and heavy-holes (see Fig. 2). Then, the E1 -LH1 optical transition starts to compete with the E1 -HH1 transition as can be seen in our spectra. When we illuminate the sample with photons whose energy overcomes the barrier energy gap, the photogenerated carriers are separated by the built-in electric field, the electrons being recaptured by the doped region in the barrier and the holes moving into the AQW where they radiatively recombine with the electrons. Then, as the power density of the pump beam increases, the 2DEG density decreases which leads to a reduced band bending in the AQW. Simultaneously, the spatial shift of the carriers envelope function is also reduced and the ratio of the optical matrix elements (E1 -HH1 )/(E1 -LH1 ) transition increases. The E1 -LH1 transition becomes less intense and, for P = 0.8 W cm−2 , vanishes completely as can be seen in Fig. 1. Moreover, when the power density of the pump beam is increased over four orders of magnitude, the observed transitions are slightly shifted towards higher energies. Indeed as the electron concentration decreases, the recombination energies increase because of both the upwards shifts of electron and hole subband levels
584
Superlattices and Microstructures, Vol. 21, No. 4, 1997 Table 1: Calculated band bending V of the AQW, recombination energy of the AQW fundamental transition Er and energy shift 1 between the light- and heavy-holes for various carrier densities n s . .
.
n s (cm−2 ) 2.5 × 1011 1.9 × 1011 1010 109
V (meV) 36 29 20 1.4
1 (meV)
Er (eV) 1.527 1.527 1.526 1.526
8.7 8.5 7.9 7.9
and the reduction of the band gap renormalization. The measured blue-shift is about 4 meV for the E1 -HH1 transition. This value is in good agreement with the one obtained from PL experiments by Chaves et al. for a similar sample in the same range of power density [3]. Our qualitative interpretations are strongly supported by self-consistent calculations which were carried out to determine the subband structure of our GaAs/AlGaAs:Si AQW. The confined states for the conduction band quantum well was calculated by numerically solving the Schr¨odinger and Poisson equations for the onedimensional motion parallel to the growth direction, in the effective mass approximation [9, 10]. Exchangecorrelation effects were taken into account within the local density approximation. The confined energy subbands for the holes were calculated by using the electrostatic potential obtained in the self-consistent calculations for electrons as an input. The values used for the effective mass of electrons, heavy- and lightholes were 0.067m 0 , 0.4m 0 and 0.087m 0 respectively, m 0 being the free electron mass [11]. The 60–40% rule was adopted for the conduction-to-valence band discontinuities. Table 1 gives the calculated values of the recombination energy Er of the E1 -HH1 transition, using the 1.507 eV value for the GaAs bandgap at 80 K, for various values of the carrier density n s in the quantum well. The transition energy has been calculated assuming that the transition occurs at k⊥ = 0 where k⊥ is the in-plane wave vector of the carrier which is assumed to be conserved. The energy difference between the value obtained for n s = 2.5 × 1011 cm−2 and the measured value at low power density is equal to 23 meV. However, it is important to bear in mind that our calculations do not include the reduction of the recombination energy due to both the bandgap renormalization and excitonic effects. The reduction value induced by the bandgap renormalization has been discussed by Delalande et al. [12] for ˚ various carrier concentrations. In the case of a one-side 150 A-thick modulation doped quantum well, it varies approximately from 10 to 20 meV when the carrier density goes from 1010 to 4 × 1011 cm−2 . Although the excitonic behaviour of optical transitions is characteristic of undoped quantum wells, it has been observed in doped quantum wells [12]. Then, taking into account the heavy-hole exciton binding energy, which in our case can be evaluated to be of the order of 8 meV [13], one can account for the difference between the calculated and measured results. Table 1 also gives the energy shift between the light- and heavy-holes levels. The calculated value for n s = 2.5 × 1011 cm−2 is equal to 8.7 meV which gives a difference of 4.7 meV with the measured one. It is probably due to both the value of the light-hole exciton binding energy, which is about 2 meV larger than the heavy-hole binding energy, and the approximations used in our theoretical approach of the valence subbands. Indeed, we do not take into account the coupling between the light- and heavy-holes states and we assume that the potential drop along the well has the same value as that obtained for the electrons. Moreover, we calculated the recombination energy for k⊥ = 0 which is not exactly true, since the Fermi energy is above the E1 electron level for such a value of carrier density. Therefore the energy shift between the light- and heavy-holes levels should be smaller than the value found in our calculations. Comparing the variation of the calculated and measured values of the recombination energies of the observed transitions, it is clear that the maximum power density of the pump beam used in our experiments .
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Superlattices and Microstructures, Vol. 21, No. 4, 1997
585
is not sufficient to completely wash out the 2DEG existing in the quantum well, which means we do not rise the flat-band conditions. Indeed the expected blue-shift deduced from our calculations between the low excitation intensity case and the flat-band one would be about 15 meV, and the measured one is equal to 4 meV. Moreover, variation of the order 11 meV has been measured in similar samples [3]. Nevertheless this level of excitation intensity is high enough to decrease the optical matrix element of the E1 -LH1 transition until vanishing. .
.
4. Conclusion We have recorded PR spectra of GaAs/AlGaAs:Si AQW for various values of the power density of the pump beam. When the power density is increased over four orders of magnitude, we measured a blue shift of the recombination energy associated to the fundamental AQW transition equal to 4 meV, a value which is in good agreement with reported results. For the first time PR experiments provide evidence of the optical control of the 2DEG density in AQW. Our theoretical results of subband calculations are in reasonably good agreement with the measured ones and show that, even in doped structures, the observed transitions can be due to excitonic recombinations rather than band-to-band ones.
References .
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