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Magneto-optical oscillations in the photoluminescence of quantum wells and the resonant polaron effect
Physica B 256±258 (1998) 367±370
Magneto-optical oscillations in the photoluminescence of quantum wells and the resonant polaron eect A.R. Alves 1, L.A. Cury, P.S.S. Guimar~ aes *, M.V.B. Moreira Dept Fõsica, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte MG, Brazil
Abstract Magneto-optical oscillations in the intensity of photoluminescence transitions in AlGaAs/InGaAs/GaAs asymmetric quantum wells with two occupied electronic subbands have been studied. The minima of the oscillations for the ®rst excited electronic subband occur at resonant polaron conditions hxLO N hxc in which the emission of LO phonons is strongly enhanced and are due to an increase of the LO phonon scattering of electrons near the Fermi level, which is con®rmed by the increase veri®ed in the photoluminescence linewidth at resonant polaron conditions. This eect can also explain the small dierence in phase observed between the magneto-optical and the Shubnikov±de Haas oscillations. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Polarons; Magneto-photoluminescence; Quantum wells
1. Introduction The oscillatory behavior of the intersubband photoluminescence (PL) intensity from asymmetric quantum wells (AQW) subjected to magnetic ®elds (B) applied perpendicular to the layers has been widely investigated [1±5]. Such magneto-optical oscillations in the PL intensity are similar to the electrical Shubnikov-de Haas (SdH) oscillations and several interpretations have been given to explain their origin. Heiman et al. [1] and Goldberg et al. [2] suggested that changes in the screening due to the crossing of the Fermi energy (EF ) between two Landau levels (LL) would be responsible for the magneto-optical oscillations. Chen et al. [3] interpreted the oscillations in the PL
*
Corresponding author. Fax: 55 31 499 5600; e-mail: pssg@®sica.ufmg.br 1 on leave from Universidade Federal de Vicßosa, MG, Brazil.
intensity for the recombination of the photoexcited electrons from the ®rst excited subband (e2 ) to the fundamental heavy hole subband (hh1 ) as an eect of the Fermi Edge Singularity (FES). Skolnick et al. [4] gave another interpretation in terms of an electron transfer mechanism. This interpretation was also corroborated by Hawrylak et al. [5]. It is important to note that these dierent interpretations come out of dierent physical regimes (dierent mobilities and the position of e2 relative to EF ). Another relevant factor that must be taken into account is the electron±phonon interaction. In the presence of a quantizing magnetic ®eld the dynamics of carriers in semiconductors is more signi®cantly aected by the polarization ®eld of longitudinal optical (LO) phonons when the frequency xLO of the LO phonon is a multiple of the cyclotron frequency xc [6,7]. Strong magneto-polaron resonances in heavily doped AQW with just one subband occupied were noticed by
0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 5 1 7 - 1
368
A.R. Alves et al. / Physica B 256±258 (1998) 367±370
Simmonds et al. [8]. Magneto-polaron resonances were also observed by Iikawa et al. [9] in AQW samples. The theoretical results of Swierkowski et al. [10] are in agreement with experimental data and explain the strong renormalization responsible for the splitting of the PL line into two components (anticrossing) at resonant polaron conditions. No mention about the association of the magneto-polaron resonances with the origin of the magneto-optical oscillations is done in the works cited above. Thus, we have revisited the magneto-optical oscillations and studied a heavily doped AlGaAs/InGaAs/GaAs AQW with two occupied electronic subbands. 2. Results and discussion wide n-type Our sample consists of a 200 A modulation doped n-Al0:3 Ga0:7 As/In0:15 Ga0:85 As/ GaAs AQW grown by molecular beam epitaxy. At B 0 T the measured two-dimensional electronic concentration is 1.56 ´ 1012 cmÿ2 under laser illumination and the energy dierence between e2 and e1 is 48 meV, with EF located about 6 meV above e2 [11]. The magnetic ®eld was applied parallel to the growth direction. The excitation light, generated by an Argon laser emitting at 514.5 nm, and the PL light were guided by optical ®bers. Due to losses in the optical ®ber medium and in the coupling of the laser beam with the optical ®ber core, the laser intensity on the sample was around 0.2 W/cm2 . The variation with magnetic ®eld of the PL intensity (IPL ) of e1 hh1 and e2 hh1 is shown in Fig. 1 together with the SdH oscillations (Rxx ) and the Hall plateaus (Rxy ), which were measured simultaneously with the PL data. It is striking to see that the oscillations from e2 hh1 PL line are strictly 180° out of phase with the oscillations from e1 hh1 . This is a direct evidence of the competitive process between them due to the limited density of photoexcited holes. The SdH oscillations do not present a phase-coherence with neither e2 hh1 nor e1 hh1 IPL oscillations. The minima (maxima) in the e2 hh1 (e1 hh1 ) IPL oscillations can clearly be seen at around B 5.3, 6.3, and 8.0 T. In the range
Fig. 1. The Shubnikov-de Haas oscillations (Rxx ), Hall plateaus (Rxy ) and the variation with magnetic ®eld of the photoluminescence intensity from the e1 hh1 and e2 hh1 transitions. The small oscillations in Rxy at low ®elds are due to a small misalignment of the Hall probe electrical contacts.
10.5 < B <12 T we have an overlap between two minima in e2 hh1 located around B 10.7 and 11.7 T, which correspond respectively to the maximum and the shoulder seen at the same B-values for the e1 hh1 curve. Chen et al. [3] investigated the magneto-optical oscillations in a sample nearly identical to ours except that in their case the subband e2 was unoccupied and it was located at 4 meV below EF . They found a very good phase-coherence between optical and electrical oscillations, in contrast with our results. The enhancement in the e2 hh1 PL line induced by the FES, as proposed by Chen et al., do not explain our results since in our case the e2 subband is not empty and EF is not signi®cantly
A.R. Alves et al. / Physica B 256±258 (1998) 367±370
aected by the position of LL's from e1 . Our results cannot either be explained by the electron transfer mechanism suggested by Skolnick et al. [4], since it implies the same phase between the optical and electrical oscillations and that is not what our results show. Fig. 2 shows the energy positions of the peaks in the PL spectra for B up to 15 T. Several PL energies E1n and E2n involving transitions from the nth LL of e1 and e2 to the nth LL of hh1 are identi®ed in Fig. 2. The lower slope observed for the E2n lines correspond to a relatively stronger excitonic eect in that case [4]. Nonparabolicity eects in the InGaAs channel can also introduce a supplementary correction that will decrease the slope of the E2n lines.
Fig. 2. The E1n and E2n transition energies (dashed lines); and the e2n polaronic lines (full lines) as a function of magnetic ®eld. The lines are only guides to the eyes.
369
The full lines e2n in Fig. 2, the polaronic lines, are obtained subtracting the energy of a GaAs LO-phonon from the E2n energies, i.e., e2n E2n ÿ hxLO . The ®rst polaron resonance occurs at B @ 5.3 T, where the e27 polaronic line crosses the E20 line, i.e., at hxLO 7hxc . Further polaron resonances with the E20 line occur at B @ 6.3, 8.0, 10.7 and 11.7 T. Notice that these values are the same B-values at which the IPL from e2 hh1 (or e1 hh1 ) present a minimum (or maximum). The e2 electrons, near the Fermi level, are the ones most sensitive to the scattering mechanisms. Our results suggest that the GaAs LO-phonons emitted during the e2n transitions increase in importance as a scattering center for electrons in e2 at polaron resonance conditions. This leads to a decrease in the IPL of e2 hh1 thus enhancing the e1 hh1 PL line intensity at the magnetic ®elds given by hxLO Nhxc , where xC eB/m is the cyclotron frequency of e2 . The SdH oscillations occur at the crossing of LL's from e1 and EF . Therefore, since the slopes of the e2n and E1n lines are dierent, the 1/B-period expected for the magneto-optical oscillations is dierent from the period of the SdH oscillations, as observed in the results shown in Fig. 1. Fig. 3 shows the changes in the linewidth of the e2 hh1 PL peak and its integrated IPL with increasing magnetic ®eld. The minima in the integrated IPL occur exactly at the magnetic ®elds at which the linewidth goes through a maximum. These are the magnetic ®elds that give the resonant pola-
Fig. 3. Linewidth and integrated IPL for the e2 hh1 photoluminescence as a function of magnetic ®eld.
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A.R. Alves et al. / Physica B 256±258 (1998) 367±370
ron condition. The increased linewidth con®rms the enhancement in LO phonon scattering at the resonant polaron magnetic ®elds. In conclusion, the competition between the e1 hh1 and e2 hh1 PL transitions, due to the limited number of photoholes, is evidenced by the clear pdephasing of their oscillations. The strict correlation between the maxima positions of the e2 hh1 linewidth and the magnetic ®elds at which the polaron resonances occur con®rms the origin of our magneto-optical oscillations as caused by enhanced phonon scattering. Acknowledgements We acknowledge the ®nancial support of FAPEMIG, CNPq and CAPES. References [1] D. Heiman, B.B. Goldberg, A. Pinczuk, C.W. Tu, A.C. Gossard, J.H. English, Phys. Rev. Lett. 61 (1988) 605.
[2] B.B. Goldberg, D. Heiman, A. Pinczuk, L. Pfeier, K. West, Phys. Rev. Lett. 65 (1990) 641. [3] W. Chen, M. Fritze, A.V. Nurmikko, D. Ackley, C. Colvard, H. Lee, Phys. Rev. Lett. 64 (1990) 2434. [4] M.S. Skolnick, P.E. Simmonds, T.A. Fisher, Phys. Rev. Lett. 66 (1991) 963. [5] P. Hawrylak, N. Pulsford, K. Ploog, Phys. Rev. B 46 (1992) 15193. [6] D.M. Larsen, Phys. Rev. B 30 (1984) 4595. [7] S. Das Sarma, A. Madhukar, Phys. Rev. B 22 (1980) 2823; S. Das Sarma, ibid 27 (1983) 2590. [8] P.E. Simmonds, M.S. Skolnick, T.A. Fisher, K.J. Nash, R.S. Smith, Phys. Rev. B 45 (1992) 9497. [9] F. Iikawa, M.L.F. Abbade, R.G. Pereira, J.A. Brum, A.A. Bernussi, A.L. Gobbi, G. Borghs, in: G.Landwehr, W.Ossau (Eds.), Proceedings of the 12th International Conference on High Magnetic Fields in the Physics of Semiconductors, vol. 2, World Scienti®c, Singapore, 1997, p. 621. [10] L. Swierkowski, J. Szymanski, P.E. Simmonds, T.A. Fisher, M.S. Skolnick, Phys. Rev. B 51 (1995) 9830. [11] A.R. Alves, P.S.S. Guimar~ aes, L.A. Cury, M.V.B. Moreira, Phys. Rev. B 58 (1998) 6720.
Magneto-optical oscillations in the photoluminescence of quantum wells and the resonant polaron eect A.R. Alves 1, L.A. Cury, P.S.S. Guimar~ aes *, M.V.B. Moreira Dept Fõsica, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte MG, Brazil
Abstract Magneto-optical oscillations in the intensity of photoluminescence transitions in AlGaAs/InGaAs/GaAs asymmetric quantum wells with two occupied electronic subbands have been studied. The minima of the oscillations for the ®rst excited electronic subband occur at resonant polaron conditions hxLO N hxc in which the emission of LO phonons is strongly enhanced and are due to an increase of the LO phonon scattering of electrons near the Fermi level, which is con®rmed by the increase veri®ed in the photoluminescence linewidth at resonant polaron conditions. This eect can also explain the small dierence in phase observed between the magneto-optical and the Shubnikov±de Haas oscillations. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Polarons; Magneto-photoluminescence; Quantum wells
1. Introduction The oscillatory behavior of the intersubband photoluminescence (PL) intensity from asymmetric quantum wells (AQW) subjected to magnetic ®elds (B) applied perpendicular to the layers has been widely investigated [1±5]. Such magneto-optical oscillations in the PL intensity are similar to the electrical Shubnikov-de Haas (SdH) oscillations and several interpretations have been given to explain their origin. Heiman et al. [1] and Goldberg et al. [2] suggested that changes in the screening due to the crossing of the Fermi energy (EF ) between two Landau levels (LL) would be responsible for the magneto-optical oscillations. Chen et al. [3] interpreted the oscillations in the PL
*
Corresponding author. Fax: 55 31 499 5600; e-mail: pssg@®sica.ufmg.br 1 on leave from Universidade Federal de Vicßosa, MG, Brazil.
intensity for the recombination of the photoexcited electrons from the ®rst excited subband (e2 ) to the fundamental heavy hole subband (hh1 ) as an eect of the Fermi Edge Singularity (FES). Skolnick et al. [4] gave another interpretation in terms of an electron transfer mechanism. This interpretation was also corroborated by Hawrylak et al. [5]. It is important to note that these dierent interpretations come out of dierent physical regimes (dierent mobilities and the position of e2 relative to EF ). Another relevant factor that must be taken into account is the electron±phonon interaction. In the presence of a quantizing magnetic ®eld the dynamics of carriers in semiconductors is more signi®cantly aected by the polarization ®eld of longitudinal optical (LO) phonons when the frequency xLO of the LO phonon is a multiple of the cyclotron frequency xc [6,7]. Strong magneto-polaron resonances in heavily doped AQW with just one subband occupied were noticed by
0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 5 1 7 - 1
368
A.R. Alves et al. / Physica B 256±258 (1998) 367±370
Simmonds et al. [8]. Magneto-polaron resonances were also observed by Iikawa et al. [9] in AQW samples. The theoretical results of Swierkowski et al. [10] are in agreement with experimental data and explain the strong renormalization responsible for the splitting of the PL line into two components (anticrossing) at resonant polaron conditions. No mention about the association of the magneto-polaron resonances with the origin of the magneto-optical oscillations is done in the works cited above. Thus, we have revisited the magneto-optical oscillations and studied a heavily doped AlGaAs/InGaAs/GaAs AQW with two occupied electronic subbands. 2. Results and discussion wide n-type Our sample consists of a 200 A modulation doped n-Al0:3 Ga0:7 As/In0:15 Ga0:85 As/ GaAs AQW grown by molecular beam epitaxy. At B 0 T the measured two-dimensional electronic concentration is 1.56 ´ 1012 cmÿ2 under laser illumination and the energy dierence between e2 and e1 is 48 meV, with EF located about 6 meV above e2 [11]. The magnetic ®eld was applied parallel to the growth direction. The excitation light, generated by an Argon laser emitting at 514.5 nm, and the PL light were guided by optical ®bers. Due to losses in the optical ®ber medium and in the coupling of the laser beam with the optical ®ber core, the laser intensity on the sample was around 0.2 W/cm2 . The variation with magnetic ®eld of the PL intensity (IPL ) of e1 hh1 and e2 hh1 is shown in Fig. 1 together with the SdH oscillations (Rxx ) and the Hall plateaus (Rxy ), which were measured simultaneously with the PL data. It is striking to see that the oscillations from e2 hh1 PL line are strictly 180° out of phase with the oscillations from e1 hh1 . This is a direct evidence of the competitive process between them due to the limited density of photoexcited holes. The SdH oscillations do not present a phase-coherence with neither e2 hh1 nor e1 hh1 IPL oscillations. The minima (maxima) in the e2 hh1 (e1 hh1 ) IPL oscillations can clearly be seen at around B 5.3, 6.3, and 8.0 T. In the range
Fig. 1. The Shubnikov-de Haas oscillations (Rxx ), Hall plateaus (Rxy ) and the variation with magnetic ®eld of the photoluminescence intensity from the e1 hh1 and e2 hh1 transitions. The small oscillations in Rxy at low ®elds are due to a small misalignment of the Hall probe electrical contacts.
10.5 < B <12 T we have an overlap between two minima in e2 hh1 located around B 10.7 and 11.7 T, which correspond respectively to the maximum and the shoulder seen at the same B-values for the e1 hh1 curve. Chen et al. [3] investigated the magneto-optical oscillations in a sample nearly identical to ours except that in their case the subband e2 was unoccupied and it was located at 4 meV below EF . They found a very good phase-coherence between optical and electrical oscillations, in contrast with our results. The enhancement in the e2 hh1 PL line induced by the FES, as proposed by Chen et al., do not explain our results since in our case the e2 subband is not empty and EF is not signi®cantly
A.R. Alves et al. / Physica B 256±258 (1998) 367±370
aected by the position of LL's from e1 . Our results cannot either be explained by the electron transfer mechanism suggested by Skolnick et al. [4], since it implies the same phase between the optical and electrical oscillations and that is not what our results show. Fig. 2 shows the energy positions of the peaks in the PL spectra for B up to 15 T. Several PL energies E1n and E2n involving transitions from the nth LL of e1 and e2 to the nth LL of hh1 are identi®ed in Fig. 2. The lower slope observed for the E2n lines correspond to a relatively stronger excitonic eect in that case [4]. Nonparabolicity eects in the InGaAs channel can also introduce a supplementary correction that will decrease the slope of the E2n lines.
Fig. 2. The E1n and E2n transition energies (dashed lines); and the e2n polaronic lines (full lines) as a function of magnetic ®eld. The lines are only guides to the eyes.
369
The full lines e2n in Fig. 2, the polaronic lines, are obtained subtracting the energy of a GaAs LO-phonon from the E2n energies, i.e., e2n E2n ÿ hxLO . The ®rst polaron resonance occurs at B @ 5.3 T, where the e27 polaronic line crosses the E20 line, i.e., at hxLO 7hxc . Further polaron resonances with the E20 line occur at B @ 6.3, 8.0, 10.7 and 11.7 T. Notice that these values are the same B-values at which the IPL from e2 hh1 (or e1 hh1 ) present a minimum (or maximum). The e2 electrons, near the Fermi level, are the ones most sensitive to the scattering mechanisms. Our results suggest that the GaAs LO-phonons emitted during the e2n transitions increase in importance as a scattering center for electrons in e2 at polaron resonance conditions. This leads to a decrease in the IPL of e2 hh1 thus enhancing the e1 hh1 PL line intensity at the magnetic ®elds given by hxLO Nhxc , where xC eB/m is the cyclotron frequency of e2 . The SdH oscillations occur at the crossing of LL's from e1 and EF . Therefore, since the slopes of the e2n and E1n lines are dierent, the 1/B-period expected for the magneto-optical oscillations is dierent from the period of the SdH oscillations, as observed in the results shown in Fig. 1. Fig. 3 shows the changes in the linewidth of the e2 hh1 PL peak and its integrated IPL with increasing magnetic ®eld. The minima in the integrated IPL occur exactly at the magnetic ®elds at which the linewidth goes through a maximum. These are the magnetic ®elds that give the resonant pola-
Fig. 3. Linewidth and integrated IPL for the e2 hh1 photoluminescence as a function of magnetic ®eld.
370
A.R. Alves et al. / Physica B 256±258 (1998) 367±370
ron condition. The increased linewidth con®rms the enhancement in LO phonon scattering at the resonant polaron magnetic ®elds. In conclusion, the competition between the e1 hh1 and e2 hh1 PL transitions, due to the limited number of photoholes, is evidenced by the clear pdephasing of their oscillations. The strict correlation between the maxima positions of the e2 hh1 linewidth and the magnetic ®elds at which the polaron resonances occur con®rms the origin of our magneto-optical oscillations as caused by enhanced phonon scattering. Acknowledgements We acknowledge the ®nancial support of FAPEMIG, CNPq and CAPES. References [1] D. Heiman, B.B. Goldberg, A. Pinczuk, C.W. Tu, A.C. Gossard, J.H. English, Phys. Rev. Lett. 61 (1988) 605.
[2] B.B. Goldberg, D. Heiman, A. Pinczuk, L. Pfeier, K. West, Phys. Rev. Lett. 65 (1990) 641. [3] W. Chen, M. Fritze, A.V. Nurmikko, D. Ackley, C. Colvard, H. Lee, Phys. Rev. Lett. 64 (1990) 2434. [4] M.S. Skolnick, P.E. Simmonds, T.A. Fisher, Phys. Rev. Lett. 66 (1991) 963. [5] P. Hawrylak, N. Pulsford, K. Ploog, Phys. Rev. B 46 (1992) 15193. [6] D.M. Larsen, Phys. Rev. B 30 (1984) 4595. [7] S. Das Sarma, A. Madhukar, Phys. Rev. B 22 (1980) 2823; S. Das Sarma, ibid 27 (1983) 2590. [8] P.E. Simmonds, M.S. Skolnick, T.A. Fisher, K.J. Nash, R.S. Smith, Phys. Rev. B 45 (1992) 9497. [9] F. Iikawa, M.L.F. Abbade, R.G. Pereira, J.A. Brum, A.A. Bernussi, A.L. Gobbi, G. Borghs, in: G.Landwehr, W.Ossau (Eds.), Proceedings of the 12th International Conference on High Magnetic Fields in the Physics of Semiconductors, vol. 2, World Scienti®c, Singapore, 1997, p. 621. [10] L. Swierkowski, J. Szymanski, P.E. Simmonds, T.A. Fisher, M.S. Skolnick, Phys. Rev. B 51 (1995) 9830. [11] A.R. Alves, P.S.S. Guimar~ aes, L.A. Cury, M.V.B. Moreira, Phys. Rev. B 58 (1998) 6720.