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AlAs multiquantum wells under high magnetic fields
PHYSICA ELSEVIER
Physica B 201 (1994) 407-410
Two-dimensional exciton states of GaAs/A1As multiquantum wells under high magnetic fields T. Yasui a'*, Y. Segawa a, Y. Aoyagi b, Y. Iimura c, G.E.W. Bauer d, I. Mogie,i~G.
Kido e
a Photodynamics Research Center, Frontier Research Program, The Institute of Physical and Chkfnical Research (RIKEN), Sendai, Japan b The Institute of Physical and Chemical Research (R1KEN), Saitama, Japan Tokyo University of Agriculture and Technology, Tokyo, Japan d Delft University of Technology, Delft, The Netherlands Institute for Materials Research, Tohoku University, Sendai, Japan
Abstract
.ydrogen-like exciton states at high magnetic fields up to/ 5 T re studied by magneto-optical spectroscopy of a multiquantum well sample with 265/~-thick wells of GaAs an~g2-60~-thick barriers of AlAs. These excitonic states are well explained by effective mass calculations which take into account residual electric fields in the sample and the valence band mixing in magnetic fields. A symmetry change of the exciton ground state is observed at a magnetic field of ~ 15 T.
1. Introduction
Since the early report by Dingle et al. [1], the study of two-dimensional (2D) exciton states confined in quantum wells has been advanced by many approaches. In particular, optical measurements in high magnetic fields are useful for investigating the 2D excitons in quantum wells, because they reveal the discrete energy levels and enhance the oscillator strengths of excitons. In the first experimental reports 1-2,3] about 2D excitons under high magnetic fields, it was pointed out that the lowest exciton levels corresponding to the heavy hole exciton and the light hole exciton show diamagnetic behavior individually. Furthermore, several peaks at higher photon energies were interpreted as Landau level transitions. Contrary to this interpretation, some researchers have proposed exciton states at higher energy under high
* Corresponding author.
magnetic fields (magnetoexcitons). Since the first theoretical reports about the magnetoexciton states in quantum wells [4-6], an excitonic nature at the higher energy region is predicted, but it has not been easy to obtain a good agreement with the experimental results [7]. Good agreement between experiment [8] and theory I-9] was later obtained by using high-quality samples. In recent years, the behavior of magnetoexcitons has been studied more precisely under intermediate 1-10] and high magnetic fields [11, 12]. These studies have shown that the magnetoexcitons in GaAs/A1As quantum wells, which reflect the complicated valence-band structure, have very complicated behavior under high magnetic fields. Since the relative importance of excitonic effects decrease with magnetic fields, this leads to the question if a Landau level model can explain the optical spectra of a quantum well under high magnetic fields. In an earlier work some of the present authors considered this problem by using a high-quality sample to determine the behavior of magnetoexcitons in
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 0 0 - A
408
T. Yasui et al./Physica B 201 (1994) 407-410
photoluminescence excitation (PLE) spectra up to 6 T [10]. The present work further addresses this problem by comparing a magneto-optical study and the calculation made by Bauer and Ando [9].
2. Experiment The sample used in this work is a multiquantum well with forty periods of 265 ,~-GaAs wells and 260/~-AlAs barriers, the details of which have been previously reported in Ref. [10]. PLE spectra were obtained by monitoring the luminescence of the lowest exciton level in a hybrid type magnet consisting of an outer superconducting magnet and an inner water-cooled resistive magnet of polyhelix type.The sample was kept at 4.2 K under magnetic fields ranging from 6 T up to 25 T. Light from a 250 W mercury lamp with a flat band in the spectral region of this study was passed through a monochromator with a spectral resolution of about 1 meV. It was circularly polarized in front of the sample in order to make a Faraday configuration with a + and a - polarization. The emitted light was detected by another monochromator at the photon energy of the lowest exciton level and led to a conventional photon counting system.
3. Results and discussion Fig. 1 shows the (r - PLE spectra at various magnetic field strengths. The a + PLE spectra were also measured but are not shown. One set of a - and (r + spectra give a complete measurement. Most of the peaks were given temporary labels, A, B, C, D, etc, and assigned to exciton states based on calculations to be discussed later. In this paper, the following notations are used for peaks: H(L) means heavy (light) holes; the first number is the electron subband and the second is the hole subband; and a hydrogenic label (nm) is used for the exciton envelope functions, where n is the total quantum number and m is the angular momentum quantum number as follows: ( . . . d - , p - , s, p + , d + , . . . ) . The spin labels are used, if necessary. To avoid complexity, this labeling system is limited to only a few cases in Fig. 1. At 0 T peaks were observed corresponding to exciton states and a step-like background was also seen. Several discrete peaks in these ]aLE spectra were clearly revealed and the background levels decreased as the magnetic field strength increased. This can be explained by the effects of the high magnetic fields, that is to say, both the increase of the binding energy with reduction of the exciton radius and quantization of the density of states. Fig. 1 also
(~--
T=4.2KI
L,~Sl "'~ H13(15)
C
L C I~CS~ A ~
25T [
g m C:
I
O
°' L11(IS)
"
---
j K
B--j%c -
D
I
L
13
H2211S}
Z,T2,,,:,
1.52 1.53 1.54 1.55 1.56 1.57 1.58 Photon Energy(eV) Fig. 1. PLE spectra of a 265/k-width GaAs quantum well sample at various magnetic fields with a - polarization. Peaks given temporary labels, A, B, C , . . . etc., are assigned to exciton states based on calculations in the literature I-9]. Other peaks were labeled as mentioned in the text.
shows the energy shifts of these peaks as the magnetic field increases. This study focuses on energy shifts and changes in oscillator strength of excitons as a function of magnetic field. To clarify these points, Fig. 2(a) and Fig. 2(b), for tr and tr + , respectively, show energy shifts in excitons as curves. Oscillator strengths are proportional to the area of the circles. The lowest states, as indicated by the bold curves, correspond to the H l l ( l s ) exciton state. Oscillator strength was normalized to the Lll(ls), which was constant throughout this measurement. Complicated energy shifts can be observed below 11 T in Fig. 2(a) and Fig. 2(b). In this region, a few exciton states mix with each other (see from 1.54 eV to 1.55 eV). Thus, peaks cannot easily be labeled by the predominant excitonic envelope function. The oscillator strengths of these peaks show very complicated changes. On the other hand, this behavior is simplified in the high magnetic field region where most peaks show a linear energy shift. This feature is a clear evidence for the reduction of exciton mixing. The crossing of H l l ( l s ) and L l l ( l s ) at 15T is shown in Fig. 2(b) but not in Fig. 2(a). It is obvious that the lowest exciton state, which is used for the monitored peak, is replaced by Lll(ls) over 15 T in a + polarization. This is explained by the effective mass of the excitons as determined by the GaAs well width ( = 265 ~). The spin splitting energy of H11(Is) is smaller than that of L11(ls)
409
T. Yasui et al./Physica B 201 (1994) 407 410 1.56
1.58
1.57
1.57 0
~"
1.56
1.56
c¢
1.56
1.55
1.54
1.54
1.53
1.53
LU
'
~
(b)
c 0
o
13..
1.52
1.52
5
10
15
20
25
5
10
Magneticfield(T)
15
20
25
Magneticfield(T)
Fig. 2. Magnetic field dependence of energy shifts of excitons up to 25 T with a - polarization (a) and a + polarization (b). The bold curves correspond to the monitored peak. The area of circles are proportional to oscillator strength of peaks in PLE spectra.
a n d it is difficult to observe by P L E measurement. Therefore the H l l ( l s ) peak crossed L l l ( l s ) in the a + configuration, but not in the a - one. This point is in good agreement with the calculation as m e n t i o n e d below. Fig. 3 shows experimental results (a) a n d calculations (b) of energy shifts as a function of magnetic fields with a + polarization. The details of the calculations are given in Ref. [9]. T h o s e calculations which are based on effec-
tive-mass theory, take into account the complicated vale n c e - b a n d structure, the effects of a residual electric field in the sample a n d magnetic fields as external p e r t u r b a tions. Since a forbidden transition ( = H12(ls)) is den o t e d in Fig. 3(a), the residual electric field should be considered in o u r sample. In earlier work, some of the present a u t h o r s estimated the value of the residual electric field to be ~ 3 k V / c m [10]. The crossing of L l l ( l s )
,o+1
1.,,
1.27
.,,,...,.,
1,54
~ 164 15a
10
L,,,,
,.,.,
IJJ
1.52
o+
t
.
.
.
.
.
.
.
.
.
.
.
.
.
.
15 20 Magneticfield (T)
'a'r
25
.
10
.
.
.
.
.
.
,
.
.
15 20 Magneticfield (T)
.
'°' 25
Fig. 3. Experimental results (a) and calculations (b) of energy shifts and oscillator strengths of excitons as a function of magnetic fields with ~r + polarization. The circles have the same meaning as in Fig. 2. The bold curve is the monitor peak in Fig. 3(a) and H1 l(ls) in Fig. 3(b), respectively. The underlined labels indicate uncertain assignments. The crossing of H1 l(ls) and L1 l(ls) is denoted.
410
T. Yasui et al./Physica B 201 (1994) 407-410
and H l l ( l s ) is well explained by the calculations as shown in Fig. 3(b). Good agreement is not obtained for the higher states of excitons at high magnetic fields as indicated by the underlined labels in Fig. 3(a). This is assumed to be due to the basis set limitations in the calculations. In other words, the basis for the radial functions in the plane of the well can perform satisfactory only for zero or intermediate magnetic fields (below 10 T) [9]. Even if some disagreement remains, it is clear that excitonic effects in our study of a 265/~-thick GaAs well remain to be significant even at high magnetic fields. These energy shifts of excitons have been observed by other researchers for various GaAs well thicknesses of 160/~ [11], 45/~ [12] and 30/~ [12]. More complicated spectra can be observed by increasing the well thickness. In these reports, the magnetoexciton states offer a good explanation of the experimental results. In the first magneto-optical study for GaAs quantum wells, however, these energy shifts were interpreted as Landau level transitions in thickness region of 50-125/~ [2] and 58-252 ~, [3]. It is difficult to identify the exact cause of this difference from our experimental results, but it is possibly caused by the poor sample quality in Refs. [2, 3], which did not allow the observation of excitonic effects. In conclusion, we have shown hydrogen-like exciton states at high magnetic fields by magneto-optical studies of a 265/~-thick GaAs well. The excitonic nature
is confirmed by effective mass calculations which take into account valence-band mixing and external perturbations.
References [1] R. Dingle, W. Wiegmann and C. H. Henry, Phys. Rev. Lett. 33 (1974) 827. [2] J.C. Maan, G. Belle, A. Fasolino, M. Altarelli and K. Ploog, Phys. Rev. B 30 (1984) 2253. [3] S. Tarucha, H. Okamoto, Y. Iwasa and N. Miura, Solid State Commun. 52 (1984) 815. [4] O. Akimoto and H. Hasegawa, J. Phys. Soc. Jpn. 22 (1967) 181. [5] M. Shinada and K. Tanaka, J. Phys. Soc. Jpn. 29 (1970) 1258. [6] R.L. Greene and K.K. Bajai, Phys. Rev. B 31 (1985) 6498. [7] S.-R. Eric Yang and L.J. Sham, Phys. Rev. Lett. 58 (1987) 2598. [8] W. Ossau, D. Jakel, E. Bangert, G~ Landwehr and G. Welmann, Surf. Sci. 174 (1986) 188. [9] G.E.W. Bauer and T. Ando, Phys. Rev. B 38 (1988) 6015. [10] Y. Iimura, Y. Segawa, G.E.W. Bauer, M.M. Lin, Y. Aoyagi and S. Namba, Phys. Rev. B 42 (1990) 1478. [11] L. Vina, G.E.W. Bauer, M. Potemski, J.C. Maan, E.E. Mendez and W. I. Wang, Surf. Sci. 229 (1990) 504. [12] M. Potemski, L. Vina, G.E.W. Bauer, J.C. Maan, K. Ploog and G. Weimann, Phys. Rev. B 43 (1991) 14707.
Physica B 201 (1994) 407-410
Two-dimensional exciton states of GaAs/A1As multiquantum wells under high magnetic fields T. Yasui a'*, Y. Segawa a, Y. Aoyagi b, Y. Iimura c, G.E.W. Bauer d, I. Mogie,i~G.
Kido e
a Photodynamics Research Center, Frontier Research Program, The Institute of Physical and Chkfnical Research (RIKEN), Sendai, Japan b The Institute of Physical and Chemical Research (R1KEN), Saitama, Japan Tokyo University of Agriculture and Technology, Tokyo, Japan d Delft University of Technology, Delft, The Netherlands Institute for Materials Research, Tohoku University, Sendai, Japan
Abstract
.ydrogen-like exciton states at high magnetic fields up to/ 5 T re studied by magneto-optical spectroscopy of a multiquantum well sample with 265/~-thick wells of GaAs an~g2-60~-thick barriers of AlAs. These excitonic states are well explained by effective mass calculations which take into account residual electric fields in the sample and the valence band mixing in magnetic fields. A symmetry change of the exciton ground state is observed at a magnetic field of ~ 15 T.
1. Introduction
Since the early report by Dingle et al. [1], the study of two-dimensional (2D) exciton states confined in quantum wells has been advanced by many approaches. In particular, optical measurements in high magnetic fields are useful for investigating the 2D excitons in quantum wells, because they reveal the discrete energy levels and enhance the oscillator strengths of excitons. In the first experimental reports 1-2,3] about 2D excitons under high magnetic fields, it was pointed out that the lowest exciton levels corresponding to the heavy hole exciton and the light hole exciton show diamagnetic behavior individually. Furthermore, several peaks at higher photon energies were interpreted as Landau level transitions. Contrary to this interpretation, some researchers have proposed exciton states at higher energy under high
* Corresponding author.
magnetic fields (magnetoexcitons). Since the first theoretical reports about the magnetoexciton states in quantum wells [4-6], an excitonic nature at the higher energy region is predicted, but it has not been easy to obtain a good agreement with the experimental results [7]. Good agreement between experiment [8] and theory I-9] was later obtained by using high-quality samples. In recent years, the behavior of magnetoexcitons has been studied more precisely under intermediate 1-10] and high magnetic fields [11, 12]. These studies have shown that the magnetoexcitons in GaAs/A1As quantum wells, which reflect the complicated valence-band structure, have very complicated behavior under high magnetic fields. Since the relative importance of excitonic effects decrease with magnetic fields, this leads to the question if a Landau level model can explain the optical spectra of a quantum well under high magnetic fields. In an earlier work some of the present authors considered this problem by using a high-quality sample to determine the behavior of magnetoexcitons in
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 0 0 - A
408
T. Yasui et al./Physica B 201 (1994) 407-410
photoluminescence excitation (PLE) spectra up to 6 T [10]. The present work further addresses this problem by comparing a magneto-optical study and the calculation made by Bauer and Ando [9].
2. Experiment The sample used in this work is a multiquantum well with forty periods of 265 ,~-GaAs wells and 260/~-AlAs barriers, the details of which have been previously reported in Ref. [10]. PLE spectra were obtained by monitoring the luminescence of the lowest exciton level in a hybrid type magnet consisting of an outer superconducting magnet and an inner water-cooled resistive magnet of polyhelix type.The sample was kept at 4.2 K under magnetic fields ranging from 6 T up to 25 T. Light from a 250 W mercury lamp with a flat band in the spectral region of this study was passed through a monochromator with a spectral resolution of about 1 meV. It was circularly polarized in front of the sample in order to make a Faraday configuration with a + and a - polarization. The emitted light was detected by another monochromator at the photon energy of the lowest exciton level and led to a conventional photon counting system.
3. Results and discussion Fig. 1 shows the (r - PLE spectra at various magnetic field strengths. The a + PLE spectra were also measured but are not shown. One set of a - and (r + spectra give a complete measurement. Most of the peaks were given temporary labels, A, B, C, D, etc, and assigned to exciton states based on calculations to be discussed later. In this paper, the following notations are used for peaks: H(L) means heavy (light) holes; the first number is the electron subband and the second is the hole subband; and a hydrogenic label (nm) is used for the exciton envelope functions, where n is the total quantum number and m is the angular momentum quantum number as follows: ( . . . d - , p - , s, p + , d + , . . . ) . The spin labels are used, if necessary. To avoid complexity, this labeling system is limited to only a few cases in Fig. 1. At 0 T peaks were observed corresponding to exciton states and a step-like background was also seen. Several discrete peaks in these ]aLE spectra were clearly revealed and the background levels decreased as the magnetic field strength increased. This can be explained by the effects of the high magnetic fields, that is to say, both the increase of the binding energy with reduction of the exciton radius and quantization of the density of states. Fig. 1 also
(~--
T=4.2KI
L,~Sl "'~ H13(15)
C
L C I~CS~ A ~
25T [
g m C:
I
O
°' L11(IS)
"
---
j K
B--j%c -
D
I
L
13
H2211S}
Z,T2,,,:,
1.52 1.53 1.54 1.55 1.56 1.57 1.58 Photon Energy(eV) Fig. 1. PLE spectra of a 265/k-width GaAs quantum well sample at various magnetic fields with a - polarization. Peaks given temporary labels, A, B, C , . . . etc., are assigned to exciton states based on calculations in the literature I-9]. Other peaks were labeled as mentioned in the text.
shows the energy shifts of these peaks as the magnetic field increases. This study focuses on energy shifts and changes in oscillator strength of excitons as a function of magnetic field. To clarify these points, Fig. 2(a) and Fig. 2(b), for tr and tr + , respectively, show energy shifts in excitons as curves. Oscillator strengths are proportional to the area of the circles. The lowest states, as indicated by the bold curves, correspond to the H l l ( l s ) exciton state. Oscillator strength was normalized to the Lll(ls), which was constant throughout this measurement. Complicated energy shifts can be observed below 11 T in Fig. 2(a) and Fig. 2(b). In this region, a few exciton states mix with each other (see from 1.54 eV to 1.55 eV). Thus, peaks cannot easily be labeled by the predominant excitonic envelope function. The oscillator strengths of these peaks show very complicated changes. On the other hand, this behavior is simplified in the high magnetic field region where most peaks show a linear energy shift. This feature is a clear evidence for the reduction of exciton mixing. The crossing of H l l ( l s ) and L l l ( l s ) at 15T is shown in Fig. 2(b) but not in Fig. 2(a). It is obvious that the lowest exciton state, which is used for the monitored peak, is replaced by Lll(ls) over 15 T in a + polarization. This is explained by the effective mass of the excitons as determined by the GaAs well width ( = 265 ~). The spin splitting energy of H11(Is) is smaller than that of L11(ls)
409
T. Yasui et al./Physica B 201 (1994) 407 410 1.56
1.58
1.57
1.57 0
~"
1.56
1.56
c¢
1.56
1.55
1.54
1.54
1.53
1.53
LU
'
~
(b)
c 0
o
13..
1.52
1.52
5
10
15
20
25
5
10
Magneticfield(T)
15
20
25
Magneticfield(T)
Fig. 2. Magnetic field dependence of energy shifts of excitons up to 25 T with a - polarization (a) and a + polarization (b). The bold curves correspond to the monitored peak. The area of circles are proportional to oscillator strength of peaks in PLE spectra.
a n d it is difficult to observe by P L E measurement. Therefore the H l l ( l s ) peak crossed L l l ( l s ) in the a + configuration, but not in the a - one. This point is in good agreement with the calculation as m e n t i o n e d below. Fig. 3 shows experimental results (a) a n d calculations (b) of energy shifts as a function of magnetic fields with a + polarization. The details of the calculations are given in Ref. [9]. T h o s e calculations which are based on effec-
tive-mass theory, take into account the complicated vale n c e - b a n d structure, the effects of a residual electric field in the sample a n d magnetic fields as external p e r t u r b a tions. Since a forbidden transition ( = H12(ls)) is den o t e d in Fig. 3(a), the residual electric field should be considered in o u r sample. In earlier work, some of the present a u t h o r s estimated the value of the residual electric field to be ~ 3 k V / c m [10]. The crossing of L l l ( l s )
,o+1
1.,,
1.27
.,,,...,.,
1,54
~ 164 15a
10
L,,,,
,.,.,
IJJ
1.52
o+
t
.
.
.
.
.
.
.
.
.
.
.
.
.
.
15 20 Magneticfield (T)
'a'r
25
.
10
.
.
.
.
.
.
,
.
.
15 20 Magneticfield (T)
.
'°' 25
Fig. 3. Experimental results (a) and calculations (b) of energy shifts and oscillator strengths of excitons as a function of magnetic fields with ~r + polarization. The circles have the same meaning as in Fig. 2. The bold curve is the monitor peak in Fig. 3(a) and H1 l(ls) in Fig. 3(b), respectively. The underlined labels indicate uncertain assignments. The crossing of H1 l(ls) and L1 l(ls) is denoted.
410
T. Yasui et al./Physica B 201 (1994) 407-410
and H l l ( l s ) is well explained by the calculations as shown in Fig. 3(b). Good agreement is not obtained for the higher states of excitons at high magnetic fields as indicated by the underlined labels in Fig. 3(a). This is assumed to be due to the basis set limitations in the calculations. In other words, the basis for the radial functions in the plane of the well can perform satisfactory only for zero or intermediate magnetic fields (below 10 T) [9]. Even if some disagreement remains, it is clear that excitonic effects in our study of a 265/~-thick GaAs well remain to be significant even at high magnetic fields. These energy shifts of excitons have been observed by other researchers for various GaAs well thicknesses of 160/~ [11], 45/~ [12] and 30/~ [12]. More complicated spectra can be observed by increasing the well thickness. In these reports, the magnetoexciton states offer a good explanation of the experimental results. In the first magneto-optical study for GaAs quantum wells, however, these energy shifts were interpreted as Landau level transitions in thickness region of 50-125/~ [2] and 58-252 ~, [3]. It is difficult to identify the exact cause of this difference from our experimental results, but it is possibly caused by the poor sample quality in Refs. [2, 3], which did not allow the observation of excitonic effects. In conclusion, we have shown hydrogen-like exciton states at high magnetic fields by magneto-optical studies of a 265/~-thick GaAs well. The excitonic nature
is confirmed by effective mass calculations which take into account valence-band mixing and external perturbations.
References [1] R. Dingle, W. Wiegmann and C. H. Henry, Phys. Rev. Lett. 33 (1974) 827. [2] J.C. Maan, G. Belle, A. Fasolino, M. Altarelli and K. Ploog, Phys. Rev. B 30 (1984) 2253. [3] S. Tarucha, H. Okamoto, Y. Iwasa and N. Miura, Solid State Commun. 52 (1984) 815. [4] O. Akimoto and H. Hasegawa, J. Phys. Soc. Jpn. 22 (1967) 181. [5] M. Shinada and K. Tanaka, J. Phys. Soc. Jpn. 29 (1970) 1258. [6] R.L. Greene and K.K. Bajai, Phys. Rev. B 31 (1985) 6498. [7] S.-R. Eric Yang and L.J. Sham, Phys. Rev. Lett. 58 (1987) 2598. [8] W. Ossau, D. Jakel, E. Bangert, G~ Landwehr and G. Welmann, Surf. Sci. 174 (1986) 188. [9] G.E.W. Bauer and T. Ando, Phys. Rev. B 38 (1988) 6015. [10] Y. Iimura, Y. Segawa, G.E.W. Bauer, M.M. Lin, Y. Aoyagi and S. Namba, Phys. Rev. B 42 (1990) 1478. [11] L. Vina, G.E.W. Bauer, M. Potemski, J.C. Maan, E.E. Mendez and W. I. Wang, Surf. Sci. 229 (1990) 504. [12] M. Potemski, L. Vina, G.E.W. Bauer, J.C. Maan, K. Ploog and G. Weimann, Phys. Rev. B 43 (1991) 14707.