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Cyclotron and plasmon emission from two-dimensional electrons in GaAs
I IS
CYCLOTRON AND PLASMON EMISSION FROM TWO-DIMENSIONAL ELECTRONS IN GaAs
Rcccived IO July
19XI :
accepted for publication
26 Augubt 19X I
The properties of the 2D electron gas in GaAs/AlG:rA~
sin&
and multilaycrs
are in~~stig~t~d
hy means of the cyclotron emission technique. The carrier heating is found to depend on the input power. In contrast to the 3D case no saturation of the heating up to 100 V/cm ia ohxrved. first
For tht
time radiative decay of plasmon excitation in an accumulation layer of <;aAs is reported. The
intensity
of the order of IO
’ W is proportional
to the applied electric field.
1. In~~uction A quasi two-dimensional (2D) carrier gas can exist at the semiconductorsemiconductor interface of GaAs,/Ga,_., Al, As heterojunctions and heterojunction superlattices [1,2]. We have investigated the narrow band emission in the far infrared (FIR) from this system. Two types of emission processes have been generated by passing a current along the channel (parallel to the interface): The first process, a single particle excitation, is due to radiative transitions between Landau levels in a magnetic field, called cyclotron emission. The 2D carriers are heated up by the current to generate some population in higher Landau levels, which results in the emission process [3]. We have studied the intensity and linewidth of this process as a function of the exciting electric field for single interface and multilayer samples. The second process is the radiative decay of collective 2D plasma oscillations generated by a current as previously reported in Si MOSFETs [4]. We have applied a grating structure in the close vicinity of the 2D electron gas to couple out the radiation. The plasma emission from a GaAs/CaAlAs single interface heterostructure is investigated. The linewidth and intensity of the plasmon emission have been measured as a function of electric field on identical samples on which cyclotron emission has been observed to give some insight in the difference between a collective and single particle excitation. * Institut Xi
fir
Allgemeinc Elektrotcchnik
Beti Laboratories,
Murray
Hill.
0039-6028/82/0000-0000/$02.75
und Elcktronik.
Technische Universit%t.
New Jersey 07974. USA
0 1982 North-Holland
Vienna. Austria.
I IY
2.Cyclotron emission The GaAs/Al.Ga,_,As heterostructures were grown by molecular beam epitaxy. A single interface sample (sample 1: n-type GaAs layer 3 pm thick. n- 1 X 1Ol6cm-3, ~(4.2 K) = 14.000 cm’/V. s and a 2pm thick n-type Al.Ga,_,As layer with x = 0.26) and several multilayer samples are investigated (sample2: d(GaAs) = 185 A, d(Al.Ga,_,As) = 211 A, x = 0.25, TV= 16.000 cm’/V . s at T = 4.2 K, center of AlGaAs in a width of 90 A doped with Si, n = 2.3 X IO" cm-2 sample 3: d(GaAs) = 234A, d(Al.Ga,_,As) = 238 A, x = 6.224, AlGaAs homogeneously doped with Si, ~(4.2 K) = 9.000 cm’/V . s. n5 = 2.7 X 10” cmP2). The samples were platelets (3 X 4 mm2) with ohmic at 400°C. The electronic contacts made by alloying In in H, atmosphere excitation is created by applying a voltage to the contacts. The radiation resulting from the excitation was detected and analysed by narrowband detectors, which are either a high purity GaAs detector at a fixed frequency of 35.5 cm-’ or a InSb cyclotron resonance detector [5] tunable between 20 and 150 cm-’ with magnetic field. Fig. 1 shows cyclotron emission spectra for two different multilayer samples taken at 4.2 K with a GaAs detector as a function of magnetic field for two electric fields. The conductivity at low electric field is also shown revealing quantum oscillations. Spectra of the single interface sample have been published previously [3]. The sample mobilities differ by a factor of two what is evident from the width of the spectra. At lower electric fields quantum oscillations are apparent in the spectra, which are washed out with increasing field. The intensity oscillates 90” out of phase from the conductivity as expected for Landau emission. From a linewidth analysis we obtain for sample 2Ai;=9cm-‘andforsample3A,1=17cm -I, If we assume the dominance of ionized impurity scattering then the linewidth is caused by certain doping levels N, in the vicinity of the 2D layer [6]. We obtain for sample 2 N, - 8 X lOI cmA3 and 3 X lOI cmP3 for sample 3. In both samples the GaAs layer is unintentionally doped to about the same level; the difference in linewidth is then onlydue to the doping of the AlGaAs. In this case the narrow linewidth of sample 2 directly reflects the effect of a center doping of AlGaAs layer as it has been shown recently with mobility data [7]. Fig. 2 shows the relative intensity of the cyclotron emission of sample 1 and 2 as a function of the exciting electric field. For sample 1 emission data for 2D and 3D electrons are included. The existence of both types of electrons has been demonstrated in ref. [5]. For the 3D electron gas a saturation of the electron heating is found for fields between 30 and 50 V/cm. The intensity increases with the square of the field for 2D electrons and no saturation is found in the investigated field range which was extended to 100 V/cm. It is evident that the heating is less efficient in the 2D system. We have normalized the spectra to the same effective number of electrons and have only included two samples with comparable mobilities. In this case the square of the electric
2
E,
20
3.0 Magnetic Field CT)
40
1
loo Electr:
Fkzld (V/cm)
field is a direct measure of the input power. Comparing the single interface sample with the multilayer sample we find that the heating is suppressed more in multilayers probably due to the stronger confinement of the electron gas. This indicates that the interface introduces some additional mechanisms for the energy relaxation. This means that for a given electric field lower electron temperatures are achieved in a 2D electron gas than compared with a 3D electron gas. This is also evident from quantum oscillations which are present in the spectra up to fields of 10 V/cm.
3. Plasmon
emission
The excitation of 2D plasma oscillations in a thin sheet of electrons embedded in a 3D dielectric has been theoretically predicted by Ritch-it: [Xl. The basic dispersion relation was given as 0; = PI~~‘~/~~I*cc,,, where q is the wave vector and wP the plasmon frequency. This relation is only valid if q c* X, (Fermi vector). The relation was later applied to real MOS systems [9- Ill. resulting in: w;x--
n,e? m*
q
I cc, c, +EZcoth(qri)
The modification
accounts
(1) for the dielectric
constants
of Si (6,) and SiO, (E? )
and the finite thickness of the oxide (d). Eq. (1) was verified with high accuracy first by Allen et al. [ 121 and by Theis et al. [13,14] in FIR transmission experiments. The coupling between the light wave and the plasma wave was obtained through a grating structure on top of the semi-transparent gate of the devices. The inverse process to the plasma excitation by absorption of light namely the radiative decay of plasma oscillations was observed for the first time by Tsui et al. [4]. The excitation was generated by passing a current through the channel of a Si MOSFET device. The coupling to the light wave was provided by a grating as in the case of absorption. Emission intensities in the order of 10 ‘W were obtained. We have applied this principle to an accumulation layer in GaAs (sample 1). The electron density in the layer is 8.25 X 10” cm -’ and can be increased by illumation with band gap radiation [2] to 8.9 X 10” by. Shubnikov-De Haas oscillations. First a 5 pm grating cm ’ as determined (1OOOA Al 1: 1) was placed on top of the GaAlAs. A current was passed through the layer and the emitted radiation was detected and analysed with a tunable InSb detector. Resonant emission was observed at a frequency of 29 cm -‘. To prove the nature of the resonant emission the 5 pm grating was replaced by a 3 pm grating which is supposed to change the emission frequency according to eq. (1). The observed spectra (at 4.2 K) are shown in fig. 3 as a function of the tunable detector magnetic field for three different exciting electric fields. A resonant signal is observed at 0.6 T corresponding to a frequency of 38 cm-‘. For comparison curve d was taken with a broadband InSb source to show the background sensitivity of the detector. The emission frequencies for the two different gratings as obtained by several experiments are displayed in fig. 4.
0.5 InSb-Detector Magnetic Field (T) Fig. 3. Plasmon grating).
emission
signal as observed
for several electric
field.\ with an InSb detector
(3 pm
I
-
1%
I
I”_’ 1
- - -Theory: $m a Experiment - - - Theory 3um A 0
Experiment lo
’
i
I
& -7s b-
*z I h I 6. I * ’ ** ’ * I
20 30 LO Frequency of Emission km-‘)
Fig. 4. Plasmnn emission frcqucncics comparison with theor]r (eq. (1)).
from
50
several
experiments
for 3 and
5 pm
grating5
in
The dashed lines give the calculated emission frequency from eq. {I) assuming an accumulation layer embedded between infinite media of GaAs (e, = 11.5) and GaAlAs (t2 = 1 I). In the real case the GaAlAs layer has a finite thickness (d< 1.0 pm) so that the plasmon will “feel”the close vacuum. An explanation for the observed higher frequency might therefore be a lower effective f2. The radiation intensity observed is the order of (2 - 3) X 10 -’ W and thus more than an order of magnitude higher than from Si MOSFETs 141. One major reason for the increased intensity is the absence of a semitransparent gate resulting in a more defined grating structure. In addition the outcoupling of the radiation might be enhanced by the better dielectric match between the plasmon and grating through the GaAlAs layer. The dependence of the intensity on the exciting electric field is shown in fig. 5. The intensity increases nearly linearly in the investigated field range (10to 20 V/cm). Cyclotron emission from the identical sample showed an intensity behaviour proportional to the square of the electric field. This indicates that the carrier heating. which is responsible for cyclotron emission, cannot fully explain the plasmon excitation. This is also evident from the experiments with Si MOSFETs, where a dependence of the radiation on the grating orientation was found (41. At fields lower than 10 V/cm the radiation intensity was too small to be detected by the InSb detector. The emission linewidth is found to increase between fields of E = 10V/cm and 40 V/cm. At low electric fields it tends toward the scattering-limited determined from cyclotron linewidth of 12 cm-‘, which was independently emission experiments 131. At very high fields (greater than 50 V/cm) the plasmon oscillation is completely washed out and no resonant emission is detectable. A further improvement in emission intensity and linewidth seems possible if samples with considerably higher mobilities are used.
&-Grating GWAS 537
GoAs -
A
E _ u +_-----__
x _ c
A ,A$”
6 -E
2 Ii=
0 5-_
A
EmissionLinewdth
_ _P
q
Intensity
-2
00
0
--I,,,,, ‘1
10
Electric
Scottwing Limited Linewdth
I 41111111
cc
L )
100 Field (Wcm)
Fig. 5. Intensity and linwidth dependence bhows the principal sample btructurcs.
of plaamon
emission
over electric
field. The insert
Acknowledgments This work was partly supported by the Fonds zur FGrderung der Wissenschaftlichen Forschung, Austria (Projekt S22/05) and by the European Research Office of the US Army (Contract No. DAJA 37-81-C-0046).
References [II [II
L.L. Chang, H. Sakaki, C.A. Chang and L. Esaki, Phys. Rev. Letters 3X (1977) 14X9. R. Dingle. H.L. StBrmer. A.C. Gossard and W. Wiegmann. Appl. Phys. Letters 7 (197X) 665: H.L. StBrmer. R. Din@, A.C. Gossard. W. Wiegmann and M.D. Sturge, Sohd State Commun. 29 (1979) 705. [31 E. Gornik. R. Schawarz. D.C. Tsui. A.C. Gossard and W. Wiegmann. Solid State Commun. 38 (1981) 541. [41 D.C. Tsui, E. Gornik and R.A. Logan. Solid State Commun. 35 (1980) X75. [51 E. Gornik, R. Schawarz, G. Lindemann and D.C. Tsui, Surface Sci. 9X (1980) 493. E. Gornik, R. Schawarz and D.C. Tsui, in: Proc. 8th Intern. Symp. on GaAa [61 G. Lindemann, and Related Compounds, Vienna, 1980. Inst. Phys. Conf. Ser. 56 (Inst. Phys.. London. 19X1) p. 63 I. I71 H.L. Stiirmer. A. Pinczuk, A.C. Gossard and W. Wiegmann, Appl. Phys. Letter 3X (19X1) 691. [Xl R.H. Ritchie, Phys. Rev. 106 (1957) X74. 191 A.V. Chaplik, Zh. Eksperim. Tear. Fiz. 62 (1972) 746 [Soviet Phys.-JETP 35 (1972) 3951. J. Phys. Sot. Japan 36 (1974) 393. [lOI M. Nakayama. [ill A. Eguiluz, T.K. Lee. J.J. Quinn and K.W. Chiu, Phys. Rev. RI I (1975) 49X9. [I21 S.J. Allen, D.C. Tsui and R.A. Logan, Phys. Rev. Letters 3X ( 1977) 980. [l31 T.N. Theis, J.P. Kotthaus and P.J. Stiles, Solid State Commun. 26 (197X) 603. [l41 T.N. Theis. Surface Sci. 9X (19X0) 5 15.
CYCLOTRON AND PLASMON EMISSION FROM TWO-DIMENSIONAL ELECTRONS IN GaAs
Rcccived IO July
19XI :
accepted for publication
26 Augubt 19X I
The properties of the 2D electron gas in GaAs/AlG:rA~
sin&
and multilaycrs
are in~~stig~t~d
hy means of the cyclotron emission technique. The carrier heating is found to depend on the input power. In contrast to the 3D case no saturation of the heating up to 100 V/cm ia ohxrved. first
For tht
time radiative decay of plasmon excitation in an accumulation layer of <;aAs is reported. The
intensity
of the order of IO
’ W is proportional
to the applied electric field.
1. In~~uction A quasi two-dimensional (2D) carrier gas can exist at the semiconductorsemiconductor interface of GaAs,/Ga,_., Al, As heterojunctions and heterojunction superlattices [1,2]. We have investigated the narrow band emission in the far infrared (FIR) from this system. Two types of emission processes have been generated by passing a current along the channel (parallel to the interface): The first process, a single particle excitation, is due to radiative transitions between Landau levels in a magnetic field, called cyclotron emission. The 2D carriers are heated up by the current to generate some population in higher Landau levels, which results in the emission process [3]. We have studied the intensity and linewidth of this process as a function of the exciting electric field for single interface and multilayer samples. The second process is the radiative decay of collective 2D plasma oscillations generated by a current as previously reported in Si MOSFETs [4]. We have applied a grating structure in the close vicinity of the 2D electron gas to couple out the radiation. The plasma emission from a GaAs/CaAlAs single interface heterostructure is investigated. The linewidth and intensity of the plasmon emission have been measured as a function of electric field on identical samples on which cyclotron emission has been observed to give some insight in the difference between a collective and single particle excitation. * Institut Xi
fir
Allgemeinc Elektrotcchnik
Beti Laboratories,
Murray
Hill.
0039-6028/82/0000-0000/$02.75
und Elcktronik.
Technische Universit%t.
New Jersey 07974. USA
0 1982 North-Holland
Vienna. Austria.
I IY
2.Cyclotron emission The GaAs/Al.Ga,_,As heterostructures were grown by molecular beam epitaxy. A single interface sample (sample 1: n-type GaAs layer 3 pm thick. n- 1 X 1Ol6cm-3, ~(4.2 K) = 14.000 cm’/V. s and a 2pm thick n-type Al.Ga,_,As layer with x = 0.26) and several multilayer samples are investigated (sample2: d(GaAs) = 185 A, d(Al.Ga,_,As) = 211 A, x = 0.25, TV= 16.000 cm’/V . s at T = 4.2 K, center of AlGaAs in a width of 90 A doped with Si, n = 2.3 X IO" cm-2 sample 3: d(GaAs) = 234A, d(Al.Ga,_,As) = 238 A, x = 6.224, AlGaAs homogeneously doped with Si, ~(4.2 K) = 9.000 cm’/V . s. n5 = 2.7 X 10” cmP2). The samples were platelets (3 X 4 mm2) with ohmic at 400°C. The electronic contacts made by alloying In in H, atmosphere excitation is created by applying a voltage to the contacts. The radiation resulting from the excitation was detected and analysed by narrowband detectors, which are either a high purity GaAs detector at a fixed frequency of 35.5 cm-’ or a InSb cyclotron resonance detector [5] tunable between 20 and 150 cm-’ with magnetic field. Fig. 1 shows cyclotron emission spectra for two different multilayer samples taken at 4.2 K with a GaAs detector as a function of magnetic field for two electric fields. The conductivity at low electric field is also shown revealing quantum oscillations. Spectra of the single interface sample have been published previously [3]. The sample mobilities differ by a factor of two what is evident from the width of the spectra. At lower electric fields quantum oscillations are apparent in the spectra, which are washed out with increasing field. The intensity oscillates 90” out of phase from the conductivity as expected for Landau emission. From a linewidth analysis we obtain for sample 2Ai;=9cm-‘andforsample3A,1=17cm -I, If we assume the dominance of ionized impurity scattering then the linewidth is caused by certain doping levels N, in the vicinity of the 2D layer [6]. We obtain for sample 2 N, - 8 X lOI cmA3 and 3 X lOI cmP3 for sample 3. In both samples the GaAs layer is unintentionally doped to about the same level; the difference in linewidth is then onlydue to the doping of the AlGaAs. In this case the narrow linewidth of sample 2 directly reflects the effect of a center doping of AlGaAs layer as it has been shown recently with mobility data [7]. Fig. 2 shows the relative intensity of the cyclotron emission of sample 1 and 2 as a function of the exciting electric field. For sample 1 emission data for 2D and 3D electrons are included. The existence of both types of electrons has been demonstrated in ref. [5]. For the 3D electron gas a saturation of the electron heating is found for fields between 30 and 50 V/cm. The intensity increases with the square of the field for 2D electrons and no saturation is found in the investigated field range which was extended to 100 V/cm. It is evident that the heating is less efficient in the 2D system. We have normalized the spectra to the same effective number of electrons and have only included two samples with comparable mobilities. In this case the square of the electric
2
E,
20
3.0 Magnetic Field CT)
40
1
loo Electr:
Fkzld (V/cm)
field is a direct measure of the input power. Comparing the single interface sample with the multilayer sample we find that the heating is suppressed more in multilayers probably due to the stronger confinement of the electron gas. This indicates that the interface introduces some additional mechanisms for the energy relaxation. This means that for a given electric field lower electron temperatures are achieved in a 2D electron gas than compared with a 3D electron gas. This is also evident from quantum oscillations which are present in the spectra up to fields of 10 V/cm.
3. Plasmon
emission
The excitation of 2D plasma oscillations in a thin sheet of electrons embedded in a 3D dielectric has been theoretically predicted by Ritch-it: [Xl. The basic dispersion relation was given as 0; = PI~~‘~/~~I*cc,,, where q is the wave vector and wP the plasmon frequency. This relation is only valid if q c* X, (Fermi vector). The relation was later applied to real MOS systems [9- Ill. resulting in: w;x--
n,e? m*
q
I cc, c, +EZcoth(qri)
The modification
accounts
(1) for the dielectric
constants
of Si (6,) and SiO, (E? )
and the finite thickness of the oxide (d). Eq. (1) was verified with high accuracy first by Allen et al. [ 121 and by Theis et al. [13,14] in FIR transmission experiments. The coupling between the light wave and the plasma wave was obtained through a grating structure on top of the semi-transparent gate of the devices. The inverse process to the plasma excitation by absorption of light namely the radiative decay of plasma oscillations was observed for the first time by Tsui et al. [4]. The excitation was generated by passing a current through the channel of a Si MOSFET device. The coupling to the light wave was provided by a grating as in the case of absorption. Emission intensities in the order of 10 ‘W were obtained. We have applied this principle to an accumulation layer in GaAs (sample 1). The electron density in the layer is 8.25 X 10” cm -’ and can be increased by illumation with band gap radiation [2] to 8.9 X 10” by. Shubnikov-De Haas oscillations. First a 5 pm grating cm ’ as determined (1OOOA Al 1: 1) was placed on top of the GaAlAs. A current was passed through the layer and the emitted radiation was detected and analysed with a tunable InSb detector. Resonant emission was observed at a frequency of 29 cm -‘. To prove the nature of the resonant emission the 5 pm grating was replaced by a 3 pm grating which is supposed to change the emission frequency according to eq. (1). The observed spectra (at 4.2 K) are shown in fig. 3 as a function of the tunable detector magnetic field for three different exciting electric fields. A resonant signal is observed at 0.6 T corresponding to a frequency of 38 cm-‘. For comparison curve d was taken with a broadband InSb source to show the background sensitivity of the detector. The emission frequencies for the two different gratings as obtained by several experiments are displayed in fig. 4.
0.5 InSb-Detector Magnetic Field (T) Fig. 3. Plasmon grating).
emission
signal as observed
for several electric
field.\ with an InSb detector
(3 pm
I
-
1%
I
I”_’ 1
- - -Theory: $m a Experiment - - - Theory 3um A 0
Experiment lo
’
i
I
& -7s b-
*z I h I 6. I * ’ ** ’ * I
20 30 LO Frequency of Emission km-‘)
Fig. 4. Plasmnn emission frcqucncics comparison with theor]r (eq. (1)).
from
50
several
experiments
for 3 and
5 pm
grating5
in
The dashed lines give the calculated emission frequency from eq. {I) assuming an accumulation layer embedded between infinite media of GaAs (e, = 11.5) and GaAlAs (t2 = 1 I). In the real case the GaAlAs layer has a finite thickness (d< 1.0 pm) so that the plasmon will “feel”the close vacuum. An explanation for the observed higher frequency might therefore be a lower effective f2. The radiation intensity observed is the order of (2 - 3) X 10 -’ W and thus more than an order of magnitude higher than from Si MOSFETs 141. One major reason for the increased intensity is the absence of a semitransparent gate resulting in a more defined grating structure. In addition the outcoupling of the radiation might be enhanced by the better dielectric match between the plasmon and grating through the GaAlAs layer. The dependence of the intensity on the exciting electric field is shown in fig. 5. The intensity increases nearly linearly in the investigated field range (10to 20 V/cm). Cyclotron emission from the identical sample showed an intensity behaviour proportional to the square of the electric field. This indicates that the carrier heating. which is responsible for cyclotron emission, cannot fully explain the plasmon excitation. This is also evident from the experiments with Si MOSFETs, where a dependence of the radiation on the grating orientation was found (41. At fields lower than 10 V/cm the radiation intensity was too small to be detected by the InSb detector. The emission linewidth is found to increase between fields of E = 10V/cm and 40 V/cm. At low electric fields it tends toward the scattering-limited determined from cyclotron linewidth of 12 cm-‘, which was independently emission experiments 131. At very high fields (greater than 50 V/cm) the plasmon oscillation is completely washed out and no resonant emission is detectable. A further improvement in emission intensity and linewidth seems possible if samples with considerably higher mobilities are used.
&-Grating GWAS 537
GoAs -
A
E _ u +_-----__
x _ c
A ,A$”
6 -E
2 Ii=
0 5-_
A
EmissionLinewdth
_ _P
q
Intensity
-2
00
0
--I,,,,, ‘1
10
Electric
Scottwing Limited Linewdth
I 41111111
cc
L )
100 Field (Wcm)
Fig. 5. Intensity and linwidth dependence bhows the principal sample btructurcs.
of plaamon
emission
over electric
field. The insert
Acknowledgments This work was partly supported by the Fonds zur FGrderung der Wissenschaftlichen Forschung, Austria (Projekt S22/05) and by the European Research Office of the US Army (Contract No. DAJA 37-81-C-0046).
References [II [II
L.L. Chang, H. Sakaki, C.A. Chang and L. Esaki, Phys. Rev. Letters 3X (1977) 14X9. R. Dingle. H.L. StBrmer. A.C. Gossard and W. Wiegmann. Appl. Phys. Letters 7 (197X) 665: H.L. StBrmer. R. Din@, A.C. Gossard. W. Wiegmann and M.D. Sturge, Sohd State Commun. 29 (1979) 705. [31 E. Gornik. R. Schawarz. D.C. Tsui. A.C. Gossard and W. Wiegmann. Solid State Commun. 38 (1981) 541. [41 D.C. Tsui, E. Gornik and R.A. Logan. Solid State Commun. 35 (1980) X75. [51 E. Gornik, R. Schawarz, G. Lindemann and D.C. Tsui, Surface Sci. 9X (1980) 493. E. Gornik, R. Schawarz and D.C. Tsui, in: Proc. 8th Intern. Symp. on GaAa [61 G. Lindemann, and Related Compounds, Vienna, 1980. Inst. Phys. Conf. Ser. 56 (Inst. Phys.. London. 19X1) p. 63 I. I71 H.L. Stiirmer. A. Pinczuk, A.C. Gossard and W. Wiegmann, Appl. Phys. Letter 3X (19X1) 691. [Xl R.H. Ritchie, Phys. Rev. 106 (1957) X74. 191 A.V. Chaplik, Zh. Eksperim. Tear. Fiz. 62 (1972) 746 [Soviet Phys.-JETP 35 (1972) 3951. J. Phys. Sot. Japan 36 (1974) 393. [lOI M. Nakayama. [ill A. Eguiluz, T.K. Lee. J.J. Quinn and K.W. Chiu, Phys. Rev. RI I (1975) 49X9. [I21 S.J. Allen, D.C. Tsui and R.A. Logan, Phys. Rev. Letters 3X ( 1977) 980. [l31 T.N. Theis, J.P. Kotthaus and P.J. Stiles, Solid State Commun. 26 (197X) 603. [l41 T.N. Theis. Surface Sci. 9X (19X0) 5 15.