- Email: [email protected]
Quantized structure in the photoinduced absorption spectra of band-edge modulated a-Si1-xNx:H films
] O U R N A b OF
Journal of Non-Crystalline Solids 137&138 (1991) 1115-1118 North-Holland
QUANTIZED STRUCI'URE IN THE PHOTOINDUCED ABSORPTION SPECTRA OF BAND-EDGE MODULATED a-Sil_xNx:H FILMS Ying LI, M. KONDO, M. YAMAGUCHI and K. MORIGAKI Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo 106, Japan The photoinduced absorption spectra have been measured for the band-edge modulated a-Sil.xNx:H films, in which the edges of the conduction and valence bands are spatially modulated with an almost sinusoidal function. The results of the quantized structure of the PA spectra are presented and discussed.
superlattices5,6.
1. INTRODUCTION Recently
we
prepared
a
new
type
of
artificial
semiconducting materials, called the band-edge modulated
2. EXPERIMENTAL
(BM) a-Sil_xNx:H films 1,2 in which the edges of the
The BM a-Sil-xNx:H films were prepared by using a
conduction and valence bands are spatially modulated with
capacitively coupled glow-discharge system. The detail of
along a direction,
the preparation method has been reported in ref.(2). The
z, perpendicular to the deposited layers, as shown in Fig. 1.
films with various modulation periods, L, ranging from 21
For the BM films whose modulation amplitude is so large
to 290 ,~. were deposited onto the fused silica substrate at
an
almost
sinusoidal
function
that optically excited carriers are located around either the
250 °C. The values of Emax and Ernin in Fig. 1 were 4.05
bottom (for electrons) or the top (for holes) of the modulated
eV and 1.91 eV, respectively. The optical gap energy for
band edge, the optical absorption spectra and luminescence
each sample, Eg, is described in each figure caption except
spectra have been measured as a function of the modulation
for sample No. 6017.
period
in the range of 30 - 300,~ 1-3. The optical gap of the
The PA measurements were carried out at 7K, using
BM films increases with decreasing modulation period in
unfocused argon ion laser light of either 514.5 nm or 488
such a way that its difference from Emin in Fig. 1 is almost
nm as an excitation light. The transmitted intensity, T, of
inversely proportional to the modulation period. This result
probe light changed with the laser excitation chopped at 80 Hz, so the change, AT, was lock-in detected by using a
indicates the quantum-size effect in the BM films and can be accounted for in terms of effective-mass equations for those electrons and holes which are affected by modulated potentials around z = 0,
harmonic oscillator potential1,2. The quantized structure in the band, however, has not yet been clarified in those BM films.
DOS
these being approximated by a
In this paper, we report, for the first time, the
observation of the quantized structure in the valence band of the BM films through the photoinduced (PA) spectra at 7 K.
c
B .ES;z-
T2yWW ~A Emax
n
*c
VB
LIJ
The PA spectra are due to optical transitions of self-trapped
Z
holes in weak Si-Si bonds (the A centres 4) into the valence
>
band, as shown in Fig. 1, where a schematic diagram of the density-of-state spectra in the conduction and valence bands is also shown. The quantized structure in the PA spectra
has
been
observed
in
a-Si:H/a-Si3N4:H
FIGURE 1 Schematic diagram for the optical transitions responsible for PA and for the density of states spectrum in BM a-Sil_xNx:H films.
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
Y. Li et aL / Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
1116
cooled Ge detector for all samples and also an InAs detector for some samples. Probe light was obtained by single prism
quantum-size effect on the edge of the valence band in the BM films.
monochromator from a tungsten lamp with a filter cutting the light of wavelength shorter than 690 nm. Interference fringes superposed over optical spectra were removed by using a
NO6008
0.e
150PERIODS L:67,~
procedure developped by Ohta 5 in our laboratory. The PA spectra correspond to -AT/T as a function of photon energy,
I.-- 0.4-
-tim, of the probe light.
//
0-2~
3. EXPERIMENTAL RESULTS Typical examples of the observed PA spectra for L
=
0.5
100
1.'0 . . . . PHOTON ENERGY(eV)
1.'5 '
2.0
67 .A and 21 .& are shown in Figs.2 - 4. In Fig. 5, the Lucovsky plot of the PA spectrum is shown for L = 290 A. The Lucovsky plot8which is well fitted to the observed PA spectra in a-Si:H bulk films 7 is given by
( - A T / T ) Z/3(ho))zo: (hm-Et~)
FIGURE 3 PA spectrum for BM film No.6008 with L = 67 _A(Eg= 2.06 eV). A dot-dashed curve and a dashed curve have ttie same definition as in Fig. 2.
(1)
where'l~e0 and Eth are the photon energy and the threshold energy, respectively. The
threshold energy taken
NO 6017
230 PERIODS L=21.~
by
extrapolation of the Lucovsky plot, as shown in Fig. 5, was obtained from the observed PA spectra, where the high energy part was fitted to the Lucovsky type, as shown in these figures. The values of Eth are shown as a function of .
t'•/ J
•5
L "1 in Fig. 6. Eth corresponds to the depth of the A centre
[ ,
1
,
I
,
.
,
I
1 PHOTON ENERGY(eV)
.
.
.
.
1.5
level in a-Si:H bulk films, but in the BM films, as will be shown below, the PA spectra deviate from the Lucovsky type and have a tail extending towards lower energy. Thus, the value of Eth has no definitive meaning, but its dependence on L -1 as shown in Fig. 6 suggests the
1.0-
No6006
FIGURE 4 PA spectrum for BM film No.6017 with L = 21 ~,. A dotdashed curve and a dashed curve have the same definition as in Fig. 2.
100PERIODS L=10OA No 6004 3
5
P
E
~
2 0.5-
2 Eth=O,525eV..I 2 0. ~
. . . .
~ .b
. . . .
ill 5
. . . .
E =0.50eV ~
2. 0
PHOTON ENERGY(eV)
FIGURE 2 PA spectrum for BM film No.6006 with L = 100 ~, (Eg = 1.97 eV). A dot-dashed curve and a dashed curve are the Lucovsky-type one fitted to the observed one and the theoretical one, respectively.
i
~ ,
0.5
.
.
.
1 PHOTON ENERGY(eV)
.
.
.
15
FIGURE 5 Lucovsky plot for BM film No.6004 with L = 290 A (Eg = 1.96 eV).
Y. Li et aL /Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
1117
where Vo is the coefficient of the harmonic oscillator potential, V~ (£
Vz= Vo(z/L) 2
Q
(6)
0
C" LtJ
0
and L is the modulation period. Using the wave function,
0
Zi(z), of the i-th quantized level, the matrix element of I
I
I
I
I
I
2
3
4
5
optical transitions is given by
L-' ( lO-Z~,-l )
M+_=
i(6)t/2yC~ _ . , [
+-------~- / -
FIGURE 6 Plot of Etla vs. L -1 for BM films.
,/2
,a_~
Zi(zj
lzl
L77~
1.
+
(~+a2)a/2]
x exp [-(~+6=)t/X]lzl dz,
(7)
4. DISCUSSION Before discussing the experimental results in detail, we 2m (E-E,i) ]1/2,
briefly present the theoretical expressions of the PA spectra
r= -~-
(8)
2m Eo)1/2, a = --~-
(9)
in the BM films. The PA is proportional to the cross section of optical absorption, o, so we calculate o, assuming that the initial state is a bound state of a hole affected by 6-potential and that the final state is a bound state of a hole affected by a harmonic oscillator potential for z-direction, being of two-dimensional free particle for the x, y plane6. The spatial position of a hole centre is assumed to be located at the centre of the harmonic oscillator potential, as shown in Fig. 1. Using the matrix element of optical transitions, M, the differential cross section, do/dg2, is given by tOme2
d•=•
IMI2f (E-E*I)
where Eo is the bound state energy of a hole afffected by 6-potential (Eo>0) and the superscripts of M* designate the direction of polarization perpendicular to the z direction.
(2) 100A 0
where f(E - Ezi) is a step function in the following expression of the density of states, n(E),
67A
/+/+A
30A
21 fl,
?/;?I
>
n
mL a (E) = ~i (2-2~ f
(3)
0.5"- . . . . . . (,9 CC hl Z la.l
and its height is proportional to (Ezi) 1/2. m and~m in eq.(2) are the effective mass of the hole and photon energy of the
1.0
probe light, respectively and Ezi is the z-component of energy of the i-th quantized level being expressed by E~i= (n++) hto0
(4)
tOo= ( Vo/mL z) i/2
(5)
FIGURE 7 Calculated quantized levels in the valence band of BM films with various values of L. The level shown by solid lines and dashed lines are optically allowed and forbidden ones, respectively.
1118
Y Li et aL / Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
The cross section, o, is obtained by integrating in the x,
superlattices.
However, free holes in the BM films are
y plane and by taking into account two directions of polarization shown above, so that o is given by 4zt times
localized at the bottom of the harmonic oscillator potential,
eq.(2). The integration of eq.(7) was numerically performed.
range compared to the modulation period. Thus, the reason
The calculated energies of the quantized levels for various
of why the quantized structure can be observed for L = 67 A,
so that the free hole's movement is limited to some narrow
values of L are shown in Fig. 7, in which Vo = 9.54 eV and
and presumably for L = 100 A, seems reasonable from the
m = free electron mass are takenl, 2.
view point of the broadening of the quantized level and the A
The calculated PA curves for L = 100 ,~, 67 ,~ and 21 .~ are shown in Figs. 2, 3 and 4, respectively. For L = 190 ~,
centre level and also comparison between the present case and the case of a-Si:H/a-Si3N4:H superlattices.
eight quantized levels participate in the PA spectrum, so the PA curve is close to the Lucovsky type of the bulk film. On the other hand, for L = 21 ~,, only the lowest quantized level (n = 0)
contributes to the PA spectrum, so the PA curve is
very different from the Lucovsky type, as shown in Fig. 4.
5. CONCLUSIONS We have observed the quantized structure in the valence band of the BM films with L = 67 ,~ and presumably for L = 100 ,~ from the PA measurements. A significant tailing
In the following, we compare the observed PA curves
towards lower photon energy of the PA spectra for BM
with the calculated ones. As shown in Fig. 3, the observed
films with shorter modulation periods may be due to the
PA spectrum for L = 67 _Aexhibits a structure which almost
broadening of the quantized levels and the A centre levels.
corresponds to a structure in the calculated PA spectrum, although it is broadened compared to the calculated one. The observed PA spectrum for L = 100 ~_ appears to exhibit a subtle structure which can be compared with the calculated
Acknowledgements We wish to thank Drs. C. Ogihara, H. Ohta and H. Yokomichi for helpful discussions.
one. On the other hand, the observed PA spectrum for BM films wiht L ranging between 44 .~, and 21 ,~, could not be
REFERENCES
fitted to the calculated ones owing to a tail extending
1. C. Ogihara, H. Ohta, M. Yamaguchi and K. Morigaki, Jpn. J. Appl. Phys. 28 (1989) L741.
towards lower energy. Such tail is due to broadening of the quantized level by disorder inherent to amorphous structure and also by some distribution of the modulation period coming from deposition processes of the BM films. These origins may be enhanced as the modulation period decreases. Furthermore, the broadening of the A centre level should be taken into account for the BM films with shorter modulation period. Finally, we compare the PA spectra for the BM films with those for a-Si:H/a-Si3N4:H superlattice films 6.
In
a-Si:H/a-Si3N4:H superlattices, where the barrier-layer thickness is fixed at 25 ,~ and the well-layer thickness, Lw, is varied, the quantized structure has been observed in the PA spectra for Lw -- 18 .~, and 36 ,~. The modulation period for which the quantized structure was observed in the BM films is longer than the well-layer thickness of the
2. C. Ogihara, H. Ohta, M. Yamaguchi and K. Morigaki, Phil. Mag. B62 (1990) 261. 3. M. Yamaguchi, C. Ogihara, H. Ohta and K. Morigaki, J. Non-Cryst. Solids 114 (1989) 705. 4. K. Morigaki, Amorphous Silicon and Related Materials, Vol. A, ed. H. Fritzsche (World Scienific, Singapore, 1989) pp. 595-631. 5. H. Ohta, Doctor Thesis, University of Tokyo, 1989, unpublished. 6. H. Ohta and K. Morigaki, Solid State Commun. 72 (1989) 425. 7. I. Hirabayashi and K. Morigaki, J. Non-Cryst. Solids 59&60 (1983) 433. 8 G. Lucovsky, Solid State Commun. 3 (1965) 299.
Journal of Non-Crystalline Solids 137&138 (1991) 1115-1118 North-Holland
QUANTIZED STRUCI'URE IN THE PHOTOINDUCED ABSORPTION SPECTRA OF BAND-EDGE MODULATED a-Sil_xNx:H FILMS Ying LI, M. KONDO, M. YAMAGUCHI and K. MORIGAKI Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo 106, Japan The photoinduced absorption spectra have been measured for the band-edge modulated a-Sil.xNx:H films, in which the edges of the conduction and valence bands are spatially modulated with an almost sinusoidal function. The results of the quantized structure of the PA spectra are presented and discussed.
superlattices5,6.
1. INTRODUCTION Recently
we
prepared
a
new
type
of
artificial
semiconducting materials, called the band-edge modulated
2. EXPERIMENTAL
(BM) a-Sil_xNx:H films 1,2 in which the edges of the
The BM a-Sil-xNx:H films were prepared by using a
conduction and valence bands are spatially modulated with
capacitively coupled glow-discharge system. The detail of
along a direction,
the preparation method has been reported in ref.(2). The
z, perpendicular to the deposited layers, as shown in Fig. 1.
films with various modulation periods, L, ranging from 21
For the BM films whose modulation amplitude is so large
to 290 ,~. were deposited onto the fused silica substrate at
an
almost
sinusoidal
function
that optically excited carriers are located around either the
250 °C. The values of Emax and Ernin in Fig. 1 were 4.05
bottom (for electrons) or the top (for holes) of the modulated
eV and 1.91 eV, respectively. The optical gap energy for
band edge, the optical absorption spectra and luminescence
each sample, Eg, is described in each figure caption except
spectra have been measured as a function of the modulation
for sample No. 6017.
period
in the range of 30 - 300,~ 1-3. The optical gap of the
The PA measurements were carried out at 7K, using
BM films increases with decreasing modulation period in
unfocused argon ion laser light of either 514.5 nm or 488
such a way that its difference from Emin in Fig. 1 is almost
nm as an excitation light. The transmitted intensity, T, of
inversely proportional to the modulation period. This result
probe light changed with the laser excitation chopped at 80 Hz, so the change, AT, was lock-in detected by using a
indicates the quantum-size effect in the BM films and can be accounted for in terms of effective-mass equations for those electrons and holes which are affected by modulated potentials around z = 0,
harmonic oscillator potential1,2. The quantized structure in the band, however, has not yet been clarified in those BM films.
DOS
these being approximated by a
In this paper, we report, for the first time, the
observation of the quantized structure in the valence band of the BM films through the photoinduced (PA) spectra at 7 K.
c
B .ES;z-
T2yWW ~A Emax
n
*c
VB
LIJ
The PA spectra are due to optical transitions of self-trapped
Z
holes in weak Si-Si bonds (the A centres 4) into the valence
>
band, as shown in Fig. 1, where a schematic diagram of the density-of-state spectra in the conduction and valence bands is also shown. The quantized structure in the PA spectra
has
been
observed
in
a-Si:H/a-Si3N4:H
FIGURE 1 Schematic diagram for the optical transitions responsible for PA and for the density of states spectrum in BM a-Sil_xNx:H films.
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.
Y. Li et aL / Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
1116
cooled Ge detector for all samples and also an InAs detector for some samples. Probe light was obtained by single prism
quantum-size effect on the edge of the valence band in the BM films.
monochromator from a tungsten lamp with a filter cutting the light of wavelength shorter than 690 nm. Interference fringes superposed over optical spectra were removed by using a
NO6008
0.e
150PERIODS L:67,~
procedure developped by Ohta 5 in our laboratory. The PA spectra correspond to -AT/T as a function of photon energy,
I.-- 0.4-
-tim, of the probe light.
//
0-2~
3. EXPERIMENTAL RESULTS Typical examples of the observed PA spectra for L
=
0.5
100
1.'0 . . . . PHOTON ENERGY(eV)
1.'5 '
2.0
67 .A and 21 .& are shown in Figs.2 - 4. In Fig. 5, the Lucovsky plot of the PA spectrum is shown for L = 290 A. The Lucovsky plot8which is well fitted to the observed PA spectra in a-Si:H bulk films 7 is given by
( - A T / T ) Z/3(ho))zo: (hm-Et~)
FIGURE 3 PA spectrum for BM film No.6008 with L = 67 _A(Eg= 2.06 eV). A dot-dashed curve and a dashed curve have ttie same definition as in Fig. 2.
(1)
where'l~e0 and Eth are the photon energy and the threshold energy, respectively. The
threshold energy taken
NO 6017
230 PERIODS L=21.~
by
extrapolation of the Lucovsky plot, as shown in Fig. 5, was obtained from the observed PA spectra, where the high energy part was fitted to the Lucovsky type, as shown in these figures. The values of Eth are shown as a function of .
t'•/ J
•5
L "1 in Fig. 6. Eth corresponds to the depth of the A centre
[ ,
1
,
I
,
.
,
I
1 PHOTON ENERGY(eV)
.
.
.
.
1.5
level in a-Si:H bulk films, but in the BM films, as will be shown below, the PA spectra deviate from the Lucovsky type and have a tail extending towards lower energy. Thus, the value of Eth has no definitive meaning, but its dependence on L -1 as shown in Fig. 6 suggests the
1.0-
No6006
FIGURE 4 PA spectrum for BM film No.6017 with L = 21 ~,. A dotdashed curve and a dashed curve have the same definition as in Fig. 2.
100PERIODS L=10OA No 6004 3
5
P
E
~
2 0.5-
2 Eth=O,525eV..I 2 0. ~
. . . .
~ .b
. . . .
ill 5
. . . .
E =0.50eV ~
2. 0
PHOTON ENERGY(eV)
FIGURE 2 PA spectrum for BM film No.6006 with L = 100 ~, (Eg = 1.97 eV). A dot-dashed curve and a dashed curve are the Lucovsky-type one fitted to the observed one and the theoretical one, respectively.
i
~ ,
0.5
.
.
.
1 PHOTON ENERGY(eV)
.
.
.
15
FIGURE 5 Lucovsky plot for BM film No.6004 with L = 290 A (Eg = 1.96 eV).
Y. Li et aL /Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
1117
where Vo is the coefficient of the harmonic oscillator potential, V~ (£
Vz= Vo(z/L) 2
Q
(6)
0
C" LtJ
0
and L is the modulation period. Using the wave function,
0
Zi(z), of the i-th quantized level, the matrix element of I
I
I
I
I
I
2
3
4
5
optical transitions is given by
L-' ( lO-Z~,-l )
M+_=
i(6)t/2yC~ _ . , [
+-------~- / -
FIGURE 6 Plot of Etla vs. L -1 for BM films.
,/2
,a_~
Zi(zj
lzl
L77~
1.
+
(~+a2)a/2]
x exp [-(~+6=)t/X]lzl dz,
(7)
4. DISCUSSION Before discussing the experimental results in detail, we 2m (E-E,i) ]1/2,
briefly present the theoretical expressions of the PA spectra
r= -~-
(8)
2m Eo)1/2, a = --~-
(9)
in the BM films. The PA is proportional to the cross section of optical absorption, o, so we calculate o, assuming that the initial state is a bound state of a hole affected by 6-potential and that the final state is a bound state of a hole affected by a harmonic oscillator potential for z-direction, being of two-dimensional free particle for the x, y plane6. The spatial position of a hole centre is assumed to be located at the centre of the harmonic oscillator potential, as shown in Fig. 1. Using the matrix element of optical transitions, M, the differential cross section, do/dg2, is given by tOme2
d•=•
IMI2f (E-E*I)
where Eo is the bound state energy of a hole afffected by 6-potential (Eo>0) and the superscripts of M* designate the direction of polarization perpendicular to the z direction.
(2) 100A 0
where f(E - Ezi) is a step function in the following expression of the density of states, n(E),
67A
/+/+A
30A
21 fl,
?/;?I
>
n
mL a (E) = ~i (2-2~ f
(3)
0.5"- . . . . . . (,9 CC hl Z la.l
and its height is proportional to (Ezi) 1/2. m and~m in eq.(2) are the effective mass of the hole and photon energy of the
1.0
probe light, respectively and Ezi is the z-component of energy of the i-th quantized level being expressed by E~i= (n++) hto0
(4)
tOo= ( Vo/mL z) i/2
(5)
FIGURE 7 Calculated quantized levels in the valence band of BM films with various values of L. The level shown by solid lines and dashed lines are optically allowed and forbidden ones, respectively.
1118
Y Li et aL / Photoinduced absorption spectra of band-edge modulated a-Sil_xNx:H films
The cross section, o, is obtained by integrating in the x,
superlattices.
However, free holes in the BM films are
y plane and by taking into account two directions of polarization shown above, so that o is given by 4zt times
localized at the bottom of the harmonic oscillator potential,
eq.(2). The integration of eq.(7) was numerically performed.
range compared to the modulation period. Thus, the reason
The calculated energies of the quantized levels for various
of why the quantized structure can be observed for L = 67 A,
so that the free hole's movement is limited to some narrow
values of L are shown in Fig. 7, in which Vo = 9.54 eV and
and presumably for L = 100 A, seems reasonable from the
m = free electron mass are takenl, 2.
view point of the broadening of the quantized level and the A
The calculated PA curves for L = 100 ,~, 67 ,~ and 21 .~ are shown in Figs. 2, 3 and 4, respectively. For L = 190 ~,
centre level and also comparison between the present case and the case of a-Si:H/a-Si3N4:H superlattices.
eight quantized levels participate in the PA spectrum, so the PA curve is close to the Lucovsky type of the bulk film. On the other hand, for L = 21 ~,, only the lowest quantized level (n = 0)
contributes to the PA spectrum, so the PA curve is
very different from the Lucovsky type, as shown in Fig. 4.
5. CONCLUSIONS We have observed the quantized structure in the valence band of the BM films with L = 67 ,~ and presumably for L = 100 ,~ from the PA measurements. A significant tailing
In the following, we compare the observed PA curves
towards lower photon energy of the PA spectra for BM
with the calculated ones. As shown in Fig. 3, the observed
films with shorter modulation periods may be due to the
PA spectrum for L = 67 _Aexhibits a structure which almost
broadening of the quantized levels and the A centre levels.
corresponds to a structure in the calculated PA spectrum, although it is broadened compared to the calculated one. The observed PA spectrum for L = 100 ~_ appears to exhibit a subtle structure which can be compared with the calculated
Acknowledgements We wish to thank Drs. C. Ogihara, H. Ohta and H. Yokomichi for helpful discussions.
one. On the other hand, the observed PA spectrum for BM films wiht L ranging between 44 .~, and 21 ,~, could not be
REFERENCES
fitted to the calculated ones owing to a tail extending
1. C. Ogihara, H. Ohta, M. Yamaguchi and K. Morigaki, Jpn. J. Appl. Phys. 28 (1989) L741.
towards lower energy. Such tail is due to broadening of the quantized level by disorder inherent to amorphous structure and also by some distribution of the modulation period coming from deposition processes of the BM films. These origins may be enhanced as the modulation period decreases. Furthermore, the broadening of the A centre level should be taken into account for the BM films with shorter modulation period. Finally, we compare the PA spectra for the BM films with those for a-Si:H/a-Si3N4:H superlattice films 6.
In
a-Si:H/a-Si3N4:H superlattices, where the barrier-layer thickness is fixed at 25 ,~ and the well-layer thickness, Lw, is varied, the quantized structure has been observed in the PA spectra for Lw -- 18 .~, and 36 ,~. The modulation period for which the quantized structure was observed in the BM films is longer than the well-layer thickness of the
2. C. Ogihara, H. Ohta, M. Yamaguchi and K. Morigaki, Phil. Mag. B62 (1990) 261. 3. M. Yamaguchi, C. Ogihara, H. Ohta and K. Morigaki, J. Non-Cryst. Solids 114 (1989) 705. 4. K. Morigaki, Amorphous Silicon and Related Materials, Vol. A, ed. H. Fritzsche (World Scienific, Singapore, 1989) pp. 595-631. 5. H. Ohta, Doctor Thesis, University of Tokyo, 1989, unpublished. 6. H. Ohta and K. Morigaki, Solid State Commun. 72 (1989) 425. 7. I. Hirabayashi and K. Morigaki, J. Non-Cryst. Solids 59&60 (1983) 433. 8 G. Lucovsky, Solid State Commun. 3 (1965) 299.