AMORPHOUS SEMICONDUCTORS IN THE Si-As-Te SYSTEM. Masahiro NUNOSHITA and Hirotsugu ARAI. Central Research Laboratory, Mitsubishi Electric ...
Journal of Non.Crystalline Solids 12 (1973) 339-352. © North-Holland Publishing Company
RELATION BETWEEN ELECTRICAL AND OPTICAL GAPS OF AMORPHOUS SEMICONDUCTORS IN THE Si-As-Te SYSTEM Masahiro NUNOSHITA and Hirotsugu ARAI
Central Research Laboratory, Mitsubishi Electric Corporation, A magasaki, Hyogo, Japan and Tateo TANEKI and Yoshihiro HAMAKAWA
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan Received 11 December 1972 and in revised form 4 April 1973
Electrical and optical properties of semiconducting Si-As-Te glasses have been investigated. Compositional dependences of the properties in the SixAsyTe z system are examined as a function of atomic percentage x (or y, z) of one element with parameters of constant atomic ratio y/z (or x/z, x/y) of the other two elements. A pre-exponential factor ao in the de conductivity formula is estimated to be (2.1 +-0.6) X 104 (g~ • cm)-I, independently of the compositions. A systematic relationship between the compositional changes in the electrical gap Eg(el) and optical gap Eg(op) has been found. The energy gaps increase linearly with increasing Si content and decreasing Te content, but are almost independent of As content. The relation between Eg(el) and Eg(op) is expressed by Eg(el) = 1.60 Eg(op) - 0.15 in eV. On the other hand, the optical absorption coefficient a(to) near the band edge follows the empirical formula, a(to) = s o exp (fito/Es). The experimentally determined factor E s increases linearly with Eg(op) and is closely related to the energy difference between the two gaps. A tentative model to explain these experimental results is proposed by taking into account of the effect of the potential fluctuations in such disordered materials.
1. Introduction A series of recent investigations on amorphous semiconductors has shown that there exists an energy-band gap and it plays an important role in the electrical and optical properties [ 1]. In order to explain the electronic processes in chalcogenide glasses, Mott et al. [2] and Cohen et al. [3] have proposed a concept of the 'mobility edge', what is sometimes called the M o t t - C F O model. The essential features of this model for the electronic structure in an amorphous semiconductor are (i) the existence of a energy pseudogap in the density of states, (ii) the electronic localized states in the pseudogap up to critical energies defining a mobility gap or electrical conductivity gap. This model, however, has not yet been experimentally confirmed,
340
M. Nunoshita et aL, S i - A s - T e system
$i
To o Glassy s t a t e • Crystalline state
Fig. 1. Synthesized glasses and glass-forming region in Si-As-Te glass system (- - - - present work, after Hilton et al. [321 ). and there is even some disagreement in the energy profile of states between the concepts of Mott et al. and Cohen et al.. Experimentally, the energy gaps in such amorphous semiconductors are usually obtained from the activation energy of dc conductivity or the optical absorption edge. Though many kinds of amorphous semi. conductors have been studied, many conflicting explanations coexist so far for the energy profiles, particularly for the localized states in these amorphous materials [4]. It is already known that a relatively large difference in magnitude always exists between the electrical and optical energy gaps. It has been found empirically by Stuke [5] that the mobility gap in many amorphous semiconductors corresponds to the photon energy at which the optical absorption coefficient has a value ~ 104 cm -1 . Moreover it has been noted that there is an energy difference between the band gaps in the crystalline and amorphous phases of a semiconductor [5]. These problems have not yet been studied systematically because of the complicated features of localized states near the band edges and inside the pseudogap. The amorphous S i - A s - T e system has a very wide glass-forming region and a suitable conductivity range compared with other tei~aary glass systems. Therefore, such S i - A s - T e glasses might be suitable materials to investigate compositional dependences of the physical properties. In our previous papers [6, 7], we have reported that there are some essential relations between the electrical gap and other inherent physical constants: glass transition temperature, softening temperature, density and dc electrical conductivity in amorphous S i - A s - T e semiconductors of different compositions, and that the electrical gap obtained is closely related to the short-range order due to Si-Te covalent bonds. We have extended the series of experiments on the S i - A s - T e system to the electrical and optical energy gaps, and
M. Nunoshita et aL, Si-As-- Te system
341
Fig. 2. Temperature dependence of dc conductivity oT of several amorphous Si-As-Te semiconductors. postulate some empirical relationships between the two gap energies. Discussions on the systematic relationships and the discrepancies between the two gaps are given and then an attempt is made to explain these phenomena by considering the localized states or potential fluctuations at the band edges of the pseudogap.
2. Experimental remits 2.1. Electrical gap Eg(el)
A series of amorphous S i - A s - T e semiconductors are prepared by the same procedures as those described in the previous papers [6, 7]. Compositions of the glasses used in the present work were selected along the lines on which the atomic ratio of the two elements is constant, as shown in fig. 1. The electrical energy gap Egtel) of amorphous semiconductors is defined as twice the activation energy AE, which is obtained from the temperature dependence of the dc electrical conductivity o T by analogy with the band-conduction process in intrinsic semiconductors. The relation is expressed in the familiar form:
M. Nunoshita et aL, S i - A s - Te system
342
Table 1 Electrical and optical properties of S i - A s - T e glasses. Compositions
o25
(~'2-1 cm -1 )
o0 Eg(el) (X 104 (eV) s2 -1 -cm -1)
Si9As4Te36 SilAS3Te12 Si4AsgTea6
1.01 X 10 -6 7.15 X 10 -s 3.05 X 10 -5
2.12 2.03 2.07
1.21 0.99 1.03
Si2As3Te12 SilASlTe4 Sil2AsTTe2a SiTAs27Te63 SiTAs12Teza Si2AsaTe 7 Si3As3Te 7 SiTAs9Te21 SilAs6Te9 SiaAssTe12 Si9Asl4Te21 Si2As2Te 3 SiaAs2Te a SiIAs9Te9 SilAs4Te 4 Si3As7Te 7 Si2AsaTe3 SilAslTe I
8.69 9.65 7.11 2.23 8.15 3.10 1.60 1.45 1.46 6.39 2.05 4.52 1.29 1.04 5.81 2.96 9.94 7.76
2.19 2.23 1.97 1.63 1.70 2.65 2.10 1.98 2.01 2.08 1.97 2.05 2.06 2.19 1.94 2.56 1.85 2.19
1.10 1.22 1.46 1.04 1.22 1.29 1.44 1.66 1.07 1.24 1.42 1.61 1.78 1.10 1.24 1.41 1.56 1.71
Sil As6Te4 Si6As21Tel4 Si4As9Te 6
3.44 X 10 -7 2.17 X 10 -8 9.10 X 10 -9
1.58 1.60 1.59
1.27 1.39 1.57
Si12 Ge loAs30Te48 (Ovonic glass)
4.05 x 10 -8
1.92
1.37
X X X X X X X X X x X × X x X x X x
10-6 10-7 10 -9 10 -s 10 -7 10 -7 10 -s 10 - l ° 10 -s 10 -7 10 -s 10 - l ° 10 -11 10 -5 10 -7 10 -s 10 -1° 10 -11
o T = o 0 e x p ( - A E I k T ) = o 0 e x p ( - Eg(el)i2kT),
Eg(op) (eV) (for a = 10)
E'g(op) (eV) .(by ~x/-~5)
0.99
(eV)
0.057
0.86 0.76 0.85 0.89 0.99 1.13 0.77 0.86 0.98 1.11 1.20 0.77 0.87 0.98 1.08 1.15
ES
0.79 0.93 1.03 0.81
0.91 1.02 1.13 1.22
0.042 0.057 0.059 0.067 0.073 0.038 0.056 0.059 0.067 0.075 0.045 0.048 0.051 0.064 0.070 0.054
(1)
w h e r e o 0 is a c o n s t a n t related t o t h e effective d e n s i t y o f states a n d t h e b a n d - c o n d u c t i o n m o b i l i t y in r e d u c e d b a n d s , k is B o l t z m a n n ' s c o n s t a n t a n d T is t h e a b s o l u t e t e m p e r a t u r e . Fig. 2 s h o w s t y p i c a l data o f o T p l o t t e d l o g a r i t h m i c a l l y against t h e reciprocals o f T f o r s o m e S i - A s - T e glasses. T h e s e p l o t s give precisely s t r a i g h t lines as i l l u s t r a t e d in t h e figure. The values o f Eg(el) a n d o 0 e s t i m a t e d f r o m t h e data are
343
M. Nunoshita et al., S i - A s - Te system
Six(A%Tea)l_x
60 ill
. . . . . . .
O Z ,~ 40 I,-
s
/ / /i
I,-
r~ .~
~..._~..
/
mo
. . , . . .......... I
•
/
.~.=-:. . . . . . .
f
....
X=0.38/ /0.29 /0,20///'lO.13......._..,e~).06 at R.T.
20
tvI,-
, J..-/,. 0.8
1.0
......... ,
1.2 1.4 WAVELENGTH
,
,
1.6 (pm)
,
,
1.8
2.0
Fig. 3. Optical transmission spectra of several Si-As--Te glasses of 350 ~m thickness at room temperature.
summarized in table 1. A remarkable result in the table is that the o 0 values are all within a range of (2.1 -+ 0.6) × 104 (~2 • cm) -1 for all the glasses used in this work. This o 0 value is relatively large and almost coincides with that for the intrinsic conduction in the single-crystalline silicon, germanium or other covalent semiconductors [5]. This fact implies that the basic factor for the electronic conduction in these amorphous semiconductors is the same as that for the band conduction in the intrinsic region of the covalent crystalline semiconductors. Due to the constant o 0value, the compositional change of the dc conductivity o T at a certain temperature T arises from the difference of the electrical gap E_,e,,. Thus the inherent dc conductivity o25 at 25°C changes widely in the range~'J10 -4 to 10 -11 (~2 • cm) -1 as a result of the compositional dependence ofEg(e D from 0.99 to 1.78 eV, as shown in table 1.
2.2. Optical gap Eg(op) The optical gap Eg(op) can be obtained from the spectral dependence of optical absorption coefficient a(o~) for interband transitions. The coefficient ct(~) can be easily calculated from the optical transmission spectrum by using t = (1 - R) 2 exp [ - a ( ~ ) d ] ,
(2)
where t is the transmittance, R the reflectivity and d the thickness in cm of the glass sample. Even without knowledge of R, ct(~) can be estimated from the transmission spectra measured for two specimens of different thickness from the same glass. Three types of specimens of thickness 100, 200 and 350/am having 5 X 5 mm 2 area were prepared from each of the glass materials listed up in table 1. Then both surfaces of the specimens were polished to a grade of optical flat with 0.3/am diamond paste. The transmittance measurement was made using SPEX No. 1700-Ili, Narumi RM 2 3 - I I - 8 4 or Shimazu 2-beam Spectrometer.
344
M.. Nunoshita et aL, S i - A s - Te system
Fig. 3 shows the transmission spectra of some amorphous Si-As-Te solids of 350/zm thickness at room temperature. As can be seen in the figure, the optical absorption edge is rather soft as compared with those of single-crystalline semiconductors. Further, the transmittance in the longer wavelength region has no spectral structure, and the value is saturated around 40 to 50%. General features in the obtained spectra and the compositional changes as shown in fig. 3 agree fairly well with the result of Minami et al. [8]. The absorption coefficients a(6o) estimated by using eq. (2) are plotted, as shown in fig. 4 for various Si-contents of the S i - A s Te glasses. A spectral change in the optical absorption near the band edge is characterized by a(6o) which increases exponentially with/iw in the range 10 _Ka(6o) < 103 cm -1 , obeying an empirical relationship of the form: or(w) = aO exp
(t~w/Es),
(3)
where a 0 and E s are constants. In the case of such an exponential absorption edge, the optical gap Eg(op) is here defined as the photon energy hw corresponding to a(6o) = 10 cm -1 . This a-value gives the upper limit of about 2.5 X 1017 states/cm 3 for the density of gap states in amorphous germanium [9]. The values of Eg(op) obtained are listed up in the 5th row of table 1.
20
-10 ¥ ¢J
0.,3/ /
Six(AS2T%)l_x
15
In Z MJ
MJ
$ix(As2Te3)l.X
X:O.O~
O,
29 o lO
10
7
o o z
o
5
i-
R.T. ra
10 (eV/cm) y2. It is thought that the eq. (4) might be more profitable in the high absorption coefficient region with a(co)~ 103 cm -1 . Unfortunately it is difficult to obtain such high values of a(¢o), because of the technical difficulty of making thin films less than 100/2m thick for the S i - A s - T e glasses. However, the small difference between the Eg(op) and E~(op) might justify the above-mentioned definition of the optical gap Eg(op). 2.3. The compositional dependences o f Eg(el) and Eg(op) Table 1 shows that both the electrical gap Eg(el) and the optical gap Eg(op) are strongly dependent upon the compositions of glass. The dependences of Eg(el) and Eg(op) on the contents of Si, As and Te (in at %) are illustrated in figs. 6a, b and c, respectively, where the parameter is the atomic ratio of the other two constituents. As shown in the figures, there are close correlations between Eg(eD and Eg(op) in spite of their differences in magnitude. Both gaps increase linearly with increasing content of Si and with decreasing content of Te, but are almost independent of the As content Therefore the atomic ratio of Si to Te determines mainly the values of the two gaps. As reported by Minami et al. [11] and Nunoshita et al. [6, 7], these glasses have the same sort of compositional dependences for other physical properties. These behaviours imply that Si-Te covalent bonds form stably the three-dimensionally cross-linked network structures with fairly strict short-range order and most of As and the excess Te atoms are randomly and loosely bound to the main networks as network modifiers. Therefore, characters of the main covalent network structures may govern the semiconducting properties such as the energy gap, the extended band states, etc. and other basic physical properties in the chalcogenide glass. It should also be expected that the As and excess Te atoms are out of the main network structures and act as electron or hole trapping centers in the gap [12, 13].
346
M. Nunoshita et aL, S i - A s - Te system
1.8 1.8
"~'x~.
Six-ASy-Te~i(~el )
~
Six-AsyTez
1.6
~ x~
1.6
~
1.4 ~.1.2 1.0 (~8
1.2
En gJ
i;/#"
1.0
~
I
I
-
.
.
a8 - . - X/z=2/3 + 3/'7 -o1/4 -e1/9
Q6
I
20
Si
F..g(op)
o
--- 3/7
I
Eg(al) " " ~ " " ' ~ .---e - --..~ _
1.4
40 0.4
(atomic %)
I
0
(a)
e'\
"
I
60
\'.-,%
>m 1.4
w
I
40 As (atomic'/,)
S ix_Asy.Tez
1.6
1.2
I
(b)
1.8
=
/
20
• ~
"~
",,
1.O
O
,~
o.e
0.6 i
20
i
i
.
io
I
i
7o
Ta (atomic°/.)
(c) Fig. 6. Compositional dependences of electrical gap Eg(el) and optical gap Eg(op) in amorphous S i - A s - T e system. (a) Eg(el) and Eg(op) as a function of Si content (in at %) with a parameter of constant atomic ratio of As/Te. Co) Eg(el) and Eg(op) as a function of As content (in at%) with a parameter of constant atomic ratio of Si/Te. (c) Eg(el) and Eg(op) as a function of Te content (in at %) with a parameter of constant atomic ratio of Si/A~
2.4. Empirical relations between Eg(e D and Eg(op) F o r all glasses used in this work, a simple linear relationship is f o u n d between Eg(el) and Eg(op) as shown in fig. 7. It is expressed b y the following empirical form: Eg(e D = 1.60 Eg(op) - 0.15
(in eV).
(5a)
M. Nunoshita et al., S i - A s - Te system
347
1.8
$i~1.(
1.4
j, 1.2 Egcel)= 1.60 Eg¢op)-O,15 1.0 I 0.8
I
1.0 Eg(op~ (eV)
I
1.2
Fig. 7. Empirical relation between Eg(el) and Eg(op) in amorphous Si-As-Te semiconductors. Then the discrepancy between the two gap energies is rewritten as Eg(el) - Eg(op) = 0.60 Eg(op) - 0.15
(in eV).
(5b)
On the other hand, the reciprocal of the slope of the exponential absorption tail, i.e. the E s value in eq. (3) at room temperature has been shown in table 1. The E s values are of the same order of 0.05 eV as that of Urbach's tail observed in ionic and covalent solids [14]. Fig. 8 shows the E s value as a function of Eg(op) for the glasses in the S i - A s - T e system. The following empirical relationship is obtained by the method of least squares as shown in fig. 8: E s = 0.068 [Eg(op) - 0.10]
(in eV).
(6)
The E s value changes linearly with the optical gap Eg(op) and in particular it is likely to increase conspicuously with Si content, as shown in fig. 8.
2.5. Temperature dependence of Eg(op) The temperature dependence of the optical absorption or(co) of Si3As3Te 7 is shown in fig. 9. The exponential tails at the lower values of ct(~) shift almost in parallel to the lower energies with increasing temperature. Fig. 10 exhibits the typical
348
M. Nunoshita et al., S i - A s - Te system
0.08
SixAS~TTez
0.06
0.04
/
,
x
1
•
2/3
O
3/7 1/4
I
1.o
112
Eg~op~ (eV)
Fig. 8. Reciprocal of slope of exponential absorption edge, E s value, as a function of optical gap Eg(op) in Si-As-Te glasses.
curves of the temperature dependence of Eg(op) , i.e. the shift with temperature o f the photon energy hco at ~(6o) = 10 cm -1 . As shown in fig. 10, Eg(op) decreases almost linearly with increasing T near room temperature and can be expressed as follows, Eg(op) "" E~g(0) - - ")'T,
(7)
where ~, is the temperature coefficient of Eg(op) near room temperature and E'g(0) is a constant but not a real optical gap at T = 0 K because the curves are expected to approach T = 0 K with zero slope. From the slope of the linear portion in fig. I0, the
291fK~lgK
Si3As3TeT////
lo' 14. LL ~//42"K 377" 42"Ki Z o
m 10
,
q)
% %%. ~.%
~.1.1 o Sh As3Te 7
1.0
0
1 O0
200 300 Temperature T ('K)
400
Fig. 10. Temperature dependence of optical gap Eg(op) in Si3As3Te 7 and Si~Asl4Te21 glasses.
-/-values of 7.7 X 10 -4 and 7.3 X 10 -4 eV/K are obtained for the Si3As3Te 7 and SigASl4Te21 glasses, respectively. According to Kolomiets [ 15] and Fagen et al. [16], the -/-value of amorphous materials is affected by the interaction of electrons with phonons rather than by lattice dilation of the substance. Mott has suggested that the -/-value in amorphous semiconductors is generally greater than that in crystalline semiconductors because of large thermal disordering of the network structures due to their spiral chain or layer-like lattices [17]. Actually the -/-values obtained here are relatively larger than those in crystalline semiconductors and almost the same as the value of about 7 X 10 -4 eV/K obtained in most chalcogenide glasses [16, 18, 19] other than a few such as Se [20] and GeTe [21].
3. Discussion
According to the 'relaxation case' theory [22, 23], the Fermi level of amorphous semiconductors with high resistivities is pinned up so as to make the dc conductivity minimum and near-intrinsic. Then the dc conductivity OT c a n be expressed by a T = 2eni(lanlap) 1A,
(8)
where lan and tZp are mobilities of electrons and holes, respectively, and n i is the intrinsic carrier density. Then n i is given by n i = n o e x p [-- Eg(T)/2kT],
(9)
where Eg(T) is the 'real energy gap' and n o is an inherent constant associated with the
350
M. Nunoshita et aL, S e - A s - T e system
effective density of states at reduced band edges. Near room temperature the real gap Eg(T) can be assumed to have the same 7-value as Eg(op): Eg(T) - E g ( 0 ) - 7T,
(10)
where Eg(0) is a constant not corresponding to the real gap at T = 0 K. Since carrier transport is mainly governed by a trap-limited drift mobility [24] due to the localized states near the band edges in an amorphous semiconductor, the effective mobility /aeff = (btn~Up)1/2 in eq. (8) may have the following temperature-dependent form: Ueff = ~n/-tp) y2 =/.tO exp ( - E t / k T ) ,
(11)
where/a 0 is the effective band-conduction mobility and E t the activation energy of the effective mobility associated with the distribution of the localized states [ 12]. Inserting eqs. (9), (10) and (11) into eq. (8) we deduce o T = O0 exp [-{Eg(0) + 2Et )/2kT],
(12a)
where o 0 = 2eno/a 0 exp (7/2k).
(12b)
Comparing eq. (12a) with eq. (1) yields Eg(eD = Eg(0) + 2E t.
(13)
The rough estimate of o 0 in eq. (12b) agrees well with the o 0 value obtained in our experiment [2]. It should be noticed here that the above Eg(el) may be fairly larger than the real gap Eg(T) in amorphous semiconductors, as shown in eq. (13). Therefore the discrepancy between the electrical gap energies obtained experimentally in crystalline and amorphous phases would be explained mainly in terms of 7- and E tvalues rather than by the change of the mean atomic spacing between the two solid phases [25]. On the other hand, the optical gap Eg(op) is assumed to be different by -+ e eV from the real gap Eg(T) at room temperature. Hence Eg(op) = Eg(T) + ~ A Eg(0) + e - "yT.
(14)
Then the energy difference between Eg(el) and Eg(op) is derived from eqs. (13) and (14) as Eg(el) - Eg(op) --- 2E t + 7 T -T-e.
M. Nunoshita et al., S t - A s - T e system
351
Eq. (15) indicates that the relatively large difference between the measured Eg(el) and Eg(op) should originate from the activation energy of the effective trap-limited drift mobility, the temperature dependence of the energy gap and an error from the procedure used to determine the optical gap. Since all amorphous Si-As-Te semiconductors used in this work are considered to have a constant 7-value of about 7 × 10 -4 eV/K, as described in the sect. 2, the term of 3'T is about 0.21 eV at 300 K and almost independent of the glass compositions. The value of e in eq. (15) will be negligible for all Si-As-Te glasses. Therefore the Et-values are estimated to be 0.04 to 0.19 eV, and thus the term of 2E t in eq. (15) seems likely to be related to the composition-dependent term on the right-hand side of the empirical eq. (5b). The energy values from 0.1 to 0.3 eV similar to the Et-values have also been observed for trap-limited drift mobility [24], Seebeck coefficient [26], photoconductivity [27], ac conductivity [28], etc. in many amorphous semiconductors. A simple correlation between E t and Eg(op) deduced from eqs. (5b) and (15) implies that in the Si-As-Te system the distribution depth of the localized states into the pseudogaps increases as the optical gaps Eg(op) increase. The above result is also supported by the linear relationship between the Es-value and the Eg(op) given by eq. (6). Two plausible explanations have been offered for the existence of such an exponential absorption edge. (i) It would be corresponding to transitions involving the localised states, which are exponentially distributed from the band edge into the pseudogap [30]. (it) It is due to an effect of internal electric field broadening on the excitonic states and band edge due to non-uniform microfields and potential fluctuations, which may be associated with various kinds of disorders [31]. Recently Olley et al. [29] have reported that the ion bombardments on amorphous As2Se 3 and Se films cause an increase in the optical absorption c~(~) and the E s value, but at the present stage of experiment there is no conclusive evidence so far. Whichever is true, it should be obvious that the existence and the Es-Value of the exponential tails are closely related to the potential fluctuations at the conduction and valence band-edges. Therefore the linear relation of eq. (6) indicates that the magnitude of the potential fluctuations increases with increasing the gaps, Egtop) and Eg(el). In particular, both the potential fluctuations and the gap energy increase notably with an increase of the St-content in the amorphous S i - A s - T e system. It can be suggested that the increase of the St-content increases not only the average bond energy in the covalent network strt~tures but also the local field fluctuations due to the compositional disorders and the large difference of electro-negativities. The potential fluctuations obviously depend selfconsistently upon the formation and occupation of the localized states, and break the k-conservation selection rule for some optical transitions. From these standpoints, the physical background of eqs. (5), (6) and (15) might be consistent. It is concluded from our experimental results that the disagreement between the electrical and optical gaps arises mainly from the potential fluctuations and their temperature dependence. Moreover an increase of the St-content and a decrease of the Te-content result in an increase of the microfields and potential fluctuations as well as the average bond energy, which play an
352
M. Nunoshita et at, S i - A s - Te system
important role in the electrical and optical properties of the amorphous S i - A s - - T e semiconductors. However the arsenic atoms seem likely to link as modulators in the main network structures and only to operate as electronic trapping centers.
Acknowledgements The authors thank Dr. T. Minami of University of Osaka Prefecture and Drs. S. Ibuki, J. Kai and H. Komiya for their helpful discussions.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [ 11 ] [12] [13] [14] [15 ] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
N.F. Mott, Phil. Mag. 19 (1969) 835. E.A. Davis and N.F. Mott, Phil. Mag. 22 (1970) 903. M.H. Cohen, H. Fritzsche and S.R. Ovshinsky, Phys. Rev. Lett. 22 (1969) 1065. H. Fritzsche, J. Non-Crystalline Solids 6 (1971) 49. J. Stuke, J. Non-CrystaUine Solids 4 (1970) 1. M. Nunoshita and H. Arai, Solid State Comm. 11 (1972) 213. M. Nunoshita and H. Arai, Solid State Comm. 11 (1972) 337. T. Minami and M. Tanaka, Bull. Univ. Osaka Prefecture A18 (1969) 165. W.E. Spicer and T.M. Donovan, J. Non-Crystalline Solids 2 (1970) 66. N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1971). T. Minami and M. Tanaka, Yogyo-Kyokai-Shi 77 (1969) 372. J.L. Hartke, Phys. Rev. 125 (1962) 1177. J. Shottmiller et al., J. Non-Crystalline Solids 4 (1970) 80. D. Redfield and M.A. Afromowitz, Appl. Phys. Lett. 11 (1967) 138. B.T. Kolomiets and E.M. Raspopava, Soviet Phys. Semi. 4 (1970) 124. E.Q. Fagen et al., Proc. 10th Int. Conf. Semiconductors (1971) p. 672. N.F. Mott, Phil. Mag. 24 (1971) 1. J.T. Edmond, Brit. J. Appl. Phys. 17 (1966) 979. N.S. Platakis et al., J. Electrochem. Soc. 116 (1969) 1436. K.J. Siemsen et al., Phys. Rev. 161 (1967) 632. R. Tsu et al., J. Non-Crystalline Solids 4 (1970) 322. H.J. Queisser, JITA Seminar, March (1972). W. Van Roosbroeck and H.C. Casey J r , Phys. Rev. B5 (1972) 2154. J.M. Marshall et al., J. Nonq~?rystalline Solids 8-10 (1972) 760. F. Herman and J.P. Van Dyke, Phys. Rev. Lett. 21 (1968) 1575. H.K. Rockstad et al., J. Non-Crystalline Solids 8-10 (1972) 326. E.A. Fagen et al., J. Non-Crystalline Solids 4 (1970) 480. H.K. Rockstad, J. Non-Crystalline Solids 8-10 (1972) 621. J.A. Olley and A.D. Yoffe, J. Non-Crystalline Solids 8-10 (1972) 850. J. Tauc et al., Phys. Rev. Lett. 25 (1970) 749. J.D. Dow and D. Redfield, Phys. Rev. B5 (1972) 594. A.R. Hilton and M.J. Brau, Infrared Phys. 3 (1963) 69.
