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The pressure and temperature dependence of electron energy-gaps in semiconductor alloys
Solid State Communications, Vol. 17, pp. 739—742, 1975.
Pergamon Press.
Printed in Great Britain
THE PRESSURE AND TEMPERATURE DEPENDENCE OF ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS R. Hill Department of Physics, Newcastle upon Tyne Polytechnic, Newcastle upon Tyne NE1 8ST, England and G.D. Pitt Standard Telecommunication Laboratories Limited, London Road, Harlow, Essex, England (Received 22 Januwy 1975 by C. W. McCombie)
The pressure and temperature dependences of the direct energy gaps of semiconductor alloys are calculated using the theory of energy gap bowing of Hill. No adjustable parameters are used, and the pressure and temperature coefficients of the bowing parameter are related to the bulk compressibilities and thermal expansion coefficients respectively. The agreement with the rather small number of experimental results is quite good. The non-linear composition dependence of the pressure coefficients of semiconductor alloys suggests that there are inconsistencies in present formulations of dielectric model theories of alloys. coefficient of 12 ~eVbar~1for coherent luminescence and 8 ~reVbar’ for incoherent luminescence.
THE PRESSURE DEPENDENCES of the energy bands of a number of semiconductors have been measured, and the pressure coefficients derived from pseudopotential and dielectric model theories have usually been in satisfactory agreement with the measured coefficients. Very little work has been done on the pressure dependence of the energy gaps of semiconductor alloys, although Pitt eta!.1 have made Hall effect measurements on Ga—InP at high pressures in an attempt to resolve the direct—indirect cross-over controversy. Hakki etaL2 estimated a pressure co efficient of l3peVbar1 for In 3 0~5Ga0~5P using Keyes scaled theory of the stiffness coefficients in the alloy system, whilst Craford et al.4 measured the pressure dependences of the resistivities of sulphur and
The temperature dependence of the energy bands of semiconductor alloys has noi been measured except for the direct gaps of Ga—InAs,6 InAs—Sb6 and Ga—InSb.78 The energy gaps of a nwnber of alloys have been measured atboth room temperature and 77°K,but unfortunately, only rarely with the same samples. It is however often possible to estimate temperature coefficients from these data although the uncertainty will be large. It is usual to write the energy gap E(x) of an alloy AXB 1...XC as
tellurium doped GaPXA51_X alloys with 1 0.3 and concluded that the direct energy gap had a pressure coefficient betweenthe 10 pressure and 10.8dependence peV bar’ of Fulton 5 investigated the eta!. wavelength emitted from GaM peak 0•7P0~3lasers and light emitting diodes, and found a pressure
E(x)
=
XEAC +
(1 —x)EBC —x(1 —x)b (1)
where EAC and EBC are the AC energy of the component semiconductors andgaps BC and b is the
.
bowing parameter. 739
740
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
Vol. 17, No.6
Table 1. Calculated values ofthe bowing parameter and its pressure and temperature dependence at 300K Alloy
b(eV)
GaP—As GaAs—Sb GaP—Sb
0.23 0.84 1.97 0.23 0.81 1.94 0.43 0.42 0.41 0.50 1.11 3.09 0.49 1.08 3.02
InP—As lnAs—Sb InP—Sb Ga—InP
Ga—InAs Ga—InSb ZnS—Se ZnSe—Te ZnS—Te CdS—Se CdSe—Te CdS—Te
~±O.3(peVbar_1)
~±O.1(l0~eVK~)
0.4 2.5 2.5 0.3 —1.0 1.2 0.3 0.3 —0.6 0.8 1.6 6.6 1.6 0.3 2.3
—0.1 0.2 —0.4 +O.l(O.O±O.1’°) _~0.3(~_0.6±0.2;b0O.0±O.l6) — 0.4 —0 3 .j.2(~0.2±0.16) _0.4(_l.5±0.58) —0.l(—0.6±0.3’~) _0.1(_1.0±0.516) —0.6 —0.3 +0.3 —0.3 —
—
The values of db/dT in brackets are experimental measurements, with uncertainties estimated by us. The uncertainties in db/dF and db/dT arise from the experimental uncertainties in the values of compressibilities and expansion coefficients. The values of the bowing parameter b are calculated using equation (3). _____________________________
l-lill~has derived an expression for the bowing parameter resulting from the non-linear dependence of the potential on the properties of the intersubstitutional ions. X-ray and electron diffraction data for alloys show that the lattice constant has a unique and well-defined value which varies approximately linearly with composition. This suggests that the alloy AXBI_XC, behaves as if the pseudo-cation A~B 1_~
i e~
1
1%
6
o~
DO
o~
o•6
i.e
COMPOSITION CX)
FIG. 1. The composition dependence of the pressure coeffIcients of Ga~In 1_~P as calculated from equations (2) and (5) and the measured values of: 0 Pitt et a!. ;1 0 Bendorius et a!. ;‘~~ Zallen and Paul ;14 ~ Camphausen er a!. ~ V Hakki eta!. ;~ S.T.L. results,
±
=
x~
dF
(1 —x) ~~—x(l
Ze TAV b
1
1
2
exp (— sr,~v) (3) ~ TA rB where Z is the valence number of the intersubstitutional =
—
— —
ions A and B, rA and TB are the Pauling covalent radii of ions A and B, TA V = ~ (rA + TB) and s is a screening constant.
The variation of E(x) with pressure is then dF
has a covalent radius equal to xrA + (1 —x)rB. Using Heine—Aberenkov type potentials for the ions, an analytical expression can be derived for the difference between the potential of the pseudo.cation and the average of the potentials of the A and B ions. 9 The bowing parameter can then be shown to be
—x) (2)
Differentiating equation (3) with respect to pressure and making the approximation that
Vol. 17, No.6 (TA
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
+ rB) —1 ( ~ db dP
—
TB) —1
2b —
TA ‘TB
en
741
________________________________
frB ~A
TA
d~B1
IrA dP
TB
dPj
(4)
This can be expressed in terms of measurable parameters with minor approximations as db =
1 b 2~J3TA
—
TB TB TA aAcy,4C
TA —
—
0 a~~y~c (5)
where CAC and aBc are the lattice constants of compounds ACandBC and y~and XBC are their compressibilities. OG
Table 1 shows the values of db/dF calculated from equation (5) for a number of alloys. The uncertainty of ±0.3 peVbar~is derived from the estimatedun-
0-4
O~2
08
06
1~0
COMPOSI11ON (Xl
~
3~ei~erature
certainties in the quoted values of compressibthties.
culated from equations (6) and (7) with the experimental values 10 taken from the Handbook ofElectronic
Figureon1 the shows the experimental results obtained at S.T.L., absorption edges of Ga—InP alloys and the curve predicted by equations (2) and (5). Whilst the theoretical curve fits the experimental results well, the uncertainties in both the experimental results and the theoretical curve are such that a wide range of values of db/dP would also fit the data. It is also apparent from Fig. 1 that the estimation by Hakki et aL2 of a pressure coefficient of 13 .zeV bar~for In 0~5Ga0 5P is too high. For GaAs0~6Po.4, coefficients of9.4and9.7peVbar~havebeenfoundintwo separate experiments4 on lightcoefficients emitting diodes S.T.L. found of 10 at and whilst Craford etfor aLGaAs 10.8 peVbar’ 0~7P0~3. The values calculated from equations (2) and (5) are 9.9 peV bar - for GaAs06Po.4 and 10.1 peV bar~for GaAs0~ 7P0.3. The 4 gave pressure electrical measurements of Craford et al. coefficients relative to (100) impurity levels, and if the perturbing effect of the (100) states were taken into account, the coefficient of the direct gap would
Materials. By methods similar to those used in deriving equations (2)—(5), one finds
be somewhat lower. The light emitting diode measurements at S.T.L. will tend to give pressure coefficients slightly lower than those for the direct gap, and thus the theoretical values are in quite good agreement with experiment, It would be instructive to investigate InAs—Sb and Ga—InSb which appear to have negative db/dF, and aidso the Il/VI alloys which have large positive db/dP. Measurements on these alloys would provide
a more rigorous test of the theory.
dE(x) dT
+
—
~ —
X
dt
~
~/3
b
~
—
~ Xj
fi —x’
~
dT
X~
‘dT (6)
and db =
-~—
—
TA
TB
l—aAcaAc—aBcaBc TB LTA
TA
where aAC and aBC are the linear coefficients of thermal expansion of the compounds AC and BC. Theare temperature coefficients calculated from equation (7) given in Table 1 together with some values derived from experimental data. The temperature variations of the direct gap of Ga—InAs have been measured7 and the room temperature values of dE 0/dT 10 These tabulated values are shown have in Fig.been 2 astabulated. a function of composition, together with the theoretical curve derived from equations (6) and (7). For ZnS—Se and ZnSe—Te, the experimental values quoted in Table 1 are calculated from the bowing parameters measured at room temperature and at low temperature. Since the expansion coefficients of these materials are strongly, and sometimes anomalously, dependent on temperature, an agreement to much better than an order of magnitude is not expected with these data.
742
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
In the dielectric theory of energy gap bowingil the bowing parameter is considered to be the sum of an intrinsic bowing term which results from the nonlinear variation of the honropolar energy gap and an extrinsic term which is proportional to the square of the electronegativity difference of the intersubstitutional ions A and B. The extrinsic bowing is thus approximately proportional to the square of the difference of the ionic energy gaps of the compounds AC and BC. Caxnphausen et aL’2 have used the dielectric model to calculate the pressure coefficients of a number of semiconductors. They showed from the pressure dependences of refractive index, ionisation potential and the E 2 energy gap that the ionic energy gap must be taken to be independent of pressure for the calculated coefficients to agree with the measured values. Their results on the pressure dependence of the direct gap was less critically dependent on the assumption of pressure independence of the ionic energy gap, but they concluded that the ionic energy gap must be nearly pressure independent. One would thus expect for an alloy that the extrrnsic bowing should be independent of pressure and since the extrinsic bowing is usually much larger than
1. 2.
Vol. 17, No.6
the intrinsic term, then l/b(db/dP) should be nearly zero for most alloys. However, the expression which Van Vechten and Bergstresser’1 derived for the cxtrinsic bowing is very similar to equation (3), and differentiating their expression with respect to pressure would give equation (5). This work, and that of Paul and co-workers indicates that the formulation used previously in the dielectric model does not give a consistent interpretation of the existing experimental data on the pressure dependence of the electron energy bands In semiconductors and semiconductor alloys. Finally, since the optical properties of semiconductors and semiconductor alloys are temperature and stress dependent, these parameters should be specified when experimental data and theoretical results.are being presented. It has often been-the case that theoretical fits to experimental data have been made with band structures selected from various temperatures, without taking account of the differences which can occur. Acknowledgements — This work has been carried out with the support of the PrOcurement Executive, Ministry of Defence. We would like to thank Professor W. Paul for his constructive comments on this work.
REFERENCES PITT G.D., VYAS M.K.R. & MABBI11~A.W., Solid State Commun. 14,621(1974). HAKKI B.W., JAYARAMAN A. & KIM C.K., I. App!. Phys. 41,5291(1970).
3. KEYES R.W.,J. AppL Phys. 33, 3371 (1962). 4. CRAFORD M.G., STILLMAN G.E., ROSS! J.W. & HOLONYAK N., Phys. Rev. 168,867(1968). 5. FULTON T.A., FITCHEN D.B. & FENNER G.E., AppL Phys. Lett. 4,9 (1964). 6. CODERRE W.M. & WOOLEY J.C., Can. /. Phys. 48,463(1970). 7. CODERRE W.M. & WOOLEY J.C., Can~J. Phys. 47,2553(1969). 8. WOOLEY J.C. & EVANS J.A.,F~oc.Phys. Soc. 78,354(1961). 9. HILL R.,J. Phys. C. Solid State Phys. 7,521(1974). 10. Handbook ofElectronic Materials (Edited by NEUBERGER M.) Vol. 7. I.F.I./Plenum, NY, (1972). 11. VAN VECHTEN J.A. & BERGSTRESSER T.K., Phys. Rev. Bi, 3361 (1970). 12. CAMPHAUSEN D.L., CONNELL G.A.N. & PAUL W., Phys. Rev. Lert. 26, 184 (1971). 13. BENDORIUS R.A. & SHILEIKA A.Y., Sop. Phys. Semicond. 6, 1042 (1972). 14. ZALLEN R. & PAUL W.,Phys. Rev. 155, 703 (1967). 15. WAGNER T.S., HECKELMANN G.H. & NELKOWSKI H., Phys. Status Solidi (b) 65, K75 (1974). 16. HECKELMANN G.H. & WAGNER T.S., Phys. Status Solidi (b) 65, Ku (1974).
Pergamon Press.
Printed in Great Britain
THE PRESSURE AND TEMPERATURE DEPENDENCE OF ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS R. Hill Department of Physics, Newcastle upon Tyne Polytechnic, Newcastle upon Tyne NE1 8ST, England and G.D. Pitt Standard Telecommunication Laboratories Limited, London Road, Harlow, Essex, England (Received 22 Januwy 1975 by C. W. McCombie)
The pressure and temperature dependences of the direct energy gaps of semiconductor alloys are calculated using the theory of energy gap bowing of Hill. No adjustable parameters are used, and the pressure and temperature coefficients of the bowing parameter are related to the bulk compressibilities and thermal expansion coefficients respectively. The agreement with the rather small number of experimental results is quite good. The non-linear composition dependence of the pressure coefficients of semiconductor alloys suggests that there are inconsistencies in present formulations of dielectric model theories of alloys. coefficient of 12 ~eVbar~1for coherent luminescence and 8 ~reVbar’ for incoherent luminescence.
THE PRESSURE DEPENDENCES of the energy bands of a number of semiconductors have been measured, and the pressure coefficients derived from pseudopotential and dielectric model theories have usually been in satisfactory agreement with the measured coefficients. Very little work has been done on the pressure dependence of the energy gaps of semiconductor alloys, although Pitt eta!.1 have made Hall effect measurements on Ga—InP at high pressures in an attempt to resolve the direct—indirect cross-over controversy. Hakki etaL2 estimated a pressure co efficient of l3peVbar1 for In 3 0~5Ga0~5P using Keyes scaled theory of the stiffness coefficients in the alloy system, whilst Craford et al.4 measured the pressure dependences of the resistivities of sulphur and
The temperature dependence of the energy bands of semiconductor alloys has noi been measured except for the direct gaps of Ga—InAs,6 InAs—Sb6 and Ga—InSb.78 The energy gaps of a nwnber of alloys have been measured atboth room temperature and 77°K,but unfortunately, only rarely with the same samples. It is however often possible to estimate temperature coefficients from these data although the uncertainty will be large. It is usual to write the energy gap E(x) of an alloy AXB 1...XC as
tellurium doped GaPXA51_X alloys with 1 0.3 and concluded that the direct energy gap had a pressure coefficient betweenthe 10 pressure and 10.8dependence peV bar’ of Fulton 5 investigated the eta!. wavelength emitted from GaM peak 0•7P0~3lasers and light emitting diodes, and found a pressure
E(x)
=
XEAC +
(1 —x)EBC —x(1 —x)b (1)
where EAC and EBC are the AC energy of the component semiconductors andgaps BC and b is the
.
bowing parameter. 739
740
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
Vol. 17, No.6
Table 1. Calculated values ofthe bowing parameter and its pressure and temperature dependence at 300K Alloy
b(eV)
GaP—As GaAs—Sb GaP—Sb
0.23 0.84 1.97 0.23 0.81 1.94 0.43 0.42 0.41 0.50 1.11 3.09 0.49 1.08 3.02
InP—As lnAs—Sb InP—Sb Ga—InP
Ga—InAs Ga—InSb ZnS—Se ZnSe—Te ZnS—Te CdS—Se CdSe—Te CdS—Te
~±O.3(peVbar_1)
~±O.1(l0~eVK~)
0.4 2.5 2.5 0.3 —1.0 1.2 0.3 0.3 —0.6 0.8 1.6 6.6 1.6 0.3 2.3
—0.1 0.2 —0.4 +O.l(O.O±O.1’°) _~0.3(~_0.6±0.2;b0O.0±O.l6) — 0.4 —0 3 .j.2(~0.2±0.16) _0.4(_l.5±0.58) —0.l(—0.6±0.3’~) _0.1(_1.0±0.516) —0.6 —0.3 +0.3 —0.3 —
—
The values of db/dT in brackets are experimental measurements, with uncertainties estimated by us. The uncertainties in db/dF and db/dT arise from the experimental uncertainties in the values of compressibilities and expansion coefficients. The values of the bowing parameter b are calculated using equation (3). _____________________________
l-lill~has derived an expression for the bowing parameter resulting from the non-linear dependence of the potential on the properties of the intersubstitutional ions. X-ray and electron diffraction data for alloys show that the lattice constant has a unique and well-defined value which varies approximately linearly with composition. This suggests that the alloy AXBI_XC, behaves as if the pseudo-cation A~B 1_~
i e~
1
1%
6
o~
DO
o~
o•6
i.e
COMPOSITION CX)
FIG. 1. The composition dependence of the pressure coeffIcients of Ga~In 1_~P as calculated from equations (2) and (5) and the measured values of: 0 Pitt et a!. ;1 0 Bendorius et a!. ;‘~~ Zallen and Paul ;14 ~ Camphausen er a!. ~ V Hakki eta!. ;~ S.T.L. results,
±
=
x~
dF
(1 —x) ~~—x(l
Ze TAV b
1
1
2
exp (— sr,~v) (3) ~ TA rB where Z is the valence number of the intersubstitutional =
—
— —
ions A and B, rA and TB are the Pauling covalent radii of ions A and B, TA V = ~ (rA + TB) and s is a screening constant.
The variation of E(x) with pressure is then dF
has a covalent radius equal to xrA + (1 —x)rB. Using Heine—Aberenkov type potentials for the ions, an analytical expression can be derived for the difference between the potential of the pseudo.cation and the average of the potentials of the A and B ions. 9 The bowing parameter can then be shown to be
—x) (2)
Differentiating equation (3) with respect to pressure and making the approximation that
Vol. 17, No.6 (TA
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
+ rB) —1 ( ~ db dP
—
TB) —1
2b —
TA ‘TB
en
741
________________________________
frB ~A
TA
d~B1
IrA dP
TB
dPj
(4)
This can be expressed in terms of measurable parameters with minor approximations as db =
1 b 2~J3TA
—
TB TB TA aAcy,4C
TA —
—
0 a~~y~c (5)
where CAC and aBc are the lattice constants of compounds ACandBC and y~and XBC are their compressibilities. OG
Table 1 shows the values of db/dF calculated from equation (5) for a number of alloys. The uncertainty of ±0.3 peVbar~is derived from the estimatedun-
0-4
O~2
08
06
1~0
COMPOSI11ON (Xl
~
3~ei~erature
certainties in the quoted values of compressibthties.
culated from equations (6) and (7) with the experimental values 10 taken from the Handbook ofElectronic
Figureon1 the shows the experimental results obtained at S.T.L., absorption edges of Ga—InP alloys and the curve predicted by equations (2) and (5). Whilst the theoretical curve fits the experimental results well, the uncertainties in both the experimental results and the theoretical curve are such that a wide range of values of db/dP would also fit the data. It is also apparent from Fig. 1 that the estimation by Hakki et aL2 of a pressure coefficient of 13 .zeV bar~for In 0~5Ga0 5P is too high. For GaAs0~6Po.4, coefficients of9.4and9.7peVbar~havebeenfoundintwo separate experiments4 on lightcoefficients emitting diodes S.T.L. found of 10 at and whilst Craford etfor aLGaAs 10.8 peVbar’ 0~7P0~3. The values calculated from equations (2) and (5) are 9.9 peV bar - for GaAs06Po.4 and 10.1 peV bar~for GaAs0~ 7P0.3. The 4 gave pressure electrical measurements of Craford et al. coefficients relative to (100) impurity levels, and if the perturbing effect of the (100) states were taken into account, the coefficient of the direct gap would
Materials. By methods similar to those used in deriving equations (2)—(5), one finds
be somewhat lower. The light emitting diode measurements at S.T.L. will tend to give pressure coefficients slightly lower than those for the direct gap, and thus the theoretical values are in quite good agreement with experiment, It would be instructive to investigate InAs—Sb and Ga—InSb which appear to have negative db/dF, and aidso the Il/VI alloys which have large positive db/dP. Measurements on these alloys would provide
a more rigorous test of the theory.
dE(x) dT
+
—
~ —
X
dt
~
~/3
b
~
—
~ Xj
fi —x’
~
dT
X~
‘dT (6)
and db =
-~—
—
TA
TB
l—aAcaAc—aBcaBc TB LTA
TA
where aAC and aBC are the linear coefficients of thermal expansion of the compounds AC and BC. Theare temperature coefficients calculated from equation (7) given in Table 1 together with some values derived from experimental data. The temperature variations of the direct gap of Ga—InAs have been measured7 and the room temperature values of dE 0/dT 10 These tabulated values are shown have in Fig.been 2 astabulated. a function of composition, together with the theoretical curve derived from equations (6) and (7). For ZnS—Se and ZnSe—Te, the experimental values quoted in Table 1 are calculated from the bowing parameters measured at room temperature and at low temperature. Since the expansion coefficients of these materials are strongly, and sometimes anomalously, dependent on temperature, an agreement to much better than an order of magnitude is not expected with these data.
742
ELECTRON ENERGY-GAPS IN SEMICONDUCTOR ALLOYS
In the dielectric theory of energy gap bowingil the bowing parameter is considered to be the sum of an intrinsic bowing term which results from the nonlinear variation of the honropolar energy gap and an extrinsic term which is proportional to the square of the electronegativity difference of the intersubstitutional ions A and B. The extrinsic bowing is thus approximately proportional to the square of the difference of the ionic energy gaps of the compounds AC and BC. Caxnphausen et aL’2 have used the dielectric model to calculate the pressure coefficients of a number of semiconductors. They showed from the pressure dependences of refractive index, ionisation potential and the E 2 energy gap that the ionic energy gap must be taken to be independent of pressure for the calculated coefficients to agree with the measured values. Their results on the pressure dependence of the direct gap was less critically dependent on the assumption of pressure independence of the ionic energy gap, but they concluded that the ionic energy gap must be nearly pressure independent. One would thus expect for an alloy that the extrrnsic bowing should be independent of pressure and since the extrinsic bowing is usually much larger than
1. 2.
Vol. 17, No.6
the intrinsic term, then l/b(db/dP) should be nearly zero for most alloys. However, the expression which Van Vechten and Bergstresser’1 derived for the cxtrinsic bowing is very similar to equation (3), and differentiating their expression with respect to pressure would give equation (5). This work, and that of Paul and co-workers indicates that the formulation used previously in the dielectric model does not give a consistent interpretation of the existing experimental data on the pressure dependence of the electron energy bands In semiconductors and semiconductor alloys. Finally, since the optical properties of semiconductors and semiconductor alloys are temperature and stress dependent, these parameters should be specified when experimental data and theoretical results.are being presented. It has often been-the case that theoretical fits to experimental data have been made with band structures selected from various temperatures, without taking account of the differences which can occur. Acknowledgements — This work has been carried out with the support of the PrOcurement Executive, Ministry of Defence. We would like to thank Professor W. Paul for his constructive comments on this work.
REFERENCES PITT G.D., VYAS M.K.R. & MABBI11~A.W., Solid State Commun. 14,621(1974). HAKKI B.W., JAYARAMAN A. & KIM C.K., I. App!. Phys. 41,5291(1970).
3. KEYES R.W.,J. AppL Phys. 33, 3371 (1962). 4. CRAFORD M.G., STILLMAN G.E., ROSS! J.W. & HOLONYAK N., Phys. Rev. 168,867(1968). 5. FULTON T.A., FITCHEN D.B. & FENNER G.E., AppL Phys. Lett. 4,9 (1964). 6. CODERRE W.M. & WOOLEY J.C., Can. /. Phys. 48,463(1970). 7. CODERRE W.M. & WOOLEY J.C., Can~J. Phys. 47,2553(1969). 8. WOOLEY J.C. & EVANS J.A.,F~oc.Phys. Soc. 78,354(1961). 9. HILL R.,J. Phys. C. Solid State Phys. 7,521(1974). 10. Handbook ofElectronic Materials (Edited by NEUBERGER M.) Vol. 7. I.F.I./Plenum, NY, (1972). 11. VAN VECHTEN J.A. & BERGSTRESSER T.K., Phys. Rev. Bi, 3361 (1970). 12. CAMPHAUSEN D.L., CONNELL G.A.N. & PAUL W., Phys. Rev. Lert. 26, 184 (1971). 13. BENDORIUS R.A. & SHILEIKA A.Y., Sop. Phys. Semicond. 6, 1042 (1972). 14. ZALLEN R. & PAUL W.,Phys. Rev. 155, 703 (1967). 15. WAGNER T.S., HECKELMANN G.H. & NELKOWSKI H., Phys. Status Solidi (b) 65, K75 (1974). 16. HECKELMANN G.H. & WAGNER T.S., Phys. Status Solidi (b) 65, Ku (1974).