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Temperature dependence of electronic and lattice properties of doping superlattices in IV–VI semiconductors
Superlattices and Microstructures, Vol. 1, No. 3, 1985
197
TEMPERATURE DEPENDENCE OF ELECTRONIC AND LATTICE PROPERTIES OF DOPING SUPERLATTICES IN IV-Vl SEMICONDUCTORS ,P. P. Ruden,*§ T . L . Reinecke, * and F. Naval Research Laboratory, Washington, §~orth Carolina State University, Raleigh, Martin Marietta Laboratories, Baltimore,
Crowne + DC 20375 NC 27650 ND 21227
(Received 13 August 1984 by J.D. Dow)
The effective band gap and the thermally excited carrier concentrations of doping superlattices in PbTe are calculated self-consistently using a semiclassical description. They show interesting temperature behaviors which arise from the temperature dependences of the lattice polarizability, of the bulk band gap, and of the equilibrium carrier concentration. The configurations of lattice polarization which are possible for doping superlattices in PbTe and in Pbl_xGexTe alloys are discussed based on a Landau free energy approach.
].
Introduction
Semiconductors with doping superlattices form a new class of synthetic materials. They have received considerable theoretical and 1 experimental study in recent years. GaAs grown by molecular beam epitaxy has been used almost exclusively for these systems. One of the attractive features of doping superlattices is that any semiconductor that can be doped both nand p-type in a well-controlled way can be used as the host material. This is an advantage over compositional superlattices for which the requirement of lattice matching of the two semiconductors involved restricts severely the choice of materials. It has been shown recently that the technique of hot wall ep%taxy allows for sufficient control over the growth process of PbTe and its alloys to make possible the growth of doping
ing of alternating layers of n- and p-doped material leads to a space charge profile which modulates the band structure of the host semiconductor. In Fig. I we show the modulation of the conduction and valence band edges for the case of a system with very thin doped layers which are separated by relatively thick undoped layers. If the total modulation is smaller than the band gap of the host material E ° and if the g system is macroscopically compensated, then all donors and all acceptors will be ionized at low temperature, and the Fermi level N will lie in the middle of the effective gap. The effective gap is given by E eff = E ° - 2V g g where V is potential.
superlattices in these semiconductors. 2 The strong temperature dependences of the dielectric properties of these materials can be expected to give rise to interesting behaviors of superlattices formed from them. Here we present calculations of the temperature dependence of the electronic properties of doping superlattices in PbTe. The configurations of lattice polarization in doping superlattices in PbTe and in Pbl_xGexTe or Pbl_xSnxTe
the
(I)
amplitude
d
of the space
charge
,
alloys are also discussed. In the bulk these alloy systems exhibit a ferroelectric phase transition at low temperature. 3 2.
Free Carrier Distribution and Effective Gap
The characteristic doping profile of a doping superlattice, which is a system consist-
0 7 4 9 - 6 0 3 6 / 8 5 / 0 3 0 1 9 7 + 04 $02.00/0
I
_
÷
--
÷
z-direction Fig. I. Schematic representation of the conduction and valence band edges of a doping superlattice with thin doped layers separated by wide intrinsic layers.
© 1 985 Academic Press Inc. (London) Limited
Superlattices and Microstructures, Vol. 1, No. 3, 1985
198 Electrons and holes present in the system at finite temperature will populate predominantly the n- and p- layers respectively. They will contribute to the total space charge potential, which is obtained as the solution of Poisson's equation:
82v(z) ~z
_ 4~e 2 {+nD(z)-nA(z)-n(z)+p(z)} K
I
o Eg ~...I~
200
/
f
I
I
I
/
¢,
(2)
E I,LI
100
with the appropriate boundary conditions. In eq. (2) nn(z ) and nA(z ) are the fixed doping profiles ~f donors arid acceptors, and the thermal equilibrium charge carrier distributions n(z) and p(z) are given by
n(z) = f~odgf(g+v(z))De(g )
(3)
_E° p ( z ) = f_ g d g ( 1 - f ( g + v ( z ) ) D h ( - g - E ~ )
(4)
Here De (g) and , D_(g) are the d e n s i t i e s of s t a t e n of the conduction and v a l e n c e bands and f ( 6 ) i s t h e Fermi-Dirac d i s t r i b u t i o n . We have solved the s e t of e q u a t i o n s (2) to (4) s e l f - c o n s i s t e n t l y f o r v a r i o u s doping s u p e r l a t t i c e c o n f i g u r a t i o n s i n PbTe. The t e m p e r a t u r e dependences of t h e d i e l e c t r i c c o n s t a n t K and of the band gap E°g p l a y an i m p o r t a n t r o l e i~ d e t e r mining the e l e c t r o n i c p r o p e r t i e s of doping superlattices. We have o b t a i n e d t h e s e q u a n t i t i e s from f i t s to e x p e r i m e n t a l data which give
These
K~I(T) = 6.67x10-4+l.72x10-5"T
(5)
E;(T)/eV = O.177+4.9x10-4.T
(6)
linear temperature
dependences
agree well
with experimental data. 3'4 The densities of states for electrons and holes were approximated by those corresponding to parabolic conduction and valence bands of equal effective mass. The effective masses were taken to be proportional to the bulk band gap which is consistent with a simple two band description. In this way the densities of state become weakly temperature dependent. In Figs. 2 and 3 we present results obtained for two doping superlattices in PbTe as functions of temperature. The doping parameters are chosen to yield the same effective gap at low temperature, but the doping profiles are different. Example A has very thin, highly doped layers separated by thick, intrinsic layers similar to the system shown in Fig. I. Example B, on the other hand, corresponds to an n-p multilayer structure without intrinsic layers. The superlattice constant is 500 nm in both cases. The two-dimensional doping concentrations per layer nD(2)__(2) -u A are 4xl0]2cm -2 for example A and 8xlO12cm-2 for example B. Figure 2 shows the temperature dependence of the effective gap for the two systems. At low temperature the decrease of the effective
J
i
0
50
100 T(K)
150
200
Fig. 2. Effective band gaps of two doping superlattices in PbTe as functions of temperature. See text for design parameters. The behavior of the bulk band gap is shown also.
1.5
,
,
' B
'
jIE o
1.0 -
I0
0.5 e-
l
0
50
I
100 T(K)
150
200
Fig. 3. Thermal equilibrium charge carrier concentration for two doping superlattices in PbTe as functions of temperature.
gap is due to the d e c r e a s e of the dielectric constant with increasing temperature. As a consequence, the chemical potential moves closer to the band edges for increasing temperature and significant population of the bands sets in. Thus the space charge becomes partially neutralized and the effective gap does not shrink further but rather increases slowly with rising temperature due to the increasing charge carrier concentration. The behavior of the effective gap with temperature should be compared to the very different behavior of the bulk band gap which is also shown in Fig. 2. Figure 3 shows the dependence of the twodimensional electron concentrations per layer on the temperature. In the two examples presented here the electron concentration always is equal
Superlattices and Microstructures, Vol. 1, No. 3, 1985 to the hole concentration. The carrier concentration at a given temperature is higher in example B due to the smoother shape of the space charge potentiaL. The temperature dependence of the electronic properties of doping superlattices in PbTe is very different from that of systems with a host material whose dielectric constant has negligible temperature dependence, e.g. GaAs. ]n the latter system the space charge potential decreases slowly with increasing temperature due to population of the bands with thermally excited charge carriers. A few remarks concerning our treatment of the problem are in order. We h a v e n e g I e c t e d quantum size effects and the resulting formation of a two-dimensionai subband structure. This is justified because the subband spiitting is small due to the large dielectric constant and theref o r e many s u b b a n d s w i l l b e p o p u l a t e d at finite temperature. We h a v e a s s u m e d c o m p l e t e macroscopic compensation. If this is not the case then a finite concentration of either electrons or holes in the n or p layers will exist in excess of the thermal carrier concentration discussed here. LastIy, it should be noted that our results pertain to the thermal equilibrium state and not to a metastable nonequilibrium state w h i c h may b e p r o d u c e d b y p h o t o e x c i t a t i o n or
charge
carrier
3.
•
.
injection.
5
Lattice Polarization
When bulk PbTe is alloyed with a few percent of Ge to form Pb. Ge Te it is found to , Ix . . undergo a ferroelectrlc p~ase transltlon at low temperatures. A spontaneous polarization appears along one of the four equivalent (III) lattice directions as the system goes from a high temperature cubic phase to a low temperature rhombohedral phase. For temperatures up to room temperature all of these systems are highly polarizable, and above their critical temperatures their inverse dielectric constants are all approximately linearly dependent on temperature. The ferroelectric transition temperature is an increasing function of the alloy composition x. In the case of PbTe the system behaves as if it would show a phase transition at -40 K, the precise value depending on the concentration of defects. The temperature dependence of the dielectric constant in eq. (5) for PbTe therefore can be associated with an incipient instability to the ferroelectric phase transition. Doping superlattices of these IV-VI materials are grown with the superlattice axis along the (111) direction. The material thus is subjected to strong electric fields, which arise from the doping, along a direction of easy polarization. The superlattice therefore may acqnire spatially varying polarizations, and these may affect the dielectric response of the system, In order to study these effects we have performed calculations of the polarizations and of the dielectric response of Pb G e T e doping
1 99 i !
i IlL
a)
I I l
IIL
i i I ÷
b)
÷
~
_ _ _ _
Fig. 4. Two examples of the configurations of lattice polarization in IV-VI doping superlattices. Case (a) is typical for temperatures above the bulk critical temperature, and (b) is an example of a low temperature phase with a net ferroelectric moment.
superlattices using a Landaul-~re~ energy approach. The superlattices have periods on the order of 100 nm and thin doping layers similar to those described above for case A (Fig. I). The free energy is written as a functional of the polarization. It contains terms corresponding to the bulk free energy, a term arising from the coupling of the polarization to the electric field of the doping distribution, a term for the depolarizing effects of the layers, and a term involving the gradient of the polarization to describe the spatial inhomogeneity of the polarization near the doping regions. For PbTe we find a spatially dependent lattice polarization which is shown schematically in Fig. 4a. The polarization is oriented parallel to the superlattice axis and alternates in direction as shown. In addition we find that for PbTe for all finite temperatures the dielec ~ tric function is given to a good approximation by that for the bulk as in eq. (5). In this case the terms in the free energy corresponding to the external field, to the gradient of the polarization, and to fourth order terms in the polarization in the bulk free energy make only small modifications to the dielectric function. For the Pbl Ge Te alloys, which have finite critical ~%~pe~atures in the bulk, we find that below the bulk critical temperature a number of interesting spatially modulated phases exist. These configurations involve polarizations along several equivalent crystal axes. An example of these is shown in Fig. 4b. For the case displayed the polarization has a constant direction but is modulated in magnitude. In these superlattice systems for temperatures on the order of or below the bulk critical temperature the dielectric response is strongly modi-
200
Superlattices and Microstructures, VoL 1, No. 3, 1985
fled compared to the simple low field bulk behavior. A detailed discussion of the spatial dependence of the polarization, of the dielectric functions and of their effects on the electronic properties of superlattices in the Pbl_xGexTe alloys will be presented elsewhere.
it is possible for the system to be switched from one to another of its polarization configurations by photoexcitation or by charge injection. This occurs because the injected charge carriers neutralize partially the space charge of the dopants and thus reduce the internal electric fields.
4.
Concluding Remarks
Quantities which are amenable to direct experimental investigation will show a marked temperature dependence as a consequence of the strong temperature dependence of the effective gap of PbTe doping superlattices. Thus, for example, the absorption coefficient for photon energies smaller than the bulk band gap but larger than the effective gap will vary strongly with temperature because it depends exponentially on the strength of the built-in electric 6 fields. In addition some rather exotic behavior may be observable in these systems due to the considerable freedom provided by the choice of superlattice design parameters. If, for example, the doping levels are sufficiently high and the superlattice period is sufficiently large, then the system may change from a semiconducting state at low temperature to a semimetallic state for which the Fermi level intersects both the conduction and valence bands at high temperature. Furthermore if the superlattice is made from a material which has a ferroelectric phase,
Acknowledgement - This work was supported partially by an ONR contract.
References 1.
For a r e c e n t review G.H. DShler, Advances
see: K. Ploog i n P h y s i c s 32,
and 285
2.
H. Kinoshita, T. Sakashita, and H. Fujiyasu, J. Appl. Phys. 52, 2869 (1981). W. Jantsch in Proceedings of the IV Int'l Conf. on Narrow Gap Semiconductorst Linz, Austria (1981), eds. E. Gornik, H. Heinrich, L. Palmetshofer (Springer-Verlag, Berlin, 1982). W. J a n t s c h , Z e i t s c h r i f t fHr P h y s i k B 40, 193 (1980). G.H. DShler, J. Vac. Sci. Technol. B I, 278 (1983). D.K. Hohnke, H. Holloway, and S. Kaiser, J. Phys. Chem. Solids 33, 2053 (1972). G.H. DShler and P.P. Ruden, submitted for publication.
(1993). 3.
4. 5. 6. 7.
197
TEMPERATURE DEPENDENCE OF ELECTRONIC AND LATTICE PROPERTIES OF DOPING SUPERLATTICES IN IV-Vl SEMICONDUCTORS ,P. P. Ruden,*§ T . L . Reinecke, * and F. Naval Research Laboratory, Washington, §~orth Carolina State University, Raleigh, Martin Marietta Laboratories, Baltimore,
Crowne + DC 20375 NC 27650 ND 21227
(Received 13 August 1984 by J.D. Dow)
The effective band gap and the thermally excited carrier concentrations of doping superlattices in PbTe are calculated self-consistently using a semiclassical description. They show interesting temperature behaviors which arise from the temperature dependences of the lattice polarizability, of the bulk band gap, and of the equilibrium carrier concentration. The configurations of lattice polarization which are possible for doping superlattices in PbTe and in Pbl_xGexTe alloys are discussed based on a Landau free energy approach.
].
Introduction
Semiconductors with doping superlattices form a new class of synthetic materials. They have received considerable theoretical and 1 experimental study in recent years. GaAs grown by molecular beam epitaxy has been used almost exclusively for these systems. One of the attractive features of doping superlattices is that any semiconductor that can be doped both nand p-type in a well-controlled way can be used as the host material. This is an advantage over compositional superlattices for which the requirement of lattice matching of the two semiconductors involved restricts severely the choice of materials. It has been shown recently that the technique of hot wall ep%taxy allows for sufficient control over the growth process of PbTe and its alloys to make possible the growth of doping
ing of alternating layers of n- and p-doped material leads to a space charge profile which modulates the band structure of the host semiconductor. In Fig. I we show the modulation of the conduction and valence band edges for the case of a system with very thin doped layers which are separated by relatively thick undoped layers. If the total modulation is smaller than the band gap of the host material E ° and if the g system is macroscopically compensated, then all donors and all acceptors will be ionized at low temperature, and the Fermi level N will lie in the middle of the effective gap. The effective gap is given by E eff = E ° - 2V g g where V is potential.
superlattices in these semiconductors. 2 The strong temperature dependences of the dielectric properties of these materials can be expected to give rise to interesting behaviors of superlattices formed from them. Here we present calculations of the temperature dependence of the electronic properties of doping superlattices in PbTe. The configurations of lattice polarization in doping superlattices in PbTe and in Pbl_xGexTe or Pbl_xSnxTe
the
(I)
amplitude
d
of the space
charge
,
alloys are also discussed. In the bulk these alloy systems exhibit a ferroelectric phase transition at low temperature. 3 2.
Free Carrier Distribution and Effective Gap
The characteristic doping profile of a doping superlattice, which is a system consist-
0 7 4 9 - 6 0 3 6 / 8 5 / 0 3 0 1 9 7 + 04 $02.00/0
I
_
÷
--
÷
z-direction Fig. I. Schematic representation of the conduction and valence band edges of a doping superlattice with thin doped layers separated by wide intrinsic layers.
© 1 985 Academic Press Inc. (London) Limited
Superlattices and Microstructures, Vol. 1, No. 3, 1985
198 Electrons and holes present in the system at finite temperature will populate predominantly the n- and p- layers respectively. They will contribute to the total space charge potential, which is obtained as the solution of Poisson's equation:
82v(z) ~z
_ 4~e 2 {+nD(z)-nA(z)-n(z)+p(z)} K
I
o Eg ~...I~
200
/
f
I
I
I
/
¢,
(2)
E I,LI
100
with the appropriate boundary conditions. In eq. (2) nn(z ) and nA(z ) are the fixed doping profiles ~f donors arid acceptors, and the thermal equilibrium charge carrier distributions n(z) and p(z) are given by
n(z) = f~odgf(g+v(z))De(g )
(3)
_E° p ( z ) = f_ g d g ( 1 - f ( g + v ( z ) ) D h ( - g - E ~ )
(4)
Here De (g) and , D_(g) are the d e n s i t i e s of s t a t e n of the conduction and v a l e n c e bands and f ( 6 ) i s t h e Fermi-Dirac d i s t r i b u t i o n . We have solved the s e t of e q u a t i o n s (2) to (4) s e l f - c o n s i s t e n t l y f o r v a r i o u s doping s u p e r l a t t i c e c o n f i g u r a t i o n s i n PbTe. The t e m p e r a t u r e dependences of t h e d i e l e c t r i c c o n s t a n t K and of the band gap E°g p l a y an i m p o r t a n t r o l e i~ d e t e r mining the e l e c t r o n i c p r o p e r t i e s of doping superlattices. We have o b t a i n e d t h e s e q u a n t i t i e s from f i t s to e x p e r i m e n t a l data which give
These
K~I(T) = 6.67x10-4+l.72x10-5"T
(5)
E;(T)/eV = O.177+4.9x10-4.T
(6)
linear temperature
dependences
agree well
with experimental data. 3'4 The densities of states for electrons and holes were approximated by those corresponding to parabolic conduction and valence bands of equal effective mass. The effective masses were taken to be proportional to the bulk band gap which is consistent with a simple two band description. In this way the densities of state become weakly temperature dependent. In Figs. 2 and 3 we present results obtained for two doping superlattices in PbTe as functions of temperature. The doping parameters are chosen to yield the same effective gap at low temperature, but the doping profiles are different. Example A has very thin, highly doped layers separated by thick, intrinsic layers similar to the system shown in Fig. I. Example B, on the other hand, corresponds to an n-p multilayer structure without intrinsic layers. The superlattice constant is 500 nm in both cases. The two-dimensional doping concentrations per layer nD(2)__(2) -u A are 4xl0]2cm -2 for example A and 8xlO12cm-2 for example B. Figure 2 shows the temperature dependence of the effective gap for the two systems. At low temperature the decrease of the effective
J
i
0
50
100 T(K)
150
200
Fig. 2. Effective band gaps of two doping superlattices in PbTe as functions of temperature. See text for design parameters. The behavior of the bulk band gap is shown also.
1.5
,
,
' B
'
jIE o
1.0 -
I0
0.5 e-
l
0
50
I
100 T(K)
150
200
Fig. 3. Thermal equilibrium charge carrier concentration for two doping superlattices in PbTe as functions of temperature.
gap is due to the d e c r e a s e of the dielectric constant with increasing temperature. As a consequence, the chemical potential moves closer to the band edges for increasing temperature and significant population of the bands sets in. Thus the space charge becomes partially neutralized and the effective gap does not shrink further but rather increases slowly with rising temperature due to the increasing charge carrier concentration. The behavior of the effective gap with temperature should be compared to the very different behavior of the bulk band gap which is also shown in Fig. 2. Figure 3 shows the dependence of the twodimensional electron concentrations per layer on the temperature. In the two examples presented here the electron concentration always is equal
Superlattices and Microstructures, Vol. 1, No. 3, 1985 to the hole concentration. The carrier concentration at a given temperature is higher in example B due to the smoother shape of the space charge potentiaL. The temperature dependence of the electronic properties of doping superlattices in PbTe is very different from that of systems with a host material whose dielectric constant has negligible temperature dependence, e.g. GaAs. ]n the latter system the space charge potential decreases slowly with increasing temperature due to population of the bands with thermally excited charge carriers. A few remarks concerning our treatment of the problem are in order. We h a v e n e g I e c t e d quantum size effects and the resulting formation of a two-dimensionai subband structure. This is justified because the subband spiitting is small due to the large dielectric constant and theref o r e many s u b b a n d s w i l l b e p o p u l a t e d at finite temperature. We h a v e a s s u m e d c o m p l e t e macroscopic compensation. If this is not the case then a finite concentration of either electrons or holes in the n or p layers will exist in excess of the thermal carrier concentration discussed here. LastIy, it should be noted that our results pertain to the thermal equilibrium state and not to a metastable nonequilibrium state w h i c h may b e p r o d u c e d b y p h o t o e x c i t a t i o n or
charge
carrier
3.
•
.
injection.
5
Lattice Polarization
When bulk PbTe is alloyed with a few percent of Ge to form Pb. Ge Te it is found to , Ix . . undergo a ferroelectrlc p~ase transltlon at low temperatures. A spontaneous polarization appears along one of the four equivalent (III) lattice directions as the system goes from a high temperature cubic phase to a low temperature rhombohedral phase. For temperatures up to room temperature all of these systems are highly polarizable, and above their critical temperatures their inverse dielectric constants are all approximately linearly dependent on temperature. The ferroelectric transition temperature is an increasing function of the alloy composition x. In the case of PbTe the system behaves as if it would show a phase transition at -40 K, the precise value depending on the concentration of defects. The temperature dependence of the dielectric constant in eq. (5) for PbTe therefore can be associated with an incipient instability to the ferroelectric phase transition. Doping superlattices of these IV-VI materials are grown with the superlattice axis along the (111) direction. The material thus is subjected to strong electric fields, which arise from the doping, along a direction of easy polarization. The superlattice therefore may acqnire spatially varying polarizations, and these may affect the dielectric response of the system, In order to study these effects we have performed calculations of the polarizations and of the dielectric response of Pb G e T e doping
1 99 i !
i IlL
a)
I I l
IIL
i i I ÷
b)
÷
~
_ _ _ _
Fig. 4. Two examples of the configurations of lattice polarization in IV-VI doping superlattices. Case (a) is typical for temperatures above the bulk critical temperature, and (b) is an example of a low temperature phase with a net ferroelectric moment.
superlattices using a Landaul-~re~ energy approach. The superlattices have periods on the order of 100 nm and thin doping layers similar to those described above for case A (Fig. I). The free energy is written as a functional of the polarization. It contains terms corresponding to the bulk free energy, a term arising from the coupling of the polarization to the electric field of the doping distribution, a term for the depolarizing effects of the layers, and a term involving the gradient of the polarization to describe the spatial inhomogeneity of the polarization near the doping regions. For PbTe we find a spatially dependent lattice polarization which is shown schematically in Fig. 4a. The polarization is oriented parallel to the superlattice axis and alternates in direction as shown. In addition we find that for PbTe for all finite temperatures the dielec ~ tric function is given to a good approximation by that for the bulk as in eq. (5). In this case the terms in the free energy corresponding to the external field, to the gradient of the polarization, and to fourth order terms in the polarization in the bulk free energy make only small modifications to the dielectric function. For the Pbl Ge Te alloys, which have finite critical ~%~pe~atures in the bulk, we find that below the bulk critical temperature a number of interesting spatially modulated phases exist. These configurations involve polarizations along several equivalent crystal axes. An example of these is shown in Fig. 4b. For the case displayed the polarization has a constant direction but is modulated in magnitude. In these superlattice systems for temperatures on the order of or below the bulk critical temperature the dielectric response is strongly modi-
200
Superlattices and Microstructures, VoL 1, No. 3, 1985
fled compared to the simple low field bulk behavior. A detailed discussion of the spatial dependence of the polarization, of the dielectric functions and of their effects on the electronic properties of superlattices in the Pbl_xGexTe alloys will be presented elsewhere.
it is possible for the system to be switched from one to another of its polarization configurations by photoexcitation or by charge injection. This occurs because the injected charge carriers neutralize partially the space charge of the dopants and thus reduce the internal electric fields.
4.
Concluding Remarks
Quantities which are amenable to direct experimental investigation will show a marked temperature dependence as a consequence of the strong temperature dependence of the effective gap of PbTe doping superlattices. Thus, for example, the absorption coefficient for photon energies smaller than the bulk band gap but larger than the effective gap will vary strongly with temperature because it depends exponentially on the strength of the built-in electric 6 fields. In addition some rather exotic behavior may be observable in these systems due to the considerable freedom provided by the choice of superlattice design parameters. If, for example, the doping levels are sufficiently high and the superlattice period is sufficiently large, then the system may change from a semiconducting state at low temperature to a semimetallic state for which the Fermi level intersects both the conduction and valence bands at high temperature. Furthermore if the superlattice is made from a material which has a ferroelectric phase,
Acknowledgement - This work was supported partially by an ONR contract.
References 1.
For a r e c e n t review G.H. DShler, Advances
see: K. Ploog i n P h y s i c s 32,
and 285
2.
H. Kinoshita, T. Sakashita, and H. Fujiyasu, J. Appl. Phys. 52, 2869 (1981). W. Jantsch in Proceedings of the IV Int'l Conf. on Narrow Gap Semiconductorst Linz, Austria (1981), eds. E. Gornik, H. Heinrich, L. Palmetshofer (Springer-Verlag, Berlin, 1982). W. J a n t s c h , Z e i t s c h r i f t fHr P h y s i k B 40, 193 (1980). G.H. DShler, J. Vac. Sci. Technol. B I, 278 (1983). D.K. Hohnke, H. Holloway, and S. Kaiser, J. Phys. Chem. Solids 33, 2053 (1972). G.H. DShler and P.P. Ruden, submitted for publication.
(1993). 3.
4. 5. 6. 7.