Conduction and switching phenomena in covalent alloy semiconductors

JOURNAL OF NON-CRYSTALLINESOLIDS4 (1970) 464--479 © North-Holland Publishing Co., Amsterdam

C O N D U C T I O N AND S W I T C H I N G P H E N O M E N A IN COVALENT ALLOY SEMICONDUCTORS* H. FRITZSCHE James Franck Institute, University o f Chicago, Chicago, Illinois 60637, U.S.A. and S. R. OVSHINSKY Energy Conversion Devices, Inc., 1675 IV. Maple Road, Troy, Michigan 48084, U.S.A. High field breakdown often leads (i) to a regenerative structural change in the material, or (ii) without any material change, to a conducting state which is maintained only above a certain holding current value. It is suggested that breakdown can be triggered by different processes depending on the temperature and the electrode configuration. The observed high field and non-equilibrium phenomena will be discussed in relation with the several proposed breakdown mechanisms. The material characteristics yielding the different switching effects will be discussed.

1. Introduction Most materials cannot withstand electric fields in excess of about 106 V/cm. In insulators such high fields usually lead to a destructive breakdown which, generally speaking, is a non-regenerative change of the material along the breakdown path. In amorphous semiconductors, electric breakdown effects have drawn particular attention because of the discovery 1-3) that electric breakdown can be a regenerative and non-destructive process. Because breakdown is quite generally expected in all high resistivity materials, it is the process, which sets in after breakdown, that sets apart the amorphous semiconductors from other materials which show destructive breakdown. The physical processes, which determine and sustain the conduction after breakdown has taken place, may be quite different from those which initiate and lead to breakdown. This distinction is quite evident when the material undergoes a change in structure after breakdown or when the electrical field distribution is drastically changed. Many theories of electric breakdown in solids have been developed during the past decades 4) and applied to various systems. A number of their explicit predictions resemble each other to a great degree, so that experimental confirmation must rest on the quantitative relationship between the current * Supported in part by the Air Force Officeof Scientific Research, AFOSR 49 (638)-1653. 464

CONDUCTION AND SWITCHING PHENOMENA

465

and voltage parameters on the one hand and on the other hand on the external parameters like temperature and sample geometry and the material characteristics which govern the electronic transport properties. Because the material parameters and the properties of contacts, which determine the low and high field conduction properties, are poorly understood in insulators and in low mobility and amorphous semiconductors, the field of electric breakdown suffers from a large degree of ambiguity. In the following the non-destructive breakdown will be discussed in detail which is observed in semiconducting covalent alloys which are used in Ovonic switching and memory devices. In particular the question will be analyzed how far the thermal breakdown theory can explain the observed phenomena. The switching and memory characteristics have been described earlier2,5,6, v) so that a full account of these can be omitted here. 2. Thermal breakdown Thermal breakdown, which is caused by Joule self-heating of the material when the heat generation exceeds the cooling term in the heat balance equation, is generally expected to occur in all materials whose resistivity decreases rapidly with increasing temperature. Additional requirements for its occurrence are of course a sample and electrode geometry which favors slow cooling and no other breakdown mechanisms which set in at a lower field. The thermal breakdown theory is particularly attractive because it is independent of the detailed conduction mechanism of the material and no further information is needed than the heat conduction and capacities, and the temperature dependence of the electrical conductivity. Such thermal runaway process, therefore, appeared to explain the fact, that we observed the switching effect in a large variety of materials such as chalcogenide glasses, arsenic and boron glasses, in transition metal containing oxides, and others. Common to all these materials is a rather low thermal conductivity and an electrical conductivity of the approximate form a = ao exp ( -

AE/2kT),

(1)

with cr0 about l0 -1 ohm -1 cm -1 for the oxides and about l0 3 ohm -1 cm -1 for most other amorphous semiconductors with values of A E between 0.6 and 1.5 eV. After ascertaining that conducting electrodes make contact with amorphous semiconductors without producing noticeable depletion layers, and that the switching phenomena are true bulk effects, we tried to explain our observations on the basis of Joule self-heating. The calculation of thermal breakdown requires the solution of the differ-

466

H.FRITZSCHE AND S.R.OVSHINSKY

ential equation c3T C 3t = aEz -

V'(KVT),

(2)

for the temperature T as a function of position and time, C being the specific heat per volume and ~: the thermal conductivity. A general solution of eq. (2) cannot be found with realistic boundary conditions. Several simplifications are commonly introduced which explains the rich literature on thermal breakdown dating back to the turn of the century. For comparison with experiments solutions to eq. (2) can most easily be found in two limiting cases: (a) Impulse thermal breakdown, which approximates eq. (2) by neglecting the heat conduction term. This is permissible when the voltage is applied rapidly enough. It yields under these conditions the delay time prior to breakdown and the critical voltage but no information about the conduction after breakdown. (b) Steady state breakdown, i.e. when the current is increased slowly, allows one to neglect the time derivative. The heat conduction term then balances the Joule heating term. Although heat is conducted in all directions, two subcases are usually treated, the case of (i) axial heat flow and (ii) radial heat flow. For a study of the dynamics of the switching process one has to include the external circuit parameters. Only subcase (b, ii) yields the generally observed phenomenon that a heated channel forms which carries most of the current after breakdown. This was realized very early, and in 1935 Spenke 8) studied in detail various boundary conditions and geometries to reduce channel formation to avoid the destructive heat generation at high currents. The temperature profile of such current channels was first measured in CdS by BSer 9) by means of the thermal shift of the absorption edge. However, the fact that channel formation is not limited to thermal breakdown but is a general consequence of current controlled I - V characteristics was pointed out by Ridleyl°). Current channels were indeed observed by recombination radiation in double injection diodesn). The analysis of several cases of thermal breakdown and a comparison with the experimental results will be presented in the appendix. We find for steady state breakdown and radial heat flow under constant current conditions the I - V curves shown in fig. 1 for several ambient temperatures. The values chosen for a o and A E are given in the figure caption and the maximum temperatures of the inner core are shown next to some curves. Since only radial heat flow is considered the current and voltage scales can easily be changed to apply to different electrode separations. This characteristic,

467

CONDUCTION AND SWITCHING PHENOMENA

-I 3 5 0 °C I

I

I

275

I so m

-2

o'=o-o exp ( - A E / k T ) AE = 0 . 6 5 eV radial heat flow only

-3 v8

-4

J

J

I

lO

20

30

~ 40

I

I

I

50

60

70

DC bias (Volts)

Fig. 1. Steady state breakdown characteristic of a cylindrical piece of semiconductor with a conductivity described by eq. (I). Axial heat flow is neglected. The cylindrical surface is held at various ambient temperatures T0.

which shows an extended negative differential resistance region, was observed very early in boronl~). Some hysteresis is observed when the current is changed too rapidly for maintaining thermal equilibrium. By using a small value of a protective load resistor R L such a device can be made to switch 13,14) along the load line from a point at which R L--- - d V/dI to the point of intersection of the load line and the I - V curve. One always finds in these cases that the breakdown voltage VB decreases rapidly with T approximately as VBoca-~, and that the highest internal temperature near VB is not much larger than ambient. Impulse breakdown discussed in the appendix yields for a voltage linearly increasing with time VB oc [L2To2/a(To)]" , (3) for the dependence of VB on electrode separation L and ambient temperature To. The temperature at breakdown near VB is Tc = T0(l + 2 kTo/AE ),

(4)

that is about 15°C above ambient for typical cases. When a square wave voltage pulse of magnitude Vp is applied, we find for the delay time t D before breakdown the relation

V2to = CLZk To2/AEa(To).

(5)

468

H.FRITZSCHE AND S.R.OVSHINSKY

We find that for thicknesses in excess of L ~ 10 pm of chalcogenide alloys of the type used in some Ovonic threshold and memory switches the thermal theory explains satisfactorily the thickness and temperature dependence of lie and of V~tD, as long as t D is sufficiently short (less than 5 psec) to permit omission of the heat conduction term. However, for thicknesses less than L = 5 /~m strong deviations from the predictions of the thermal theory are observed. In agreement with Kolomiets 15) we find that lib is first proportional to L and for L > 10 pm, Va~zL", with 0.5 ~
t2n

2

"~

o

-0

e Itherm0|)

thickness

L

Fig. 2. When two or more breakdown processes are possible, which scale differently with temperature and electrode separation, the process having lower VB will dominate. Thermal breakdown, which is always one of these processes in semiconductors, is favored in larger samples and under poor heat sinking conditions.

processes scale differently with thickness. The critical L dividing the two regions will depend on the material and on geometrical and thermal parameters of the whole system. The observation16,17) of an isothermal nonlinear current increase before the voltage reaches breakdown suggests but does not prove an electrical initiation of breakdown at small thicknesses. Let us now consider the phenomena which occur after breakdown has been initiated. Switching is observed in a 1 #m thick semiconducting layer contacted by pyrolytic carbon electrodes to occur from 20 V and 20/~A to a conducting condition of 1 V and 10 mA within a time interval ts ~<10 - 9 sec. Let us assume as the best condition for self-heating that no heat is conducted

CONDUCTION

AND SWITCHING

PHENOMENA

469

away. Under this favorable circumstance we shall determine whether or not a sufficient volume of the layer can be heated within t s to a sufficiently high temperature T above the temperature TB to yield the conducting state 2 specified in the example above. The energy available for heating is z1 C o Vd, the energy stored on the capacitance of the device Co = 2 p F in addition to joule heating. We obtain C A L ( T - T.) = ' ~CoV B 2 + f I V dr.

(6)

ts

The energy stored on the capacitance of the device is about ten times larger than the Joule heating term, hence even a considerably longer switching time t s does not alter significantly the following conclusions. Since the cross section A of the conducting region is uncertain, we express A in terms of R and a, the resistance and conductivity, respectively, of the conducting region. Writing E s for the right-hand side of eq. (6), r - T B = E s R a ( T ) / L 2 C = 4ao e x p ( - A E / 2 k T ) ,

(7)

if one inserts for the heat capacity C = 1 J/cm 3 deg and the values R = 100 ohm and L = 10 -4 cm for the example chosen. Both sides of eq. (7) with TB = 325 °K are plotted in fig. 3. One finds no solution for eq. (7) unless the conductivity jumps abruptly to a high value at a certain finite temperature, as for instance at the crystallization temperature. The occurrence of a 1o'

I

I

W

I

2

3

_= -o 1(5I o

16~

b

~r 163

c

1o" J6" 0

103IT (*K -j) Fig. 3. The left and right-hand side of eq. (7) of text are plotted against reciprocal temperature. One notices that no solution exists. This means that even with most favorable assumptions the thermal breakdown theory is incapable of explaining the observed fast switching to the highly conducting state.

470

H.FRITZSCHE AND S.R.OVSHINSKY

structure change during the time ts can, however, be excluded because in those cases which show a structural transition, this change is always observed to occur some time after switching has taken place, as will be explained later. Regardless of the mechanism which initiates breakdown the short time within which the highly conducting state is reached poses a challenging problem. Several qualitative explanations have been offered 6, 7,18) but in view of our poor understanding of the conduction processes in amorphous semiconductors, it is not surprising that many questions remain unanswered. Once the conducting state has been established, with a constriction of the current path as predicted by Ridley, Joule heating will naturally take place. The holding voltage is about 1 V, independent of electrode separation. This means the voltage drop is not uniform but it occurs near one or most likely near both electrodes. Ambient temperature has a negligible effect on this value. It appears to be always slightly larger than the mobility gap of the amorphous semiconductor. In the case of the Ovonic switching device, the unit switches back to the high resistance state as the current falls below a minimum holding value of about 0,5 mA. If a switching voltage is applied immediately after turn off, the former conducting channel is still warm which results in a somewhat lower switching voltage 5). After about 1 #sec recovery time the original cool state is reestablished. This recovery time sets the upper limit to the high frequency response.

3. Memory effects Let us now consider the switching element with memory. Here a permanently conducting state is established a short time after fast switching into the conducting state has taken place. This lock-on process is usually observable as an additional slight decrease of the resistance and as a lowering of the level of the noise spectrum. The memory device can be returned to its high resistance state by the application of a current pulse. The switching into the oN state and resetting into the OFF state can be repeated at liberty. After measuring the differential thermal analysis curve of such memory type glass we first 6) came to the conclusion that the current channel in the conducting state gets warm enough to reach the crystallization temperature T1, transforming the channel region into a well conducting degenerate semiconductor. The short reset pulse would then bring the crystallized channel quickly above the melting temperature TM, after which the channel region is quickly cooled by its environment, establishing by quenching the original glassy state. The process appears to be much more subtle and interesting, however:

CONDUCTION AND SWITCHING PHENOMENA

471

By placing two electrodes on the surface of a piece of polished memory material obtained from us, Uttecht et al. 19) first saw at breakdown evidence of heating in the region between the electrodes. Because the electrode spacing was as large as 100 #m and heat conduction was poor, this probably was thermal breakdown. Then, as sketched in fig. 4, starting from the anode, a + switch on

o

lock

switch-on

(7--------

on

time

C- . . . . . . . . . . . . . .

---O

lock-on completed

Fig. 4. Processes observed in Ovonic memory type material. Only after the breakdown or "switch-on" process has occurred does a partially crystallized and conducting filament grow from the anode. When it has reached the cathode, conducting state is locked-on. Sketch according to Kikuchi20).

15 pm thick filament proceeded to grow towards the cathode. Only after this filament, which turned out to be crystalline, reached the cathode was the memory set or locked-on. If one reverses polarity before lock-on was established, the half-grown filament retracted and a new filament started at the new anode. Depending on the memory material speeds of filament growth between 10-2 cm/sec and 102 cm/sec were subsequently observed. Kikuchi 20) observed the same phenomena. He and his collaborators found that the filament cross section increased in proportion with the lock-on current. This is a macroscopic simulation of Ovshinsky's "adaptive memory". Different conducting resistances can be reproducibly established using different lock-on currents. Kikuchi placed there and four electrodes on the surface of this macroscopic device and showed in slow motion the three or four terminal device which one of us (S.R.O.) described zl). Fig. 5 shows a sketch of Kikuchi's experiment: First switch and lock-on between AB. Then switchon AM without locking on, this causes AB to unlock. Or one can make a

472

H.FRITZSCHE AND S.R.OVSHINSKY

A

M

B

A

(2)

(2)

(I)AB: Lock-On (2) AM: Switch-On (5) AM: Switch-Off Result, AB Unlocked

(I) AM: (2) MB: (5) MB: Result,

M

B

Lock-On Switch-On Lock-On AM Unlocked

Fig. 5. Sketch of Kikuchi's three electrode experiment2o).

flip-flop device: Lock-on AM, then switch-on action between MB causes AM to unlock. But then the applied voltage is kept on sufficiently long to lock-on MB. Switching on AM unlocks MB and the process can be repeated forth and back. 4. Conclusions The foregoing discussion emphasizes that one may have to distinguish between the process which initiates breakdown and the phenomena which take place after breakdown has taken place. Moreover, thermal phenomena and electrical breakdown obey different scaling laws and may be observed under different experimental conditions. Macroscopic models have to be taken with caution since thermal effects are greatly enhanced and shortening the time scales by as much as factors of 10 6 (in Kikuchi's experiments lock-on took place after many minutes) may eliminate some diffusion processes completely. The macroscopic models are instructive, however, since they can make important effects visible. The fact that crystallization proceeded in some of the experiments on memory material from the anode emphasizes the importance of the electric field and of the presence of holes in the structural changes taking place. The large densities of holes to be expected in the conducting state represent broken valence bonds. These can facilitate crystallization 22) or a very fast and subtle structural change as described by Krebs2a). The effects of fields and of electron excitations on structure changes are still poorly understood and may open an interesting and new area of study in amorphous and glassy semiconductors.

CONDUCTION AND SWITCHING PHENOMENA

473

Acknowledgments We gratefully acknowledge the advice of many of our colleagues, in particular that of M. H. Cohen, N. F. Mott, and A. Bienenstock, and the devoted help of the staff of Energy Conversion Devices, Inc.

Appendix. Impulse thermal breakdown Let us consider a piece of semiconducting material of cross section A between flat electrodes separated by a distance L. The material has a specific heat per volume C and its conductivity follows eq. (1). We assume that breakdown occurs rapidly enough that the heat conduction term in eq. (2) can be ignored. It turns out that the temperature TB at the point of breakdown is only 10-20°C above ambient which also minimizes the importance of heat conduction. After breakdown has occurred, T starts to increase exceedingly rapidly until a new steady state is reached which is governed within the framework of thermal breakdown by the efficiency of heat conduction. Since this is neglected altogether, the following treatment cannot yield any information about the state of affairs after breakdown. It also is obvious that the important phenomenon of current channeling cannot be treated by a theory which neglects heat conduction. It appears, however, that the channel formation sets in after the voltage has reached the breakdown value VB. The resistance of the device at breakdown is R(TB). If the load resistor R L is larger or comparable to this value, then the voltage across the device is reduced to V~--IRL, where V~ is the applied voltage, and breakdown is considerably delayed. The case of large and small R L will be treated separately and two voltage forms will be considered: (A) square wave voltage pulse of height Vp and (B) voltage increasing linearly with time as Va= Vowt; the second case approximates the beginning of a sinusoidal wave V, = Vo sin

(wt). l.

A)

S M A L L L O A D RESISTOR

RL~R(Ta)

Square wave voltage Vp From eq. (2) one obtains immediately the delay time to Tc

CAL~ R(T) dT

ID = Vp2-P2

(A1)

,a

To

The critical temperature Tc is not known. However, its value is unimportant

474

H.FRITZSCHE AND S.R.OVSHINSKY

for the evaluation of to because o f the exponential decrease of R with increasing T. In other words, T increases slowly first, then exceedingly rapidly, the borderline is t o. Fig. 6 shows the dependence of the integral of eq. (A1) as a function of its upper temperature limit. This particular behavior of the integral is determined by the exponential T dependence of the resistivity p and constitutes the basic reason for thermal breakdown. 400 590 Exarnpte:

R : IO'%nm R(5OO*K)=ZSxtOT

580

ohm

570

AE= 1.3 eV. V = I00 V. CO = 6 0 Hz. C: 1.5 d/cm3 A=2xl~cm z L= 1~3cm

560 m 55O

~- 340 330 320 510 300

Io

s.o ~

,o~

~oo Time (#sec.)

Fig. 6. Because of the exponential decrease of resistance with increasing T, the major contribution to the integral of eq. (A1) and hence to the delay time to is accumulated at lower temperatures. The ordinate is used for the independent variable T.

The integral can be solved approximately and one obtains very nearly

VpZto = CL2 p (To) 2kT2/AE. B)

(A2)

Va = VoWt

Neglecting the heat conduction term in eq. (2) and separating time and temperature variables yields tD

Tc

vow

0

R(T)dT.

~ dt=CAL

(A3)

To

Here the same remarks about the integral on the right-hand side apply.

475

CONDUCTION AND SWITCHING PHENOMENA

One obtains 3 ½V~)2 w 2 t D = CL2p(To) 2kTo2/AE.

(A4)

Since the breakdown voltage is Va = VoWtD one obtains Va = (6CL2 P (To) VowkTE/AE) ~ •

(A5)

One notices the relation between Va of the linearly increasing voltage and V2ID for an applied square wave pulse. Hence

V2to = V3/3Vo w .

(A6)

The temperature at the point of breakdown can be estimated from eqs. (A2) and (A4) as Ta = 7"o(1 + 2kTo/AE ).

(AT)

C) Comparison with experimental results The temperature dependence of t D and of VB are dominated by the p(To). Figs. 7 and 8 show respectively the dependence of V2tD and of VB on the resistance of a device carrying a L = l0/~m thick film having a cross section of about A = 10-5 cm 2. Its resistance was changed by changing the ambient temperature To. One observes good agreement with eqs. (A2) and (A5).

i01

I

-~ I0 o c~

/~....--

v~ ,0 o. R

/

I

i0 -I 10 6

10 7

Resistonee

R

10 8

(~)

Fig. 7. Comparison of a device having L -- I0/tm with the thermal breakdown theory under square wave impulse condition. The resistance R is changed by using different ambient temperatures To.

476

H.FRITZSCHE

AND S.R.OVSHINSKY

iO~

o >

g o

I0 2

j

o rn

/~-theoreticol

I0'

IOs

slope

VB o~ R Vs

I0 7 Resistance (Q,)

i0 8

Fig. 8. The breakdown voltage VB plotted against resistance R of the same device used for previous figure. Here the applied voltage is increased linearly with time yielding VBoC R (To)~.

2. LARGE LOAD RESISTOR R L Only the case Va= Vowt will be discussed. The case of a square wave pulse is less interesting since a large RE causes the voltage across the device to decrease more gradually with time so that it is difficult to define a definite delay time t D. B) V. = Vowt Neglecting the heat conduction term one obtains

3 CAL B(T), V~w 2

t3 -

(A8)

T

B ( T ) = I" d T ( R + RL)Z/R .

(A9)

To

Eq. (A8) relates T in the semiconducting material with the time t after beginning of the voltage V.. Knowing this relation one can calculate the I - V curve since V.(t) = Vowt = [3 CAL VowB(T)] ~, (A10)

R(T) V = Va(t) R ( T ) + RL ,

(All)

477

CONDUCTION AND SWITCHING PHENOMENA

I -

v.(0 +

R(T)

R L"

(AI2)

The f u n c t i o n B ( T ) has been o b t a i n e d by m a c h i n e c o m p u t a t i o n . It is plotted in fig. 9 for A E = 1.3 eV a n d for different R E = ]03 to l07 ohm. U s i n g C = 1.5 J/cm 3, A = 2 × l0 -6 cm 2, L = ]0 -3 cm, Vo = 100 V a n d w = 3 6 0 sec -1, i0 I0

~ il \,o' ~,o~/o'

t

\

109

.

/

V,o'\

T

\\ )\

t"\ \

107 300

-

/

2 .,,r"x ~ 108

y ~ -/;o ~

\ \ \ I\ \

~,o: ,o~

\ \ \ \1

I

400 Absolute Ternperoture (°K)

Fig. 9. The functions B (T) and C (T) for various load resistors RE. The intersections of two corresponding curves mark the breakdown point for a particular choice of R[,.

I

- 2

o

Io

20

Volts

3O

40

Fig. 10, Thermal breakdown curves for different load resistors. Because of the omission of heat conduction in this case of impulse breakdown, the results cannot be extended much beyond breakdown.

478

H.FRITZSCHE AND S.R.OVSHINSKY

the resulting I - V curves have been plotted in fig. 10. After breakdown the I - V curves follow the load line corresponding to R L but neglection of the heat conduction term invalidates conclusions about the time dependence of I and V after breakdown. The breakdown voltage VB is defined as the maximum voltage across the device. At this point one has dV/dt=O with dV R dVa RE dR d T dt - R + R L dt + ( R + R r ) 2 E~dT dt

(AI3)

One obtains from eq. (2) dt Vaz R d T - CAL (R + RL) 2

(A14)

Substituting (A14) into (A13) one obtains dV. dt -

V,? RL dR CAL (R + RE) 3 dT"

(AI5)

Using Va= Vowt and eq. (l) it follows that CAL (R + RL) 3 2kT~ tg = ([/oW) 2 RRL~ AE

(A16)

This equation is the condition for breakdown. We therefore have added the subscript B to the time symbol. Eq. (A8) relates t and T for all times and hence also at the point of breakdown. Combining (A8) and (Al6) one obtains for the breakdown condition B(T)=

2kT 2 (R + RE) 3 3AE - RRL

(AlT)

This equation is particularly convenient because it is independent of Vo and w and the parameters A and L. The right-hand side of eq. (A17) is called C(T) and is plotted together with B ( T ) in fig. 9. At the crossing point of B ( T) and C(T) for a particular choice of R L the eq. (A17) is satisfied. This point defines TB and B(Ta) from which tB and hence Va, V a n d / a t the point of breakdown can be obtained using eqs. (A10), (All), and (A12). References

1) Early work by S. R. Ovshinsky was reported in Electronics 32 (1959) 76; Control Engineering 6 (1959) 121; in: Anodic Oxide Films by L. Young (Academic Press, New York, 1961); in: IV Symp. on Vitreous ChalcogenideSemiconductors (Acad. Sci., U.S.S.R., Leningrad, 1967); and in: Intern. Colloquiumon Amorphousand Liquid Semiconductors (Acad. Soc. Repub., Rumania, Bucharest, 1967). 2) S. R. Ovshinsky, Phys. Rev. Letters 21 (1968) 1450.

CONDUCTION AND SWITCHING PHENOMENA

479

3) A. D. Pearson, W. R. Northover, J. F. Dewald and W. F. Peck, Jr., in: Advances in Glass Technology (Plenum Press, New York, 1962) p. 357. 4) See review of R. Stratton, Progress in Dielectrics 3 (1961) 234. 5) A detailed description of their properties is found in R. R. Shanks, J. Non-Crystalline Solids 2 (1970) 504. 6) H. Fritzsche, Symposium on Instabilities in Semiconductors, I.B.M. Watson Research Laboratory, March 1969, to be published in the IBM J. Res. Develop. 7) H. Fritzsche and S. R. Ovshinsky, J. Non-Crystalline Solids 2 (1970) 393. 8) E. Spenke, Z. Techn. Phys. 16 (1935); 373 Wiss. Ver6ffentl. Siemenskonzern 15 (1936) 92. 9) K. W. BOer, Festk6rperprobleme 1 (1962) 38. 10) B. K. Ridley, Proc. Phys. Soc. (London) 82 (1963) 996. l l) A. M. Barnett and H. A. Jensen, Appl. Phys. Letters 12 (1968) 341. 12) E. Weintraub, J. Ind. Eng. Chem. (Feb. 1913) 109; F. W. Lyle, Phys. Rev. 11 (1918) 253; J. H. Bruce and A. Hickling, Trans. Faraday Soc. 35 (1939) 1436. 13) W. Dietz and H. Helmberger, in: Boron, Vol 2, Ed. G. K. Gaul6 (Plenum Press, New York, 1965) 13. 301. 14) C. Feldman and W. A. Gutierrez, J. Appl. Phys. 39 (1968) 2474; C. Feldman, Mater. Res. Bull 3 (1968) 93. 15) B. T. Kolomiets, E. A. Lebeder and I. A. Taksami, Soviet Phys.-Semicond. 3 (1969) 267, 731. 16) P.J. Walsh, R. Vogel and E. J. Evans, Phys. Rev. 178(1969) 1274. 17) E. A. Fagen and H. Fritzsche, J. Non-Crystalline Solids 2 (1970) 170. 18) F. W. Schmidlin, to be published; K. B6er, to be published; W. Heywang and D. R. Haberland, to be published. 19) R. Uttecht, H. Stevenson, C. H. Sie, J. D. Griener and K. S. Raghaven, J. NonCrystalline Solids 2 (1970) 358. 20) M. Kikuchi, S. Iizima, M. Sugi and K. Tanaka, to be published; M. Kikuchi and S. lizima, to be published. 21) S. R. Ovshinsky, U.S. Patent 3, 3,336,486 (1967). 22) J. Dresner and G. B. Stringfellow, J. Phys. Chem. Solids 29 (1968) 303. 23) H. Krebs, FestkOrper probleme 9 (1969) 1.