Electron beam heating in amorphous semiconductor beam memory

:. 6C IEEI: TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-20, NO. 2, FEBRUARY 1973

V. PRESSURE DEPENDENCE Observations of Walsh et aZ. [20] show that threshold

voltage is a linear decreasing function of the hydro- static pressure. Our observation is the same. The first voltage at which switching occurs is a linear decreasing function of the weight on the contact as the diode is charged, in cases both of diode with or without evap3- rated top electrode. This effect is well known with p,.n and Schottky diodes, where i t is interpreted as a change o f the energy gap or as an interlayer effect. Furthermore, pulse measurement shows that the switching energy will be decreased with an increased pressure on the top contact. We have, at this time, no explanation for th i s quite reproducible change of the switching energy.

ACKNOWLEDGMENT The author would like to thank Dr. G. Goldbach for.

his discussions, and K. Wedermann for the sample preparation.

REFEREXCES [l] Proc. Semiconductor Effects in Amor@hous Semiconductors (SEW.

York), 1969; see also J . Non-Cryst. Solids, vol. 2, 1970. [2] Proc. Int . Conf. Amorphous and Liquid Semiconductors (Carn-

bridge, England), 1969; see also J . Non-Cryst. Solids, vol. 4, 1970.

[3] A. Csillag and H. Jager, “Energy controlled switching process in the amorphous system Te-As-Ge-Si,” J . Non-Cryst. Solids, vol.

[4] A. Csillag, Investigation of the switching characteristics of the Te-As-Ge-Si glass-films,” J . Non-Cryst. Solids, vol. 4, pp. 518- 522, 1970.

2, pp. 133-tf0, 1970.

[51

[71

S. R. Ovshinsky, E. J . Evans, D. L. Nejson, and H. Fritzsche,

Sci . (Annual Conference on Nuclear and S@ace Radiation Effects), “Radiation hardness of Ovonic devices, IEEE Trans. Nucl.

S. R. Ovshinsky, Reversible electrical switching phenomena in disordered structures,” Phys. Rev. Lett. , vol. 21, no. 20, pp. 1450- 1453, 1968. V. T. Kolomiets, E. A. Lebedev, and I. A. Taksami, “Principal parameters of switches based on glassy chalcogenide semiconductors,” Sov. Phys.-Semicond., vol. 3, no. 5 , pp. 621-624, 1969. H. J . Stocker, “Bulk and thin film switcking and memory effects in semiconducting chalcogenide glasses, Ap@l. Phys. Let t . , vol.

J. .D. ,,Mackenzie, “Electronic conduction in non-crystalline 15, no. 2, pp. 55-57, 1969.

sollds, J . Non-Cryst. Solids, vol. 2, pp. 16-26, 1970. B. Eckstein, “The inner parameter of glassy system,” J . Non-

A. D. Pearson, lecture presented at the NATO Summer School, Cryst. Solids, VOI. 4, pp. 366-369, 1970.

Ghent, Belgium, 1969. M. H. Cohen, H. Fritsche, and S. R. Ovshintky, “Simple band model for amorphous semiconducting alloys, Phys. Rev. Lett. , vol. 22, no. 20, pp. 1065-1068, 1969. H. Fritzsche, paper presented in Stuttgart, Germany, Apr;,1969.

Amer . , pp. 30-41, Nov. 1969. H. K. Henisch, lLAmorphous-semiconductor switching, Sci .

A. Engel and 0. Holzinger, “Schalt-, und Verstarkerelemente aus Glas,” Frequenz, vol. 23, no. 10, pp. 294-301, 1969.

bleitenden Chalcogenid-Glasern,” paper presented at the 1970 M. Guntersdorfer, “Thermische Effekte beim Schalten in hal-

A. D. Pearson, “Memory and switching in semiconducting Friihjahrstagung, Freudenstadt, Germany.

A. Csillag, ‘LA,,Ccumulation effects with Te-Ge-As and Te-As- glasses,” J . Non.-Cryst. Solids, vol. 2, pp. 1-15, 1970.

Ge-Si glasses, in Proc. 2nd Int . Conf. on Conduction in LOW- Mobility Materials. London: Eilat/Israel International Scien- tific Publishers, 1971. D. R. Haberland, “Ladungsbedinger Schaltmechanismus in Glashalbleitern” Solid-state Electron., vol. 13, pp. 207-217, 1970. P. J . Walsh, J . E. Hall, R. Ni;olaides, S. DeFeo, P. Calella, J. Kuchmas, and W. Doremus, Experimental results in amorphous semiconductor switching,” J . Non-Cryst. Solids, vol. 2, pp.

VOI. NS-15, pp. 31;-321, 1968.

107-124, 1970.

Electron Beam Heating in Amorphous Semiconductor

Beam Memory

ARTHUR C. M. CHEN

Abstract-The high-speed electron beam heating and the subs+ quent cooling processes in an amorphous semiconductor target of a beam memory have been studied by computer simulation. Such a memory would utilize the amorphous and the crystalline phases of chalcogenide thin films as the binary states of the memory. For an electron source of 1-p radius, the results suggest that a storage target, consisting of a chalcogenide thin film whose thickness is twice the electron penetration range on a good heat sinking substrate, is the optimum target configuration. Possible high-speed memory operating characteristics with present long-life high-brightness electron guns are described.

1971.

Development Center, Schenectady, N. Y . 12301.

Manuscript received September 3, 1971; revised December 11,

The author is with the General Electric Corporate Research and

I. ISTRODUCTION

ISTORICALLY, computers have shown an almost insatiable need for more on-line storage- capacity because of increasingly complex system

and application requirements. This need has been re- strained primarily by the cost of these memories [l ]. In anticipation of future memory requirements a t lower cost, a substantial research effort has been devoted to the development of large capacity optical or electron beam access memories. Among the potential optical beam memory techniques, Feinleib and Ovshinsky have shown that amorphous semiconductors can be used as the memory storage medium [ 2 ] . The memory mech-

CHEN: ELECTRON BEAM HEATING 161

anism is the change in the optical reflectivity that accompanies the amorphous-to-crystalline phase transition in the chalcogenide glasses. Because of the com- plexity of electronic optical deflection techniques, however, many of the proposed optical beam memory systems will use, in part, electromechanical scanning techniques to address the memory sites.

Recent advances in electron beam access technology, particularly the development of the Fly's Eye Electron Optics [SI, have made a fast electronic access electron beam memory feasible. A principal concern, however, has been the form of the memory storage targets. Vari- ous approaches, such as magnetic films and charge storage in insulating films as potential memory media, have been discussed by various workers [4]-[6].

Alternatively, the use of amorphous-to-crystalline phase transition in the chalcogenide thin films as a possible memory mechanism in an electron beam memory recently has been proposed [7] . Generally speaking, the binary states of the memory are the crystalline and the amorphous phases. Switching between the memory states can be achieved by the use of an electron beam, at the same voltage, as the access means for reading and writing, and as the source of switching energy. Some possible advantages in the use of the chalcogenide thin- film memory targets are simplified electronoptics because of the constant beam voltage, nondestructive readout, nonvolatility, and high bit density. The memory may operate either in the Read-Mostly mode or in the archival, i.e., permanent storage mode [8].

T h e basic operational elements of such a memory are shown in Fig. 1. The amorphous semiconductor thin- film storage target is structureless in that no physical entities, such as metallic spots or holes, are required to define the memory sites. Thus, the bit position is defined by the electron beam, and its size is limited only by the beam diameter and the possible interaction between the thin film and the electron beam. Viewed simply, writing is accomplished by electron beam heating to induce the amorphous-to-crystalline transition. Readout by the electron beam is possible by the use of a lower beam current, at the same beam voltage, to measure the difference in secondary electron yields of the two phases. Such a difference in thin films of Ge-Te-As has recently been reported [7]. Erasing is possible by using the electron beam to heat the material to above its melting point and quenching the material to its amorphous phase.

An important concept in such a memory is that one need only switch or change the state of the surface of the film as secondary electrons are generated within a few hundred angstroms from the surface. Thus, i t is hoped that the electron beam heating duration can be short in order to obtain a memory spot size approximately equal to the beam diameter.

This simple picture of the operation of the memory

f Fig. 1. Basic operation elements of the electron beam memory

using amorphous semiconductor thin film as the storage target. I p is the incident primary electron beam current, I. is the secondary electron current, and I T is the target- current. 6 O is the secondary yield of the amorphous phase and 61 is that of the crystalline phase.

will be modified if electron-beam-enhanced crystallization, similar to photocrystallization, occurs during the write process [9], [lo]. Fast (510 ps ) electron-beam- induced memory switching observed in. the chalcogenide thin films suggests that some form of enhanced crystallization process may occur. Before any crystallization can occur, however, the amorphous semiconductor must be heated to above T,, the glass transition temperature. Nondestructive readout would requi.re that any beam heating that may occur during thle read process be limited to below T,. The possible rol~es of the electron- beam-enhanced crystallization process in the memory operation will be described later.

Even with the possible more conlplex operational characteristics described above, a good understanding of the electron beam heating and cooling processes is necessary to realize such a memory. Among the important characteristics are the minimum beam energy required to induce the crystallization process, the amount of heat spread beyond the beam diameter during this process, and the design of the thermal characteristics of the target so the quenching of the material can be accomplished. In addition, an understanding of these processes will be important in the study of the crystallization kinetics in these materials and other devices utilizing these materials. In the beam memory applications, these problems must be examined with time duration in the microsecond region and spatial variation of micron and submicron dimensions. Further- more, the changes in the thermal parameters as the materials undergo these phase transitions also must be considered.

Experimental determination of the details of the heating and cooling processes within the above time and

162 :EZE TXASSACTTONS OX ELECTROS DEVICES, FEBRGARY 19'73

Fig. 2. Schematic of t1.e computer simulation model.

spatial constraints appear to be extremely difficult, if not impossible. Analytical investigation of similar electron beam heating problems have been made b:7 various workers [11]-[13]. Most of these treatments, however, were restricted to idealized geometrical situa- tions, and none of them treated the problem with temperature-dependent thermal parameters. Computer simulation offers an attractive and perhaps the only alternative solution to this problem. The simulation of the heating and cooling processes in an amorphouj semiconductor beam memory by the use of a generalized transient heat transfer program1 is the subject of t h k paper.

11. COMPUTER SIMULATION MODEL

The geometry considered in the computer simulation model is shown in Fig. 2. I t is a layer structure in which a thin film of amorphous semiconductor is deposited upon a molybdenum-coated silicon substrate. This corn,. bination was chosen to prevent any potential chemicai reaction between the chalcogenide glasses and the silicor, substrate. The electron beam is assumed to have uniform current density with a finite radius, and to dissipate its energy within the amorphous semiconductor to the depth of the electron penetration range.

T h e physical bodies, amorphous semiconductor, and substrates are partitioned into small volume segment:' that constitute the temperature modes of the problem. The simulation program is based upon heat balance at each node such that for t h e j t h node

n

Qilc = 0. (1)

Q j k are the effective heat transfer rates from j to itself

k-1

gram deveIoped within the General Electric Company. This simulation uses a generalized transient heat transfer pro-

and to n adjacent nodes. These rates include heat ex- changes due to temperature differences and boundary conditions, internal heat generation, and change in the internal stored energy at j .

A finite difference approximation to the time deriva- tive is used, and the centroid temperature Tj for each node is computed at a given time using an iterative solution technique until (1) is satisfied within a given cri- terion for all nodes. Transient solutions are obtained by finding Tj for successive incremental time intervals. For each temperature change, the program takes into account any temperature variation in the thermal properties of the material.

For the particular geometry shown in Fig. 2 , the volume was partitioned into 260 segments of various sizes. Fine segment sizes were used at the boundaries of the volume heated by the electron beam to account for the expected large thermal gradient. All external surfaces had adiabatic boundary conditions. To simulate the large size of the memory target accurately, the temperature of the peripheral segments cannot change from its initial value (room temperature) for any valid solution.

For our particular problem, the electron is assumed to dissipate all its energy into heat uniformly within the volume defined by its diameter and the penetration range of the electron. The penetration range used is based on the empirical relationship given by Kobetich and Katz [14].

A particularly troublesome problem in our simulation is the values of the thermal properties of the target materials. I n general, we have used the values for silicon and molybdenum tabulated by the T P R C D a t a Series [ l S ] . For the amorphous semiconductor that will undergo amorphous-to-crystalline and crystalline-to- liquid phase transitions, we have used the thermal conductivity and specific heat shown in Fig. 3. As we are concerned with tellurium-based chalcogenide glasses,


K 0 . 0 5 ~ 1 0.03 CRYSTALLINE

0.01 AMORPHOUS (0.0035)

I

0 100 200 300 400 500 600 700 800 900 1000

Fig. 3. Thermal properties as a function of the temperature of an amorphous semiconductor used in the computer simulation program.

the crystalline and liquid thermal conductivity and specific heat shown in Fig. 3 are those of T e given in the T P R C D a t a Series [IS]. The value of thermal conductivity K in the amorphous phase is one tenth that of crystalline Te. This extrapolation is based on the similar ratio measured for Se [I 51, and is close to the value of the commercial Ge-Sb-Se infrared glasses [16].

T h e melting point, 425OC, is near that of the Ge-Te eutectic. As we are concerned with the minimum or the worst case electron beam energy necessary to crystallize amorphous semiconductor thin film a t a heating rate (> lOO"C/ps) much faster than the normal DTA mea- surelment rates, we have chosen arbitrarily a high crystallization temperature of -315°C. Crystallization is assumed to occur immediately a t this temperature because its rate will be enhanced by the electron beam excitation. The crystallization process was assumed to occur over a span of 50°C. T o simulate the heat of fusion upon melting, the specific heat has a large "spike" a t t he melting point. T h e base width was 50°C wide and the peak value was based on a heat of fusion of 11 cal/g. This value is close to the measured heat of crystallization of Ge-Te-As glasses [I 71, but may be too small by a factor of two. The inclusion of this large heat of fusion, however, is needed and does provide a realistic simulation of the effect of the heat of fusion on the heating and cooling processes.

By our choice of the thermal boundary conditions, we have neglected the possible heat loss due to radiation. Even though the emissivity from these materials may be high,2 this loss will be orders of magnitude less than the conduction losses for the temperature region ( < 1000 K) under consideration.

Perhaps a more serious problem is that we have not included the possible effects of the heat of crystallization in our simulation. In part, this is due to our ignorance of the rate of this heat release and in part to the diffi-

culty in incorporating this effect in our simulation program in concert with the time transient response. Physi- cally, the effect of any heat released upon crystallization will increase our simulated heating rate and perhaps the peak temperature. The magnitude of this effect will depend in part on the time duration of this heat release. For these reasons, our results of the surface temperature will be the minimum attainable for the given electron beam excitation.

T h e electron beam parameters were chosen to reflect the state of the art of electron gun sources and the de- sirable data rate of a potential memory. Thus, the electron beam was assumed to be a t 5 kV with a diameter of 2 p, T h e pulse duration was 1 ps with less than 10-ns rise and fall time. Thus, the heating and cooling processes needed to achieve a data rate of greater than 1 MHz can be studied. The maximum beam current studied was 1 pA, and reflects the present state of the a r t for long-life high-brightness electron guns [18]. The penetration range of the 5-kV electron used is 1750 A and is based on a thin-film density of (-5 g/cm3.

Instead of varying the beam parameters, it is more instructive to examine the thermal behavior of the various amorphous semiconductor targets for the above electron beam source. As the physics of this problem is complex and not amenable to analytical solutions, the simulation results will enable us to develop a qualitative understanding of the heating and cooling processes and some basis to judge the tradeoffs involved in the potential memory characteristics.

111. COMPUTER SIMULATION RESULTS A . Effects of Temperature Dependence of Thermal Con- ductivity and Specific Heat

The operation of the beam memory as previously described depends primarily on the change induced on the surface of the amorphous semicon'ductor thin film. Thus, the temperature of the surface (-250 A deep) as a function of time and as a function of radial distance they may be expected to have similar behavior as silicon. Silicon has

No values are available for the chalcogenide glasses. However,

a total normal emittance of 0.3-0.6 between 251-1000 K. will be our primary concern.

i--, , , ' 7_

TEMPERATURE AT BEAU CENTER

8001 I ,

E. B.- 5 kV, 0.3~ A I

LL AMORPHOUS

DISTANCE (MICRON)

(b) Fig. 4. Surface temperature distribution of a thick amorphous semicon-

ductor for three different thermal properties. Amorphous parameters- constant K and C, independer.t of temperature, K(T)-only tempera-

&. (a) Temperature a t beam center versus time. (b) Temperature ture-dependent K, LH and K(T)-include latent heat in C,. I, =0.3

pxofiles a t 0.1, 0.3, and 1.0 ps .

T h e effect of the temperature dependence of the ther- m8sl properties on the surface temperature was ex- ,ar.lined. The target was a thick homogeneous (80 ,L) .amorphous semiconductor, so that no extraneous effects (due to the high thermal conductivity of the substrate are introduced. The effect of the heat of fusion (i.e., Li7 for latent heat) and the change in K upon phase transitions are shown in Fig. 4(a) and (b). The beam currer.t was 0.3 pA in these figures. A t 0.3 pA, an all amorphom parameter ( K = 0.0035 W/cm .It(, C, = 0.05 cal/g"C:) would have suggested that the 1.0-ps-long electrcn beam is capable of heating the beam center surface to approximately 870°C. Taking into account the increase in K upon crystallization and melting alone (i.e., the K ( T ) curve), the peak temperature at 1.0 ps is only about 425°C. As the peak temperature is near the me1 t- ing point, the effect of latent heat (LH) and K(2') curve) on the temperature distribution is small. A hint of the effect of the latent heat in delaying the coo1ir.g ra.te as the beam is cu t off can be seen in Fig. 4(a). The effect of the increase in thermal conductivity upon crys- taJlization at 315°C can be seen in the decrease in the ra.te a t which the temperature rises a t t he crystallizaticm te:mperature.

The radial distribution of the surface temperature or the temperature profile a t a few time frames is shown ,111

Fig. 4(b). The grid line on the abscissa indicates the nodal dimensions. The knee in the temperature profile at 1 .O ps reflects the thermal interface where the thermal conductivity changes its value. 4 s expected, the high?r thermal conductivity in the crystalline phase causs; more heat spread in the radial direction [t = 1 ps in Fig. 4(b) 1. However, this additional spread is surprisingly small in comparison with the large differences in tlle pleak temperatures because the mass increases with the square of the radius. The small additional spread may

cause a slight loss, if any, in the bit density of the potential beam memory.

B. Electron Beam Writing and Reading Processes The temperature profiles were determined for various

targets to evaluate the necessary beam power for writing and the maximum permissible beam current for reading. The amorphous semiconductor must be heated to its crystallization temperature across the entire beam diameter to write. In contrast, the materials cannot be heated to above their glass transition temperature T, during reading. As a reference, the surface temperatures versus time and the temperature profiles for various beam currents for the thick (80 p) amorphous semiconductor target were evaluated. The results are shown in Fig. 5(a), (b), (c), and (d). As one can see, a beam current of 0.2 p A is sufficient to heat the material to the crystallization temperature, and at the same time no surface is heated to the melting point. The reading current, however, will have to be less than 0.1 pA if we assume T, < 200°C.

The temperature profiles at three time frames are shown in Fig. 5(b), (c), and (d). As expected, a t 0.6 ps after the beam cutoff ( t = 1.6 ps), the temperature has a diffusion-like profile, modified, of course, by the effects of the phase transitions. Although low beam currents can be used to write, the long cooling time of the surface temperature from above the melting point is a serious handicap for fast data rate. Furthermore, whether this long cooling time would be fast enough to quench the heated volume to the amorphous phase for memory information erasure is questionable. For these reasons, thinner amorphous semiconductor films on a good heat- sinking substrate were investigated. The substrate as previously described had molybdenum film thickness of 2000-4000 A.


700 t I : 0.1 ps 1

600 - -

I 1 I I I I I I 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

TIME IPS)

1 I BEAM EDGE 500

L 400- V - I-

-

0 I I 1 I I

0 I .o 2.0 3.0 RADIAL DISTANCE IMICffONl

- I I 1 I I

0 I .o 2.0 3.0 RADIAL DISTANCE IMICffONl

(a) ( b l I I I I I I T

700 - - - t =l.Ops 700 - t : 1.6 ps

( e ) 8op ( d l B o p - 600 - -

BEAM EDGE

- 500 - - I b ' l . O p A

- -

- -

-

100 -

0- 1 I 0- - 0 I .o 2.0 3 .O 0 I .o 2 .o 3 .O

- I 1 I I L

RADIAL DISTANCE (MICRON1 RADIAL DISTANCE IMICRON)

(Cl ( 4 Fig. 5. Surface temperature distribution of a thick amorphous semiconductor for various beam currents. (a) Temperature at

beam center versus time. (b) Temperature profile at 0.1 ps, (c) Same as (b) at 1.0 ps. (d) Same as (b) at 1.6 ps.

The temperature distributions for 3750, 2750, and 1750-2050-A films are shown in Figs. 6(a)-8(b). As expected, the beam current required to write has increased with decreasing film thickness, and the cooling decay time has decreased considerably (-0.5 p s ) from that of the thick amorphous semiconductor. An additional benefit of the heat sinking substrate is that the heat spread beyond the beam edge is also smaller.

The peak in the temperature versus time curve observed for certain beam currents, i.e., l.OpcA in Fig. 6(a), occurs at the time when the temperature at the beam edge crosses the melting point. Physically, we can postu- late that at that time, the material adjacent to the beam

increased its thermal conductivity, and that under this condition, the beam power is insufficient to support the high peak temperature. Whether this temperature peak will actually develop in a real life situation is an open question.

The loss in heating efficiency as measured by the difference in the peak temperature of 3750-A film in comparison to the thick film is very small. This loss appears to be a weak function of the film thickness until a certain minimum threshold level is rea.ched. A t 2050 A, even a beam current of 1.0 p A is insuEicient to heat the 2-p-diameter surface to the melting point. Qualitatively speaking, at 5 kV, a film thickness of twice the penetra-

166 PEEE TRANSACTIOXS O N ELECTROE; DEVICES, FEBRURRY 1973

0 0.2 0.4. 0.6 0.8 1.0 1.2 1.4 1.6 1 . L -2.0 TIME I p s )

(4

700

BEAM EOGE

600

500

4 00

300

2 00

I D 0

0 0 I .o 2.0 3.0

RADIAL DISTANCE lYlCRONl

(b) Fig. 6. Surface temperature distribution of 3750- i i amorphous semiconductor thin-film memory target on 4000-A-Mo-coated

Si wafer for various beam currents. (a) Temperature a t b?am center versus time. (b) Temperature profile a t t = 1.0 MS.

7001 1

RADIAL DISTANCE (MICRON)

(b) Fig. 7. Same as Fig. 6 for 2750-A amorphous semiconductor thin-film target. (a) Temperature at beam center versus time.

(b) Temperature profile a t t = 1.0 ps.

CHEN: ELECTROK BEAM HEATING

700

600

500

5 400 e I-

30 O

200

IO0

0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

TIME ( P S I

(a)

167

Fig. 8. Same as Fig. 6 for 1750-2050-A amorphous semicynductor thin-film target. 1,=0.2-, 0.4-, and 0.6-~A. curves are for 1750 A, Ip=l.O-, 1.5-, and 2.0-fiA curves are for 2050 A. (a) Temperature a t beam center versus time. (b) Temperature profile at t = 1 . O ,US.

tion range of the electrons appears to be an optimum choice in the balance between the high beam heating efficiency and the fast cooling thermal time constant desired.

Th.e maximum reading beam current depends on the glass transition temperature. If this temperature is 150°C, then 0.1 pA is too high for 3750 A, but permissible for a 27.50-W film target.

C. Electron Beam Erasing Process T o erase the written information in this beam mem-

ory, the crystalline memory bits or spots must be heated to above the melting point and quenched to the amorphous phase. The results of the previous section have shown that a fast cooling time (50.5 ps) from the liquid phase to the amorphous phase is possible with submicron thick film on a heat-sinking substrate. The beam current required to heat such a crystalline spot to the melting point was simulated using the following model. T h e memory bit was assumed to be a 2.24-p diameter, 1750- A-thick crystalline disk with the 3750-A-thick amorphous thin film. The thermal conductivity of this disk from room temperature to the crystallization temperature was increased to that of the crystalline phase, while the melting point and heat of fusion remained the same. The result is surprising in that the heating behavior of this memory bit is almost identical to that of the amorphous phase alone. The only difference is in the cooling rate; i t is now controlled by the larger thermal conductivity. This cooling rate will not occur in memory operation because the room temperature phase will be the uniform amorphous phase rather than the crystalline disk assumed in this model. The temperature profile,

almost identical to that shown in Fig. 6(b), indicates tha t 1.0 p A will be needed in order to heat the entire crystalline surface to above the melting point. This is the minimum required beam current since there will be no heat of crystallization released during the erasure process.

IV. E EMORY OPERATING CHARACTERISTICS The operating characteristics of a memory based on a

thermally induced phase transition is unique in the large switching energies required. Althlough, in general, such a requirement may be undesirable, i t has an advantage of permitting large margins in the switching energy source. This is especially true during the erasure process in this memory, as the heat of fusion will act as a sink for any excess energy.

In their study of reversible photoinduced crystallization in amorphous semiconductors, Feinleib et al. proposed a model that permitted crystallization only during the short laser excitation when electron-hole pairs are created to enhance the crystallization process [lo]. As direct evidence that the thermal time constant is too short for thermal transformation, no crystallite halo was observed around a memory site after repeated reversible transformations were induced by laser pulses.

Measurement of the time dependence of the photocrystallization and carrier trapping processes in amorphous Se by Dresner and Stringfellow have suggested that trapped holes with a thermal release time of seconds are responsible for the enhanced crystallization rate [9]. If a similar mechanism is applicable to the multicomponent chalcogenide glasses, then the model of Feinleib et al. cannot explain the absence of the crys-

’callite halo; photocrystallization will proceed after the xrmination of the laser excitation when the material is ‘xtween the melting point and T,.

An alternative model for the absence of the halo ‘2ased upon the temperature profile of the heated crysta: - .‘,me spot is possible. During erasure, the entire crystal- .me spot, which will extend beyond the beam diameter, :must be heated to above the melting point. In the molten state, the trapped holes-the broken crosslink- .ing bonds-are released immediately so tha t no er.- hanced crystallization can occur after the beam is turned off. During this heating process, some material outside the beam diameter is heated to above T,. As these arezs were not subjected to any beam excitation, no trapped charge and thus no enhanced crystallization can occu:-. If thermal transformation cannot take place during the short time period, no crystallization halo will appe2.r during the erasure process.

The computer simulation described in this paper and the possible roles of enhanced crystallization processcs described previously show that the possible interactiorm in this memory are complex, and no single paran1etc:r or group of parameters appear to be able to describe tf e operation accurately. For example, the temperature attained for a given excitation cannot be ascribed eithcr to a power or to an energy dependence. In addition, our present understanding of electron- or photon-enhanced crystallization is so rudimentary that no quantitati7.e role can be ascribed to this mechanism. Computer simulation as described in this paper together with experi-, mental verification will help in our understanding tlle dynamics of the processes involved.

In general, a beam memory would operate with a.1-

alog scanning. That is, the beam will scan the target ;n a continuous fashion. Digital scanning, where the beam is step-scanned from memory spot to memory spot, is possible but difficult a t a high data rate, and will I x more expensive. Our simulation results are directly applicable to digital scanning and should correlate to the results obtained using analog scanning.

For a typical memory operation, we will use the 3750- A-thick target as a specific example [Fig. 6(a) and (b> 1. T o write a “1” will require a pulsed beam current of 0.4 pA with -0.5-ps duration. For the same beam duration, the reading current will have to be less than 0.1 A A if To<15O”C. An alternative tactic would take advantage of the long thermal time constant at 0.1 pA and use this current to read by decreasing the dwell time of the beam to 0.2 ps. Erasure or writing a “0” will require 1.0 pA with about 0.5-ps duration.

From the temperature profile shown in Fig. 6(b), the temperature at 1.5 p from the beam center will be less than the 150°C glass transition temperature during erasure. As maximum heating occurs during the-erasL.re process, 3.0-p center-to-center bit spacing is a reasonalde expectation with the 2-p-diameter electron beam. Thus,

I “

., *

for the given electron beam parameters used in our simulation, a S t density of 1 X IO7 bits/cm2 is achiev- able. This bit (density is imposed by the beam diameter rather than b~7 the physics of the memory mechanism, as crystallite size of less than 1000 A has been observed in these films.. If higher brightness electron guns are available, one can easily envision submicron memory bit sizes with resultant memory densities of greater than lo8 bits/cmZ.

In comparing the possible beam access technologies for mass memory, the electron beam has the advantage of easy electronic control-modulation and deflection- in its favor. Our computer simulation has shown that these attributes are needed since variable beam ampli- tude and short time duration will be necessary in the operation of amorphous semiconductor electron beam memory. I t is hoped that the studies described herein will help in th’e realization of such a memory.

ACKNOWLEDGMENT

The invalua.ble help of V I , H. Meiklejohn, who set up the simulation program, is gratefully acknowledged. Stimulating discussions with Mi. D. Barber, bV. C. Hughes, and J . M. Wang, and the encouragement of W. L. Chu are deeply appreciated.

REFERENCES [l] E. W. Pugh, “Storage hierarchies; Gaps, cliffs and trends,”

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Analysis of an Inhomogeneous Bulk “S-shaped*’ Negative

Differential Conductivity Ele ent in a Circuit

Containing Reactive

&!I. P. SMAW, R. L. GRUBIN, AND I. J. GASTMAN

Abstracf-This paper analyzes the time and space evolution of the current density distribution in an inhomogeneous bulk “S- shapecl” negative differential conductivity (SNDC) element and the response of the surrounding lumped element circuit. The SNDC element, in series with a package inductance, is in parallel with a package capacitance, the loop being in series with a load resistance and a battery. First the presence of isothermal current density filamentation in SNDC elements is demonstrated. By approximating the SNDC element as an appropriate conductive voltage curve in series with an appropriate intrinsic inductance, it is next shown that various modes of behavior (switching, relaxation oscillations, and a bias induced transition between the two) can all occur in the same SNDC element for appropriate values of the circuit parameters. A major aspect of the circuit theory is that it transforms directly between S and N shaped NDC elements when the important reactive components are identified in each case (duals). The techniques used are applicable to all SNDC elements, such as p-n-p-n and p-i-n diodes, and Ovonic threshold switches; emphasis is placed on the latter.

I. ISTRODUCTION H E EXISTEXCE of semiconducting devices .with regions of negative differential conductivity (NDC) has led to the development of a vast tech-

nology. T h e devices fall into two distinct groups: “N” and “Si” shaped, where the letter describes the shape of the conduction current density-electric field relation. NDC in inhomogeneous bulk material can lead, in the case oi NNDC, to stationary [ l ] or steady-traveling [ 2 ] high electric-field domains [3], or sustained circuit- controlled oscillations [4], [SI. For SXDC, either circuit-controlled oscillations [6] or stationary high cur-

Manuscript received November 6, 1971 ; revised March l, 1972. M. P. Shaw and 1 . J. Gastman are with the Department of Elec

trical Engineering, Wayne State University, Detroit, Mich. 48202. H. L. Grubin is with United Aircraft Research Laboratories, East

Hartford, Conn. 06108.

rent density filaments usually result [7]-[9]. In either case, S or N, there are three aspects of the problem that must be considered to understand the myriad of in- stabilities possible in these systems. They are: 1) the bulk properties of the material; 2) the boundary conditions; and 3) the circuit interaction. The major thrust of this paper is the SNDC circuit interaction. Pre- liminary results have been reported in [6], where comparison is made with experiments on p,-n-p-n diodes and Ovonic threshold switches. The Clvonic threshold switches were shown to exhibit: 1) considerably faster switching times; 2 ) a narrower range of threshold voltage variation from pulse to pulse (stability); and 3) much higher frequency relaxation oscillations than the p-n-p-n diode. Considering these factors and the recent great interest in amorphous semiconductors, i t is clearly necessary to develop a detailed circuit model for the Ovonic threshold switch.

Our task is to determine the conditions necessary for either a high current density filament (switching to the “on” state [lo]) or circuit-controlled oscillations to occur. We examine the situation where oscillations occur in the absence of filament formation and then establish the additional limitation imposed by filamentation, which is demonstrated for an idealized situation. The techniques used are applicable to a n y SNDC element. W e find that either switching or relaxation oscillations can occur for the same S N D C element in the same circuit with appropriate circuit parameters. A major aspect of the investigation i s the fact that the circuit theory transforms directly between the S and N case when the important reactive components are identified f o r each case. The important circuit parameters in each ca.se produce a “dual” circuit system where the voltage acyoss the N N D C element in its

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