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The switching mechanisms in amorphous chalcogenide memory devices
Journal of Non-CrystaUine Solids 21 (1976) 319-329 © North-Holland Publishing Company
THE SWITCHING MECHANISMS IN AMORPHOUS CHALCOGENIDE MEMORY DEVICES A.G. STEVENTON Post Office Research Centre, Martlesham lteath, Ipswich, Suffolk IP5 7RE, UK
Received 29 September 1975 Revised manuscript received 26 November 1975
Measurements of the resistance of chalcogenide memory devices switched with pulses which have a long or very short trailing edge, showed no significant difference. This contradicts the switching model as proposed by Cohen et al. Experimental data is presented and a discussion of the complexity of crystallization suggests a modification in which the inner zone of the filament is usually quenched below the crystallization temperature during the set pulse, as a result of current redistribution. Further modifications to the model for the reset event take account of an annulus around the reset filament which is at the optimum temperature for crystallization. Crystallization in that annulus results in shifting of the filament axis. The use of multiple-pulse resetting reduces the chance of crystal growth in the annulus.
1. Introduction Switching processes in amorphous semiconductors have been a topic of considerable interest and controversy since they were first observed. General reviews are given by Adler [1] and b y Fritzsche [2]. In this paper we are concerned with the mechanism by which the stable low-resistance state is produced in a memory switch (setting) and the reverse change to a high-resistance state (resetting). Cohen et al. [3] have suggested a clear model (the CNP model) of crystallization processes for these transformations, and Sie et al. [4] have made microscopic observations which support it. In the model, the memory device is first switched into a filamentary threshold-on state and then the current is maintained long enough to allow the amorphous material in the hot filament to crystallize. The central part o f the filament can be too hot for crystallization and will then only satisfactorily crystallize when it is cooled slowly. If it is rapidly quenched, the set state, which is formed b y a chain of conductive crystallites linking the electrodes, may contain weak links or even be incomplete. In resetting, the crystallites are removed by dissolving them in the background matrix, using a short high-current pulse which produces a relatively hot filament. In this paper we report additional observations inconsistent with this description and suggest modifications to the model to explain them. 319
320
A.G. Steventon / Switching mechanisms in memory devices
2. Effect o f set-pulse trailing edge
Cohen et al. [3J consider that crystallization of the filament is incomplete without a slow fall time on the set pulse. We have attempted to measure this effect from the change in resistance o f the set switch. Initially ECD switches were tested with a 15 ms set pulse with (additional) fall times o f 100 ns or 5 ms at two different current levels. The results are given in table I and show no distinguishable resistance change with fall time. Another group of ECD devices (type MS115) was checked in greater detail at various current levels, using pulses of total duration o f 20 ms including either a 100 ns fall time or a 5 ms fall time. The results are shown in fig. 1. The erratic current dependence of resistance above 10 mA is probably due to variations in incompletely crystallized filaments as suggested by Cohen et al., but in all cases there is no systematic effect due to the trailing edge. The smooth change o f resistance R with set current I s below 10 mA can be fitted to the expression R - 1 / 2 = a In I s + b which is functionally the same as the filament diameter as measured by Sie et al. [4]. Although the trailing edge does not generally have much effect on the resistance
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Fig. 1. On-state resistance as a function of current for set pulses with and without a trailing edge.
321
A.G. Steventon / Switching mechanisms in memory devices
Table 1 Influence of set-pulse trailing edge on device on-state resistance. Set current (mA)
7.5 15
Resistance (s2) with 100 ns ramp
with 5 ms ramp
119 -+ 2
118
121 -+ 1
122.6 ± 0.5
+2
Table 2 Reliability of devices tested with or without a set-pulse trailing edge. Fall time
5 ms 100 ns
No. of successful cycles to first failure for each device
195 299 14
385 971 48
Geometrical mean
555 632
710 498
2 076 338
573 034
196 526
272 481
401 863
6792
it changes the failure rate o f the set pulse. This is shown by the results in table 2, in which 10 devices were set with a 7.5 mA pulse o f 20 ms total duration and either a 5 ms or a 100 ns fall time. A standard reset train of nine 150 mA pulses o f 6/~s duration and 10 kHz prf was used. It is seen that the longer fall time has significantly improved the chances of turning the device on: this implies that on rare occasions the device resistance is affected by the fall time.
3. Crystallization of the filament Consider the progress o f crystallization o f the filament in setting a memory switch. Crystallization o f glasses is well studied [5] and is inhibited at b o t h low and high temperatures. At low temperatures the atoms are frozen in position, but with increasing temperature above the glass transition temperature the mobility permits rearrangement into a regular lattice. The interaction o f diffusing species is closely measured by viscosity and, over a limited part o f this viscosity-controlled region, the crystal growth rate increases exponentially with temperature [6]. At high temperatures the growth rate declines fairly sharply as the reduction in free energy produced b y crystallization becomes small. A typical growth rate curve is shown in fig. 2. This illustrates that there is a temperature Tp at which the growth rate is a maximum, and temperatures T c and T d at which the growth rate is nearly zero. Above T d the crystals begin to dissolve. Nucleation and growth are separate processes and a significant induction period is normally needed to form stable nuclei before growth can proceed.
322
A.G. Steventon / Switching mechanisms in memory devices
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Fig. 2. Schematic curve of the crystallization rate of a typical glass. However, in chalcogenide switches which are reset using only a single pulse, we believe such nuclei are readily available in the filament region, and their initial development is part of the forming process. The thermal time constant of the filament region is of the order of 1 ~s in most thin-film switches on silicon substrates, so that fairly stable patterns are expected to be present for most of the set-pulse time. The bulk of crystallization, however, occurs within 1 ms before and after lock-on, when considerable thermal disturbance must occur. A major source of this disturbance arises from the difference in properties of the hot amorphous filament and the crystals it forms. Fig. 3, after Krebs and Fischer [7], shows a typical curve of temperature variation of electrical resistivity in a memory chalcogenide. The dashed line represents the resistivity of the hot amorphous chalcogenide before crystallization. Depending on the temperature, crystallization produces an increase in conductivity of 5-500-fold. We follow Kroll and Cohen [8] in assuming that the Wiedemann-Franz law applies to these chalcogenides, and so we may expect comparable changes in thermal conductivity. The electrical discontinuity during the set pulse at lock-on is quite small, and to the first approximation both current and voltage across the switch are unchanged. However, the current density in the crystalline filament must be greatly increased, and since the power is nearly constant the power density must also increase. This interaction will tend to produce a temperature rise which might be sufficient to dissolve the crystals, but it is mitigated by the greatly enhanced heat sinking to the electrodes due to the accompanying increase in thermal conduction along a now continuous crystalline path to the electrodes. At the beginning of crystallization
A.G. Steventon / Switching mechanisms in memory devices
323
AnioRPHOUS //"'~"~ 1/T Fig. 3. Schematic curve of the resistivity of a typical memory chalcogenidematerial. (After Krebs and Fischer [7].)
when crystals are growing from isolated nuclei, we expect the initial growth rate to be increased by the release of latent heat. If the latent heat released in l/Is from a 10 nm dia. crystal growing at 2.5 × 10 -5 m/s were retained in the crystal, it would raise its temperature by 10°C and so provide a positive feedback mechanism which would be reduced by loss of growth area and finally by cooling to the electrodes. Precipitation of tellurium-rich crystals causes the composition of the inner parts of the hot filament to change rapidly during lock-on and so further modify the crystallization dynamics, but the outer edge will grow under more stable conditions. Messier and Roy [9] have shown how certain glasses expected to precipitate GeTe from the phase diagram can crystallize, instead, a tellurium phase during warming. In view of the collapse of isothermals at lock-on the outer regions of the filament will in fact be cooling.
4. Experimental In section 3 some of the basic factors affecting crystallization were identified. It is now necessary to consider what extra experimental evidence can be obtained to elucidate their interaction. The large difference between the electrical conductivity of crystals and of the glass means that the on-resistance of a switch, measured at room temperature, is a useful guide to the cross-sectional area of a crystalline filament. We have also used the threshold voltage as a measure of the uncrystallized (high-resistance) path length between
324
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electrodes during switching [6,10]. Fig. 4 shows the changes of resistance R and threshold voltage VT during multiple-set pulses on an experimental switch based on Ge12Te78As10. This illustrates that while the isolated crystals are growing VT gradually decreases but R remains high, until VT ~ 0 when R rapidly decreases. Devices based on Ge15Te81S2Sb 2 exhibit an induction period during which VT and R remain high. During that time the isolated crystals are too small to affect VT. If multiple pulses are used to reset'the device, the induction period will include a "nucleation time" of about 700/2s. It is clear that during all the substantial induction period before lock-on there is no continuous crystalline path between the two electrodes though some crystal growth occurs, but after lock-on crystallization progresses very rapidly and is nearly complete within a few milliseconds. Steventon [6] has distinguished irregular variations between six different electrical lock-on patterns, which are perhaps too complex to analyse, but subsequent changes are fairly straightforward. The on-resistance gradually decreases with time and stabilizes at a value determined by the set current. We assume that the highest temperature occurs on the filament axis and increases with the set current so that the diameter of the isothermal representing minimum temperature for crystallization (Tc) expands with current. Sie et al. [4] noted that the filament dimensions fit a logarithmic expression for
A.G. Steventon / Switching mechanisms in memory devices
325
set currents up to 18 mA, but the diameter calculated for a crystalline cylinder of the observed resistance (fig. 1) fits the expression only up to 10 mA. Thus, above 10 mA not all of the volume of the filament is crystalline. We assume, therefore, that the set filament develops an uncrystallized core above this value.
5. The modified model for the set event When the threshold voltage is exceeded the current through the switch condenses into a filament which is hot enough to permit crystallization. At low set currents the temperature in the filament is lower than the temperature for maximum crystal growth rate (Tp) and crystals will first form on the axis at the hottest part of the filament. In this zone individual crystallites will grow somewhat irregularly, according to local conditions of available nuclei, etc. Variations are shown by the changes in threshold voltage illustrated in fig. 4. Their growth ~produces little change in the overall thermal or electrical pattern. When the individual crystallites first join up to form a continuous chain there is an electrical discontinuity generally signalled by a small discontinuity (lock-on) in the current or voltage trace. The much lower resistance of the continuous chain causes most of the current to leave the outer zones of the filament and concentrate in it, while the corresponding increase of thermal conductivity greatly enhances removal of heat from the chain via the electrodes. The actual temperatures developed will depend on the interplay of these two factors.
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326
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These changes are indicated schematically in fig. 5, which shows the change with time of the radii of isotherms (assumed circular) about the filament. The actual values of the radii will increase with set current and there will also be some variations along the axis of the filament, but the diagram is expected to be valid until the set
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A.G. Steventon / Switching mechanisms in memory devices
327
current causes the temperature Tp to be exceeded in the filament before lock-on. If the current pulse is terminated before the stabilization of crystallization the filament will have a reduced radius indicated by the dashed line in fig. 5 (see also fig. 4). With higher set currents the initial crystallization will not occur on the filament axis, which is too hot, but on the Tp isotherm annulus. The thermal and electrical redistribution already described will now occur about the annulus, and in many cases will result in quenching the central region quickly enough to prevent it crystallizing. This produces the hollow filaments described by Cohen et al. [3]. The addition of a slow fall time to set pulse can only help crystallization of the central core when its temperature is still too hot at the end of the set pulse. In our experiments the trailing edge had no effect on the filament resistance and we assume that the central zone was already quenched to below T e. An alternative view of this model, in the form used by Cohen et al. [3] is given in fig. 6. The experimentally observed improvement in the success rate for setting, when the set pulse includes a trailing edge, has been tentatively attributed to the occurrence of microfilaments linking crystallites [11]. On rare occasions these may be distributed in such an arrangement that one of a few microfilaments must crystallize in order to complete the chain, but that because of high local current density crystallization is inhibited. Cooling, by using a trailing edge, will then be successful. Steventon [11 ] has also attributed observations of the resetting ability of reverse polarity set pulses to electromigration in such microfilaments. Without such an explanation neither the model of Cohen et al. nor the above modifications to their model, could explain this effect.
6. The reset event
In the reset event, the current is immediately channelled through the pre-existing crystalline filament and causes considerable local heating. The crystals dissolve and a hot conductive channel of amorphous material is produced with a diameter much greater than the original crystal f'dament. The whole of the original filament lies within the Ta isotherm of the reset pulse, but of course a narrow annulus exists outside this in which optimum conditions for crystallization exist. The reset pulse is short enough for the central area to quench into the glassy state, but the possibility of some small increment of crystallization in the outer annulus must be admitted. With repeated cycling, enough conductive material is expected to accumulate to displace the filament axis. The following set (and reset) pulse will then be recentred on a point on the Tp annulus of the previous reset pulse, while the next reset pulse based on the new position, will have a Tp isotherm which passes through the original axis. Successive elimination of the crystallites in the Tp annulus of the earlier reset pulses will result in shifting of the axis in the annulus about the original axis, but always intersecting near the original axis. Thus the original axis will be a favourable position for crystal growth thus causing the filament to return. This mechanism explains the ad-
328
A.G. Steventon / Switching mechanisms in memory devices
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Fig. 7. Plan view of the suggested elimination of crystallites from the crystallization annulus using multiple reset pulses. vantages of multiple-pulse resetting, as illustrated in fig. 7. The initial pulse removes the main filament, and successive pulses remove the larger regions Of crystalline debris in the annulus. There will be second- and third-order effects but these will be much weaker. Evidence that significant crystallization can occur during the very short reset pulse (~6/as) is provided by the effect of a trailing edge on the reset pulse [12]. This edge can affect the subsequent set operation if it is greater than 1 Dis long and can cause failure to reset if it is >5/as, thus implying that the crystallization rate at Tp is sufficient to grow substantial quantities of crystalline material. Separately reset pulses of I0/as have an increasing proportion of failures. This is attributed to the formation of a crystalline link in the Tp annulus.
A.G. Steventon /Switching mechanisms in memory devices
329
Buckley et al. [13] have observed device degradation with floral patterns in the top electrode, which could be attributed to electrode damage while the filament changes in the manner of fig. 7.
7. Conclusions Some limitations o f the CNP switching model have been described and some modifications suggested which take account o f the change in local conductivity and heat dissipation due to crystallization. The improved reliability obtained when a set pulse trailing edge is used, and the influence o f reverse polarity set pulses can be explained by postulating, in addition, the existence o f microfilaments.
Acknowledgement The author wishes to acknowledge the help o f Mr. D.C. Shotton in the preparation o f this paper and the Director o f Research o f the British Post Office for permission to publish it. The author also wishes to thank Dr. J. Allison and Dr. M. Thompson of Sheffield University for their supervision during the preparation of his thesis from which this work was taken.
References [1] D. Adler, Amorphous semiconductors (Butterworth, London 1971). [2] H. Fritzsche, in: Electronic and structural properties of amorphous semiconductors, eds. P. LeComber and J. Mort (Academic Press, London and New York, 1973) p. 557. [3] M.H. Cohen, R.G. Neale and A. Paskin, J.Non-Crystalline Solids 8-10 (1972) 885. [4] C.H. Sie, M.P. Dugan and S.C. Moss, J. Non-Crystalline Solids 8-10 (1972) 877. [5] P.W. McMillan, Glass ceramics (Academic Press London and New York, 1964). [6] A.G. Steventon, in: Amorphous and liquid semiconductors, eds. J. Stuke and W. Brenig (Taylor and Francis, London 1974) p. 675. [7] H. Krebs and P. Fischer, Discuss. Faraday Soc. no. 50 (1970) 35. [8] D.M. Kroll and M.H. Cohen, J. Non-Crystalline Solids 8-10 (1972) 544. [9] R. Messier and R. Roy, Mater. Res. BuU 6 (1971) 749. [10] A.G. Steventon and D.J. Bond, J. Phys. D; Appl. Phys. 7 (1974) L167. [11] A.G. Steventon, J. Phys. D; Appl. Phys. 8 (1975) L120. [12] A.G. Steventon, J. Phys. D; Appl. Phys. 8 (1975) 1869. [13] W.D. Buckley, F.H. Holmbery, R.G. Neale, R.R. Shanks and K.E. van Landingham, Final Report. Contract No. N 60921-72-C-0165 (US Naval Ordnance Laboratory, 1974).
THE SWITCHING MECHANISMS IN AMORPHOUS CHALCOGENIDE MEMORY DEVICES A.G. STEVENTON Post Office Research Centre, Martlesham lteath, Ipswich, Suffolk IP5 7RE, UK
Received 29 September 1975 Revised manuscript received 26 November 1975
Measurements of the resistance of chalcogenide memory devices switched with pulses which have a long or very short trailing edge, showed no significant difference. This contradicts the switching model as proposed by Cohen et al. Experimental data is presented and a discussion of the complexity of crystallization suggests a modification in which the inner zone of the filament is usually quenched below the crystallization temperature during the set pulse, as a result of current redistribution. Further modifications to the model for the reset event take account of an annulus around the reset filament which is at the optimum temperature for crystallization. Crystallization in that annulus results in shifting of the filament axis. The use of multiple-pulse resetting reduces the chance of crystal growth in the annulus.
1. Introduction Switching processes in amorphous semiconductors have been a topic of considerable interest and controversy since they were first observed. General reviews are given by Adler [1] and b y Fritzsche [2]. In this paper we are concerned with the mechanism by which the stable low-resistance state is produced in a memory switch (setting) and the reverse change to a high-resistance state (resetting). Cohen et al. [3] have suggested a clear model (the CNP model) of crystallization processes for these transformations, and Sie et al. [4] have made microscopic observations which support it. In the model, the memory device is first switched into a filamentary threshold-on state and then the current is maintained long enough to allow the amorphous material in the hot filament to crystallize. The central part o f the filament can be too hot for crystallization and will then only satisfactorily crystallize when it is cooled slowly. If it is rapidly quenched, the set state, which is formed b y a chain of conductive crystallites linking the electrodes, may contain weak links or even be incomplete. In resetting, the crystallites are removed by dissolving them in the background matrix, using a short high-current pulse which produces a relatively hot filament. In this paper we report additional observations inconsistent with this description and suggest modifications to the model to explain them. 319
320
A.G. Steventon / Switching mechanisms in memory devices
2. Effect o f set-pulse trailing edge
Cohen et al. [3J consider that crystallization of the filament is incomplete without a slow fall time on the set pulse. We have attempted to measure this effect from the change in resistance o f the set switch. Initially ECD switches were tested with a 15 ms set pulse with (additional) fall times o f 100 ns or 5 ms at two different current levels. The results are given in table I and show no distinguishable resistance change with fall time. Another group of ECD devices (type MS115) was checked in greater detail at various current levels, using pulses of total duration o f 20 ms including either a 100 ns fall time or a 5 ms fall time. The results are shown in fig. 1. The erratic current dependence of resistance above 10 mA is probably due to variations in incompletely crystallized filaments as suggested by Cohen et al., but in all cases there is no systematic effect due to the trailing edge. The smooth change o f resistance R with set current I s below 10 mA can be fitted to the expression R - 1 / 2 = a In I s + b which is functionally the same as the filament diameter as measured by Sie et al. [4]. Although the trailing edge does not generally have much effect on the resistance
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Fig. 1. On-state resistance as a function of current for set pulses with and without a trailing edge.
321
A.G. Steventon / Switching mechanisms in memory devices
Table 1 Influence of set-pulse trailing edge on device on-state resistance. Set current (mA)
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195 299 14
385 971 48
Geometrical mean
555 632
710 498
2 076 338
573 034
196 526
272 481
401 863
6792
it changes the failure rate o f the set pulse. This is shown by the results in table 2, in which 10 devices were set with a 7.5 mA pulse o f 20 ms total duration and either a 5 ms or a 100 ns fall time. A standard reset train of nine 150 mA pulses o f 6/~s duration and 10 kHz prf was used. It is seen that the longer fall time has significantly improved the chances of turning the device on: this implies that on rare occasions the device resistance is affected by the fall time.
3. Crystallization of the filament Consider the progress o f crystallization o f the filament in setting a memory switch. Crystallization o f glasses is well studied [5] and is inhibited at b o t h low and high temperatures. At low temperatures the atoms are frozen in position, but with increasing temperature above the glass transition temperature the mobility permits rearrangement into a regular lattice. The interaction o f diffusing species is closely measured by viscosity and, over a limited part o f this viscosity-controlled region, the crystal growth rate increases exponentially with temperature [6]. At high temperatures the growth rate declines fairly sharply as the reduction in free energy produced b y crystallization becomes small. A typical growth rate curve is shown in fig. 2. This illustrates that there is a temperature Tp at which the growth rate is a maximum, and temperatures T c and T d at which the growth rate is nearly zero. Above T d the crystals begin to dissolve. Nucleation and growth are separate processes and a significant induction period is normally needed to form stable nuclei before growth can proceed.
322
A.G. Steventon / Switching mechanisms in memory devices
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Fig. 2. Schematic curve of the crystallization rate of a typical glass. However, in chalcogenide switches which are reset using only a single pulse, we believe such nuclei are readily available in the filament region, and their initial development is part of the forming process. The thermal time constant of the filament region is of the order of 1 ~s in most thin-film switches on silicon substrates, so that fairly stable patterns are expected to be present for most of the set-pulse time. The bulk of crystallization, however, occurs within 1 ms before and after lock-on, when considerable thermal disturbance must occur. A major source of this disturbance arises from the difference in properties of the hot amorphous filament and the crystals it forms. Fig. 3, after Krebs and Fischer [7], shows a typical curve of temperature variation of electrical resistivity in a memory chalcogenide. The dashed line represents the resistivity of the hot amorphous chalcogenide before crystallization. Depending on the temperature, crystallization produces an increase in conductivity of 5-500-fold. We follow Kroll and Cohen [8] in assuming that the Wiedemann-Franz law applies to these chalcogenides, and so we may expect comparable changes in thermal conductivity. The electrical discontinuity during the set pulse at lock-on is quite small, and to the first approximation both current and voltage across the switch are unchanged. However, the current density in the crystalline filament must be greatly increased, and since the power is nearly constant the power density must also increase. This interaction will tend to produce a temperature rise which might be sufficient to dissolve the crystals, but it is mitigated by the greatly enhanced heat sinking to the electrodes due to the accompanying increase in thermal conduction along a now continuous crystalline path to the electrodes. At the beginning of crystallization
A.G. Steventon / Switching mechanisms in memory devices
323
AnioRPHOUS //"'~"~ 1/T Fig. 3. Schematic curve of the resistivity of a typical memory chalcogenidematerial. (After Krebs and Fischer [7].)
when crystals are growing from isolated nuclei, we expect the initial growth rate to be increased by the release of latent heat. If the latent heat released in l/Is from a 10 nm dia. crystal growing at 2.5 × 10 -5 m/s were retained in the crystal, it would raise its temperature by 10°C and so provide a positive feedback mechanism which would be reduced by loss of growth area and finally by cooling to the electrodes. Precipitation of tellurium-rich crystals causes the composition of the inner parts of the hot filament to change rapidly during lock-on and so further modify the crystallization dynamics, but the outer edge will grow under more stable conditions. Messier and Roy [9] have shown how certain glasses expected to precipitate GeTe from the phase diagram can crystallize, instead, a tellurium phase during warming. In view of the collapse of isothermals at lock-on the outer regions of the filament will in fact be cooling.
4. Experimental In section 3 some of the basic factors affecting crystallization were identified. It is now necessary to consider what extra experimental evidence can be obtained to elucidate their interaction. The large difference between the electrical conductivity of crystals and of the glass means that the on-resistance of a switch, measured at room temperature, is a useful guide to the cross-sectional area of a crystalline filament. We have also used the threshold voltage as a measure of the uncrystallized (high-resistance) path length between
324
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Fig. 4. Device resistance and threshold voltage during multiple short set pulses.
electrodes during switching [6,10]. Fig. 4 shows the changes of resistance R and threshold voltage VT during multiple-set pulses on an experimental switch based on Ge12Te78As10. This illustrates that while the isolated crystals are growing VT gradually decreases but R remains high, until VT ~ 0 when R rapidly decreases. Devices based on Ge15Te81S2Sb 2 exhibit an induction period during which VT and R remain high. During that time the isolated crystals are too small to affect VT. If multiple pulses are used to reset'the device, the induction period will include a "nucleation time" of about 700/2s. It is clear that during all the substantial induction period before lock-on there is no continuous crystalline path between the two electrodes though some crystal growth occurs, but after lock-on crystallization progresses very rapidly and is nearly complete within a few milliseconds. Steventon [6] has distinguished irregular variations between six different electrical lock-on patterns, which are perhaps too complex to analyse, but subsequent changes are fairly straightforward. The on-resistance gradually decreases with time and stabilizes at a value determined by the set current. We assume that the highest temperature occurs on the filament axis and increases with the set current so that the diameter of the isothermal representing minimum temperature for crystallization (Tc) expands with current. Sie et al. [4] noted that the filament dimensions fit a logarithmic expression for
A.G. Steventon / Switching mechanisms in memory devices
325
set currents up to 18 mA, but the diameter calculated for a crystalline cylinder of the observed resistance (fig. 1) fits the expression only up to 10 mA. Thus, above 10 mA not all of the volume of the filament is crystalline. We assume, therefore, that the set filament develops an uncrystallized core above this value.
5. The modified model for the set event When the threshold voltage is exceeded the current through the switch condenses into a filament which is hot enough to permit crystallization. At low set currents the temperature in the filament is lower than the temperature for maximum crystal growth rate (Tp) and crystals will first form on the axis at the hottest part of the filament. In this zone individual crystallites will grow somewhat irregularly, according to local conditions of available nuclei, etc. Variations are shown by the changes in threshold voltage illustrated in fig. 4. Their growth ~produces little change in the overall thermal or electrical pattern. When the individual crystallites first join up to form a continuous chain there is an electrical discontinuity generally signalled by a small discontinuity (lock-on) in the current or voltage trace. The much lower resistance of the continuous chain causes most of the current to leave the outer zones of the filament and concentrate in it, while the corresponding increase of thermal conductivity greatly enhances removal of heat from the chain via the electrodes. The actual temperatures developed will depend on the interplay of these two factors.
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326
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These changes are indicated schematically in fig. 5, which shows the change with time of the radii of isotherms (assumed circular) about the filament. The actual values of the radii will increase with set current and there will also be some variations along the axis of the filament, but the diagram is expected to be valid until the set
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current causes the temperature Tp to be exceeded in the filament before lock-on. If the current pulse is terminated before the stabilization of crystallization the filament will have a reduced radius indicated by the dashed line in fig. 5 (see also fig. 4). With higher set currents the initial crystallization will not occur on the filament axis, which is too hot, but on the Tp isotherm annulus. The thermal and electrical redistribution already described will now occur about the annulus, and in many cases will result in quenching the central region quickly enough to prevent it crystallizing. This produces the hollow filaments described by Cohen et al. [3]. The addition of a slow fall time to set pulse can only help crystallization of the central core when its temperature is still too hot at the end of the set pulse. In our experiments the trailing edge had no effect on the filament resistance and we assume that the central zone was already quenched to below T e. An alternative view of this model, in the form used by Cohen et al. [3] is given in fig. 6. The experimentally observed improvement in the success rate for setting, when the set pulse includes a trailing edge, has been tentatively attributed to the occurrence of microfilaments linking crystallites [11]. On rare occasions these may be distributed in such an arrangement that one of a few microfilaments must crystallize in order to complete the chain, but that because of high local current density crystallization is inhibited. Cooling, by using a trailing edge, will then be successful. Steventon [11 ] has also attributed observations of the resetting ability of reverse polarity set pulses to electromigration in such microfilaments. Without such an explanation neither the model of Cohen et al. nor the above modifications to their model, could explain this effect.
6. The reset event
In the reset event, the current is immediately channelled through the pre-existing crystalline filament and causes considerable local heating. The crystals dissolve and a hot conductive channel of amorphous material is produced with a diameter much greater than the original crystal f'dament. The whole of the original filament lies within the Ta isotherm of the reset pulse, but of course a narrow annulus exists outside this in which optimum conditions for crystallization exist. The reset pulse is short enough for the central area to quench into the glassy state, but the possibility of some small increment of crystallization in the outer annulus must be admitted. With repeated cycling, enough conductive material is expected to accumulate to displace the filament axis. The following set (and reset) pulse will then be recentred on a point on the Tp annulus of the previous reset pulse, while the next reset pulse based on the new position, will have a Tp isotherm which passes through the original axis. Successive elimination of the crystallites in the Tp annulus of the earlier reset pulses will result in shifting of the axis in the annulus about the original axis, but always intersecting near the original axis. Thus the original axis will be a favourable position for crystal growth thus causing the filament to return. This mechanism explains the ad-
328
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Fig. 7. Plan view of the suggested elimination of crystallites from the crystallization annulus using multiple reset pulses. vantages of multiple-pulse resetting, as illustrated in fig. 7. The initial pulse removes the main filament, and successive pulses remove the larger regions Of crystalline debris in the annulus. There will be second- and third-order effects but these will be much weaker. Evidence that significant crystallization can occur during the very short reset pulse (~6/as) is provided by the effect of a trailing edge on the reset pulse [12]. This edge can affect the subsequent set operation if it is greater than 1 Dis long and can cause failure to reset if it is >5/as, thus implying that the crystallization rate at Tp is sufficient to grow substantial quantities of crystalline material. Separately reset pulses of I0/as have an increasing proportion of failures. This is attributed to the formation of a crystalline link in the Tp annulus.
A.G. Steventon /Switching mechanisms in memory devices
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Buckley et al. [13] have observed device degradation with floral patterns in the top electrode, which could be attributed to electrode damage while the filament changes in the manner of fig. 7.
7. Conclusions Some limitations o f the CNP switching model have been described and some modifications suggested which take account o f the change in local conductivity and heat dissipation due to crystallization. The improved reliability obtained when a set pulse trailing edge is used, and the influence o f reverse polarity set pulses can be explained by postulating, in addition, the existence o f microfilaments.
Acknowledgement The author wishes to acknowledge the help o f Mr. D.C. Shotton in the preparation o f this paper and the Director o f Research o f the British Post Office for permission to publish it. The author also wishes to thank Dr. J. Allison and Dr. M. Thompson of Sheffield University for their supervision during the preparation of his thesis from which this work was taken.
References [1] D. Adler, Amorphous semiconductors (Butterworth, London 1971). [2] H. Fritzsche, in: Electronic and structural properties of amorphous semiconductors, eds. P. LeComber and J. Mort (Academic Press, London and New York, 1973) p. 557. [3] M.H. Cohen, R.G. Neale and A. Paskin, J.Non-Crystalline Solids 8-10 (1972) 885. [4] C.H. Sie, M.P. Dugan and S.C. Moss, J. Non-Crystalline Solids 8-10 (1972) 877. [5] P.W. McMillan, Glass ceramics (Academic Press London and New York, 1964). [6] A.G. Steventon, in: Amorphous and liquid semiconductors, eds. J. Stuke and W. Brenig (Taylor and Francis, London 1974) p. 675. [7] H. Krebs and P. Fischer, Discuss. Faraday Soc. no. 50 (1970) 35. [8] D.M. Kroll and M.H. Cohen, J. Non-Crystalline Solids 8-10 (1972) 544. [9] R. Messier and R. Roy, Mater. Res. BuU 6 (1971) 749. [10] A.G. Steventon and D.J. Bond, J. Phys. D; Appl. Phys. 7 (1974) L167. [11] A.G. Steventon, J. Phys. D; Appl. Phys. 8 (1975) L120. [12] A.G. Steventon, J. Phys. D; Appl. Phys. 8 (1975) 1869. [13] W.D. Buckley, F.H. Holmbery, R.G. Neale, R.R. Shanks and K.E. van Landingham, Final Report. Contract No. N 60921-72-C-0165 (US Naval Ordnance Laboratory, 1974).