Melting and quenching during RESET are essential to the operation of a phase change memory (PCM) device. This follow-up article explores the role of melting during threshold switching and the post-threshold switching conducting state prior to SET state crystallization.
In a recent EE Times article [Ref 1] a couple of phase change memory (PCM) questions were raised and left unresolved. One was the degree to which localized melting might be involved in threshold switching. With a possible discontinuity in electrical conductivity on melting able to provide provide a more powerful feedback mechanism than would be the case with Joule heating and Poole-Frenkel conduction alone; the thermistor-like model proposed by IBM. The second was the question regarding the possible existence of a separate post-threshold switching conducting state, melting or otherwise, and prior to crystallization for a PCM and by definition the only post-switching state in a threshold switch.
There has been a considerable amount of follow up interest on the thermal aspect of threshold switching. Especially with Intel confirming [Ref 2] that the basic element in 3DXPoint is a stack of four devices where it now appears threshold switching for each will make a significant contribution to the thermal budget. Figure 1 illustrates a PCM memory stack with the option of the threshold switch filament serving as heater electrode.
Figure 1: A possible double stack of PCM-threshold switch cells with the hot threshold switch filament serving as the heater electrode and some questions.
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A more powerful feedback mechanism driving the switching transition would result in a faster transition, required for shorter read and write times; especially in those cases where the memory cell consists of a threshold switch stacked above a memory cell. Melting would only be of an additional value to the thermal hysteresis effect alone as described in [Ref 1], if there was a discontinuity in conductivity towards a higher value at the melting point. The possible downside with melting and current localization in a hotspot is the possibility that even at low device currents damaging levels of current density and electro-migration could be experienced.
Although there remains some disagreement as to exactly when melting occurs during the memory SET operation, Figure 2 brings together in one set of I-V characteristics what might be considered a 2016 enlightened view of threshold switching. This for illustrative purposes is an example threshold switching for a pulse with insufficient time for any significant crystallization to occur in the case of (PCM) memory device.
Four types of characteristics are shown: the first (yellow) is what must now be called the LeGallo [Ref 1] hysteresis a purely thermal threshold switching effect; the second (blue) when there are no reactive components and after reaching the threshold voltage the I-V characteristics rapidly follow a transition path determined by the series resistor and the third (light blue dashed) is when stray capacitance is present and a current i = CdV/dt is determined by the value of any reactive component. The fourth (purple) is a direct tunnelling current. If the IBM results are generally applicable to all threshold switching, three of these characteristics will have one thing in common it is what I have designated as the thermal trigger point at the threshold voltage. Vts and Vtl are the threshold voltages for pulses of short and longer duration respectively.
Quantitative values will be structure and material composition dependant. In [Ref 3] it was suggested that at some voltage either by thermal means or tunnelling from the traps all carriers will have contributed to the conductivity. Beyond that point (marked with a blue dot in Figure 2) and assuming the pulses were of short enough duration direct tunnelling might be observed, the purple curve.
In Figure 2 the two thin red lines are notional representation of constant power and used to mark the value of current where molten material is present during writing of the memory SET state. The lower of the two would mark the value of current when molten material first appears; initially as some form of initiating hotspot. As the current is increased the volume of molten material will increase. In my model of Figure 2 as the current is reduced the size of the molten region is reduced and what might be considered molten hysteresis or“latching” has occurred. That is a persistence of molten material at current levels where it might not have been present during the initial part of the switching transition. Until finally at very low power it cannot be maintained and the material returns to the amorphous state.
It still leaves open the question as to when the first molten material appears during threshold switching and with it any discontinuity in electrical conductivity, the latter either providing a more powerful feedback mechanism to drive the switching transition or even responsible for it. If melting is present at the threshold voltage it would require moving the lower of the two thin red lines of Figure 2 to coincide with the threshold voltage and the drop-out point.
Figure 2: Four threshold switching I-V options and possible conditions for melting, with from left to right pulses of progressively shorter duration and varying amplitude.
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With all of the 50 years of experience of phase change memory, thousands of published papers and promises for future devices and products it should have been a simple task to find if this is the case, not so. It would appear to be very dangerous even now to make “ just round the corner” PCM product promises if the answers to these rather basic questions with supporting evidence could not be provided almost instantly.
In support of the thermal model [Ref 1] a spokesperson from IBM offered by way of a suggestion a view that the electrical conductivity of amorphous material would not change significantly at the solid-to-liquid melting point. However it was possible to find examples in the literature of other materials, for example silicon [Ref 4] and tellurium [Ref 5] with discontinuities in conductivity at the crystal to liquid melting point. These are elements and will not have the possibility of mixed crystal-liquid phases before they become completely molten.
GST, the material which has been the material composition of choice for many PCM developments, and discontinuities in its electrical conductivity on melting has been the focus of the work of Luca Crespi and colleagues at the Politecnico di Milano, Milan, Italy. [Ref 6] They looked at the results for a number of different crystal structures of GST, from different sources, and from them developed a model with a discontinuity in electrical conductivity at the crystal-to-melt transition.
The answer to one of our PCM questions will surely be found in the curve which traces the activated electrical conductivity of amorphous GST in its solid state meet any discontinuity. Figure 3 shows the original curves of Crespi with superimposed my extrapolated alternatives for the memory chalcogenide as it is heated towards its melting point. The yellow shaded area is the transition region and the dashed mauve curves are merely illustrative examples of many possible trajectories for crystal-to-liquid and amorphous-to-crystal-to- liquid region transitions.
Figure 3: The crystal or amorphous state to melting, speculative curves of possible transitions (dashed purple) overlaid on the original Crespi crystal- to-molten model data.
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The actual paths will be complicated by the consideration that any curves of this type will have a different form depending the rate at which the temperature is changed. Clearly at any point above the crystallization temperature there will be a conductivity discontinuity as a function of crystal growth rate from the amorphous to crystal state if that temperature is maintained at a constant value for a fixed time.
I asked Luca Crespi for his view on my speculative extrapolations of his work, he replied:
“The problem is way more complicated than it might appear to be at first sight, and is much more evident on a the “line” structure architecture, which I am now investigating. The area you call Crystal-Liquid or Amorphous-Liquid, is a really critical area of interest with regard to its electrical conductivity. Based on my experience, when I start from a crystalline cell in a virgin state, with a uniform material, an electrical conductivity is the one I published (with a discontinuity) and necessary to describe the experimental data.
After the first programming, ion migration may vary the local stoichiometry, so much that the melting point and the properties of the material can change considerably, as published by Legendre and Bordas in 1984 and 1986, in Thermochimica Acta. Once this happens, during an electrical pulse, the different local stoichiometry melts at different temperatures, and therefore may lead to a much smoother transition in electrical conductivity. Locally, a discontinuity would still be present, but not all the material would melt at the same time, therefore leading to a smoother transition.
This requires a complex numerical model that takes into account the local melting point dependent on the stoichiometry, in order to obtain a clear description of the experimental data. Unfortunately, that is still a work in progress, but I presented a preliminary study at the last year Spring MRS, where, with a simplified model, the material properties of a GST line structure were changed and showed that the Te-rich area melts at a lower temperature than the rest of the line.
Concerning the amorphous conductivity, looking at your speculative transitions in Figure 2, you show a large transition that goes from 10 S/cm up to 2000 S/cm in roughly 100 K. That could be considered as a discontinuity, due to the large change in conductivity values. For the HCP phase I have electrical evidence, supported by numerical modelling, that a discontinuity at melt is still present, otherwise I would not be able to properly fit the experimental data collected. I can certainly affirm that, starting from a HCP phase or FCC phase, a discontinuity at melt is present.”
I also raised the question with Dr Crespi as to the possibility that if, before complete melting within a mixed crystal-liquid hotspot, there was a large difference between the electrical conductivities at a 33% volume fraction of liquid percolation paths might give rise to a discontinuity and in a device act to localize the current. He commented:
“About percolation paths, that is a possibility, but until now, I haven't found hard evidence that they are present. It's a possibility, but I have no data to sustain it.”