Pitfalls and alternative models
Before looking at experimental results, we must consider a number of aspects of the proposed back-extrapolation. The first is the mathematical safety of the magnitude of the back extrapolation of over seven decades from three data points spread over two decades that is required to get from the minutes and hours of the accelerated ETDR tests to the PCM “set” times on the order 50 ns to 200 ns. After seven decades of extrapolation, small errors can become large errors. To further complicate matters, there is actually more than one extrapolation involved in obtaining the characteristics of a representative or average PCM device in a population. This is because the three or so data points of the ETDR test and the associated extrapolation to the claimed data retention performance are not those of real devices; instead, they represent what should perhaps be called a probability or confidence device, obtained by extrapolation of log normal-distribution plots. It is the device that will probably appear if a large enough sample is tested. Although for the purpose of the model presented here we can consider it as a real device, the average device can be up to two decades away in time, displacing the line for the fully “set” device by that amount.
There is an additional and even more important consideration that could act to distort any seven-decade back-extrapolation of the type proposed here. It would come about if the devices from which the original data was derived are of a mixed population with two different failure mechanisms in play; for example, if a small part of the population has a fabrication defect that results in what appears to be more rapid crystallization, or even if two different crystallization process are involved, one for a minority of devices and the other for the majority or normal devices. Shih  highlighted this two-mechanism failure problem for PCM devices in a paper at IEDM 2008 and suggested that in one case, crystallization was caused by local spontaneous nucleation and growth in the body of the reset material, and in the other, growth from the crystal electrode.
For the normal forward extrapolation of the ETDR test, the tails of the distribution are of extreme importance and for the back extrapolation to be undistorted and valid requires that only one crystallization process can be in play. In terms of the validity of the back-extrapolation and its relation to the “set” pulse for normal devices, it is necessary to establish whether the original ETDR data used as the source material is from the tail bits, the average population, or a mixture of both; and whether the particular device structure has two mechanisms in play. In the event that any ETDR test data points are for outliers, then the displacement in time of the line for a fully “set” normal device will need to be corrected by half the width of the distribution in time.
In the work of Shih, the possibility that element separation caused by electric current or field might have created regions in the reset amorphous material with lower crystallization temperatures was not considered to be an option to account for the results.
Is dual crystallization a fundamental property of the active material composition or, in the context of a device, a combination of the effects of the history of operation, element separation related composition changes, and the electrode surface structure? The closeness of the activation energies of the tail bits and the normal bits in Shih’s work is surprising when two separate processes are involved, nucleation and growth, versus just growth. There are two possible explanations. The first is that at some point near the surface of the hemispherical crystal electrode, the changed amorphous material composition acts to in effect catalyze localized enhanced crystal growth from the spherical crystal electrode, creating a dendrite structure. The second possibility, and in my view more likely, is that on a statistical basis, the reset process leaves a very small crystal nucleating site on the surface of the bottom electrode (BE); not large enough to affect the two-terminal resistance. Because a very small amount of crystal growth from that nucleating site will have a very large effect on the overall resistance of a hemispherical reset region, it will appear to as a failure much earlier than in the case of those devices in which the same growth is occurring from the hemispherical crystal electrode surface. I think one could argue that the reason why a very small crystal nucleating site might be left on the surface of the BE is because the rate of cooling, especially if the BE is a heater, might be just slow enough.