Avoiding unsafe extrapolation
The question as to the safety of extrapolation can perhaps be turned on its head by questioning the safety and accuracy of the forward extrapolation. Ideally, for the forward extrapolation, the data points should be qualified with the sample size. In the context of the requirement for PCM devices of capacity greater than 1 Gb, a sample size that allows high confidence parts per billion (ppb) is mandatory. This avoids the problem of the unsafe extrapolation of the results for a small sample for failures at the level of parts per million or parts per billion; e.g. a hundred devices producing percentage failure rates over three decades extrapolated to parts-per-billion levels.
One recent publication  has even used the word “unlimited” to describe the magnitude of their forward extrapolation. Another aspect of the forward extrapolation that is often overlooked is that PCM devices subjected to the ETDR test are usually above the glass transition temperature, not arrived at by quenching; while devices at the temperature to which the forward extrapolation is made are always in the rapidly quenched “reset” state.
It is also important is to consider and eliminate other possible models for “set,” of which there are a number of candidates. We can eliminate two of those because of the seed condition. The first model, involving a slower process, is based on homogenous growth in which incubation-nucleation and growth occur in each region of the temperature gradient. The second model, involving a faster process, is based on a model in which crystal growth starts from nucleation sites on the sidewalls and both electrodes and even remnant crystallites. Those opposing the use of my “seeded-bridge” model must answer the key question: Why can the presence of a massive crystal nucleus be ignored as the dominant starting point for crystal growth?
Because crystal growth rate is an activated function of temperature, the optimum set pulse will be one that maintains the region close to the growing crystal interface at a temperature that results in the highest growth rate, as illustrated in figure 2. A “set” pulse with a trailing edge is best suited to achieve the required result and will represent the optimum pulse as far as minimizing set time. Historically, there is indirect support for the “seeded-bridge” model of PCM “set”—a trailing edge has always been part of any empirically optimized “set” pulse. Why would a trailing edge be necessary, when a square pulse should be able to raise the temperature to the crystallization temperature? There are a number of possible explanations. Threshold switching is an inherent part of the “set” step. If the assumption is made that, post-threshold switching, the switched material is relatively cool, as would be the case for a purely electronic process, then a hotspot at a temperature higher than the crystallization temperature for maximum growth rate must be created. That hotspot must be created to raise the temperature of the extreme regions of the amorphous material in the device structure to the temperature for the highest crystal growth rate. To bring that hotspot back to crystallization temperature requires a trailing edge.
Alternatively, and in accord with the view of this author, the result of threshold switching is a hotspot and although crystal growth can occur in the material around the hotspot, a trailing edge is necessary to complete crystallization process. In both examples above, the hotspot must be at a temperature higher than that required for crystallization because crystals grow up temperature gradients in order to dump the latent heat of crystallization.