Using a seeded-bridge model
Given the correctness of the model used to provide the close link between ETDR failure results and a fully crystallized “set” device, such a back extrapolation should be able to point to the “set” times and the crystallization temperatures of the materials involved and a possible means of optimizing those variables. In the event that there is there is a large anomaly between the expected and predicted values, it would suggest that another process is involved that either assists or impedes the crystallization process in the PCM device structure in the presence of electric current and field.
Modern PCM device structures that feature one electrode formed of the memory material that remains in its crystallized state introduce a thermal asymmetry that is sometimes enhanced by making one electrode a heater. This makes consideration of the crystal-growth model the special case of “seeded” growth, in which there is always present a massive nucleation site on which crystal growth can start.
For this investigation, I have used what I have termed a seeded-bridge model for the PCM “set” process. In this model, crystal growth for both “set” and ETDR test failures starts on the crystallized active material electrode as the seed and grows to bridge, or reduce, the inter-electrode gap to result in a particular “set” resistance or a designated failure condition, respectively. While growth from the crystal electrode as a seed is not new idea, the term seeded-bridge better describes what occurs during PCM “set” (see figure 2).
Figure 2: The device cross sections show the crystallization of germanium-antimony-tellurium (GST)—the “set” process—of the seeded-bridge model correlated to the shape and form of an optimized “set” pulse.
The seeded-bridge model makes establishing a close link and a numerical relationship between the fractionally crystallized device of the ETDR test and a fully crystallized “set” device a simple step. I assume the result of an ETDR test failure represents crystal growth that extends into one tenth of the “reset” material; thus, the black line in Figure 1 that represents a fully “set” device is displaced one decade to longer times. Implicit in the accuracy of the seeded-bridge model is a linear relationship between resistance and fractional crystal growth into the inter-electrode space. I am aware that the values of resistance change that are used to define an ETDR test failure do vary between different groups and this will change the parallel position of the fully “set” line (black) to the back extrapolated line (blue) in figure 1 and the later figures from real devices (see part 2) in a proportional manner.
Back extrapolation of the type I propose must end when the a value of 1/kT
representing the melting temperature Tm
is reached; by definition at Tm
crystal growth rate must drop to zero, meaning the lines of t = f (1/kT)
for PCM devices must reach a minimum “set” time. The question, for which at this time I do not have an answer, is that at the temperatures involved, does the crystal growth rate go through a maximum that would cause the back-extrapolated line enter a gentle minimum or does it continue with the same activation energy to Tm
? For the moment, and until other evidence comes to light, I consider the minimum in “set” time, where seeded crystal growth is at its maximum rate, to be located at the start of a discontinuity to infinite time at Tm
(see figure 1).
If we can establish that crystal growth rates go through a minimum at temperatures well below Tm
and when translated into times for the seeded-bridge to cross a given electrode gap, the result is values much greater than known set times, we can consider that to be an indication that effects other than temperature (e.g. electro-crystallization) are assisting the crystallization process.
Outside of any consideration of the true shape of the t = f (1/kT)
curve, there is an absolute minimum “set” time dictated by the time required to bring the device and its immediate environs up to the required crystallization temperature in a controlled manner, determined quantitatively by the thermal mass of the device and associated thermal time constant.