TEM (left) and simulated (right) grain images for three different ramp-rates (380, 7.5, and 0.17 °C/min). All images are shown at the same scale, each corresponding to an area of 886 nm × 886 nm. For the fast ramp, a 15 nm SiN membrane (Ted Pella, Inc.) was used, for the medium ramp a 9 nm amorphous silicon membrane (TEM windows, SimPore, Inc.), and for the long ramp, a 30 nm SiN membrane (SPI). In the grain images from our classical nucleation theory simulator, yellow represents a crystalline voxel and brown a grain boundary.
Cumulative distribution of area covered by polycrystalline grains, from largest to smallest, according to image analysis of (a) the TEM images from Figure 1 and (b) the grain sizes obtained directly from simulation. For each simulated ramp-rate, ten different simulations with different random seeds were run. Large grains will lead to a steep curve, while numerous small grains will result in a much more gentle curve.
(a) Resistance vs. temperature, and (b) temperature vs. time for experimental truncated ramp-anneals. For comparison, part (b) also includes, plotted in red squares, the piecewise-linear temperature-vs-time trajectory used for numerical simulation of the 146 °C truncated anneal.
TEM (left) grain images for five different peak temperatures (138, 143, 148, 150, and 152 °C), and simulated (right) grain images at every 2 °C between 142 and 150 °C, using temperature-time trajectories similar to the one shown in Figure 3. Except for the TEM of the still-amorphous sample (truncated at 138 °C) which shows a 90 nm × 90 nm region, all images areshown at the same scale, corresponding to an area of 886 nm × 886 nm. Aslight sample-to-sample non-repeatability of ramp profile, ramp-rate (67–96 °C/min), and precise crystallization temperature due to stoichiometry fluctuations may be why the membranes with anneals truncated at 143 °C and 148 °C both appear to be only slightly crystallized. In the grain images from our classical nucleation theory simulator, yellow represents a crystalline voxel, brown a grain boundary, and cyan a voxel which is still amorphous (for which sub-critical nucleation is tracked).
Crystal growth velocity, , and steady-state nucleation rate, , as a function of temperature. The inset replots on a linear scale in the high temperature regime. Both the melting temperature and glass transition temperature are shown. Symbols at lower left show low-temperature crystal growth velocities obtained experimentally with AFM measurements.44
The TTT diagram for Ge2Sb2Te5 according to numerical simulations, showing the temperature and time-at-temperature combinations where crystal fraction reaches 10−6, 10−5, 10−4, 0.1%, 1%, 10%, 50%, and 99%. The top horizontal axis shows the corresponding linear ramp-rate in °C/min. The use of a constant, rate-independent in the simulations means that this TTT diagram becomes inherently less accurate as the ramp-rate increases. The inset plots at upper right show the evolution of the simulated crystal fraction and device resistance as a function of temperature for a simulation run at a constant ramp-rate of 81 °C/min. Insets at upper left show the evolution of the aggregate population of sub-critical nuclei at four different temperatures; insets at lower left illustrate the distribution of partially established grains at five different temperature/time points, during this same simulation.
TEM grain images and cumulative distribution of area covered by poly crystalline grains, from largest to smallest, for membrane samples exposed to 3, 30, or 300 min of additional annealing at 220 °C after a ramp-rate of 7.5 °C/min. All images are shown at the same scale and correspond to an area of 886 nm × 886 nm. The cumulative distribution for 7.5 °C/min from Figure 2, corresponding to no additional annealing at 220 °C, is also shown for comparison.
Median grain area and effective diameter, as obtained from the slope of the inset plots in Figure 2, for both the TEM and simulated grain images in Figure 1. For the simulations, the median grain area was computed for each instance separately and then averaged across the ten simulations run at the same ramp-rate.
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