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HH2.08 - Modeling of Phase Change Memory Devices Using a Dynamic Crystal Density Approach 
April 22, 2014   4:45pm - 5:00pm

Unlike conventional solid-state devices, phase change memory (PCM) devices experience large variations in temperature and the material dynamically changes between the amorphous, crystalline and liquid phases. The gradual transitions from the amorphous to crystalline phase and between the different crystalline phases lead to local variations in material states that depend on the thermal history. Hence, modeling of PCM operation requires a component that dynamically tracks the local crystallinity state of the material.The changes in the phase-change material can be modeled using a finite element tool by generating crystalline domains and growing them in time based on the theoretically predicted nucleation-growth dynamics [1]. However, this is computationally intensive approach as the boundaries of the nucleated domains need high-density meshing for the calculations. Alternatively, the crytallinity state of individual mesh points can be tracked and get switched between the amorphous and crystalline states in a binary fashion. However, this mesh-based approach requires a uniform mesh as variations in mesh sizes in the structure would result in variations in grain sizes. Hence, this is also computationally intensive.We have developed a model that uses a crystal density approach where each point is tracked with a variable that represents a crystal density, rather than a binary switch between amorphous and crystalline states. Hence, the approach is immune to variations in mesh and allows non-uniform meshing of a device geometry. The model is calibrated to increase the crystal density based on the temperature-dependent nucleation-growth parameters of Ge2Sb2Te5 [1] as the material crystallizes, and rapidly decrease the crystal density upon melting. The reset-set cycling behavior of the phase change memory cells simulated for several cycles using this model is very much in-line with the experimental findings.This model is built upon the electro-thermal models we have developed in our group which accounts for temperature-dependent material parameters, thermoelectric effects, thermal boundary resistances and field dependent electrical conductivity (dielectric breakdown) leading to threshold switching [2,3]. [1] G. W. Burr, et al. “Observation and modeling of polycrystalline grain formation in Ge2Sb2Te5” Journal of Applied Physics 111, 104308 (2012); doi: 10.1063/1.4718574[2] A Faraclas, N Williams, A Gokirmak, H Silva, “Modeling of Set and Reset Operations of Phase-Change Memory Cells”, IEEE Electron Device Letters, 1-3[3] N Kan'an, A Faraclas, N Williams, H Silva, A Gokirmak “Computational Analysis of Rupture-Oxide Phase-Change Memory Cells” IEEE Trans. Electr. Dev., 60 (5), 1649-1655

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