We model electrical conductivity in metastable amorphous $Ge_{2}Sb_{2}Te_{5}$ using independent contributions from temperature and electric field to simulate phase change memory devices and Ovonic threshold switches. 3D, 2D-rotational, and 2D finite element simulations of pillar cells capture threshold switching and show filamentary conduction in the on-state. The model can be tuned to capture switching fields from ~5 to 40 MV/m at room temperature using the temperature dependent electrical conductivity measured for metastable amorphous GST; lower and higher fields are obtainable using different temperature dependent electrical conductivities. We use a 2D fixed out-of-plane-depth simulation to simulate an Ovonic threshold switch in series with a $Ge_{2}Sb_{2}Te_{5}$ phase change memory cell to emulate a crossbar memory element. The simulation reproduces the pre-switching current and voltage characteristics found experimentally for the switch + memory cell, isolated switch, and isolated memory cell.
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