Modeling Filamentary Conduction in Reset Phase Change Memory Devices

We performed a computational analysis on percolation transport and filament formation in amorphous $Ge_2Sb_2Te_5$ (a-GST) using 2D finite-element multi-physics simulations with 2 nm out-of-plane depth using an electric-field and temperature dependent electronic transport model with carrier activation energies that vary locally around 0.3 eV and as a function of temperature. We observe the snapback (threshold switching) behavior in the current-voltage (I-V) characteristics at ~50 MV/m electric field with 0.63 $\mu$A current for 300 K ambient temperature, where current collapses onto a single molten filament with ~ 2 nm diameter, aligned with the electric field, and the device switches from a high resistance state (108 $\Omega$) to a low resistance state (103 $\Omega$). Further increase in voltage across the device leads to widening of the molten filament. Snap-back current and electric field are strong functions of ambient temperature, ranging from ~ 0.53 $\mu$A at 200 K to ~ 16.93 $\mu$A at 800 K and ~ 85 MV/m at 150 K to 45 MV/m at 350 K, respectively. Snap-back electric-field decreases exponentially with increasing device length, converging to ~ 38 MV/m for devices longer than 200 nm.