Phase change memory (PCM) is considered as one of the most promising candidate for future non-volatile memory (NVM) technology . Among the emerging NVMs, PCM is also the first which has reached the industrial maturity . PCM devices are based on the reversible crystalline-amorphous transition in a chalcogenide material such as Ge2Sb2Te5 (GST). While the crystalline (set) state is stable, the amorphous (reset) state is metastable, showing spontaneous thermally-activated crystallization. Crystallization can be obtained either by increasing the ambient temperature or by electrical pulses, where the T increase due to Joule heating leads to phase transition in the 10 ns timescale. For this reason, crystallization plays an important role not only in data retention  and programming speed , but also in reset transition , read disturb  and program disturb .
In this work, we propose a unified finite element model able to predict electrically induced crystallization in PCM devices. The simulated structure is a mushroom cell with confined bottom electrode contact (heater). Literature values for electrical and thermal conductivities were used. To correctly describe Joule-heating in PCM from ambient temperature to melting point (around 900 K), also the T-dependence of GST electrical and thermal conductivities were taken into account . The model relies on continuity and Fourier equations for electrical and thermal transport, while a first order differential equation describes the thermal activated evolution of the crystalline fraction. The fragile nature of GST glass was modeled by considering the non-Arrhenius-activated kinetic constant driving crystallization equation . To model the reset state during set transition, we have described threshold switching by the formation of a highly conducting filament within the amorphous cap . The model is able to predict the measured resistance R evolution in set experiments even at extremely low currents near the hold current Ih (around 40 μA), which is the minimum current necessary for the self-sustaining threshold switching mechanism. In addition, the model also describes crystallization in the subthreshold regime (I < 5 μA), where T is below 500 K and R decay in the 1000 s time-scale. This unified approach is important to predict read disturb effect in PCM devices, which must be thoroughly understood to avoid data loss under repeated read operations .
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