Analytical Modeling of Chalcogenide Crystallization for PCM Data-Retention Extrapolation

Phase-change memory (PCM) reliability is affected by the crystallization of the amorphous chalcogenide material. To reduce measurement time, crystallization of the active material, usually a chalcogenide alloy, is generally studied at high temperature (T > 160degC), while data retention is to be predicted for lower temperatures (T > 120degC). Therefore, a physically based procedure to extrapolate crystallization dynamics from high to operation temperatures is required. This paper shows a simple analytical model for predicting the maximum PCM-operation temperature compatible with a ten-year retention lifetime of the device. Experiments are first analyzed to extract the average retention lifetime and average size of crystalline particles at crystallization in the PCM cell; this allowed the extraction of nucleation rate and growth velocity in the Ge₂Sb₂Te₅ phase-change material. The classical theory for crystallization based on nucleation and growth (N/G) is then used to extrapolate lifetime data to relatively low temperatures for reliability assessment. Our study shows that the temperature dependence of retention lifetime may not obey to the Arrhenius law, as a result of non-Arrhenius nucleation. The dependence of reliability on N/G parameters is finally discussed with reference to different crystallization modes in phase-change materials.