Analytical modeling of chalcogenide crystallization for PCM data-retention extrapolation

Chalcogenide materials are receiving increasing interest for their many applications as active materials in emerging memories, such as phase-change memories, programmable metallization cells, and cross-point devices. The great advantage of these materials is the capability to appear in two different phases, the amorphous and the crystalline phases, with rather different electrical properties. The aim of this work is to provide a physically based model for conduction in the amorphous chalcogenide material, able to predict the current-voltage I−V characteristics as a function of phase state, temperature, and cell geometry. First, the trap-limited transport at relatively low currents subthreshold regime is studied, leading to a comprehensive model for subthreshold conduction accounting for a the shape of the I−V characteristics, b the measured temperature dependence, c the dependence of subthreshold slope on the thickness of the amorphous phase, and d the voltage dependence of the activation energy. The threshold switching mechanism is then explained by the nonequilibrium population in high-mobility shallow traps at high electric field and by the nonuniform field distribution along the amorphous layer thickness. A single analytical model is then shown which is able to account for subthreshold conduction, threshold switching, negative differential resistance region, and ON regime. The model can be applied for fast yet physically based computation of the current in chalcogenide-based devices e.g., phase change memory cells and arrays as a function of applied voltage, temperature, and programmed state.