Thermal memory driven compact electro-thermal modelling of phase-change memristors

Compact models of phase-change memristive devices are important for circuit- and system-level simulations. Despite this, most of the approaches available today depend on threshold-based switching or experiential conductance updates. These models reproduce fundamental SET/RESET behaviour, but these models overlook the conductance changes influenced by pulse history, which governs gradual analog switching. In particular, residual heat build-up between consecutive programming pulses is often neglected or absorbed into model parameters, which disguises their role in governing analog conductance changes. This study proposes a compact electro–thermal–kinetic model that directly incorporates residual thermal memory as a dynamic state variable. This model stores the excess local temperature that is maintained in the phase-transition area and combines it with Johnson-Mehl-Avrami-Kolmogorov (JMAK) crystallization kinetics. This shows a direct relation among pulse timing, thermal accumulation, and phase-change dynamics. This permits the device to imitate pulse-history-dependent conductance modulation under similar electrical excitation. Time-domain MATLAB simulations show that incorporating thermal memory enables gradual, reproducible analog switching and produces characteristic pinched current–voltage hysteresis. In contrast, deactivating the thermal state in control simulation causes abrupt and binary-like switching behavior, which highlights the importance of thermal accumulation. By varying the pulse width, amplitude, and thermal parameters, it is found that the conditions under which analog behavior occurs, saturates, or collapses. By treating residual thermal memory as a state variable, the model provides a physically grounded framework for understanding analog switching in phase-change memristive devices. The proposed compact formulation is computationally efficient and material-agnostic, and well-suited for large-scale circuit and neuromorphic-level simulations that require pulse-history dependence.