Equivalent Circuit of Electrothermal Memristor Model Based on HfO₂

Memristor devices have obtained significant attention within the electronics design community due to their switching properties and nonvolatile storage capabilities. This paper presents a comprehensive 3D modeling approach for a memristor device based on HfO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>, aiming at studying its electrical and thermal behaviors. An electrothermal model is implemented in COMSOL Multiphysics to investigate the RESET process and the rupture of the conductive filament under combined electrical and thermal effects. However, capturing the dynamic switching behavior from the low to high resistance states of the memristor proves challenging. To address this, an equivalent circuit model is developed and implemented in SPICE, based on a mathematical representation, to characterize the memristor switching behavior. The study analyzes the pinched hysteresis loop (I-V) and the total resistance of the memristor using both pulse and sinusoidal voltage waveforms to evaluate the impact of the input on the characteristics of the device achieving good agreement with COMSOL analyses. Additionally, the circuit model incorporates temperature effects, demonstrating the dynamic switching behavior under varying thermal conditions.