Experimentally Validated, Predictive Monte Carlo Modeling of Ferroelectric Dynamics and Variability

A physics-based, circuit-compatible Monte Carlo simulation framework, capable of predicting the dynamic response of a ferroelectric (FE) under any arbitrary input waveform, is developed by extending the nucleation-limited switching model. Measured polarization reversal data from fabricated FE W/Hf_0.5Zr_0.5O₂ (HZO)/W capacitors is used to extract the statistical distribution of FE grains, which show negligible variation with film thickness. After parameter extraction, the model is able to predict the dynamics of HZO and bilayer HZO/HfO₂ (FE-DE) thin films without further calibration. Unlike prior models, the proposed model is able to predict device-to-device variability, and quantify the resultant reduction in the memory window for highly scaled devices, revealing a significant reduction for FE capacitors having <; 20 grains (~40×40 nm²). The memory window is further reduced in FE-DE stacks for the same programming voltage and pulse duration due to the dielectric depolarizing field.