Heracles: A HfO ₂ Ferroelectric Capacitor Compact Model for Efficient Circuit Simulations

The growing use of ferroelectric-based technology, extending beyond conventional memory storage applications, necessitates the development of compact models that can be easily integrated into circuit simulation environments. These models assist circuit designers in the design and the early assessment of the performance of their systems. The Heracles model is a physics-based compact model for circuit simulations in a SPICE environment for HfO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>-based ferroelectric capacitors (FeCaps). The model has been calibrated based on experimental data obtained from HfO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>-based FeCaps. A thermal model with an accurate description of the device parasitics is included to derive precise device characteristics based on first principles. The incorporation of statistical device data enables Monte Carlo analysis based on realistic distributions, thereby rendering the model particularly well-suited for design-technology co-optimization (DTCO). The model’s efficacy is further demonstrated in circuit simulations using an integrated circuit with current programming, wherein partial switching of the ferroelectric polarization is observed. Finally, the model was benchmarked in an array simulation, reaching convergence in 1.8 s with an array size of 100 kb.