Random polarization distribution of multi-domain model for polycrystalline ferroelectric HfZrO₂

Device dimension scaling down to be comparable to the domain size of polycrystalline ferroelectric HfZrO2 (HZO) is evaluated for subthreshold swing (SS) and drain-induced barrier lowering (DIBL) by numerical simulation. The proposed multi-domain modeling involves polarization random location in HZO and probability with Gaussian distribution, as well as being integrated with the Landau-Khalatnikov equation. A small device with a few domains exhibits steep SS compared with large dimension with many domains. The N-DIBL (negative-DIBL) is also estimated by using this model, and the negative capacitance effect retards the short-channel effects significantly. The trend of the experimental data and simulation results of fin field-effect transistors and planar field-effect transistors is consistent with nano-scale and micro-scale devices, respectively.