A Wide Temperature Range Unified Undoped Bulk Silicon Electron and Hole Mobility Model

For decades, there is no unified model developed for Silicon carriers from 4 K to above room temperature. In this article, a unified undoped silicon low field and high field mobility model for both electron in the ⟨100⟩ and ⟨111⟩ directions from 8 to 300 K and 430 K, respectively, and hole in the ⟨100⟩ direction from 6 to 430 K is proposed and calibrated to the experiment. It is found that the Canali high field saturation model is sufficient to fit the ⟨111⟩ experimental data but not the ⟨100⟩ data due to the anisotropy-induced plateaus and negative differential velocity. Therefore, a modified Farahmand model is used. To allow parameter interpolation in anisotropic simulation, the modified Farahmand model is also calibrated for the ⟨111⟩ direction. The model is then used to predict the mobility of electrons and holes in undoped Si at 4 K, which can be served as the initial calibration parameters when reliable experimental data is available for the technology computer-aided design (TCAD) model development.