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
$\langle 100\rangle $
and
$\langle 111\rangle $
directions from 8 to 300 K and 430 K, respectively, and hole in the
$\langle 100\rangle $
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
$\langle 111\rangle $
experimental data but not the
$\langle 100\rangle $
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
$\langle 111\rangle $
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.