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

TL;DR

This paper introduces a comprehensive undoped silicon mobility model valid from cryogenic to high temperatures, accurately capturing anisotropic effects for electrons and holes in different crystal directions.

Contribution

It presents the first unified low and high field mobility model for silicon across a wide temperature range, incorporating anisotropy and calibration to experimental data.

Findings

The model fits experimental data for <100> and <111> silicon directions.

Modified Farahmand model improves anisotropic mobility predictions.

Predicted mobility at 4K provides initial parameters for TCAD simulations.

Abstract

For decades, there is no unified model developed for Silicon carriers from 4K to above room temperature. In this paper, a unified undoped Silicon low field and high field mobility model for both electron in the <100> and <111> directions from 8K to 300K and 430K, respectively, and hole in the <100> direction from 6K to 430K 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 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 4K, which can be served as the initial calibration parameters when reliable experimental data is available for the TCAD model development.