# Cryogenic MOSFET Threshold Voltage Model

## TL;DR

This paper introduces a physics-based threshold voltage model for bulk MOSFETs operating from room temperature down to cryogenic temperatures, crucial for cryo-CMOS and quantum computing applications.

## Contribution

The paper develops a novel threshold voltage model incorporating bandgap widening, carrier-density scaling, and incomplete ionization, validated with experimental data at 4.2 K.

## Key findings

- Model accurately predicts threshold voltage at cryogenic temperatures
- Incomplete ionization significantly affects threshold voltage estimation
- Validated with 28-nm CMOS process experimental data

## Abstract

This paper presents a physics-based model for the threshold voltage in bulk MOSFETs valid from room down to cryogenic temperature (4.2 K). The proposed model is derived from Poisson's equation including bandgap widening, intrinsic carrier-density scaling, and incomplete ionization. We demonstrate that accounting for incomplete ionization in the expression of the threshold voltage is critical for an accurate estimation of the current. The model is validated with our experimental results from nMOSFETs of a 28-nm CMOS process. The developed model is a key element for a cryo-CMOS compact model and can serve as a guide to optimize processes for high-performance cryo-computing and ultra-low-power quantum computing.