# Cryogenic Subthreshold Swing Saturation in FD-SOI MOSFETs described with Band Broadening

## TL;DR

This paper investigates the saturation of subthreshold swing in 28nm FD-SOI MOSFETs at cryogenic temperatures, proposing a disorder-induced band tail model that explains experimental observations and aids future cryogenic circuit design.

## Contribution

It introduces a novel disorder-induced band tail model to explain subthreshold swing saturation at cryogenic temperatures in FD-SOI MOSFETs, validated by experimental data.

## Key findings

- Model accurately fits experimental SS(T) data from 300K to 4K.
- Band tail width estimated at approximately 3 meV.
- Provides a method to determine band-tail extension for cryogenic device modeling.

## Abstract

In the standard MOSFET description of the drain current $I_{D}$ as a function of applied gate voltage $V_{GS}$, the subthreshold swing $SS(T)\equiv dV_{GS}/d\log I_{D}$ has a fundamental lower limit as a function of temperature $T$ given by $SS(T) = \ln10~k_BT/e$. However, recent low-temperature studies of different advanced CMOS technologies have reported $SS$(4K or lower) values that are at least an order of magnitude larger. Here, we present and analyze the saturation of $SS(T)$ in 28nm fully-depleted silicon-on-insulator (FD-SOI) devices for both n- and p-type MOSFETs of different gate oxide thicknesses and gate lengths down to 4K. Until now, the increase of interface-trap density close to the band edge as temperature decreases has been put forward to understand the saturation. Here, an original explanation of the phenomenon is presented by considering a disorder-induced tail in the density of states at the conduction (valence) band edge for the calculation of the MOS channel transport by applying Fermi-Dirac statistics. This results in a subthreshold $I_{D}\sim e^{eV_{GS}/k_BT_0}$ for $T_0=35$K with saturation value $SS(T<T_0) = \ln 10~k_BT_0/e$. The proposed model adequately describes the experimental data of $SS(T)$ from 300 down to 4K using $k_BT_0 \simeq 3$meV for the width of the exponential tail and can also accurately describe $SS(I_{D})$ within the whole subthreshold region. Our analysis allows a direct determination of the technology-dependent band-tail extension forming a crucial element in future compact modeling and design of cryogenic circuits.