  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.
