Physics-based model for scaled cryogenic FETs with band-tail-assisted carrier statistics

Abstract

Accurate transistor models that remain predictive at cryogenic temperatures are essential for developing large-scale cryogenic complementary metal-oxide-semiconductor platforms that support quantum computing and other low-temperature electronic systems. However, existing cryogenic field-effect transistor (cryo-FET) models struggle to simultaneously reproduce threshold-voltage shifts, gradual subthreshold turn-on, and above-threshold transport in scaled devices because these behaviors originate from distinct physical mechanisms. This study presents a physics-based model for scaled cryo-FETs that integrates the temperature-dependent electrostatic alignment, continuous interface-trap energy distribution, band-tail-assisted carrier statistics, and effective field-dependent mobility degradation within a unified charge-based framework. The model explicitly incorporates bandgap widening and incomplete dopant ionization into the metal-semiconductor work-function difference while representing interface traps through a physically consistent continuous energy spectrum. The study further demonstrates that interface-trap electrostatics alone cannot account for the experimentally observed subthreshold broadening at deep cryogenic temperatures owing to the excessively sharp Maxwell-Boltzmann carrier response. To resolve this limitation, a band-tail-assisted statistical carrier formulation that broadens the subthreshold carrier formation while naturally recovering the conventional conduction-band transport in strong inversion is introduced. The model accurately reproduced the transfer characteristics of 65-nm silicon bulk transistors from 250 to 12 K over multiple decades of drain current, with excellent agreement in both the threshold behavior and the subthreshold slope. These results establish a physically interpretable and quantitatively accurate modeling framework for scaled cryo-FETs, thereby providing a foundation for predictive cryogenic circuit design and future compact-model development.