Hyewon Park, Dokyoung Lee, Hyeonsik Ahn, Jusung Kim and Sungho Kim
Physics-based model for scaled cryogenic FETs with band-tail-assisted carrier statistics
SciRep (2026)
DOI: 10.1038/s41598-026-65834-5
1. Division of Electronic and Semiconductor Engineering, Ewha Womans University (KR)
2. Institute for Multiscale Matter and Systems (IMMS), Ewha Womans University (KR)
3. Department of Electronic Engineering, Hanbat National University, Daejeon (KR)
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 K 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.
Fig.1: Physical origin of transfer-characteristic deviations in scaled cryo-FETs and the corresponding model extensions. Schematic of the logarithmic ID–VG characteristics comparing the measured behavioral characteristics with those of the baseline cryo-FET model. At cryogenic temperatures, the baseline model shows three key mismatches: threshold-voltage shift, overly steep subthreshold turn-on, and inaccurate above-threshold current. These arise from distinct mechanisms. The threshold shift is linked to temperature-dependent electrostatics, including bandgap widening and incomplete ionization. The subthreshold mismatch reflects the sharp Maxwell–Boltzmann carrier response at low thermal voltages, motivating a band-tail-assisted formulation. The above-threshold error results from insufficient transport-field coupling, requiring effective-field-dependent mobility.
Acknowledgements: This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT and MOE) (RS-2024-00449412 and RS-2025-16063688). Data supporting the findings of this study are available from the corresponding author upon reasonable request.
