Beyond the interface: Persistent Hopping Transport and Frequency Dispersion in Strong-inversion Cryogenic MOSFETs
Cryogenic complementary metal-oxide-semiconductor (cryo-CMOS) technology is essential for quantum computing interfaces, which require precise modeling of dynamic device behavior. The output impedance of MOS field-effect transistors (MOSFETs) is frequency dependent, which has been conventionally attributed to extrinsic parasitics. Here, we report an intrinsic frequency dispersion in the channel impedance of cryogenic MOSFETs that persists deep into the strong-inversion region. Through a Cole-Cole analysis, we characterize this dispersion as a depressed semicircle in the impedance plane and attribute its behavior to variable-range hopping through band-tail localized states. Unlike conventional models where band-tail states are confined to the oxide interface, we demonstrate that in MOSFETs with high channel doping the band-tail states are induced by ionized impurities and distributed throughout the depletion region. Our paradigm accounts for frequency dispersion under strong inversion. This work demonstrates that ionized-impurities-induced hopping governs the dynamic response of cryo-MOSFETs channel impedance even when drift conduction dominates, offering critical insights for accurate small-signal modeling and high-frequency cryo-CMOS circuit design.