Building a useful quantum computer is, in large part, a classical-electronics problem: the qubits need control and readout circuitry, and the cleanest place to put much of that circuitry is right next to the qubits, at cryogenic temperatures. That has made cryogenic CMOS — cryo-CMOS — a serious sub-field of device engineering, and it carries an unforgiving requirement. The transistor models that circuit designers rely on were validated at room temperature, and at a few kelvin the devices behave in ways those models do not anticipate. A June 2026 arXiv preprint, Beyond the interface: Persistent Hopping Transport and Frequency Dispersion in Strong-inversion Cryogenic MOSFETs, by Keito Yoshinaga, Wataru Miyagi, Ryo Toyoshima, Munehiro Tada and Ken Uchida, identifies one such surprise and explains its physical origin.
The observation concerns output impedance. A MOSFET's channel impedance is known to depend on the frequency of the small signal you probe it with, and the conventional explanation is that this dispersion comes from extrinsic parasitics — the unavoidable capacitances and resistances of the wiring and contacts around the device, not the transistor channel itself. If that were the whole story, you could model the dispersion as an external network bolted onto an ideal device. The authors report that at cryogenic temperatures this is not the whole story.
"Here, we report an intrinsic frequency dispersion in the channel impedance of cryogenic MOSFETs that persists deep into the strong-inversion region."— arXiv:2606.17547 (Yoshinaga et al.), source
Why strong inversion is the surprising part
The phrase "persists deep into the strong-inversion region" is what makes this result notable rather than routine. Strong inversion is the operating regime where the transistor is fully turned on, the channel is densely populated with carriers, and conduction is supposed to be dominated by ordinary drift — carriers flowing smoothly under the applied field. Anomalies tied to localized states and trapping are normally expected near threshold or in weak inversion, where carrier populations are sparse and disorder matters most. Finding an intrinsic, disorder-driven dispersion that survives into the heart of strong inversion contradicts the comfortable assumption that, once the device is fully on, the channel behaves cleanly.
To characterize it, the authors use a Cole-Cole analysis, a technique borrowed from impedance spectroscopy that plots the complex impedance and looks at the shape of the resulting arc. They report a depressed semicircle in the impedance plane — a flattened arc rather than a perfect half-circle. That shape is diagnostic: a depressed semicircle is the signature of a distribution of relaxation times rather than a single clean time constant, which is exactly what you expect when transport proceeds through a spread of localized states with different energies and spatial separations rather than through one uniform mechanism.
Variable-range hopping, and where the states live
The mechanism the authors assign is variable-range hopping through band-tail localized states. Band-tail states are energy levels that smear below the conduction band edge because of disorder in the material; at cryogenic temperatures, where thermal energy is tiny, carriers can move through these states by hopping — quantum-mechanically tunneling from one localized site to another, preferentially choosing hops that optimize the trade-off between distance and energy difference, which is what "variable-range" denotes. Hopping is inherently a frequency-dependent, distributed process, so it produces precisely the depressed-semicircle, multiple-relaxation-time impedance the Cole-Cole analysis reveals.
The most important claim is about where these states are. Conventional models confine band-tail states to the oxide interface — the boundary between the silicon channel and the gate dielectric, long understood as the dirtiest part of the device. The authors instead argue that in MOSFETs with high channel doping, the band-tail states are induced by ionized impurities and distributed throughout the depletion region, not pinned to the interface. That relocation of the responsible physics, from a thin interfacial layer to the bulk of the depletion region, is the conceptual core of the paper, and it is what explains why the dispersion survives strong inversion: the responsible states are everywhere the dopants are, not just at a surface that strong inversion would screen.
Why a circuit designer should care
For cryo-CMOS circuit design, the consequence is concrete. The authors conclude that ionized-impurity-induced hopping governs the dynamic response of the cryo-MOSFET channel impedance even when drift conduction dominates, and that this offers critical insights for accurate small-signal modeling and high-frequency cryo-CMOS circuit design. In practice, that means a designer building a cryogenic amplifier or readout stage cannot treat the transistor's frequency dispersion as an external parasitic to be calibrated away; part of it is intrinsic to the channel and depends on doping and on the distribution of impurity-induced states. A small-signal model that omits this term will mispredict gain, bandwidth and impedance matching at exactly the cryogenic, high-frequency operating point that quantum control electronics demand.
The abstract leaves room for the questions independent groups will want answered. It does not, in summary form, specify the exact temperatures and frequency ranges measured, the doping levels at which the effect becomes significant, or how universal the behavior is across device geometries and fabrication processes — all of which determine how broadly the conclusion generalizes. Nor does it offer a closed-form compact-model term ready to drop into a circuit simulator; translating a physical mechanism into a SPICE-ready parameter is a separate body of work.
Even so, the contribution is the kind that quietly improves an entire design discipline. By insisting that an observed dispersion is intrinsic rather than parasitic, and by tracing it to impurity-induced hopping distributed through the depletion region, the work tells cryo-CMOS designers where a real modeling error has been hiding. As quantum-computing systems push more control electronics down to cryogenic temperatures, the accuracy of those transistor models stops being an academic nicety and becomes a limit on how well the qubits can be controlled. Knowing that the channel itself disperses — and why — is precisely the sort of device-physics correction that has to land before the circuit models can be trusted.