Inter-Site 1/f Fluctuation Mechanics in Cryogenic MESFETs and Junction Field-Effect Transistors (JFETs)

Cryogenic low-noise readout electronics operating at liquid-helium and millikelvin temperatures form the foundational signal-processing backbone for advanced radio astronomy, bolometer interfaces, and space-based instrumentation. While Metal-Semiconductor Field-Effect Transistors (MESFETs) and Junction Field-Effect Transistors (JFETs) are selected for their exceptionally low gate leakage and minimal high-frequency noise, their performance at deep cryogenic temperatures is severely constrained by low-frequency flicker noise and random telegraph signals (RTS). Conventional empirical models—such as the classical Hooge mobility formulation or phenomenological trap-density parameters—fail to predict the anomalous spectral upturns and bias-dependent plateau transitions observed below . Here, we present a first-principles derivation of inter-site fluctuation mechanics applied specifically to cryogenic MESFET channels and JFET gate-junction depletion boundaries. By modeling carrier transport as a stochastic hopping process through a disordered inter-site potential landscape we eliminate heuristic fitting parameters. We derive the exact spectral density governing channel conductance fluctuations, incorporate freeze-out defect relaxation kinetics via non-Hermitian master equations, and establish closed-form expressions for the input-referred voltage noise spectral density in cryogenic single-crystal channels. This framework provides device designers with a robust predictive tool for optimizing ultra-low frequency radio astronomy readout chains and bolometric detector front-ends.