First-Principles Resolution of 1/f Excess Noise and Quantum Bremsstrahlung in Cryogenic HEMT Channels: Inter-Site Potential Landscapes, Non-Equilibrium Quasi-Fermi Convolutions, and Radio Astronomy Receiver Limits

In modern radio astronomy and ultra-sensitive quantum instrumentation, receiver noise temperatures and spectral baseline stability are critically limited by low-frequency excess noise and its upconversion into phase noise in cryogenic Low-Noise Amplifiers (LNAs) and High-Electron-Mobility Transistors (HEMTs). Traditional device engineering has historically relied on empirical Hooge scaling or non-physical single-time-constant trap distributions that fail to predict high-field bias runaway and unshrinkable sub-Kelvin noise plateaus. This work presents a complete first-principles field theory of fluctuation phenomena in cryogenic two-dimensional electron gas (2DEG) channels by reformulating transport across a continuous inter-site electrostatic potential manifold. Key contributions include: First-Principles GDOS Derivation: Applying the Lindeberg–Feller Vector Central Limit Theorem to remote dopant multi-pole fields and heterointerface roughness to yield an emergent Gaussian Density of States (GDOS) with alloy disorder width . Non-Equilibrium Quasi-Fermi Convolutions: Convolving the spatial de-alignment of quasi-Fermi levels under drain-source bias () with the GDOS to derive a closed-form error-function Hooge parameter that accurately captures high-field bias runaway. Quantum Bremsstrahlung Floor: Accounting for non-stationary phase agitation across Morse saddle crossings to establish a regularized soft-phonon quantum bremsstrahlung floor (), explaining the irreducible noise plateau at sub-Kelvin and operating stages. Operando DJS Inversion Toolbox: Providing a fully integrated, open-access MATLAB simulation and bounded trust-region optimization toolbox (forward_hemt_dns, extract_hemt_parameters, and DEMO_HEMT_PIPELINE) for robust parameter extraction and metrology. Value Proposition for Radio Astronomy: Beyond theoretical illumination, transitioning from empirical curve-fitting to a rigorous first-principles noise model carries profound economic value. Given the extraordinary capital expenditures and multi-year integration timelines required for ground-based telescope arrays, design ambiguity introduces severe financial risk. By providing closed-form analytical control over noise baselines, this methodology equips instrument engineers with an exact design framework—eliminating trial-and-error tuning and ensuring that cryogenic LNA front-ends meet optimal performance limits prior to fabrication.