We formulate a simple, yet accurate, model for a non-uniform mobile charge density ρ(z) giving rise to a mean potential Ψ* across an inversion layer of finite extent, which we measure by means of a novel, sensitive, experimental method involving nulls of harmonic distortion components (D2 ≈ D3 ≈ 0) of the drain current under sinusoidal excitation below saturation. We thus establish analytically and experimentally, that the low-field, “universal” effective mobility µeff varies as ~(E*T)-1/3 for transversal fields ET*= -(1/εsi)·[ɳQi + Qb] ≤ 0.5 MV/cm, wherein ɳ varies continuously between 1/2 and 1/3. We also establish and observe that the higher order, derivative, parameter θT quantifying µeff’s modulation by E*T varies as ~(E*T)-5/3 under laminar flow conditions, thereby further corroborating the foregoing effects and interpretations thereof.

The salient properties of charge flow (or current) along the MOSFET’s inversion layer are shown to be consilient with a river’s flow in a gravitational potential field, insofar as both are fundamentally governed by energy conservation principles, and their laminar and turbulent conditions determined by friction losses at shallow depths. We establish analytically that the low-field, “universal” effective mobility, μeff , long reported to vary as ~(E*T)-1/3 for transversal fields below 0.5 MV/cm, is manifestation and consequence of both energy and momentum conservation under laminar flow conditions and quantum mechanical effects, in which case the inversion layer’s mean thickness also varies as ~(E*T)-1/3 up to a maximum value E*T ≈ 0.35 MV/cm at 300K, determined only by interface “terrain” amplitude and fundamental constants.

The salient properties of charge flow (or current) along the MOSFET’s inversion layer are shown to be analogous to a river’s flow in a gravitational potential field, insofar as both are fundamentally governed by energy conservation principles, and their laminar and turbulent conditions determined by friction losses at shallow depths. We formulate an accurate model for a non–uniform mobile charge density giving rise to a mean potential across an inversion layer of finite extent, which we measure by a sensitive experimental method …