Physical Origins of Universal Mobility in MOSFET Inversion Layers: Conservation Laws

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, μ_eff , 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.