Modeling the MOSFET’s Inversion Layer and its Universal Mobility: A New Experimental Method1

Abstract

<div>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 µ<sub>eff</sub> varies as ~(E*<sub>T</sub>)<sup>-1/3 </sup>for transversal fields E<sub>T</sub>*= <b>-</b>(1/ε<sub>si</sub>)<b>·</b>[ɳQ<sub>i</sub> + Q<sub>b</sub>] <b>≤ </b>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 θ<sub>T</sub> quantifying µ<sub>eff</sub>’s modulation by E*<sub>T</sub> varies as ~(E*<sub>T</sub>)<sup>-5/3</sup> under laminar flow conditions, thereby further corroborating the foregoing effects and interpretations thereof.</div>