Extraction of MOSFET carrier mobility characteristics and calibration of a mobility model for numerical device simulation

Abstract

Results of an investigation on the methodology for calibrating parameters of the carrier mobility model in a 2-D numerical device simulator are presented. The effective channel mobility and gate field, μ eff and E eff, in the inversion charge layer determined from terminal drain currents using a commonly adopted extraction method are compared with values obtained directly from distributions of carriers and electric field given by numerical device simulation. The results have shown excellent agreement in the inversion and depletion charge densities, μ eff and E eff. It is also found that the gate field given by the commonly used expression E eff = ( Q inv 2+Q b ) ϵ si , where Q inv is the inversion charge density, Q b is the bulk depletion charge density and ϵ si is the dielectric constant of silicon, should be interpreted as the effective gate field, and not the average field in the inversion layer as has been previously suggested. The effect of nonlinear distributions of charge carriers and electric field in the inversion layer on E eff is implicitly included in this simple expression. It is also shown that parameters for a local-field mobility model should not be obtained through a direct fit of the mobility model to the μ eff vs E eff relation extracted from measured I DS. Instead, an optimization of the fit between the simulated and measured I DS should be used. This is due to the non-uniform distribution of both charge carriers and electric field in the inversion charge layer. The feasibility of predictive device simulation is also demonstrated by the universality of the μ eff vs E eff extracted from simulated I DS of transistors with different T ox and N s. The “charge sheet” approach in modeling carrier mobility for numerical device simulation is also briefly discussed.