Quantum mechanical effects correction models for inversion charge and current-voltage (I-V) characteristics of the MOSFET device

Analytic 1-D quantum mechanical effects correction formulae for the MOSFET inversion charge and I-V characteristics are derived from the density gradient (DG) model using matched asymptotic expansion techniques. Results for the classical drift-diffusion (DD) equations using asymptotic techniques have been achieved by Please [1], Ward [2] and Markowich [3]. Ward's results were improved in [4] to achieve explicit formulae for MOSFET I-V characteristics, which are accurate over the range of device voltages. Ancona, [6], introduced the DG theory to model quantum effects in electron and hole transport equations. The numerical simulation results of the I-V and the capacitance-voltage (C-V) characteristics using the DG model showed good comparison with data, see [7,8]. This numerical approach has been useful at the device simulation level. However, for circuit analysis applications a simple analytic model is required