Abstract
The operation of metal-oxide-semiconductor-field-effect transistors (MOSFETs) cannot be conceived without the prior formation of inversion layers. Charge, potential, and current distributions in this layer are important quantities for all types of MOSFET configurations. The mathematical difficulty to solve analytically the nonlinear Poisson equation in Kingston-Neustadter (KN) model, where the charge density includes electrons and holes, led to Hauser and Littlejohn (HL) to consider a simplified but solvable model, of only electrons or only holes, and to numerous HL-like compact analytical models. Recently, a new and simple method that overcomes the mathematical difficulty to solve the nonlinear Poisson equation in the inversion layer of a MOS has been introduced, and the more accurate Kingston-Neustadter model was successfully solved. We summarize here the new method and given the analytical solutions for the KN and HL models, we compare the potential and charge distribution predictions and show that they may differ by orders of magnitude. We also briefly outline the analytical results for the inversion layer width, the effective ionized atoms concentration, and the drift-diffusion currents in single and double gate junctionless (JL) MOSFETs. Specific calculations of these quantities, as functions of impurity concentration, gate potential, and oxide layer width, will be shown and compared with the predictions of the most exemplary simplified model, the Hauser-Littlejohn model.