Analytical model of inversion layer quantization effect in heavily doped N-channel MOSFETs

Abstract

MOSFETs are extensively used in Ie fabrications. Improvement of the VLSI technology has resulted in device dimens-ions of the order of fractions of a micron. With increased substrate doping levels and reduced gate oxide thicknesses the classical treatment of MOSFETs is no longer accurate. If the substrate is heavily doped then the inversion layer thickness falls below the classica1 critical width and under that situation the quantization effects cannot be neglected. The effects of quantization can be most accurately modeled by numerically solving Schrodinger's and Poisson's equations self-consistently. But this approach involves much computational time. It is important to develop a computer efficient method that can derive a result that approximates the quantum mechanical calculation resul ts. In this thesis WKB approximate method is used to determine the eigen energy of the inversion layer potential well. The average penetration of the inversion layer charges in the potential well from the semiconductor-insul<;ltor interface is determined using the results of the WKB method. The surface potential at the semiconductor-insulator interface is then related to the threshold voltage by using the calculated_ eigen energy and the average penetration of the inversion layer charges from the semiconductor-insulator interface. The derived relations . , ~. -are used to develop a computer efficient analytical model to study the quantum mechanical effects in various parameters of MOSFETs including threshold voltage. The threshold voltage is found to be larger than the classical value if quantization effects are considered. Also quantization effects are found to become prominent for higher substrate doping levels and thinner gate oxide thicknesses.