Study of inversion layer quantum capacitance of MOS structures

Abstract

MOSFETs are extensively used in Ie fabrication. Improvement of the~ VLSI technology has resulted in device dimensions of the order of fractions of a micron. In MOSFETs with increased substrate doping levels and reduced gate oxide thicknesses the energy-band bending at the Si/SiOZ interface, under inversion condition, is very steep. Quantum effects arise when the confinement of inversion layer carriers in this potential well yields ~nincreasingly two-dimensional carrier system and the classical treatment of MOSFETs is no longer accurate. The effects o.f quantization can be most accurately modeled by solving the Schrodinger's and Poisson I s equations. self-consistently. The quantum mechanical calculation is very time. consuming and therefore it is necessary to develop a simple model which includes the quantization effects and requires less computational time. In this thesis the eigen energies of the potential well are determined by solving Schrodinger's wave equation for a triangular potential well by Airy function approximations. To find an analytical expression for quantum capacitance, the electron population in two sub-bands are considered. The capacitance calculated considering quantum effects is found to .deviate from the classical value.