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.
