An analytical expression for the threshold voltage of a small geometry MOSFET

A closed form analytical expression for the threshold voltage of a small geometry MOSFET is developed. The threshold voltage expression is derived from a three dimensional geometrical approximation of the bulk charge. The threshold voltage is expressed as a function of gate oxide thickness, channel doping concentraton, junction-depth, backgate bias and channel length and width. The theory is compared with experimental results and the agreement is close.