Drain-voltage effects on the threshold voltage of a small-geometry MOSFET

Closed form analytical expressions are developed to predict the threshold voltage of a small geometry MOSFET with a nonzero drain voltage. Two expressions are developed. The first expression is for an abrupt oxide transition from the thin gate to thick field oxide with uniform doping and the second expression includes the effects of a tapered recessed field oxide, and field doping encroachment at the channel edges. The theory is compared with experimental results obtained from n-channel small geometry MOSFETs.