On the threshold voltage of metal-oxide-semiconductor field-effect transistors

It is shown that the classical threshold criterion based on critical band-bending leads to an inaccurate estimation of the linearly extrapolated threshold voltage VTe of metal-oxide-semiconductor (MOS) devices. With the use of a properly defined and physically accurate condition for effective surface potential pinning, an approximate but explicit expression is derived for VTe. Good agreement is obtained between the values of VTe calculated using this expression and those extracted from the numerically simulated current-voltage characteristics of long-channel MOS field-effect transistors. Instead of increasing monotonically with the gate dielectric thickness, VTe of an MOS device with a finite substrate doping concentration is found to exhibit a global minimum.