Effects of substrate doping on the linearly extrapolated threshold voltage of symmetrical DG MOS devices

With the use of a properly defined physical criterion for surface potential pinning, an approximate but explicit expression is derived for the linearly extrapolated threshold-voltage of fully depleted, symmetrical double-gate metal-oxide-semiconductor (DG MOS) capacitors with intrinsic or doped silicon bodies. Good agreement is obtained between the values of threshold-voltage calculated using this expression and those extracted from the numerically simulated current-voltage characteristics of DG MOS field-effect transistors. Instead of increasing monotonically with the gate oxide thickness, the linearly extrapolated threshold-voltage of a DG MOS device with a doped silicon body is found to exhibit a global minimum. The dependence of this minimum threshold-voltage on body doping concentration is evaluated. It is also verified using numerical simulation that even after considering quantum mechanical confinement and short-channel effects, the nonmonotonic dependence of the linearly extrapolated threshold-voltage on gated oxide thickness for a silicon body with finite doping is qualitatively maintained.