Overview

We give below some expressions often used in MOS transistor models. The symbols used but not defined below are explained in Sec. 3.2. The device type is assumed to be nMOS. Further information and numerous references can be found elsewhere [ ^[1]].

V _T0 and ? ₀ for Unimplanted Devices

A common approximation is

where V _FB is the flat-band voltage, given by

with ? _MS being the potential corresponding to the gate-body work function difference, Q' ₀ the effective semiconductor-insulator interface charge, and

where ? _F is the body's Fermi potential, given by

with n _i the intrinsic carrier concentration (1.45 10 ¹⁰ cm ^?3 at room temperature).

These results are not valid for implanted devices. A "quick fix" often used for such devices, consisting of adding the implant charge per unit area to Q' _o in Eq. (A.2), does not work if the implant is not extremely shallow. The effective value of ( ? _O for implanted devices can be smaller or larger than 2 ? _F, depending on implantation details.

Built-in Potential for n ⁺p or p ⁺n Junctions

where V _Gap is the potential corresponding to the energy gap (1.12 V for silicon at room temperature) and ? _F is given by Eq. (A.4), with N _B being the doping concentration of the lightly doped side.

Zero-Bias Capacitance per Unit...