TABLE OF CONTENTS One of the most important physical parameters of a MOSFET is its threshold voltage V th, defined as the gate voltage at which the device starts to turn on. The accurate modeling of threshold voltage is important to predict correct circuit behavior from a circuit simulator. Since V th has profound effect on circuit operation, it is often used to monitor process variations. Present day MOS process invariably use ion implantation into the channel region, a step often called the threshold adjust implant, that alter the doping profile near the surface of silicon substrate. By changing dose and energy of the threshold implant a desired threshold voltage is achieved. The threshold voltage is by no means a constant quantity but varies with the back bias. With larger back bias, circuits have slower transitions due to decreased drain current and as a result, noise margins decrease.
In this chapter we develop models for the threshold voltage of MOSFETs. First, we will derive the expression for V th for a uniformly doped substrate. We will modify the model for channel implanted devices. The effect of device channel length and width on V th is then modeled from a circuit simulation point of view.
In this section we will develop a basic threshold voltage expression for large and wide MOSFETs, neglecting edge effects due to short channel and narrow widths. Let us consider an n-channel device with a uniformly doped...
