Model for the channel-implanted enhancement-mode IGFET

A simple dc four-terminal "channel-implanted model" is developed for the enhancement-mode IGFET. The model accurately predicts the dependence of transistor threshold voltage and current gain on substrate bias. Modeled and measured threshold voltages are shown to agree to within 25 mV across a 15-V range of V
SB
. Modeled and measured transistor currents agree to within 5 percent across a 10-V range of V
SB
for medium- to long-channel length transistors (
L_{drawn} \ge 2.5
µm). The channel impurity profile is approximated as a constant effective impurity concentration N
AE
extending from the semiconductor surface through the implanted region to an effective implant depth X
DE
("box" profile approximation). At depths greater than X
DE
, the bulk substrate impurity concentration is approximated as a constant, N
A
. The model is composed of two threshold voltage equations, three drain current equations, two saturation voltage equations, and two boundary equations. All first-order model equations and all of their first derivatives are continuous at all boundaries. The model's continuity and its accuracy make it useful for circuit simulation. Extrapolation of channel concentration profile parameters N
AE
, X
DE
, and N
A
from measured threshold voltages yields information on implant profile and on field-implant impurity encroachment into the transistor channel.