174
Compact Models for Integrated Circuit Design
b. Write down the expressions for the inversion carrier density n(0)
and n(L) in terms of the surface potential f ss , bulk potential f B ,
and the appropriate channel potential V ch (y) at the respective
terminal.
c. Assuming that the depth of the inversion layer is given by
X
v K
qN
inv
k T
s i
bss
=
ε
φ
0 2
, show that the subthreshold region drain
current is given by Equation 4.114; where the parameters have
their usual meanings as described in Section 4.4.4.4.
d. Following the procedure in Section 4.4.4.4, show that I ds is given
by Equation 4.118.
e. In the subthreshold region, a MOSFET device includes an oxide
capacitor C ox in series with a depletion capacitor C d and any
change in gate voltage V gs causes corresponding change in f ss ;
consider a voltage divider between C ox and C d , and show that the
ideality factor n is given by Equation 4.121.
f. Show that the final I ds in the subthreshold region is given by
Equation 4.122.