203
Compact Models for Small Geometry MOSFETs
Since the saturation region I ds depends weakly on V ds , we can use Taylor
series expansion of I ds @ V ds  = V dsat and neglect the higher order terms to get
I V V
I V V
dI V V
dV
V V
I
ds
gs
ds
ds
gs
dsat
ds
gs
ds
ds
ds
dsat
,
,
,
(
) = (
) + (
) −
(
)
= d dsat
dsat
ds
gs
ds
ds
ds
dsat
dsat
I
dI V V
dV
V V
I
V
1
1
1
+
(
) −
(
)








=
+
,
d ds
dsat
A
V
V
−






(5.82)
where I dsat and V A are given by
I
I V V
V I
dI
dV
dsat
ds
gs
dsat
A
d sat
ds
ds
= (
)
=






−
,
1
(5.83)
In Equation 5.83, the expression for I dsat is given by Equations 5.76 and 5.77.
In Equation 5.82, V A is called the early voltage (following the original term
0
0.0
0.5
1.0
1.5
2.0
2.5
Triode
CLM
D IBL
S CBE
3.0
1
2
V ds (V)
R
out (KΩ)
I
ds (mA)
3
4
0
2
4
6
8
10
12
14
FIGURE 5.13
MOSFET output characteristics: drain current, I ds , and output resistance, R out , of an nMOSFET device divided into different operating regions based on different physical mechanisms.
(Reproduced with permission from J.H. Huang et al., International Electron Devices Meeting 1992,
Technical Digest, pp. 569–572, IEEE, 1992. Copyright 1992 IEEE.)