185
Compact Models for Small Geometry MOSFETs
where N CH and N SD are the effective channel and S/D doping concentrations,
respectively, and l t represents the characteristic length given by
l
K T W
K
t
si ox d
ox
=
η
(5.23)
With depletion width W
K
V qN
d
s i
s
bs
CH
=
−
(
)
2
0
ε φ
and η (ETA) is a fitting
parameter so that W d /η = average width of the depletion region along the
length of the channel.
Equation 5.20 shows that ΔV th depends linearly on V ds showing that V th
decreases as V ds increases due to DIBL. In order to improve modeling flexibility for different technologies, different model parameters are introduced
to get
θ th
eff t
L l
(
)
.
cosh
.
SCE
DVT
DVT
=
(
) −
0 5
0
1
1
(5.24)
∆V
V
th
th
bi
s
(
)
(
)
SCE
S CE
= −
−
(
)
θ
φ
(5.25)
l
K T W
K
V
t
si ox d
ox
bs
=
+
(
)
1
2
DVT .
(5.26)
Similarly, the shift in threshold voltage due to DIBL is described by
θ th
eff t
L l
(
)
.
cosh
.
DIBL
DSUB
=
(
) −
0 5
1
0
(5.27)
V s
V g
V g
Gate
Electron barrier height reduction in the
conduction band (CB) at the edge of source
Gate
Depletion
CB
p-Substrate
n + Source
n + Source
n + Drain
n + Drain
Depletion
p-Substrate
n + Source
n + Drain
V d
V d
V d
V s
(a)
(b)
(c)
FIGURE 5.6
Short channel effect in MOSFETs due to drain voltage V ds –DIBL in an n-channel device:
(a) V gs  = 0 and V ds  = 0, (b) V gs  = 0 and V ds  = supply voltage, V dd , and (c) plot of conduction bands
along the length of the device under zero bias (top curve) and at drain bias conditions (bottom
curve).