157
Large Geometry MOSFET Compact Models
dash curve. Then substituting for V ds = V dsat from Equation 4.80 in Equation 4.72,
we get the drain current I dsat at the pinch-off point as
I
V V
V V
V V
dsat
gs
th
ds
dsat
gs
th
=
−
(
)
=
=
−
β
2
2 ; at
(4.81)
Thus, the simplified compact model requires two separate expressions for
I ds given by Equations 4.72 and 4.81 to model the MOSFET device characteristics in strong inversion region in contrast to Pao-Sah and Brews models
described earlier.
Saturation Region Operation: Thus, we find that for a given V gs , as V ds
increases the channel charge Q i decreases near the drain end, and when
V ds = V dsat = (V gs − V th ), the channel is pinched off. For V ds > V dsat , the pinchedoff region moves away from the drain end of the channel, widening the drain
depletion region as shown in Figure 4.11c. Thus, as V ds increases beyond
pinch-off, the pinched-off region l d between the channel pinch-off point
P and the n+ drain region causes the effective channel length to decrease
from L to (L − l d ). Since the channel can support only V dsat , any voltage greater
than V dsat is absorbed by the l d region of the channel. Clearly, l d is bias-dependent parameter, modulating the effective channel length (L eff = L − l d ). This
phenomenon is called the channel length modulation (CLM). For long channel
devices with L >> l d , the drain current I ds remains approximately constant at
I dsat for any V ds > V dsat . Thus, to a first order, for V ds beyond the pinch-off value,
the current I ds = I dsat and is given by Equation 4.81 and is repeated below:
I
V V
V V
dsat
gs
th
ds
dsat
=
−
(
)
>
β
2
2 ;
(4.82)
The region of operation of the MOSFETs beyond pinch-off (V ds > V dsat ) is
referred to as the saturation region because I ds ideally does not increase in
this region. And, the region below V dsat is called the linear region or triode
region. Note that Equation 4.82 predicts that I ds in saturation varies as the
square of the effective gate voltage and hence often referred to as the square
law model of the MOSFETs. Equations 4.72, 4.80, and 4.82 when plotted
together result the output characteristics of a MOSFET device as shown by
the continuous lines in Figure 4.12.
Figure 4.12 shows that the calculated value of I ds by Equation 4.82 saturates
beyond V dsat . This is because Equation 4.82 is based on the assumption that
the current is independent of V ds . In reality, I ds depends on V ds > V dsat due
to CLM due to the change in the effective channel length L eff = L − l d . Then
using L eff for L in Equation 4.82, we get
I
C
W
L l
V V
V V
ds
s ox
d
gs
th
ds
dsat
=
−
(
)
−
(
)
>
µ
2
2 ;
(4.83)
Equation 4.83 shows that as l d increases with the increasing V ds > V dsat , the
drain current increases. We can express Equation 4.83 as
Large Geometry MOSFET Compact Models
dash curve. Then substituting for V ds = V dsat from Equation 4.80 in Equation 4.72,
we get the drain current I dsat at the pinch-off point as
I
V V
V V
V V
dsat
gs
th
ds
dsat
gs
th
=
−
(
)
=
=
−
β
2
2 ; at
(4.81)
Thus, the simplified compact model requires two separate expressions for
I ds given by Equations 4.72 and 4.81 to model the MOSFET device characteristics in strong inversion region in contrast to Pao-Sah and Brews models
described earlier.
Saturation Region Operation: Thus, we find that for a given V gs , as V ds
increases the channel charge Q i decreases near the drain end, and when
V ds = V dsat = (V gs − V th ), the channel is pinched off. For V ds > V dsat , the pinchedoff region moves away from the drain end of the channel, widening the drain
depletion region as shown in Figure 4.11c. Thus, as V ds increases beyond
pinch-off, the pinched-off region l d between the channel pinch-off point
P and the n+ drain region causes the effective channel length to decrease
from L to (L − l d ). Since the channel can support only V dsat , any voltage greater
than V dsat is absorbed by the l d region of the channel. Clearly, l d is bias-dependent parameter, modulating the effective channel length (L eff = L − l d ). This
phenomenon is called the channel length modulation (CLM). For long channel
devices with L >> l d , the drain current I ds remains approximately constant at
I dsat for any V ds > V dsat . Thus, to a first order, for V ds beyond the pinch-off value,
the current I ds = I dsat and is given by Equation 4.81 and is repeated below:
I
V V
V V
dsat
gs
th
ds
dsat
=
−
(
)
>
β
2
2 ;
(4.82)
The region of operation of the MOSFETs beyond pinch-off (V ds > V dsat ) is
referred to as the saturation region because I ds ideally does not increase in
this region. And, the region below V dsat is called the linear region or triode
region. Note that Equation 4.82 predicts that I ds in saturation varies as the
square of the effective gate voltage and hence often referred to as the square
law model of the MOSFETs. Equations 4.72, 4.80, and 4.82 when plotted
together result the output characteristics of a MOSFET device as shown by
the continuous lines in Figure 4.12.
Figure 4.12 shows that the calculated value of I ds by Equation 4.82 saturates
beyond V dsat . This is because Equation 4.82 is based on the assumption that
the current is independent of V ds . In reality, I ds depends on V ds > V dsat due
to CLM due to the change in the effective channel length L eff = L − l d . Then
using L eff for L in Equation 4.82, we get
I
C
W
L l
V V
V V
ds
s ox
d
gs
th
ds
dsat
=
−
(
)
−
(
)
>
µ
2
2 ;
(4.83)
Equation 4.83 shows that as l d increases with the increasing V ds > V dsat , the
drain current increases. We can express Equation 4.83 as