159
Large Geometry MOSFET Compact Models
We notice from Equation 4.86 that when V ds = −1/λ, I ds = 0. This means that
when I ds is extrapolated backward from the saturation region, it will intersect the V ds axis at a value of −1/λ as shown in Figure 4.13. However, this
is an ideal case and generally the value of λ is obtained by curve fitting
the measurement data to Equation 4.86 to minimize the error between the
measured data and model.
Equation 4.86 is a first-order approximation for modeling CLM effect in
MOSFETs. It provides the basic feature of nonzero slope for the saturated
drain current as shown in Figure 4.13. However, the use of Equation 4.86
for calculating I ds in the saturation region results in a discontinuity of the
current at V ds = V dsat . The SPICE model Level 1 corrects for the discontinuity
by multiplying the linear region current by the factor (1 + λV ds ). Other methods include use of mathematical smoothing functions to make the liner and
saturation curve at the transition point at V ds = V dsat .
To summarize, we have developed a first-order MOSFET model, which can
be described by the following expressions
I
V V
ds
gs
th
=
−
(
) <
;
0
0
β V V V
V V
V V
V
V V
V
gs
th
ds
ds
gs
th
ds
gs
th
ds
−
−
<
−
(
) ≥
−
(
) +
(
1
2
0
2
1
2
;
β
λ ) )
<
−
(
) ≤
; 0 V V
V
gs
th
ds
(4.87)
In Equation 4.87, β depends on κ [Equation 4.73], W, L, and C ox [Equation 4.74]
whereas, V th depends on V th0 , 2f B , and γ [Equation 4.14]. Since C ox depends on
T ox , the parameter set of SPICE Level 1 model is {V th0 , κ, γ, λ, 2f B }.
1/λ
0
Increasing V gs
V ds
V gs1
V gs2
V gs3
V gs4
I ds
FIGURE 4.13
A typical I ds − V ds characteristics of an nMOSFET device showing the effect of channel length
modulation and CLM factor, λ.
Large Geometry MOSFET Compact Models
We notice from Equation 4.86 that when V ds = −1/λ, I ds = 0. This means that
when I ds is extrapolated backward from the saturation region, it will intersect the V ds axis at a value of −1/λ as shown in Figure 4.13. However, this
is an ideal case and generally the value of λ is obtained by curve fitting
the measurement data to Equation 4.86 to minimize the error between the
measured data and model.
Equation 4.86 is a first-order approximation for modeling CLM effect in
MOSFETs. It provides the basic feature of nonzero slope for the saturated
drain current as shown in Figure 4.13. However, the use of Equation 4.86
for calculating I ds in the saturation region results in a discontinuity of the
current at V ds = V dsat . The SPICE model Level 1 corrects for the discontinuity
by multiplying the linear region current by the factor (1 + λV ds ). Other methods include use of mathematical smoothing functions to make the liner and
saturation curve at the transition point at V ds = V dsat .
To summarize, we have developed a first-order MOSFET model, which can
be described by the following expressions
I
V V
ds
gs
th
=
−
(
) <
;
0
0
β V V V
V V
V V
V
V V
V
gs
th
ds
ds
gs
th
ds
gs
th
ds
−
−
<
−
(
) ≥
−
(
) +
(
1
2
0
2
1
2
;
β
λ ) )
<
−
(
) ≤
; 0 V V
V
gs
th
ds
(4.87)
In Equation 4.87, β depends on κ [Equation 4.73], W, L, and C ox [Equation 4.74]
whereas, V th depends on V th0 , 2f B , and γ [Equation 4.14]. Since C ox depends on
T ox , the parameter set of SPICE Level 1 model is {V th0 , κ, γ, λ, 2f B }.
1/λ
0
Increasing V gs
V ds
V gs1
V gs2
V gs3
V gs4
I ds
FIGURE 4.13
A typical I ds − V ds characteristics of an nMOSFET device showing the effect of channel length
modulation and CLM factor, λ.