173
Large Geometry MOSFET Compact Models
4.8 Consider an MOS transistor on a uniformly doped p-type silicon
substrate with doping concentration N a = ×
−
1 10
16
3
cm at room temperature and W = L = 10 μm. Assume V fb = 0, T ox = 20 nm; threshold
voltage, V th = 0.7 V, electron mobility = 600 cm 2 V –1 sec −1 ; λ = 0.01 V −1
a. Calculate and plot I ds versus V ds for 0.0 ≤ V ds ≤ 5.0 V with V gs = 2,
3, 4 and 5 V on the same plot using following equations at different limits of V gs shown:
i. I
V V
V
V
V
V
V
V V
ds
gs
th
ds
ds
gs
th
ds
gs
th
=
−
− (
)
(
)
>
≤
−
β
2
; for
a nd
ii. I
V V
V
V
V
V V
ds
gs
th
gs
th
ds
gs
th
= ( ) −
(
)
(
)
>
≥
β 2
2 ; for
and
_
iii. I
V V
V
V
V
V
V V
ds
gs
th
ds
gs
th
ds
gs
th
= ( ) −
(
) +
(
)
>
≥ (
)
β
λ
2
1
2
; for
and
−
iv. Superimpose I dsat versus V dsat on the same plot;
where β µ
=
( )
s ox
C W L ; clearly, label different operating regimes all
different operating regions of MOSFETs and explain
4.9 Measured device data for a silicon nMOSFET are shown in Table E4.1
Considering the bulk-charge effect (α) in drain current I ds calculate:
a. V th0
b. λ
c. γ
d. β
using regional drain current model
4.10 In Section 4.4.4.4, the subthreshold region drain current is modeled
using inversion charge at the source and drain ends. In this exercise,
formulate the subthreshold region drain current (I ds ) model using
the inversion carrier density at the source end n(0) and drain end
n(L). Clearly state any assumptions you make.
a. Write an expression for the subthreshold region I ds from Fick’s
first law of diffusion; assume that the concentration gradient of
inversion carriers dn dy
/
(
) is constant along the channel to maintain a constant current flow through the device.
TABLE E4.1
Measurement Data to Extract the Basic
nMOSFET Device Model Parameters
V gs (V)
V ds (V)
V bs (V)
I ds (mA)
2
5
0
40
5
5
0
536
5
5
−5
360
5
8
0
644
5
5
−3
420
Large Geometry MOSFET Compact Models
4.8 Consider an MOS transistor on a uniformly doped p-type silicon
substrate with doping concentration N a = ×
−
1 10
16
3
cm at room temperature and W = L = 10 μm. Assume V fb = 0, T ox = 20 nm; threshold
voltage, V th = 0.7 V, electron mobility = 600 cm 2 V –1 sec −1 ; λ = 0.01 V −1
a. Calculate and plot I ds versus V ds for 0.0 ≤ V ds ≤ 5.0 V with V gs = 2,
3, 4 and 5 V on the same plot using following equations at different limits of V gs shown:
i. I
V V
V
V
V
V
V
V V
ds
gs
th
ds
ds
gs
th
ds
gs
th
=
−
− (
)
(
)
>
≤
−
β
2
; for
a nd
ii. I
V V
V
V
V
V V
ds
gs
th
gs
th
ds
gs
th
= ( ) −
(
)
(
)
>
≥
β 2
2 ; for
and
_
iii. I
V V
V
V
V
V
V V
ds
gs
th
ds
gs
th
ds
gs
th
= ( ) −
(
) +
(
)
>
≥ (
)
β
λ
2
1
2
; for
and
−
iv. Superimpose I dsat versus V dsat on the same plot;
where β µ
=
( )
s ox
C W L ; clearly, label different operating regimes all
different operating regions of MOSFETs and explain
4.9 Measured device data for a silicon nMOSFET are shown in Table E4.1
Considering the bulk-charge effect (α) in drain current I ds calculate:
a. V th0
b. λ
c. γ
d. β
using regional drain current model
4.10 In Section 4.4.4.4, the subthreshold region drain current is modeled
using inversion charge at the source and drain ends. In this exercise,
formulate the subthreshold region drain current (I ds ) model using
the inversion carrier density at the source end n(0) and drain end
n(L). Clearly state any assumptions you make.
a. Write an expression for the subthreshold region I ds from Fick’s
first law of diffusion; assume that the concentration gradient of
inversion carriers dn dy
/
(
) is constant along the channel to maintain a constant current flow through the device.
TABLE E4.1
Measurement Data to Extract the Basic
nMOSFET Device Model Parameters
V gs (V)
V ds (V)
V bs (V)
I ds (mA)
2
5
0
40
5
5
0
536
5
5
−5
360
5
8
0
644
5
5
−3
420