139
Large Geometry MOSFET Compact Models
geometry device so that the short channel and narrow width effects can be
neglected. We will develop a generalized large geometry MOSFET drain
current model using several simplifying assumptions.
4.4.1 Drain Current Formulation
In general, the static and dynamic characteristics of a semiconductor device
under the influence of external fields can be described by the following three
sets of coupled differential equations
1. The Poisson’s equation for electrostatic potential ϕ is described in
Equation 4.2 and is given by
∇ = −
2
0
φ
ρ
ε
K si
(4.15)
where:
ρ is the charge density
K si is the dielectric constant of silicon
ε 0 is the permittivity of free space
2. The current density equations for electron current density (J n ) and
hole current density (J p ),
J q nE qD n
J q pE qD p
n
n
n
p
p
p
=
+
∇
=
−
∇
µ
µ
(electrons)
(holes)
(4.16)
Equation 4.16 under nonequilibrium condition is represented by
J
qn
J
qp
n
n
n
p
p
p
= −
∇
= −
∇
µ φ
µ φ
(electrons)
(holes)
(4.17)
Depletion
region
V bs
p-Substrate, N b
Inversion
layer
x
y
z
W
V ds
V gs
T ox
V s
X j
n+
n+
Gate
Oxide
Q i (y)
Q b (y)
dy
L
FIGURE 4.6
Schematic of an nMOSFET device showing different biases and reference direction; x, y, and z
distance into the silicon, along the channel, and along the channel width of the device, respectively.