34
Compact Models for Integrated Circuit Design
concentrations plots are shown in Figure 2.6 for uniformly doped silicon at
300° K. The plot for n-type is lower than p-type doped silicon because electron mobility is higher than the hole mobility.
2.2.5.3 Sheet Resistance
The resistance of a uniform conductor of length L, width W, and thickness t
is given by
R
L
tW
= ρ
(2.35)
where:
ρ is the resistivity of the conductor in ohm-centimeter
Typically, in an IC technology, the thickness t of a diffusion region is uniform and normally much less than both L and W of the region. Therefore, it
is useful to define a new variable ρ sh , called the sheet resistance, which has the
dimension of Ohm (Ω) and is given by
ρ
ρ
sh
t
=
(2.36)
Then Equation 2.35 becomes
R
L
W
sh
= ρ
(2.37)
10
12
10
13
10
14
10
15
10
16
10
17
Impurity concentration (cm
−3 )
10
18
10
19
10
20
10
21
10
−4
10
−3
10
−2
10
−1
10
0
10 1
10
2
10
3
10
4
Silicon
300° K
Resistivity (Ohm-cm)
p-Type (boron)
n-Type
(phosphorus)
FIGURE 2.6
Impurity concentration versus resistivity for n-type and p-type silicon at 300° K. (After Sze 2007.)