EE143
N. Cheung
Ion Implantation Profile and Range Data
In EE143, we use a gaussian function to approximate the ion implantation concentration depth
profile:
C(x) =
2
R
p
exp [
 (x R
p
)
2
2
R
p
2
]
where
is the implantation dose ( in # /
cm
2
),
R
p
is the projected range and
R
p
is the longitudinal straggle.
This gaussian approximation is reasonably good for sheet resistance calculations because the integral
quantity R
s
(
1
q
) is less sensitive to details of the distribution. However, the gaussian function has too
rapid a decay with distances from
R
p
and can lead to smaller calculated junction depths
x
j
.
The rationales to choose the gaussian approximation are: (1) only two parameters (
R
p
and
R
p
)
are used to describe the shape of the depth profile; (2) the gaussian function is a natural solution of the
diffusion equation, which we have to deal with when further annealing steps are encountered after
implantation. A better approximation for the implantation profile is the PearsonIV distribution which
requires the first four spatial moments of the distribution but such calculations will require numerical
procedures [see more advanced texts such as Plummer et al].
Projected Range
R
p
and Longitudinal Straggle
R
p
for common dopants used in IC technology, B,
P and As implanted into Si are shown in the following graphs (solid lines). The ranges (in
ﾅ
) are also fitted
to a polynomial (dashed lines) of the form:
a0+a1*E+a2*E
2
+a3*E
3
+a4*E
4
with E in keV
10
100
1000
100
1000
10000
R
p
=185.34201 +6.5308 E 0.01745 E
2
+2.098e5 E
3
8.884e9 E
4
R
p
=51.051+32.60883 E 0.03837 E
2
+3.758e5 E
3
1.433e8 E
4
R
p
R
p
B
11
into Si
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 Spring '04
 ee142

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