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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 ee142

Click to edit the document details