Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1999-05-12
2004-01-27
Thomson, William (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S006000, C703S013000, C703S012000
Reexamination Certificate
active
06684181
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an ion implantation simulation method, and especially relates to an ion implantation simulation method for determining by simulation the impurity distribution and point defect distribution when carrying out ion implantation for a multilayer substrate used in the production of semiconductors.
2. Background Art
In semiconductor device manufacturing processes, ion implantation is widely used to form impurity regions in semiconductor substrates. In order to suitably carry out such ion implantation, there is a need to know in advance how the concentration of ions in the substrate will be distributed, in other words, to ascertain what the impurity distribution will be, and what the distribution of point defects in the substrate will be, and for this purpose, ion implantation simulations are carried out to determine, by means of the simulation, the impurity distribution and the point defect distribution.
The conventional ion implantation simulation method for determining the impurity distribution and point defect distribution in a multilayer substrate shown in
FIG. 2
is carried out as follows. In
FIG. 2
, in a multilayer substrate composed of layers from the first to the k-th layers, k=1 is set and Q
1
is set as the dose implanted into the first layer, next it is judged whether k>(the number of layers), and if k>(the number of layers), the procedure is stopped, and if k≦(the number of layers), a Gaussian distribution, a combined Gaussian distribution, a Pearson distribution, a dual Pearson distribution or the like is used to determine the normalized impurity distribution I
k
(x) in the material of the k-th layer. If the impurity distribution I
k
(x) is obtained using a Gaussian distribution, the impurity distribution I
k
(x) is expressed by the following equation.
I
k
(
x
)
=
C
k
2
π
σ
k
exp
[
-
(
x
-
Rp
k
)
2
2
σ
k
2
]
Eq
.
(
1
)
In Eq. (1), Rp
k
is the range of ions defined for the material of the k-th layer for obtaining the impurity distribution, &sgr;
k
is a moment defined for the material of the k-th layer used for obtaining the impurity distribution, and x represents the coordinate in the depthwise direction. Further, C
k
is determined so as to satisfy the following equations, when XS
k
is the transformed surface coordinate of a layer for which the material is converted into that of the k-th layer of the device,
∫
x
k
∞
I
k
(
x
-
xs
)
ⅆ
x
=
1
Eq
.
(
2
)
xs
k
=
x
i
+
∑
i
=
1
k
-
1
(
1
-
Rp
k
Rp
i
)
di
Eq
.
(
3
)
where, in Eq. 3, d
i
is the width (layer thickness) of the i-th layer, and d
i
=x
i+1
−x
i
. Then, the impurity distribution in the k-th layer f
k
(x) is determined by the following equation.
f
k
(
x
)
=
Q
k
I
k
(
x
-
xs
k
)
Eq
.
(
4
)
Next, the point defect distribution is determined. The point defect distribution can be determined by the following equation, which corresponds to the Eq. (35) of Japanese Unexamined Patent Application, First Publication No. Hei 9-45630, previously proposed by the inventor of the present invention.
f
dk
(
x
)
=
F
k
Q
k
J
dk
(
x
-
(
∑
i
=
1
k
-
1
d
i
[
1
-
Rp
k
Rp
i
]
)
-
(
-
Rp
k
+
Rp
dk
)
)
Eq
.
(
5
)
Here, in Eq. (5), f
dk
(x) is the point defect distribution in the k-th layer, F
k
is (the total amount of point defects)/(the total amount of impurities), Q
k
is, as mentioned above, the dose of impurities in the k-th layer, J
dk
(x) is the normalized point defect distribution calculated from the moments Rp
k
, &sgr;
dk
, &ggr;
dk
, and &bgr;
dk
; and &sgr;
dk
, &ggr;
dk
, &bgr;
dk
are moments defined for the material of the k-th layer used for obtaining the point defect distribution, respectively representing the standard deviation, distortion and sharpness. Further, Rp
dk
is a range defined for the material of the k-th layer used for obtaining the point defect distribution.
The normalized point defect distribution J
dk
used in Eq. (5) is defined as being calculated from the moments Rp
k
, &sgr;
dk
, &ggr;
dk
, and &bgr;
dk
, but this definition is unnatural because these moments are a mixture of moments in terms of the impurity distribution and moments in terms of the point defect distribution, therefore a new function referred to as I
dk
will be explained, in which the definition of the normalized point defect distribution is calculated from Rp
dk
, &sgr;
dk
, &ggr;
dk
, and &bgr;
dk
. In this way, the relationship between J
dk
(x) and I
dk
(x) is
I
dk
(
x
)
=
J
dk
(
x
+
Rp
k
-
Rp
dk
)
Eq
.
(
6
)
and Eq. (5) can be rewritten as follows.
f
dk
(
x
)
=
F
k
Q
k
I
dk
(
x
-
(
∑
i
=
1
k
-
1
d
i
[
1
-
Rp
k
Rp
i
]
)
)
Eq
.
(
7
)
Here, by analogy to the impurity distribution f
k
(x) which is
∫
xk
∞
f
k
(
x
)
ⅆ
x
=
Q
k
Eq
.
(
8
)
the point defect distribution f
dk
(x) is defined by the following equation.
∫
xk
∞
f
dk
(
x
)
ⅆ
x
=
F
k
Q
k
Eq
.
(
9
)
As a result, the normalized point defect distribution I
dk
is obtained by the following equation.
∫
xk
∞
I
dk
(
x
-
(
∑
i
=
1
k
-
1
d
i
[
1
-
Rp
k
Rp
i
]
)
)
ⅆ
x
=
1
Eq
.
(
10
)
As a result, the point defect distribution in, for example, the second layer can be obtained by eliminating Q
k
using both Eqs. (8) and (9), and by setting k=2, as follows.
∫
x2
∞
f
d2
(
x
)
ⅆ
x
=
F
2
∫
x2
∞
f
2
(
x
)
ⅆ
x
Eq
.
(
11
)
This ion implantation simulation method, proposed by the present inventor, is an analytical simulation method which is carried out using analytical equations such as Gaussian distributions, combined Gaussian distributions, and Pearson distributions.
On the other hand, the Monte Carlo ion implantation simulation method is also disclosed in the literature (Masami Hane and Masao Fukuma, “Ion Implantation Model Considering Crystal Structure Effects”, IEDM (1988)) as a method of ion implantation simulation. In the Monte Carlo ion implantation simulation method, as ions are implanted into the semiconductor substrate and the implanted ions advance, they are subjected to scattering by atomic nuclei, and to energy loss, and they are further subjected to energy loss by scattering by electrons present around the nuclei. Such a process is simulated for one particle at a time, and it is possible to obtain the impurity distribution after ion implantation by calculating the distribution of particles finally remaining in the semiconductor substrate.
Further, it is possible to calculate the distribution of point defects such as vacancies or interstitial atoms in a crystal after ion implantation by simulating the process by which ions expel electrons which constitute the crystal lattice.
In the Monte Carlo ion implantation simulation method, a simulation of the scattering process is made for each implanted ion, one at a time, and therefore, there is the problem that it takes a long time to obtain the results of the simulation. The present inventor disclosed an ion implantation simulation method in Japanese Unexamined Patent Application, First Publication No. Hei 9-45630, which makes it possible to obtain, in a short time, simulation results of the impurity distribution and point defect distribution by the above-mentioned analytical ion implantation simulati
NEC Electronics Corporation
Scully Scott Murphy & Presser
Thomson William
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