Data processing: structural design – modeling – simulation – and em – Simulating nonelectrical device or system
Reexamination Certificate
1997-10-20
2003-02-18
Jones, Hugh M. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Simulating nonelectrical device or system
C703S003000, C703S004000
Reexamination Certificate
active
06522997
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of simulation and particularly relates to the method of simulating a target in a sputtering arrangement and also to the method of simulating a track of a sputtered particle in the arrangement.
2. Description of the Related Art
In the field of semiconductor integrated circuits, there has been a growing trend toward the design of high-density integrated circuits, as the technology of integrating electronic circuits progresses. This trend has brought about an urgent requirement to develop a technique for growing a semiconductor thin film in a finely formed contact hole of a highly integrated IC.
Optimization of a sputtering arrangement is imperative in order to meet the above requirement. Since the actual construction of and experimentation with the arrangement of the sputtering apparatus are problematic from the viewpoint of cost and development time, the optimization has been attempted by means of simulation.
In connection with the design of the sputtering arrangement, it has been required to improve the direction-dependent distribution characteristic of the particles ejected from the target, as well as to improve the shapes of components of the arrangement, such as a collimator. These improvements have been desired more anxiously, particularly as a high aspect ratio of a circuit element is required for fine-structuring of an IC. Hereinafter, the direction-dependent distribution of the particles ejected from the target is referred to as an angular distribution.
There have been presented methods of simulating the angular distribution using a method of the molecular dynamics (MD). Yamada H., the present inventor, has invented such a simulation method of sputtering, which method was disclosed in Japanese Patent Application. No. 55682/96 (filed by the present applicant) filed before the present application. Since the simulation method is relevant to the present invention, it will be referred to, hereinafter, as Yamada's former method.
FIG. 1
is a flow chart to illustrate Yamada's former method.
Referring to
FIG. 1
, the method includes steps P
1
, P
2
and S
5
. In step P
1
, an angular distribution of the particles ejected from a target is calculated using the MD method and stored in a data file. In step P
2
, the angular distribution of ejection is successively read out. In step S
5
, a track of the sputtered particle in the sputter arrangement is calculated from the vertical and horizontal components of the direction of ejection by means of the Monte Carlo (MC) method, wherein the angular distribution of ejected particles read out in Step P
2
is taken as an initial value.
In step P
1
, the velocity of the ion incident on the target is calculated from the applied voltage, and the surface temperature of the target is calculated by means of thermoanalysis. The initial velocity of the atoms in the interior of the target is derived from the surface temperature. The track of an interior atom of the target is calculated by means of the MD method on the basis of the derived initial velocity (step S
11
). The track of an atom farther than a cut-off distance from the surface of the target is next extracted as a sputtered atom (step S
12
), the horizontal and vertical components of the ejected directions of the sputtered atoms are extracted (step P
13
), and are stored in a data file (step S
14
). The steps S
11
-S
14
are repeated until the number of data points reachs a predetermined number-N (step S
15
). The number of extracted sputtered atoms, i.e., the number of ejected angles of the particles N is of the order of 100-200 in order for the calculation to be carried out within a practical calculation time.
Next, the ejected direction is successively read out in step P
2
. In this step, the ejection angle data is read out successively from the data file starting with #
01
data (step P
21
). It is judged then whether the number of the read-out data n reaches N (step P
22
). The read-out ejection angle data is successively served to the calculation of the tracks of sputtered atoms in the sputtering arrangement (step S
51
) until the number of data points read-out reaches N. Upon the number reaching N, #
01
data is employed again for the calculation of the tracks (step P
23
), and the N data are repeatedly employed for the calculation of the tracks of the sputtered atoms.
The tracks of the sputtered particle in the sputtering apparatus are calculated by applying the MC method to each of the ejection angle data. In this calculation, the collision of the particles through a central force of a Lennard-Jones type potential and the trapping of the sputtered atom by the collimator and the wall of the arrangement are taken into account (step S
51
).
Finally, of the sputtered particles that have kept the tracks thus calculated, the particles, which arrive at a specific region on a wafer, are extracted (steps S
52
, S
53
). The shape of the region where the particles are actually to arrive is then calculated in step S
6
with the aid of the string model or the like.
In this calculation, steps P
21
to S
53
are repeated until M ejection angle data are served to the MC calculation (step S
54
), wherein M is the number of the ejection angle data desirable to minimize the random number error in the MC calculation. M need be of the order often millions. Here, the random number error refers to an error originating from the deviation from a result of calculation carried out on the assumption of an infinite number of random numbers.
In the foregoing method of simulation, substantial sampling errors in directional components (direction cosines with respect to x-, y- and z-axes) of the possible tracks of the sputtered particles at their ejection points depend on the number of ejection angle data N.
Since the value of N, however, is taken as small as 100-200 because of the limitation in practical calculation time, a random number error is as large as 1/N
½
(≅10
−1
) can occur in this case. As a result, the calculated shape of the formed film becomes deformed due to a 20 to 30% error as compared with an ideal shape (the shape assumed in the case of a negligible-random number error) of the film.
The problem to be solved by the present invention is summarized as follows:
The foregoing method of simulation needs ejection angle data of the order of ten millions to be taken into the calculation (the desirable number of the ejection angle data to be taken into calculation will be hereinafter denoted as M) in order to minimize the random number error. In addition, because the sampling error decreases as N is increased, it is advantageous to make the number of the ejection angle data N as great as possible in order to minimize the sampling error. (The sampling error refers to an error which is likely to occur when directional components of the possible tracks of the particles are sampled at their ejected points). The value of the ejection angle data N, however, needs to be kept as small as 100-200 because of the limitation in calculation time, as described above. Consequently, a problem in Yamada's former method has been that a large random number error takes place from such a small value of N.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method of simulating sputtering by which a random number error can be reduced and thus a film with a shape of a precise size can be formed by sputtering.
In order to realize the above object, the present invention is directed to calculating an direction-dependent distribution of ejected particles, effecting a calculation of tracks of the sputtered particles according to the MC method within a practically performable time and accuracy and obtaining an accurate shape of a produced film.
In order to attain the objects of the invention, the method of simulating sputtering according to the present invention, comprises:
a first step of calculating a direction-dependent distribution of ejected particles from the ta
Jones Hugh M.
NEC Corporation
Sughrue & Mion, PLLC
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