Single-crystal – oriented-crystal – and epitaxy growth processes; – Processes of growth from liquid or supercritical state – Having pulling during growth
Reexamination Certificate
2001-02-26
2002-09-17
Kunemund, Robert (Department: 1765)
Single-crystal, oriented-crystal, and epitaxy growth processes;
Processes of growth from liquid or supercritical state
Having pulling during growth
C117S013000, C117S014000, C117S029000, C117S202000, C117S932000
Reexamination Certificate
active
06451107
ABSTRACT:
This application claims Paris Convention priority of Japanese Application Nos. 2000-125840 filed Apr. 26, 2000 and 2000-230850 filed Jul. 31, 2000, the complete disclosure of which is(are) hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for computer-simulating the shape of the solid-liquid interface between a single crystal and a molten liquid of silicon or the like, said single crystal being pulled by Czochralski (hereinafter referred to as CZ) method, and the distribution of point defects in the single crystal.
2. Description of the Related Art
As a simulation method of this kind, as shown in
FIG. 7
, there has been known a conventional method which estimates the internal temperature distribution of a silicon molten liquid
2
by operating the thermal conductivity of the molten silicon liquid
2
on the basis of the structure of a hot zone and the pulling speed of a silicon single crystal
4
in a pulling apparatus
1
when pulling the silicon single crystal
4
by means of CZ method using an overall heat transfer simulator and which obtains the shape of the solid-liquid interface between the silicon single crystal
4
and the silicon molten liquid
2
from this internal temperature distribution by means of a computer.
And there has been known another conventional method of obtaining the coordinates and temperature of meshes of a silicon single crystal
4
from the internal temperature distribution of said silicon molten liquid
2
and then solving a diffusion equation on the basis of the diffusion coefficients and the boundary conditions of interstitial silicon atoms and atomic vacancies in the silicon single crystal
4
, and thereby obtaining the density distributions of said interstitial silicon atoms and vacancies by means of a computer.
In these methods, each member in the hot zone is mesh-divided and modeled as a mesh structure. Particularly, the silicon molten liquid
2
is divided into comparatively rough meshes of about 10 mm so as to shorten the computation time.
In the above-mentioned conventional methods, however, since the convection of a molten silicon generated in an actual pulling apparatus is not considered and the meshes of the molten silicon are comparatively rough, there has been a problem that a simulation result and an actual measurement result of the shape of a solid-liquid interface are greatly different from each other, and a simulation result (FIG.
6
(
b
)) and an actual measurement result (FIG.
6
(
e
)) of the density distributions of interstitial silicon atoms and vacancies are also greatly different from each other.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a method for simulating the shape of the solid-liquid interface between a single crystal and a molten liquid, in which a computation result and an actual measurement result of the shape of the solid-liquid interface between the single crystal and the molten liquid coincide very well with each other.
Another object of the present invention is to provide a method for simulating the distribution of point defects in a single crystal, in which a computation result and an actual measurement result of the distribution of point defects in the single crystal coincide very well with each other.
A first aspect of the present invention is characterized, as shown in
FIGS. 1 and 2
, by a method for simulating the shape of the solid-liquid interface between a single crystal and a molten liquid using a computer, comprising;
a first step of modeling as a mesh structure a hot zone in a pulling apparatus
11
of the single crystal
14
to be computed,
a second step of combining meshes for each member in the hot zone and inputting physical property values of each member corresponding to the combined meshes into the computer,
a third step of obtaining the surface temperature distribution of each member on the basis of the calorific power of a heater and the emissivity of each member,
a fourth step of obtaining the internal temperature distribution of each member by solving a heat conduction equation on the basis of the surface temperature distribution and the thermal conductivity of each member, and then further obtaining the internal temperature distribution of a molten liquid
12
being in consideration of convection by simultaneously solving a turbulent model equation obtained on the assumption that the molten liquid
12
is a turbulent flow and Navier-Stokes equation, a fifth step of obtaining the shape of the solid-liquid interface between the single crystal
14
and the molten liquid
12
in accordance with an isothermal line including a tri-junction S of the single crystal
14
, and
a sixth step of repeating the third to fifth steps until the tri-junction S becomes the melting point of the single crystal
14
, wherein;
some or all of the meshes of the molten liquid
12
which are in the radial directions of the single crystal
14
and are directly under the single crystal
14
are set at 0.01 to 5.00 mm, and
some or all of the meshes of the molten liquid
12
which are in the longitudinal direction of the single crystal
14
are set to 0.01 to 5.00 mm.
Since the method for simulating the solid-liquid interface between a single crystal and a molten liquid according to the first aspect of the present invention takes account of convection of the molten liquid
12
and sets comparatively fine meshes of the molten liquid
12
, the shape of the solid-liquid interface between the single crystal
14
and the molten liquid
12
obtained by computation coincides very well with an actual measurement result.
It is preferable that the physical property values to be given to each member in the second step are the thermal conductivity, emissivity, viscosity, coefficient of thermal expansion, density and specific heat of each member.
Further, it is preferable that the turbulent model equation is a kl-model equation represented by equation (1), and an optional value within a range of 0.4 to 0.6 is used as a turbulent parameter C of this model equation:
κ
t
=
c
Pr
t
×
ρ
×
C
×
d
k
(
1
)
Here, &kgr;
t
is the turbulent thermal conductivity of a molten liquid, c is the specific heat of the molten liquid, Pr
t
is Prandtl number, &rgr; is the density of the molten liquid, d is a distance from the inner wall of a crucible containing the molten liquid, and k is the sum square of variable components to the average flow speed of the molten liquid.
As shown in
FIGS. 2
to
4
, a second aspect of the present invention is a method for simulating the distribution of point defects of a single crystal using a computer, comprising;
a first step of modeling as a mesh structure a hot zone in a pulling apparatus
11
of a single crystal
14
in a state in which the single crystal
14
has been pulled to a specified length by the pulling apparatus
11
,
a second step of combining meshes for each member in the hot zone, and inputting the physical property values of each member corresponding to the combined meshes, the pulled length of the single crystal
14
and the pulling speed of the single crystal
14
corresponding to the pulled length into the computer,
a third step of obtaining the surface temperature distribution of each member on the basis of the calorific power of a heater and the emissivity of each member,
a fourth step of obtaining the internal temperature distribution of each member by solving a heat conduction equation on the basis of the surface temperature distribution and the thermal conductivity of each member, and then further obtaining the internal temperature distribution of a molten liquid
12
being in consideration of convection by simultaneously solving a turbulent model equation obtained on the assumption that the molten liquid
12
is a turbulent flow and Navier-Stokes equation,
a fifth step of obtaining the shape of the solid-liquid interface between the single crystal
14
and the molten liquid
12
in accordance with an isothermal line including a tri-junction S o
Kitamura Kounosuke
Ono Naoki
Kunemund Robert
Mitsubishi Materials Silicon Corporation
Reed Smith LLP
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