U.S. patent application number 14/482502 was filed with the patent office on 2015-12-17 for topography simulation apparatus, topographysimulation method and recording medium.
The applicant listed for this patent is KABUSHIKI KAISHA TOSHIBA. Invention is credited to Masanori TAKAHASHI, Hirotaka TSUDA.
Application Number | 20150363516 14/482502 |
Document ID | / |
Family ID | 54609256 |
Filed Date | 2015-12-17 |
United States Patent
Application |
20150363516 |
Kind Code |
A1 |
TSUDA; Hirotaka ; et
al. |
December 17, 2015 |
TOPOGRAPHY SIMULATION APPARATUS, TOPOGRAPHYSIMULATION METHOD AND
RECORDING MEDIUM
Abstract
In one embodiment, a topography simulation apparatus includes a
division module configured to divide topography of a substance of a
semiconductor device into first to n-th layers, where n is an
integer of two or more. The apparatus further includes a flux
calculation module configured to calculate, for each of the first
to n-th layers, a flux of particles which reach a surface of the
substance in each layer. The apparatus further includes a
topography calculation module configured to calculate, for each of
the first to n-th layers, an amount of change of the topography of
the substance in each layer based on the flux.
Inventors: |
TSUDA; Hirotaka; (Tokyo,
JP) ; TAKAHASHI; Masanori; (Yokohama, JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
KABUSHIKI KAISHA TOSHIBA |
Tokyo |
|
JP |
|
|
Family ID: |
54609256 |
Appl. No.: |
14/482502 |
Filed: |
September 10, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62011836 |
Jun 13, 2014 |
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Current U.S.
Class: |
716/136 |
Current CPC
Class: |
G06F 30/398 20200101;
G06F 30/367 20200101 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A topography simulation apparatus comprising: a division module
configured to obtain data representing topography of a substance of
a semiconductor device and to divide the topography of the
substance in the data into first to n-th layers, where n is an
integer of two or more; a flux calculation module configured to
calculate, for each of the first to n-th layers, a flux of
particles which reach a surface of the substance in each layer and
contribute to processing of the topography of the substance; and a
topography calculation module configured to calculate, for each of
the first to n-th layers, an amount of change of the topography of
the substance in each layer based on the flux, wherein the flux
calculation module calculates the flux in a k-th layer based on the
flux in a (k-1)-th layer adjacent to the k-th layer and a
transmission probability of the particles in the k-th layer, where
k is an integer from 2 to n.
2. The apparatus of claim 1, wherein the division module divides
the topography of the substance which includes a concave portion
into the first to n-th layers.
3. The apparatus of claim 2, wherein topography of a region of the
concave portion in each layer is a columnar shape, and the
topography calculation module calculates an amount of change of a
radius of the concave portion in each layer.
4. (canceled)
5. The apparatus of claim 1, wherein the transmission probability
is a function of a topography parameter representing the topography
of the substance in the k-th layer.
6. The apparatus of claim 5, wherein the topography parameter is an
aspect ratio of a region of a concave portion of the substance in
the k-th layer.
7. The apparatus of claim 1, wherein the transmission probability
is a function of a topography parameter representing the topography
of the substance in the k-th layer and a distribution parameter
representing distribution of the particles.
8. The apparatus of claim 7, wherein the distribution parameter is
a half width of the distribution of the particles.
9. The apparatus of claim 1, wherein the division module varies a
value of the division number n of the first to n-th layers with a
change of the topography of the substance.
10. The apparatus of claim 1, wherein the flux calculation module
calculates the flux in the k-th layer based on the flux in the
(k-1)-th layer, the transmission probability of the particles in
the k-th layer, and a reaction probability of the particles.
11. A topography simulation method performed by an apparatus
comprising: obtaining data representing topography of a substance
of a semiconductor device by the apparatus, and dividing the
topography of the substance in the data into first to n-th layers
by the apparatus, where n is an integer of two or more;
calculating, for each of the first to n-th layers, a flux of
particles which reach a surface of the substance in each layer and
contribute to processing of the topography of the substance, by the
apparatus; and calculating, for each of the first to n-th layers,
an amount of change of the topography of the substance in each
layer based on the flux, by the apparatus, wherein the flux in a
k-th layer is calculated based on the flux in a (k-1)-th layer
adjacent to the k-th layer and a transmission probability of the
particles in the k-th layer, where k is an integer from 2 to n.
12. (canceled)
13. The method of claim 11, wherein the transmission probability is
a function of a topography parameter representing the topography of
the substance in the k-th layer.
14. The method of claim 13, wherein the topography parameter is an
aspect ratio of a region of a concave portion of the substance in
the k-th layer.
15. The method of claim 11, wherein the transmission probability is
a function of a topography parameter representing the topography of
the substance in the k-th layer and a distribution parameter
representing distribution of the particles.
16. The method of claim 15, wherein the distribution parameter is a
half width of the distribution of the particles.
17. The method of claim 11, further comprising varying a value of
the division number n of the first to n-th layers with a change of
the topography of the substance.
18. The method of claim 11, wherein the flux in the k-th layer is
calculated based on the flux in the (k-1)-th layer, the
transmission probability of the particles in the k-th layer, and a
reaction probability of the particles.
19. A non-transitory computer-readable recording medium containing
a topography simulation program which causes a computer to perform
a topography simulation method, the method comprising: obtaining
data representing topography of a substance of a semiconductor
device by the computer, and dividing the topography of the
substance in the data into first to n-th layers by the computer,
where n is an integer of two or more; calculating, for each of the
first to n-th layers, a flux of particles which reach a surface of
the substance in each layer and contribute to processing of the
topography of the substance, by the computer; and calculating, for
each of the first to n-th layers, an amount of change of the
topography of the substance in each layer based on the flux, by the
computer, wherein the flux in a k-th layer is calculated based on
the flux in a (k-1)-th layer adjacent to the k-th layer and a
transmission probability of the particles in the k-th layer, where
k is an integer from 2 to n.
20. The medium of claim 19, wherein the flux in the k-th layer is
calculated based on the flux in the (k-1)-th layer, the
transmission probability of the particles in the k-th layer, and a
reaction probability of the particles.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application is based upon and claims the benefit of
priority from the prior U.S. Provisional Patent Application No.
62/011,836 filed on Jun. 13, 2014, the entire contents of which are
incorporated herein by reference.
FIELD
[0002] Embodiments described herein relate to a topography
simulation apparatus, a topography simulation method and a
recording medium.
BACKGROUND
[0003] In a topography simulation for a semiconductor device, it is
required to calculate a flux of particles that reach a surface of a
substance of the semiconductor device and contribute to the
processing of topography of the substance in short time. The flux
is called surface incident flux. For example, there is known a
method of calculating the flux by using an aspect ratio of a
concave portion formed in the substance. This method can calculate
the flux in short time by approximating topography of the concave
portion formed in the substance with one columnar shape, and
analytically calculating the flux on a bottom surface of the
concave portion.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] FIG. 1 is a flow chart showing a procedure of a topography
simulation method of a first embodiment;
[0005] FIGS. 2A and 2B are cross sectional views showing an example
of an initial structure of a substance in the first embodiment;
[0006] FIGS. 3A and 3B are cross sectional views showing an example
of a topography change of the substance in the first
embodiment;
[0007] FIG. 4 is a perspective view for illustrating an aspect
ratio x;
[0008] FIG. 5 is a graph showing an example of a relationship
between the aspect ratio x and a flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in FIG. 4;
[0009] FIGS. 6A to 6C are cross sectional views for illustrating a
method of calculating surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 of the
first embodiment;
[0010] FIG. 7 is a cross sectional view showing another example of
the topography change of the substance in the first embodiment;
[0011] FIG. 8 is a cross sectional view for illustrating a
topography simulation method of a second embodiment;
[0012] FIG. 9 is a perspective view for illustrating a topography
simulation method of a third embodiment;
[0013] FIG. 10 is a graph for illustrating a relationship between
the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in FIG. 9;
[0014] FIG. 11 is a graph showing an example of angle distribution
of ions used for processing a semiconductor device;
[0015] FIG. 12 is a perspective view for illustrating a
relationship between the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in a case of using the ions;
[0016] FIG. 13 is a graph for illustrating the relationship between
the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in the case of using the ions;
[0017] FIGS. 14A and 14B are cross sectional views for illustrating
a topography simulation method of a modification of the first to
third embodiments;
[0018] FIG. 15 is an external view showing a configuration of a
topography simulation apparatus of a fourth embodiment; and
[0019] FIG. 16 is a block diagram showing a configuration of a
controller in FIG. 15.
DETAILED DESCRIPTION
[0020] Embodiments will now be explained with reference to the
accompanying drawings.
[0021] In one embodiment, a topography simulation apparatus
includes a division module configured to divide topography of a
substance of a semiconductor device into first to n-th layers,
where n is an integer of two or more. The apparatus further
includes a flux calculation module configured to calculate, for
each of the first to n-th layers, a flux of particles which reach a
surface of the substance in each layer. The apparatus further
includes a topography calculation module configured to calculate,
for each of the first to n-th layers, an amount of change of the
topography of the substance in each layer based on the flux.
First Embodiment
[0022] FIG. 1 is a flow chart showing a procedure of a topography
simulation method of a first embodiment. The topography simulation
method of the present embodiment is performed by using an
information processing apparatus such as a personal computer and a
workstation.
[0023] The topography simulation method of the present embodiment
will be described below with reference to FIG. 1. In this
description, FIGS. 2A to 3B will be also referred to as
appropriate.
[0024] In the topography simulation method of the present
embodiment, the initial structure of a substance of a semiconductor
device is inputted into the information processing apparatus (step
S1). Although examples of a method of inputting the initial
structure include various possible formats, the present embodiment
uses a method in which topography of a surface of the substance is
represented in a point sequence, and the information processing
apparatus reads this point sequence.
[0025] FIG. 2A is a cross sectional view showing an example of the
initial structure of the substance in the first embodiment. The
initial structure in FIG. 2A includes a substrate 1, a mask layer 2
formed on the substrate 1, and a concave portion 3 formed in the
substrate 1 and the mask layer 2. Examples of the substrate 1
include a semiconductor substrate, and a workpiece substrate in
which a workpiece layer is formed on a semiconductor substrate.
Examples of the mask layer 2 include a hard mask layer and a resist
mask layer. Topography of the concave portion 3 in FIG. 2A (initial
topography) is a columnar shape. Reference character G denotes the
central axis of the concave portion 3. Reference character R
denotes the radius of the concave portion 3 (initial radius).
[0026] FIG. 2A shows an X direction and a Y direction that are
parallel to a main surface of the substrate 1 and are perpendicular
to each other, and a Z direction that is perpendicular to the main
surface of the substrate 1. In the present specification, the +Z
direction is treated as an upward direction, and the -Z direction
is treated as a downward direction. For example, the positional
relationship between the substrate 1 and the mask layer 2 is
expressed that the substrate 1 is positioned below the mask layer
2.
[0027] The topography of the initial structure of the substance is
divided into first to n-th layers L.sub.1 to L.sub.n, where n is an
integer of two or more (step S2). A block in the information
processing apparatus for performing a process of step S2 is an
example of a division module of the present disclosure.
[0028] FIG. 2B is a cross sectional view showing, similarly to FIG.
2A, the example of the initial structure of the substance in the
first embodiment. FIG. 2B shows the example in which the topography
of the initial structure of the substance is divided into the first
to eighth layers L.sub.1 to L.sub.8 having the same thickness T.
Reference character d denotes the depth of the concave portion 3.
Reference characters r.sub.1 to r.sub.8 denote radii r.sub.1 to
r.sub.8 of the concave portion 3 in the first to eighth layers
L.sub.1 to respectively. All the values of the radii r.sub.1 to
r.sub.8 in FIG. 2B are R. In the present embodiment, the start
position of dividing the topography of the substance (the upper
surface of the first layer L.sub.1) is set at the aperture face of
the concave portion 3, and the end position of dividing the
topography of the substance (the lower surface of the eighth layer
L.sub.8) is set at the bottom surface of the concave portion 3.
[0029] Steps S3 to S6 of the topography simulation method in the
present embodiment will be described below with reference to the
initial structure in FIGS. 2A and 2B as an example. Therefore, the
division number n of the topography of the substance is set at
eight.
[0030] Step 3 is performed to calculate, for each of the first to
eighth layers L.sub.1 to L.sub.8, a flux of particles that reach
the surface of the substance in each layer. The flux is called
surface incident flux. In the initial structure in FIGS. 2A and 2B,
step 3 is performed to calculate the flux of the particles that
reach the side surface of the concave portion 3 in each layer. A
block in the information processing apparatus for processing a
process of step S3 is an example of a flux calculation module of
the present disclosure.
[0031] Reference character .GAMMA..sub.in denotes the flux of the
particles that reach the upper surface of a region of the concave
portion 3 in the first layer L.sub.1. Reference characters
.GAMMA..sub.out.sub.--.sub.1 to r.sub.out.sub.--.sub.8 denote the
fluxes of the particles that reach the lower surfaces and the side
surfaces of regions of the concave portion 3 in the first to eighth
layers L.sub.1 to L.sub.8, respectively. Therefore, the fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8
correspond to the surface incident fluxes in the first to eighth
layers L.sub.1 to L.sub.8, respectively. A method of calculating
the surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 will be described later.
[0032] The particles treated in step S3 in the present embodiment
are particles that contribute to the processing of the topography
of the substance. Examples of such particles include ions or
radicals that contribute to deposition, oxidation, nitriding,
epitaxial growth, etching, aching or the like.
[0033] Step 4 is performed to calculate, for each of the first to
eighth layers L.sub.1 to L.sub.8, an amount of change of the
topography of the substance in each layer based on the surface
incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8. Specifically, step 4 is performed to
calculate the amounts of change .DELTA.r.sub.1 to .DELTA.r.sub.8 of
the radii r.sub.1 to r.sub.8 of the concave portion 3 in the
respective layers after the lapse of a time .DELTA.t from an
initial time t.sub.0. A block in the information processing
apparatus for processing a process of step S4 is an example of a
topography calculation module of the present disclosure.
[0034] In step S4 of the present embodiment, it is assumed that
topography of a region of the concave portion 3 in each layer
changes isotropically in a radial direction of a columnar shape,
and the columnar shape changes into another columnar shape. In
other words, it is assumed that the radius of the concave portion 3
in each layer changes in step S4 of the present embodiment. The
amount of change .DELTA.r.sub.m of the radius r.sub.m of the
concave portion 3 in an arbitrary m-th layer among the first to
eighth layers L.sub.1 to L.sub.8 is provided by the following
expression 1):
.DELTA. r m = .GAMMA. out _ m .GAMMA. i n R p .DELTA. t ( 1 )
##EQU00001##
[0035] where m is an integer from one to eight, and reference
character R.sub.p denotes the processing rate of the substance. In
the present embodiment, since the flux .GAMMA..sub.in is set at
one, the expression (1) is replaced with the following expression
(2).
.DELTA.r.sub.m=.GAMMA..sub.out.sub.--.sub.m)R.sub.p.DELTA.t (2)
[0036] In the present embodiment, the processes of the step S3 and
step S4 are repeated until a preset process time elapses (step S5).
Thereby, the topography of the substance changes as shown in FIGS.
3A and 3B. FIGS. 3A and 3B are cross sectional views showing an
example of a topography change of the substance in the first
embodiment.
[0037] FIG. 3B shows the topography of the region of the concave
portion 3 in each layer after the time t elapses from the initial
time t.sub.0 (=0). FIG. 3B shows a state in which the topography of
the region of the concave portion 3 in each layer has changed with
maintaining the columnar shape. It is noted that since the values
of the radii r.sub.1 to r.sub.8 have differently changed, the
topography of the entire concave portion 3 in FIG. 3B has changed
into a shape different from the columnar shape.
[0038] In this way, the present embodiment makes it possible to
simulate a process that the concave portion 3 having the columnar
shape changes into a shape different from the columnar shape. For
example, the present embodiment makes it possible to simulate a
process that the initial topography in FIG. 2A changes into the
topography in FIG. 3A.
[0039] FIG. 3B shows a state in which the concave portion 3 expands
to a new nin-th layer L.sub.9. In the present embodiment, it is
also possible to simulate the change in depth d of the concave
portion 3 by applying the expression (2) to the bottom surface of
the concave portion 3. In this way, the present embodiment may vary
the division number n of the topography of the substance with the
change of the topography of the substance with the lapse of the
time t. Such a process will be described later in detail in a
second embodiment.
[0040] When the process time has elapsed, the final topography of
the substance is outputted (step S6), and the calculation is
finished.
[0041] (1) Method of Calculating Surface Incident Fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8
[0042] In the present embodiment, the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 are
calculated by using an aspect ratio of the region of the concave
portion 3 in each layer. The method of calculating the surface
incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 of the present embodiment will be
described below with reference to FIGS. 4 to 6C.
[0043] FIG. 4 is a perspective view for illustrating an aspect
ratio x.
[0044] FIG. 4 shows an example of the concave portion 3 having a
columnar shape. Reference characters .GAMMA..sub.in and
.GAMMA..sub.out denote the fluxes of the particles that reach the
upper surface and the lower surface of the concave portion 3,
respectively. Reference character H denotes the height of the
concave portion 3. Reference character W denotes the aperture width
(diameter) of the concave portion 3. Reference character x denotes
the aspect ratio of the concave portion 3. The aspect ratio x of
the concave portion 3 is given by the expression of x=H/W.
[0045] FIG. 5 is a graph showing an example of a relationship
between the aspect ratio x and a flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in FIG. 4. In the present
embodiment, since the flux .GAMMA..sub.in is set at one, the flux
ratio .GAMMA..sub.out/.GAMMA..sub.in is the same value as that of
the flux .GAMMA..sub.out.
[0046] FIG. 5 shows the relationship between the aspect ratio x and
the flux ratio .GAMMA..sub.out/.GAMMA..sub.in in the case where the
flow of the particles in the concave portion 3 is represented by
Knudsen transport model. Knudsen transport model represents the
flow of the particles in a case where a mean free path of the
particles is sufficiently longer than the aperture width W
(molecular flow). In this case, the flow of the particles is not
much influenced by the collision between the particles, but is
influenced by the collision between the particles and the inner
surface of the concave portion 3.
[0047] The relationship between the aspect ratio x and the flux
ratio .GAMMA..sub.out/.GAMMA..sub.in in Knudsen transport model is
given by the following expression (3).
.GAMMA. out .GAMMA. i n = K ( x ) = ( 1 + 3 4 x ) - 1 ( 3 )
##EQU00002##
[0048] K(x) in the expression (3) is called Clausing factor
representing a transmission probability that the particles pass
from the upper surface to the lower surface of the concave portion
3.
[0049] In the present embodiment, the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to F.sub.out.sub.--.sub.8 are
calculated assuming that the flow of the particles in each of the
first to eighth layers L.sub.1 to L.sub.8 is represented by Knudsen
transport model of the expression (3).
[0050] FIGS. 6A to 6C are cross sectional views for illustrating a
method of calculating the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to F.sub.out.sub.--.sub.8 of the first
embodiment.
[0051] FIG. 6A shows a method of calculating the surface incident
flux L.sub.out.sub.--.sub.2 of the second layer L.sub.2. Reference
characters x.sub.1 and x.sub.2 denote the aspect ratios of the
regions of the concave portion 3 in the first and second layers
L.sub.1 and L.sub.2, respectively. The aspect ratios x.sub.1 and
x.sub.2 are given by T/2r.sub.1 and T/2r.sub.2, respectively.
Reference character T represents the thickness of each layer shown
in FIGS. 2A to 3B.
[0052] Reference character K.sub.1 denotes the transmission
probability that the particles pass from the upper surface to the
lower surface of the region of the concave portion 3 in the first
layer L.sub.1. Reference character K.sub.2 denotes the transmission
probability that the particles pass from the upper surface to the
lower surface of the region of the concave portion 3 in the second
layer L.sub.2. The transmission probabilities K.sub.1 and K.sub.2
are respectively given by the following expressions (4) and (5) by
using the expression (3).
K 1 ( x 1 ) = ( 1 + 3 4 x 1 ) - 1 ( 4 ) K 2 ( x 2 ) = ( 1 + 3 4 x 2
) - 1 ( 5 ) ##EQU00003##
[0053] As seen from the above, the transmission probabilities
K.sub.1 and K.sub.2 are functions of the aspect ratios x.sub.1 and
x.sub.2, respectively.
[0054] Reference character K.sub.out.sub.--.sub.2 denotes the
transmission probability that the particles pass through the
regions of the concave portion 3 in the first and second layers
L.sub.1 and L.sub.2. The transmission probability
K.sub.out.sub.--.sub.2 is given by the following expression (6) of
the sum of an infinite series, taking the incidence and reflection
of the particles in each layer into consideration as shown in FIG.
6A.
K.sub.1K.sub.2
K.sub.1K.sub.2+K.sub.1K.sub.2(1-K.sub.1)(1-K.sub.2)
K.sub.1K.sub.2+K.sub.1K.sub.2(1-K.sub.1).sup.2(1-K.sub.2).sup.2
. . .
K.sub.1K.sub.2+K.sub.1K.sub.2(1-K.sub.1).sup.p(1-K.sub.2).sup.p
(6)
[0055] By calculating the sum of the infinite series of the
expression (6), the transmission probability K.sub.out.sub.--.sub.2
is given by the following expression (7).
K out _ 2 = K 1 K 2 K 1 + K 2 - K 1 K 2 ( 7 ) ##EQU00004##
[0056] Therefore, the surface incident flux
.GAMMA..sub.out.sub.--.sub.2 in the second layer L.sub.2 is given
by the following expression (8) obtained by substituting the
expression (7) into the expression (3).
.GAMMA. out _ 2 .GAMMA. i n = K out _ 2 = K 1 K 2 K 1 + K 2 - K 1 K
2 ( 8 ) ##EQU00005##
[0057] It is noted that the transmission probability
K.sub.out.sub.--.sub.1 that the particles pass through the region
of the concave portion 3 in the first layer L.sub.1 is the same
value as that of the transmission probability K.sub.1
(K.sub.out.sub.--.sub.1=K.sub.1). Therefore, the surface incident
flux .GAMMA..sub.out.sub.--.sub.2 of the first layer L.sub.1 is
given by the expression (9) obtained by substituting
K.sub.out.sub.--.sub.1=K.sub.1 into the expression (3).
.GAMMA. out _ 1 .GAMMA. i n = K out _ 1 = K 1 ( 9 )
##EQU00006##
[0058] FIG. 6B shows a method of calculating the surface incident
flux .GAMMA..sub.out.sub.--.sub.3 in the third layer L.sub.3.
Reference character x.sub.3 denotes the aspect ratio of the region
of the concave portion 3 in the third layer L.sub.3. Reference
character K.sub.3 denotes the transmission probability that the
particles pass from the upper surface to the lower surface of the
region of the concave portion 3 in the third layer L.sub.3. The
transmission probability K.sub.3 is given by the following
expression (10) by using the expression (3).
K 3 ( x 3 ) = ( 1 + 3 4 x 3 ) - 1 ( 10 ) ##EQU00007##
[0059] As seen from the above, the transmission probability K.sub.3
is a function of the aspect ratio x.sub.3.
[0060] Reference character K.sub.out.sub.--.sub.3 denotes the
transmission probability that the particles pass through the
regions of the concave portion 3 in the first to third layers
L.sub.1 to L.sub.3. When the transmission probability
K.sub.out.sub.--.sub.3 is calculated, the first and second layers
L.sub.1 and L.sub.2 are considered to be one layer L.sub.2' having
the transmission probability K.sub.out.sub.--.sub.2. Therefore, the
transmission probability K.sub.out.sub.--.sub.3 is given by the
following expression (11) as with the expression (7).
K out _ 3 = K out _ 2 K 3 K out _ 2 + K 3 - K out _ 2 K 3 ( 11 )
##EQU00008##
[0061] Therefore, the surface incident flux
.GAMMA..sub.out.sub.--.sub.3 of the third layer L.sub.3 is given by
the expression (12) obtained by substituting the expression (11)
into the expression (3).
.GAMMA. out _ 3 .GAMMA. i n = K out _ 3 = K out _ 2 K 3 K out _ 2 +
K 3 - K out _ 2 K 3 ( 12 ) ##EQU00009##
[0062] FIG. 6C shows a method of calculating a surface incident
flux .GAMMA..sub.out.sub.--.sub.k in a k-th layer L.sub.k where k
is an integer from two to n (=8). Reference character x.sub.k
denotes the aspect ratio of the region of the concave portion 3 in
the k-th layer L.sub.k. Reference character K.sub.k denotes the
transmission probability that the particles pass from the upper
surface to the lower surface of the region of the concave portion 3
in the k-th layer L.sub.k. The transmission probability K.sub.k is
given by the following expression (13) by using the expression
(3).
K k ( x k ) = ( 1 + 3 4 x k ) - 1 ( 13 ) ##EQU00010##
[0063] As seen from the above, the transmission probability K.sub.k
is a function of the aspect ratio x.sub.k. The aspect ratio x.sub.k
is an example of a topography parameter representing the topography
of the substance in the k-th layer.
[0064] Reference character K.sub.out.sub.--.sub.k denotes the
transmission probability that the particles pass through the
regions of the concave portion 3 in the first to k-th layers
L.sub.1 to L.sub.k. When the transmission probability
K.sub.out.sub.--.sub.k is calculated, the first to (k-1)-th layers
L.sub.1 to L.sub.k-1 are considered to be one layer L.sub.k-1'
having the transmission probability K.sub.out.sub.--.sub.k-1.
Therefore, the transmission probability K.sub.out.sub.--.sub.k is
given by the following expression (14) as with the expression
(7).
K out _ k = K out_k - 1 K k K out _ k - 1 + K k - K out _ k - 1 K k
( 14 ) ##EQU00011##
[0065] Therefore, the surface incident flux
.GAMMA..sub.out.sub.--.sub.k in the k-th layer L.sub.k is given by
the following expression (15) obtained by substituting the
expression (14) into the expression (3).
.GAMMA. out _ k .GAMMA. i n = K out _ k = K out _ k - 1 K k K out _
k - 1 + K k - K out _ k - 1 K k ( 15 ) ##EQU00012##
[0066] In this way, the surface incident flux
.GAMMA..sub.out.sub.--.sub.k in the k-th layer L.sub.k of the
present embodiment is calculated based on the surface incident flux
.GAMMA..sub.out.sub.--.sub.k-1 (=K.sub.out.sub.--.sub.k-1) in the
(k-1)-th layer L.sub.k-1 adjacent to the k-th layer L.sub.k, and
the transmission probability K.sub.k in the k-th layer L.sub.k.
[0067] The surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 calculated in this way are
respectively used for calculating the amounts of change
.DELTA.r.sub.1 to .DELTA.r.sub.8 in the radii r.sub.1 to r.sub.8 in
step S4.
[0068] It is noted that the values of the transmission
probabilities K.sub.1 to K.sub.8 and the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 change
with the lapse of the time t. The reason for this is that since the
radii r.sub.1 to r.sub.8 change with the lapse of the time t, the
aspect ratios x.sub.1 to x.sub.8 also change with the lapse of the
time t.
[0069] (2) Details of Method of Calculating Surface Incident Fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8
[0070] The method of calculating the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 of the
present embodiment will be described in detail with reference to
the same FIGS. 6A to 6C.
[0071] As described above, the present embodiment calculates the
surface incident fluxes .GAMMA..sub.out-1 to
.GAMMA..sub.out.sub.--.sub.8 using Knudsen transport model. Knudsen
transport model well fits the behavior of the particles moving
isotropically like radicals. Furthermore, Knudsen transport model
well fits the behavior of the particles moving in a low-pressure
atmosphere close to vacuum. Therefore, the method of calculating
the surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 of the present embodiment is suitable
for, for example, simulating a plasma process in manufacturing a
semiconductor device. An example where the present embodiment is
applied to the particles moving anisotropically like ions will be
described later.
[0072] The present embodiment can analytically calculate the
surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 by using Knudsen transport model as
shown by the expression (15) for example. However, the present
embodiment may use a model other than Knudsen transport model. In
this case, the surface incident fluxes .GAMMA..sub.out.sub.--.sub.1
to .GAMMA..sub.out.sub.--.sub.8 may be given by a form other than
analytical formula, for example, by a form of an empirical formula
obtained by experimentation.
[0073] In the present embodiment, the initial topography of the
concave portion 3 is set to have a columnar shape. However, the
initial topography of the concave portion 3 of the present
embodiment may be set to have a shape other than the columnar
shape. Examples of such an initial topography of the concave
portion 3 include a prism shape having a quadrilateral or another
polygonal cross section, and a cylindrical shape having an annular
cross section.
[0074] In the present embodiment, the change of the topography of
the region of the concave portion 3 in each layer is calculated
such that it changes from a columnar shape into another columnar
shape. However, the present embodiment is applicable to other
topography changes by introducing amounts of change of the
topography other than the amounts of change .DELTA.r.sub.1 to
.DELTA.r.sub.8 of the radii r.sub.1 to r.sub.8, and topography
parameters other than the aspect ratios x.sub.1 to x.sub.8.
Examples of such amounts of change of the topography include an
amount of change of the length of an edge of the concave portion 3
having a prism shape. In addition, examples of such topography
parameters include a ratio of the length of the edge of the concave
portion 3 to the height (thickness) of the concave portion 3.
[0075] In the present embodiment, the thicknesses of the first to
eighth layers L.sub.1 to L.sub.8 are set at the same thickness T.
However, the thicknesses of the first to eighth layers L.sub.1 to
L.sub.8 of the present embodiment may be set to be different from
one another. An example will be described later in which the
thicknesses of these layers are set to be different from one
another.
[0076] In the present embodiment, the radii r.sub.1 to r.sub.8 of
the initial topography of the concave portion 3 in the first to
eighth layers L.sub.1 to L.sub.8 are set at the same value.
However, the radii r.sub.1 to r.sub.8 of the initial topography of
the concave portion 3 of the present embodiment may be set to be
different from one another. In other words, in the initial
topography of the concave portion 3 in the present embodiment, the
cross sectional shapes of the concave portion 3 in the first to
eighth layers L.sub.1 to L.sub.8 may be set to be different from
one another.
[0077] (3) Modification of First Embodiment
[0078] FIG. 7 is a cross sectional view showing another example of
the topography change of the substance in the first embodiment.
[0079] Reference character U denotes the surface of the concave
portion 3 at the time t. Arrows A denote directions in which the
surface U of the concave portion 3 changes with the lapse of the
time t. Reference character B denotes an end portion of the surface
U of the concave portion 3.
[0080] The present embodiment can simulate a process that the side
surface of the concave portion 3 is etched in a horizontal
direction by calculating the amounts of change .DELTA.r.sub.1 to
.DELTA.r.sub.8 of the radii r.sub.1 to r.sub.8. For example, in a
dry etching by using fluorine-containing etching gas, it is known
that the substrate 1 is etched isotropically both in the depth
direction and the horizontal direction. As shown in FIG. 7, the
present embodiment makes it possible to simulate such dry etching.
FIG. 7 shows the result of simulating an undercut process that the
substrate 1 below the mask layer 2 is etched by using the mask
layer 2 which has a processing rate lower than that of the
substrate 1.
[0081] As described above, the topography simulation method of the
present embodiment divides the topography of the substance into the
first to n-th layers L.sub.1 to L.sub.n, calculates the surface
incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.n for the respective layers, and
calculates the amounts of change .DELTA.r.sub.1 to .DELTA.r.sub.n
of the radii r.sub.1 to r.sub.n of the concave portion 3 for the
respective layers.
[0082] Therefore, the present embodiment makes it possible to
handle the topography change of the side surface of the concave
portion 3, for example, in the case where the topography of the
concave portion 3 changes from the columnar shape into a shape
other than the columnar shape. In other words, the present
embodiment makes it possible to handle the topography change of the
substance that is to be processed into various shapes.
[0083] Furthermore, the present embodiment makes it possible to
calculate the surface incident fluxes .GAMMA..sub.out.sub.--.sub.1
to .GAMMA..sub.out.sub.--.sub.n in short time, because the surface
incident flux in each layer is calculated by using the aspect ratio
of each layer. In other words, the present embodiment makes it
possible to handle various topography changes of the substance,
while shortening the calculating time of the surface incident
fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.n. This is also applied to the case
where a topography parameter other than the aspect ratio is
used.
[0084] In the present embodiment, it is assumed that the flux on
the side surface of the region of the concave portion 3 in each
layer is the same as the flux (.GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.n) on the bottom surface of the region
of the concave portion 3 in each layer. Therefore, each of the
fluxes .GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.n
in the present embodiment is used as the surface incident flux on
the side surface of the region of the concave portion 3 in each
layer. The precision of such an approximation is considered to
become finer by setting the division number n of the topography of
the substance to be sufficiently large and making the thickness T
of the layers sufficiently small. However, the division number n
and the thickness T in the present embodiment can be arbitrarily
set in accordance with the precision required for individual
topography simulations.
Second Embodiment
[0085] FIG. 8 is a cross sectional view for illustrating a
topography simulation method of a second embodiment.
[0086] Reference character U denotes the surface of the concave
portion 3 in the initial structure of the substance. Arrows C
denote directions in which the surface U of the concave portion 3
changes with the lapse of a time t. Reference character D denotes a
point of closure of the concave portion 3. FIG. 8 shows a state
that the concave portion 3 is closed by embedding an insulating
material in the concave portion 3 while a void 3a is left. FIG. 8
further shows a process that the insulating material is deposited
on the substrate 1 outside the concave portion 3. Examples of the
concave portion 3 include an isolation trench.
[0087] FIG. 8 illustrates five layers L.sub.A to L.sub.E. The layer
L.sub.A is positioned at a height where the layer L.sub.A includes
the point of closure D. The layers L.sub.B and L.sub.C are
positioned below the layer L.sub.A. The layers L.sub.D and L.sub.E
are positioned above the layer L.sub.A. The layer L.sub.D is
positioned at a height where the layer L.sub.D includes the main
surface of the substrate 1, and the layer L.sub.E is positioned
above the main surface of the substrate 1.
[0088] In the present embodiment, when the concave portion 3 is
closed at the point of closure D, it is useless to perform the
processes of steps S3 and S4 in FIG. 1 to the layers L.sub.B and
L.sub.C.
[0089] Therefore, if the concave portion 3 is closed at the point
of closure D at the time t, a process of removing the layers
L.sub.B and L.sub.C below the layer L.sub.A is performed between
steps S3 and S4 at the time t and steps S3 and S4 at the time
t+.DELTA.t.
[0090] In the present embodiment, if the insulating material is
deposited on the substrate 1 outside the concave portion 3, it is
desirable that the layers L.sub.D and L.sub.E including this
insulating material are added. Therefore, when the insulating
material is deposited on the substrate 1 outside the concave
portion 3 at the time t, a process of adding the layer L.sub.D (as
well as the layer L.sub.E if needed) between steps S3 and S4 at the
time t and steps S3 and S4 at the time t+.DELTA.t.
[0091] The timing to add the layers L.sub.D and L.sub.E may be
arbitrarily set. For example, the layer L.sub.E may be added at the
time when the surface of the insulating material reaches the inside
of the layer L.sub.E, or may be added at the time when the surface
of the insulating material reaches the middle point between the
upper surface and the lower surface of the layer L.sub.E. This is
also applied to the timing to add the above-described nin-th layer
L.sub.9 (FIG. 3B).
[0092] As described above, the topography simulation method of the
present embodiment varies the division number n of the topography
of the substance with the change of the topography of the substance
with the lapse of the time t. Therefore, the present embodiment
makes it possible to realize a faster and more precise topography
simulation by deleting a useless layer and adding a required
layer.
Third Embodiment
[0093] FIG. 9 is a perspective view for illustrating a topography
simulation method of a third embodiment.
[0094] FIG. 9 shows an example of the concave portion 3 having a
columnar shape, similarly to FIG. 4. Reference characters 17, and
.GAMMA..sub.out denote the fluxes of the particles that reach the
upper surface and the lower surface of the concave portion 3,
respectively. Reference character K is the Clausing factor, which
denotes the transmission probability that the particles pass from
the upper surface to the lower surface of the concave portion 3.
Reference character S denotes a reaction probability that the
particle react with the substance inside the concave portion 3 or
outside the concave portion 3. The reaction probability S is also
called sticking probability.
[0095] FIG. 9 shows the flow of the particles in a case where the
flow of the particles in the concave portion 3 is represented by
Coburn reactive transport model. Coburn reactive transport model is
a compensation model in which the reaction probability S is
introduced into Knudsen transport model. Knudsen transport model is
equivalent to Coburn reactive transport model in which the reaction
probability S is one.
[0096] FIG. 9 shows a flux S.GAMMA..sub.out that reacts with the
substance after passing through the concave portion 3, a flux
(1-K).GAMMA..sub.in that is reflected without passing through the
concave portion 3, and a flux K(1-S).GAMMA..sub.out that is
reflected without reacting with the substance after passing through
the concave portion 3. The following expression (16) holds among
these fluxes.
.GAMMA..sub.in-(1-K)-.sub.in-K(1-S).GAMMA..sub.out=S.GAMMA..sub.out
(16)
[0097] Therefore, a flux ratio .GAMMA..sub.out/.GAMMA..sub.in in
Coburn reactive transport model is given by the following
expression (17).
.GAMMA. out .GAMMA. i n = C ( x ) = K ( x ) K ( x ) + S - SK ( x )
( 17 ) ##EQU00013##
[0098] The expression (17) indicates that the Clausing factor K(x)
is replaced with a factor C(x) by replacing Knudsen transport model
with Coburn reactive transport model. The relationship between the
aspect ratio x and the Causing factor K(x) is expressed by the
above-described expression (3).
[0099] FIG. 10 is a graph for illustrating a relationship between
the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in FIG. 9.
[0100] A curve K shows the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in when S=1. Curves C.sub.1 to C.sub.4
show flux ratios .GAMMA..sub.out/.GAMMA..sub.n when S=0.5, S=0.1,
S=0.01 and S=0, respectively. The curve K is the same as the curve
in FIG. 5.
[0101] (1) Topography Simulation Method of Third Embodiment
[0102] The topography simulation method of the present embodiment
is performed in the same manner as the topography simulation method
of the first embodiment. However, the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 in the
present embodiment are calculated assuming that the flow of the
particles in each of the first to eighth layers L.sub.1 to L.sub.8
can be represented by Coburn reactive transport model of the
expression (17).
[0103] Therefore, the surface incident flux
.GAMMA..sub.out.sub.--.sub.k in a k-th layer L.sub.k of the present
embodiment is given by the following expression (18) obtained by
replacing K(x) of the expression (15) with C(x).
.GAMMA. out _ k .GAMMA. i n = C out _ k = C out _ k - 1 C k C out _
k - 1 + C k - C out _ k - 1 C k ( 18 ) C k ( x ) = K k ( x ) K k (
x ) + S - SK k ( x ) ( 19 ) ##EQU00014##
[0104] In this way, the surface incident flux
.GAMMA..sub.out.sub.--.sub.k in the k-th layer L.sub.k of the
present embodiment is calculated based on the surface incident flux
.GAMMA..sub.out.sub.--.sub.k-1 (=C.sub.out.sub.--.sub.k-1) in a
(k-1)-th layer L.sub.k-1 adjacent to the k-th layer L.sub.k, the
transmission probability K.sub.k of the k-th layer L.sub.k, and the
reaction probability S of the particles.
[0105] The surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 calculated in this way are used for
calculating the amounts of change .DELTA.r.sub.1 to .DELTA.r.sub.8
of the radii r.sub.1 to r.sub.8 in step S4.
[0106] As described above, the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 in the
present embodiment are calculated using Coburn reactive transport
model. Therefore, the present embodiment makes it possible to
simulate the topography change of the substance to be processed
into various topography with high precision by taking the reaction
probability S of the particles into consideration.
First Modification of First to Third Embodiments
[0107] In the first embodiment, the surface incident fluxes
.GAMMA..sub.out.sub.--.sub.1 to .GAMMA..sub.out.sub.--.sub.8 are
calculated using Knudsen transport model. Knudsen transport model
well fits the behavior of the particles moving isotropically like
radicals. Therefore, when the present embodiment is applied to the
particles moving anisotropically like ions, it is desirable that
the surface incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 are calculated using a model different
from Knudsen transport model.
[0108] FIG. 11 is a graph showing an example of angle distribution
of the ions used for processing a semiconductor device. The
vertical axis in FIG. 11 denotes an ion intensity I. The horizontal
axis in FIG. 11 denotes an angle .theta.. FIG. 11 shows an example
that the angle distribution of the ions follows a normal
distribution. Reference character .sigma. denotes the standard
deviation of the normal distribution. The unit of the angle .theta.
and the standard deviation .sigma. is radian, for example. A width
2.sigma. shown in FIG. 11 corresponds to a half width of the angle
distribution of the ions.
[0109] FIG. 12 is a perspective view for illustrating a
relationship between the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in in the case of using the ions.
[0110] FIG. 12 shows an example of the concave portion 3 having a
columnar shape, similarly to FIGS. 4 and 9. Reference characters
.GAMMA..sub.in and .GAMMA..sub.out denote the fluxes of the
particles that reach the upper surface and the lower surface of the
concave portion 3, respectively. Reference character x denotes the
aspect ratio of the concave portion 3. An angle 2.alpha. shown in
FIG. 12 corresponds to an angular aperture in a case where the
aperture is looked up at from the bottom portion of the concave
portion 3 having the aspect ratio x.
[0111] When the ions are used for processing the semiconductor
device, there is a problem with the ratio of the angular aperture
2.alpha., to the half width 2.sigma.. In a case where the ratio
.alpha./.sigma. is small, since the angular aperture 2.alpha. of
the concave portion 3 is large relative to the half width 2.sigma.,
many ions can reach the bottom surface of the concave portion 3. In
contrast, in a case where the ratio .alpha./.sigma. is large, since
the angular aperture 2.alpha. of the concave portion 3 is small
relative to the half width 2.sigma., many ions cannot reach the
bottom surface of the concave portion 3. Therefore, when the ions
are used for processing the semiconductor device, the surface
incident fluxes .GAMMA..sub.out.sub.--.sub.1 to
.GAMMA..sub.out.sub.--.sub.8 depend on the half width 2.sigma..
[0112] The flux ratio .GAMMA..sub.out/.GAMMA..sub.in in FIG. 12 is
given by the following expression (20) when the angle distribution
of the ions in FIG. 11 is applied:
.GAMMA. out .GAMMA. i n = erf ( arctan ( 1 / ( 2 x ) ) .sigma. 2 )
( 20 ) ##EQU00015##
[0113] where "erf" denotes an error function, "arc tan" denotes arc
tangent, ".sigma." denotes the standard deviation of the normal
distribution, and "x" denotes the aspect ratio.
[0114] FIG. 13 is a graph for illustrating the relationship between
the aspect ratio x and the flux ratio
.GAMMA..sub.out/.GAMMA..sub.in the case of using the ions.
[0115] Curves C.sub.1 to C.sub.4 the flux ratios
.GAMMA..sub.out/.GAMMA..sub.in when .sigma.=0.1, .sigma.=0.05,
.sigma.=0.02 and .sigma.=0, respectively. When comparing FIG. 5 and
FIG. 13, the flux ratios .GAMMA..sub.out/.GAMMA..sub.in with the
same aspect ratio x are larger in the case of FIG. 5 than in the
case of FIG. 13. It is therefore understood that the ions are more
likely to reach the bottom surface of the concave portion 3 than
the radicals.
[0116] The first embodiment can be applied to the particles moving
anisotropically like the ions by replacing the function form of the
transmission probability K(x) of the expression (3) with a function
form shown in FIG. 13. In this case, the transmission probability
K(x) is a function of the aspect ratio and the half width 2.alpha..
The half width 2.sigma. is an example of a distribution parameter
representing the distribution of the particles.
[0117] In addition, the third embodiment can be applied to the
particles moving anisotropically like the ions by using the
function form shown in FIG. 13.
Second Modification of First to Third Embodiments
[0118] FIGS. 14A and 14B are cross sectional views for illustrating
a topography simulation method of a modification of the first to
third embodiments.
[0119] In FIGS. 2A and 2B, the main surface of the substrate 1 in
the initial structure of the substance is set to be a flat plane.
In contrast, in FIGS. 14A and 14B, the main surface of the
substrate 1 in the initial structure of the substance includes a
difference in level. Therefore, the mask layer 2 in FIGS. 14A and
14B includes a first upper surface which is a higher upper surface,
and a second upper surface which is a lower upper surface. The
first to third embodiments can be also applied to such an initial
structure.
[0120] When the substance as shown in FIG. 14A is actually
processed, the aperture is likely to be closed in the vicinity of
the side surface of the mask layer 2. Therefore, when the
processing of the topography of such a substance is simulated, it
is desirable that a calculation with high precision is performed to
the vicinity of the side surface of the mask layer 2. Therefore, in
FIG. 14B, a thickness T.sub.1 of layers L.sub.1 to L.sub.4 close to
the side surface of the mask layer 2 is set to be small, and a
thickness T.sub.2 of layers L.sub.5 to L.sub.9 far from the side
surface of the mask layer 2 is set to be large. In the present
modification, the start position of dividing the topography of the
substance (the upper surface of the first layer L.sub.1) is set at
the second upper surface (lower upper surface) of the mask layer 2,
the end position of dividing the topography of the substance (the
lower surface of the nin-th layer L.sub.9) is set at the bottom
surface of the concave portion 3.
[0121] When the substance as shown in FIG. 14A is actually
processed, the topography change of the concave portion 3 is often
affected by forming a deposition layer on the side surface and the
mask layer 2 or etching the side surface of the mask layer 2.
Therefore, the present modification may handle, as a target of the
topography simulation, the topography change of the mask layer 2 as
well as the topography change of the substrate 1. In this case, it
is desirable to separately set, as a processing rate R.sub.p in the
expression (1), the processing rate of the substrate 1 and the
processing rate of the mask layer 2.
Fourth Embodiment
[0122] FIG. 15 is an external view showing a configuration of a
topography simulation apparatus of a fourth embodiment.
[0123] The topography simulation apparatus in FIG. 15 includes a
controller 11, a display module 12, and an input module 13.
[0124] The controller 11 controls the operation of the topography
simulation apparatus. For example, the controller 11 performs one
of the topography simulation methods of the first to third
embodiments. The controller 11 will be described in detail
hereafter.
[0125] The display module 12 includes display devices such as a
liquid crystal monitor. For example, the display module 12 displays
a screen for inputting setting information for the topography
simulation, and calculation results of the topography
simulation.
[0126] The input module 13 includes input devices such as a
keyboard 13a and a mouse 13b. For example, the input module 13 is
used for inputting the setting information for the topography
simulation. Examples of the setting information include information
on calculation expressions, information on experimental values or
predicted values, information on the structure of the substance,
information on the flux of the particles, and instruction
information on conditions or procedures of the topography
simulation.
[0127] FIG. 16 is a block diagram showing a configuration of the
controller 11 in FIG. 15.
[0128] The controller 11 includes a central processing unit (CPU)
21, a read only memory (ROM) 22, a random access memory (RAM) 23, a
hard disk drive (HDD) 24, a memory drive 25 such as a compact disc
(CD) drive or digital versatile disk (DVD) drive, and a memory
interface (I/F) 26 such as a memory port or a memory slot.
[0129] In the present embodiment, a topography simulation program
for one of the topography simulation methods of the first to third
embodiments is stored in the ROM 22 or the HDD 24. When
predetermined instruction information is inputted from the input
module 13, the CPU 21 reads the program from the ROM 22 or the HDD
24, expands the read program on the RAM 23, and performs the
topography simulation under this program. Various types of data
generated with this process are held in the RAM 23.
[0130] In the present embodiment, a non-transitory computer
readable recording medium in which the topography simulation
program is stored may be prepared to install the topography
simulation program to the ROM 22 or the HDD 24 from the recording
medium. Examples of such a recording medium include CD-ROMs and
DVD-ROMs.
[0131] In the present embodiment, the topography simulation program
may be installed into the ROM 22 or the HDD 24 by downloading it
via a network such as the Internet.
[0132] As described above, the present embodiment makes it possible
to provide the topography simulation apparatus and the topography
simulation program for performing the topography simulation methods
of the first to third embodiments.
[0133] While certain embodiments have been described, these
embodiments have been presented by way of example only, and are not
intended to limit the scope of the inventions. Indeed, the novel
apparatuses, methods and media described herein may be embodied in
a variety of other forms; furthermore, various omissions,
substitutions and changes in the form of the apparatuses, methods
and media described herein may be made without departing from the
spirit of the inventions. The accompanying claims and their
equivalents are intended to cover such forms or modifications as
would fall within the scope and spirit of the inventions.
* * * * *