TOPOGRAPHY SIMULATION APPARATUS, TOPOGRAPHY SIMULATION METHOD AND RECORDING MEDIUM
In one embodiment, a topography simulation apparatus includes a division module to divide a substance surface into plural computing elements, a determination module to extend straight lines in plural directions from each computing element, and to determine whether each straight line contacts the substance surface and determine which computing element each straight line contacts, and a calculation module to calculate, based on results of the determinations, a direct flux of a reactive species directly reaching each computing element, and a form factor indicating a positional relationship between the computing elements. When the determinations are performed to calculate the form factor in a case where an ionic species reaching each computing element is reflected, the determinations are performed by setting a cut-off angle for a reflection direction of the ionic species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle.
1 . A topography simulation apparatus comprising:
a division module configured to divide a surface of a substance into a plurality of computing elements;
a determination module configured to extend straight lines in a plurality of directions from each computing element, and configured to determine whether each straight line contacts the surface of the substance and determine which computing element each straight line contacts; and
a calculation module configured to calculate, based on results of the determinations, a direct flux which is a flux of a reactive species directly reaching each computing element, and a form factor indicating a positional relationship between the computing elements,
wherein
when the determinations are performed to calculate the form factor in a case where an ionic species reaching each computing element is reflected, the determination module performs the determinations by setting a cut-off angle for a reflection direction of the ionic species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle, and
when a straight line from a first computing element among the plurality of computing elements contacts a second computing element, the determination module judges whether a straight line from the first computing element contacts a third computing element surrounding the second computing element, and judges whether the third computing element is positioned within the range of the cut-off angle of the first computing element,
the determination module selecting, as the third computing element, a computing element directly adjacent to the second computing element, and a computing element indirectly adjacent to the second computing element through one or more computing elements each having positive results of the judgments, and repeating the judgments until there is no candidate for the third computing element to be selected.
2 . The apparatus of claim 1 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species is generated by sputtering using the ionic species reaching each computing element, the determination module performs the determinations by setting a cut-off angle for a generation direction of the neutral species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle.
3 . The apparatus of claim 1 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species reaching each computing element is scattered from each computing element again, the determination module performs the determinations without performing cut-off for the directions in which the straight lines are extended.
4 . The apparatus of claim 1 , wherein the determination module sets the cut-off angle to be dependent on a number of the computing elements.
5 . The apparatus of claim 1 , wherein the calculation module calculates, by using the direct flux and the form factor, at least one of a total flux which is a flux of the reactive species directly or indirectly reaching each computing element, and a local surface growth rate of the substance.
6 . The apparatus of claim 5 , wherein
the calculation module calculates, based on the results of the determinations, a visibility factor indicating whether the computing elements are visible to each other, and
the calculation module calculates, by using the direct flux, the visibility factor and the form factor, at least one of the total flux and the surface growth rate.
7 . The apparatus of claim 5 , wherein the calculation module performs a time evolution on a level set function defined with a distance from the surface of the substance by using at least one of the total flux and the surface growth rate to calculate a change of topography of the substance.
8 . The apparatus of claim 5 , wherein the calculation module expresses the form factor by a form factor matrix in which half or more of matrix elements are zero, and solves a matrix equation including the matrix elements of the form factor matrix to calculate at least one of the total flux and the surface growth rate.
9 . A topography simulation method comprising:
dividing a surface of a substance into a plurality of computing elements;
extending straight lines in a plurality of directions from each computing element, and determining whether each straight line contacts the surface of the substance and determining which computing element each straight line contacts; and
calculating, based on results of the determinations, a direct flux which is a flux of a reactive species directly reaching each computing element, and a form factor indicating a positional relationship between the computing elements,
wherein
when the determinations are performed to calculate the form factor in a case where an ionic species reaching each computing element is reflected, the determinations are performed by setting a cut-off angle for a reflection direction of the ionic species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle, and
when a straight line from a first computing element among the plurality of computing elements contacts a second computing element, it is judged whether a straight line from the first computing element contacts a third computing element surrounding the second computing element, and judged whether the third computing element is positioned within the range of the cut-off angle of the first computing element,
the judgments comprising selecting, as the third computing element, a computing element directly adjacent to the second computing element, and a computing element indirectly adjacent to the second computing element through one or more computing elements each having positive results of the judgments, and the judgments being repeated until there is no candidate for the third computing element to be selected.
10 . The method of claim 9 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species is generated by sputtering using the ionic species reaching each computing element, the determinations are performed by setting a cut-off angle for a generation direction of the neutral species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle.
11 . The method of claim 9 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species reaching each computing element is scattered from each computing element again, the determinations are performed without performing cut-off for the directions in which the straight lines are extended.
12 . The method of claim 9 , wherein the cut-off angle is set to be dependent on a number of the computing elements.
13 . The method of claim 9 , wherein further comprising calculating, by using the direct flux and the form factor, at least one of a total flux which is a flux of the reactive species directly or indirectly reaching each computing element, and a local surface growth rate of the substance.
14 . The method of claim 13 , wherein further comprising calculating, based on the results of the determinations, a visibility factor indicating whether the computing elements are visible to each other,
wherein at least one of the total flux and the surface growth rate is calculated by using the direct flux, the visibility factor and the form factor.
15 . The method of claim 13 , further comprising performing a time evolution on a level set function defined with a distance from the surface of the substance by using at least one of the total flux and the surface growth rate to calculate a change of topography of the substance.
16 . The method of claim 13 , further comprising expressing the form factor by a form factor matrix in which half or more of matrix elements are zero, and solving a matrix equation including the matrix elements of the form factor matrix to calculate at least one of the total flux and the surface growth rate.
17 . 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:
dividing a surface of a substance into a plurality of computing elements;
extending straight lines in a plurality of directions from each computing element, and determining whether each straight line contacts the surface of the substance and determining which computing element each straight line contacts; and
calculating, based on results of the determinations, a direct flux which is a flux of a reactive species directly reaching each computing element, and a form factor indicating a positional relationship between the computing elements,
wherein
when the determinations are performed to calculate the form factor in a case where an ionic species reaching each computing element is reflected, the determinations are performed by setting a cut-off angle for a reflection direction of the ionic species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle, and
when a straight line from a first computing element among the plurality of computing elements contacts a second computing element, it is judged whether a straight line from the first computing element contacts a third computing element surrounding the second computing element, and judged whether the third computing element is positioned within the range of the cut-off angle of the first computing element,
the judgments comprising selecting, as the third computing element, a computing element directly adjacent to the second computing element, and a computing element indirectly adjacent to the second computing element through one or more computing elements each having positive results of the judgments, and the judgments being repeated until there is no candidate for the third computing element to be selected.
18 . The medium of claim 17 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species is generated by sputtering using the ionic species reaching each computing element, the determinations are performed by setting a cut-off angle for a generation direction of the neutral species, and limiting the directions in which the straight lines are extended within a range of the cut-off angle.
19 . The medium of claim 17 , wherein when the determinations are performed to calculate the form factor in a case where a neutral species reaching each computing element is scattered from each computing element again, the determinations are performed without performing cut-off for the directions in which the straight lines are extended.
20 . The medium of claim 17 , wherein the cut-off angle is set to be dependent on a number of the computing elements.