Topography simulation apparatus, topography simulation method, and topography simulation program

1. A topography simulation apparatus comprising a processor and a memory connected to the processor, the memory storing instructions executable by the processor to:

input two-dimensional data indicating a layout of a pattern into the memory;

set topographies of a material at N times T 1 to T N within a calculation region, N being an integer of two or more;

develop the topographies of the material at the times T 3 to T N over time independently, and calculate first to N-th values respectively representing a change in topography of the material from the times T 1 to T N to times T 1 ′to T N ′; and

calculate a topography of the material at time T N+1 , based on the first to N-th values,

wherein the topography of the material at the time T i (i=2, . . . N) is developed before, after, or during the development of the topography of the material at the time T i−1 .

2. The apparatus according to claim 1 ,

wherein the instructions to set the topographies of the material include instructions executable by the processor to set the topographies of the material, based on the two-dimensional data indicating a layout of a pattern of a photomask for processing the material.

3. The apparatus according to claim 2 ,

wherein the instructions to set the topographies of the material include instructions executable by the processor to derive an equation that represents a topography of the material as a function over time, by using the two-dimensional data, and set the topographies of the material, by using the equation.

4. The apparatus according to claim 3 ,

wherein the equation is a function of a distance between a boundary surface in the two-dimensional data and a boundary surface of the material, over time.

5. The apparatus according to claim 1 ,

wherein the instructions to develop the topographies of the material include instructions executable by the processor to develop the topographies of the material at the times T 1 to T N over time in parallel.

6. The apparatus according to claim 1 ,

wherein the first to N-th values respectively represent surface movement amounts at a plurality of locations of the material from the times T 1 to T N to times T 1 ′ to T N ′.

7. The apparatus according to claim 6 ,

wherein the instructions to develop the topographies of the material include instructions executable by the processor to

divide a surface of the material into a plurality of surface segments,

calculate at least one of a total flux of particles that directly or indirectly reach each surface segment, or a local surface movement speed of the material, and

calculate a local surface movement amount of the material, based on the total flux or the local surface movement speed.

8. The apparatus according to claim 1 .

wherein the times T 1 ′ to T N ′ respectively match the times T 2 to T N+1 .

9. The apparatus according to claim 1 ,

wherein the instructions to calculate the topography of the material include instructions executable by the processor to output two-dimensional data that represents a three-dimensional topography of the material at the time T N+1 by contour lines.

10. The apparatus according to claim 1 ,

wherein the instructions to calculate the topography of the material include instructions executable by the processor to calculate a total value of the first to N-th values, and calculate the topography of the material at the time T N+1 based on the total value.

11. The apparatus according to claim 1 ,

wherein the instructions to set the topographies of the material include instructions executable by the processor to correct the topographies of the material at the times T 1 to T N , based on the topography of the material at the time T N+1 ,

wherein the instructions to develop the topographies of the material include instructions executable by the processor to develop the corrected topographies of the material at the times T 1 to T N over time independently, and correct the first to N-th values, and

wherein the instructions to calculate the topography of the material include instructions executable by the processor to correct the topography of the material at the time T N+1 , based on the corrected first to N-th values.

12. A non-transitory computer-readable storage medium storing instructions as a topography simulation program executable by a processor to:

input two-dimensional data indicating a layout of a pattern into a memory;

set topographies of a material at N times T 1 to T N within a calculation region, N being an integer of two or more;

develop the topographies of the material at the times T 1 to T N over time independently, and calculate first to N-th values respectively representing a change in topography of the material from the times T 1 to T N to times T 1 ′ to T N ′; and

calculate a topography of the material at time T N+1 , based on the first to N-th values,

wherein the topography of material at the time T i (i=2. . . N) is developed before, after, or during the development of the topography of the material at the time T i− 1.

13. The non-transitory computer-readable storage medium according to claim 12 ,

wherein the instructions to set the topographies of the material include instructions executable by the processor to set the topographies of the material, based on the two-dimensional data indicating a layout of a pattern of a photomask for processing the material.

14. The non-transitory computer-readable storage medium according to claim 13 ,

wherein the instructions to set the topographies of the material include instructions executable by the processor to derive an equation that represents a topography of the material as a function over time, by using the two-dimensional data, and set the topographies of the material, by using the equation.

15. The non-transitory computer-readable storage medium according to claim 14 ,

wherein the equation is a function of a distance between a boundary surface in the two-dimensional data and a boundary surface of the material, over time.

16. The non-transitory computer-readable storage medium according to claim 12 ,

wherein the instructions to develop the topographies of the material include instructions executable by the processor to develop the topographies of the material at the times T 1 to T N over time in parallel.

17. A topography simulation method comprising:

inputting two-dimensional data indicating a layout of a pattern into a memory;

setting topographies of a material at N times T 1 to T N within a calculation region, wherein N is an integer of two or more;

developing the topographies of the material at the times T 1 to T N over time independently;

calculating first to N-th surface movement amounts of the material from the times T 1 to T N to times T 1 ′ to T N ′, respectively; and

calculating a topography of the material at time T N+1 , based on the first to Nth surface movement amounts,

wherein the topography of the material at the time T i (i=2 , . . . , N) is developed before, after, or during the development of the topography of the material at the time T i−1 .

18. The method according to claim 17 ,

wherein the first to N-th surface movement amounts respectively represent surface movement amounts at a plurality of locations of the material from the times T 1 to T N to times T 1 ′ to T N ′.

19. The method according to claim 18 ,

wherein the developing the topographies of the material includes:

dividing a surface of the material into a plurality of surface segments,

calculating at least one of a total flux of particles that directly or indirectly reach each surface segment, or a local surface movement speed of the material, and

calculating a local surface movement amount of the material based on the total flux or the local surface movement speed.

20. The method according to claim 19 , wherein

calculating the local surface movement amount of the material is based on a function of a distance between a boundary surface of the material at time Ta (Ta=0 seconds ) and a boundary surface of the material at time Tb (Tb>0 seconds ).