# US 10,482,190 B2 · Topography simulation apparatus, topography simulation method, and topography simulation program > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,482,190 B2 - Document ID: US10482190B2 - Status: Granted - Kind: B2 - Application number: 15/254,077 - Filed: 2016-09-01 - Published: 2017-09-14 - Granted: 2019-11-19 - Earliest claimed: 2016-03-10 - Assignees: Toshiba Memory Corporation - Applicants: Toshiba Memory Corporation - Inventors: Takashi Ichikawa - Web page: https://patentgrep.com/patent/US10482190B2 ## CPC - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - G06F 30/25: using particle-based methods - G06F 30/00: Computer-aided design [CAD] - G06F 2111/10: Numerical modelling - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A topography simulation apparatus includes a processor and a memory connected to the processor. The memory stores instructions executable by the processor to set topographies of a material at N times T1 to TN (N is an integer of two or more) within a calculation region. The memory further stores instructions executable by the processor to develop the topographies of the material at the times T1 to TN over time independently, calculate first to N-th values respectively representing a change in a topography of the material from the times T1 to TN to times T1′ to TN′, and calculate a topography of the material at time TN+1, based on the first to N-th values. ## Claims ### Claim 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 T1 to TN within a calculation region, N being an integer of two or more; develop the topographies of the material at the times T3 to TN over time independently, and calculate first to N-th values respectively representing a change in topography of the material from the times T1 to TN to times T1′to TN′; and calculate a topography of the material at time TN+1, based on the first to N-th values, wherein the topography of the material at the time Ti (i=2, . . . N) is developed before, after, or during the development of the topography of the material at the time Ti−1. ### Claim 2 (depends on 1) 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. ### Claim 3 (depends on 2) 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. ### Claim 4 (depends on 3) 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. ### Claim 5 (depends on 1) 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 T1 to TN over time in parallel. ### Claim 6 (depends on 1) 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 T1 to TN to times T1′ to TN′. ### Claim 7 (depends on 6) 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. ### Claim 8 (depends on 1) The apparatus according to claim 1. wherein the times T1′ to TN′ respectively match the times T2 to TN+1. ### Claim 9 (depends on 1) 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 TN+1 by contour lines. ### Claim 10 (depends on 1) 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 TN+1 based on the total value. ### Claim 11 (depends on 1) 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 T1to TN, based on the topography of the material at the time TN+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 T1 to TN 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 TN+1, based on the corrected first to N-th values. ### Claim 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 T1 to TN within a calculation region, N being an integer of two or more; develop the topographies of the material at the times T1 to TN over time independently, and calculate first to N-th values respectively representing a change in topography of the material from the times T1 to TN to times T1′ to TN′; and calculate a topography of the material at time TN+1, based on the first to N-th values, wherein the topography of material at the time Ti (i=2. . . N) is developed before, after, or during the development of the topography of the material at the time Ti−1. ### Claim 13 (depends on 12) 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. ### Claim 14 (depends on 13) 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. ### Claim 15 (depends on 14) 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. ### Claim 16 (depends on 12) 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 T1 to TN over time in parallel. ### Claim 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 T1 to TN within a calculation region, wherein N is an integer of two or more; developing the topographies of the material at the times T1 to TN over time independently; calculating first to N-th surface movement amounts of the material from the times T1 to TN to times T1′ to TN′, respectively; and calculating a topography of the material at time TN+1, based on the first to Nth surface movement amounts, wherein the topography of the material at the time Ti (i=2 , . . . , N) is developed before, after, or during the development of the topography of the material at the time Ti−1. ### Claim 18 (depends on 17) 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 T1 to TN to times T1′ to TN′. ### Claim 19 (depends on 18) 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. ### Claim 20 (depends on 19) 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 ).