Simulation method and simulation program

• US 8,209,155 B2
• Filed: 08/15/2008
• Issued: 06/26/2012
• Est. Priority Date: 08/16/2007
• Status: Active Grant

• Current Assignee: Kioxia Corporation
• Original Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Inventors: Ichikawa, Takashi, Tamaoki, Naoki, Takase, Toshiro
• Primary Examiner(s): ALHIJA, SAIF A
• Application Number:
  US12/192,179
• Publication Number:
  US 20090055143A1
• Time in Patent Office: 1,411 Days
• Field of Search: 703/2
• US Class Current: 703/2
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]

Abstract

A simulation method includes dividing a material surface into finite computational elements, and calculating a deposition rate or etching rate at each of the computational elements to simulate a feature profile of the material surface, the calculating including calculating an indirect effect of a first computational element on the deposition rate or etching rate of a second computational element. The calculating the indirect effect includes correcting a surface profile at the first computational element on the basis of a surface structure around the first computational element, and calculating the indirect effect on the basis of the corrected surface profile at the first computational element.

Claims

1. A simulation method comprising:

dividing a material surface into finite computational elements using a computer; and

calculating a rate of one of deposition and etching at each of the computational elements to simulate a feature profile of the material surface using the computer, the calculating including calculating an indirect effect of a first computational element on the rate at a second computational element,

the calculating the indirect effect including;

correcting a surface profile at the first computational element on the basis of a surface structure around the first computational element using a level set method; and

calculating the indirect effect on the basis of the corrected surface profile at the first computational element,

wherein the correction of the surface profile includes approximating at least part of the surface profile at the first computational element to a curved surface which is continuous to the surface around the first computational element.

2. The method according to claim 1, wherein the indirect effect is a flux of species reflected at the first computational element and reaching the second computational element.

3. The method according to claim 1, wherein the indirect effect is a component of a rate for species reflected at the first computational element and reaching the second computational element.

4. The method according to claim 3, wherein the calculating the indirect effect includes calculating an angular distribution of species reflected at the first computational element.

5. The method according to claim 1, wherein the indirect effect is a flux of sputtered material which is sputtered by species impinging on the first computational element and reaches the second computational element.

6. The method according to claim 1, wherein the indirect effect is a component of a rate for sputtered material which is sputtered by species impinging on the first computational element and reaches the second computational element.

7. The method according to claim 6, wherein the calculating the indirect effect includes calculating an angular distribution of the sputtered material which is sputtered at the first computational element.

8. The method according to claim 1, wherein the correction of the surface profile includes approximating the curved surface with a normal vector.

9. A simulation method comprising:

dividing a material surface into finite computational elements using a computer; and

calculating a rate of one of deposition and etching at each of the computational elements to simulate a feature profile of the material surface using the computer, the calculating including calculating an indirect effect on the rate at one computational element exerted by all the other computational elements,

the calculating the indirect effect including;

correcting a surface profile at the all the other computational elements on the basis of a surface structure around each of the all the other computational elements using a level set method; and

calculating the indirect effect for a plurality of reflections on the basis of the corrected surface profile at the all the other computational elements,

wherein the correction of the surface profile includes approximating at least part of the surface profile of at least one of the all the other computational elements to a curved surface which is continuous to the surface around the one of the all the other computational elements.

10. The method according to claim 9, wherein geometrical factors at the at least one of the all the other computational elements are expressed in a form dependent on the curvature of the curved surface.

11. A simulation program configured to cause a computer to perform a simulation, the simulation including:

dividing a material surface into finite computational elements; and

calculating a rate of one of deposition and etching at each of the computational elements to compute a feature profile of the material surface, the calculating including calculating an indirect effect of a first computational element on the rate at a second computational element,

in calculating the indirect effect, the simulation program causing the computer to perform;

correcting a surface profile at the first computational element on the basis of a surface structure around the first computational element using a level set method; and

calculating the indirect effect on the basis of the corrected surface profile at the first computational element,

wherein the correction of the surface profile includes approximating at least part of the surface profile at the first computational element to a curved surface which is continuous to the surface around the first computational element.

12. The program according to claim 11, wherein the indirect effect is a flux of species reflected at the first computational element and reaching the second computational element.

13. The program according to claim 11, wherein the indirect effect is a component of a rate for species reflected at the first computational element and reaching the second computational element.

14. The program according to claim 13, wherein the calculating the indirect effect includes calculating an angular distribution of species reflected at the first computational element.

15. The program according to claim 11, wherein the indirect effect is a flux of sputtered material which is sputtered by species impinging on the first computational element and reaches the second computational element.

16. The program according to claim 11, wherein the indirect effect is a component of a rate for sputtered material which is sputtered by species impinging on the first computational element and reaches the second computational element.

17. The program according to claim 16, wherein the calculating the indirect effect includes calculating an angular distribution of the sputtered material which is sputtered at the first computational element.

18. The program according to claim 11, wherein the correction of the surface profile includes approximating the curved surface with a normal vector.