Skip to main content
Log in

Accelerated redistancing for level set-based process simulations with the fast iterative method

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

The finite iterative method is compared to an industry-hardened fast marching method for accelerating the redistancing step essential for Level Set-based process simulations in the area of technology computer-aided design. We discuss our implementation of the finite iterative method and depict extensions to improve the method for process simulations, in particular regarding stability. Contrary to previously published work, we investigate real-world structures with varying resolutions, originating from the area of process simulation. The serial execution performance as well as error norms are used to compare our approach with an industry-hardened fast marching method implementation. Parallel scalability is discussed based on a shared-memory OpenMP implementation. We show that our approach of the finite iterative method is an excellent candidate for accelerating Level Set-based process simulations, as it offers considerable performance gains both in serial and parallel execution mode, albeit being inferior with respect to accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Suvorov, V., Hössinger, A., Djurić, Z., Ljepojevic, N.: A novel approach to three-dimensional semiconductor process simulation: application to thermal oxidation. J. Comput. Electron 5(4), 291 (2006). doi:10.1007/s10825-006-0003-z

    Article  Google Scholar 

  2. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12 (1988). doi:10.1016/0021-9991(88)90002-2

    Article  MATH  MathSciNet  Google Scholar 

  3. Ertl, O., Selberherr, S.: A fast level set framework for large three-dimensional topography simulations. Comput. Phys. Commun. 180(8), 1242 (2009). doi:10.1016/j.cpc.2009.02.002

    Article  Google Scholar 

  4. Radjenović, B., Radmilović-Radjenović, M.: 3D simulations of the profile evolution during anisotropic wet etching of silicon. Thin Solid Films 517(14), 4233 (2009). doi:10.1016/j.tsf.2009.02.007

    Article  Google Scholar 

  5. Filipovic, L., Selberherr, S.: A method for simulating atomic force microscope nanolithography in the level set framework. Microelectron. Eng. 107, 23 (2013). doi:10.1016/j.mee.2013.02.083

    Article  Google Scholar 

  6. Montoliu, C., Ferrando, N., Gosálvez, M., Cerdá, J., Colom, R.: Level set implementation for the simulation of anisotropic etching. J. Micromech. Microeng. 23(7), 075017 (2013). doi:10.1088/0960-1317/23/7/075017

    Article  Google Scholar 

  7. Silvaco.: Victory Process (2014). http://www.silvaco.com/products/tcad/process_simulation/victory_process/victory_process.html

  8. Jeong, W.K., Whitaker, R.T.: A fast iterative method for Eikonal equations. SIAM J. Sci. Comput. 30(5), 2512 (2008). doi:10.1137/060670298

    Article  MATH  MathSciNet  Google Scholar 

  9. Adalsteinsson, D., Sethian, J.: The fast construction of extension velocities in level set methods. J. Comput. Phys. 148(1), 2 (1999). doi:10.1006/jcph.1998.6090

    Article  MATH  MathSciNet  Google Scholar 

  10. Mauch, S.: A fast algorithm for computing the closest point and distance transform. Tech. Rep. 077. California Institute of Technology (2000)

  11. Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl Acad. Sci. 93(4), 1591 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sethian, J.A., Vladimirsky, A.: Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes. Proc. Natl Acad. Sci. 97(11), 5699 (2000). doi:10.1073/pnas.090060097

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhu, Y.: Adaptively Refined Meshes for Level Set Function. University of British Columbia, Tech. rep (2004)

  14. Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sethian, J.A.: Evolution, level set and fast marching methods for advancing fronts. J. Comput. Phys. 169(2), 503 (2001). doi:10.1006/jcph.2000.6657

    Article  MATH  MathSciNet  Google Scholar 

  16. Herrmann, M.: A domain decomposition parallelization of the fast marching method, annual research briefs. Center for Turbulence Research, pp. 213–225 (2003)

  17. Tugurlan, M.C.: Fast Marching Methods—Parallel Implementation and Analysis. Ph.D. thesis, Louisiana State University (2008)

  18. Breuß, M., Cristiani, E., Gwosdek, P., Vogel, O.: An adaptive domain-decomposition technique for parallelization of the fast marching method. Appl. Math. Comput. 218(1), 32 (2011). doi:10.1016/j.amc.2011.05.041

    Article  MATH  MathSciNet  Google Scholar 

  19. Gunnarsson, J.: Algorithms for representation of 3d regions in radiotherapy planning software. Master’s thesis, Uppsala Universitet (2013)

  20. Li, S., Mueller, K., Jackowski, M., Dione, D., Staib, L.: Physical-space refraction-corrected transmission ultrasound computed tomography made computationally practical. Lect. Notes Comput. Sci. 5242, 280–288 (2008). doi:10.1007/978-3-540-85990-1_34

  21. Fu, Z., Jeong, W.K., Pan, Y., Kirby, R., Whitaker, R.T.: A fast iterative method for solving the Eikonal equation on triangulated surfaces. SIAM J. Sci. Comput. 33(5), 2468 (2011). doi:10.1137/100788951

  22. Jeong, W.K., Whitaker, R.T.: A fast Eikonal equation solver for parallel systems. In Proceedings of the SIAM Conference on Computational Science & Engineering (CSE) (2007)

  23. Dang, F., Emad, N., Fender, A.: A fine-grained parallel model for the fast iterative method in solving eikonal equations. In Proceedings of the International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC) (2013), pp. 152–157. DOI:10.1109/3PGCIC.2013.29

  24. Dang, F., Emad, N.: Multi-level parallel upwind finite difference scheme for anisotropic front propagation. In Proceedings of the International Meeting on High Performance Computing for Computational Science (VECPAR) (2014)

  25. Zhao, H.: A fast sweeping method for Eikonal equations. Math. Comput 74(250), 603 (2005). doi:10.1090/S0025-5718-04-01678-3

    Article  MATH  Google Scholar 

  26. Detrixhe, M., Gibou, F., Min, C.: A parallel fast sweeping method for the Eikonal equation. J. Comput. Phys. 237, 46 (2013). doi:10.1016/j.jcp.2012.11.042

    Article  MathSciNet  Google Scholar 

  27. Hysing, S.R., Turek, S.: The Eikonal equation: numerical efficiency vs. algorithmic complexity on quadrilateral grids. In: Proceedings of Algoritmy, pp. 22–31 (2005)

  28. Sussman, M., Fatemi, E.: An efficient. Interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comput. 20(4), 1165 (1999). doi:10.1137/S1064827596298245

    Article  MATH  MathSciNet  Google Scholar 

  29. Ausas, R.F., Dari, E.A., Buscaglia, G.C.: A geometric mass-preserving redistancing scheme for the level set function. Int. J. Numer. Methods Fluids 65(8), 989 (2011). doi:10.1002/fld.2227

  30. Losasso, F., Fedkiw, R., Osher, S.: Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids 35(10), 995 (2006). doi:10.1016/j.compfluid.2005.01.006

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Austrian Science Fund (FWF) through the Grant P23296. The authors thank Florian Dang from the Université de Versailles, France for valuable discussions concerning the FIM.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Josef Weinbub.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weinbub, J., Hössinger, A. Accelerated redistancing for level set-based process simulations with the fast iterative method. J Comput Electron 13, 877–884 (2014). https://doi.org/10.1007/s10825-014-0604-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-014-0604-x

Keywords

Navigation