Skip to main content

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 43))

Abstract

A non-linear hyperbolic conservation law, used to model the Ion etching process in a single material, is solved using an Essentially Non-Oscillatory (E.N.O.) scheme with a Runge Kutta time stepping routine. The model is extended to deal with a two material configuration which is separated by a moving boundary. The numerical solution of this problem involves the introduction of a co-ordinate stretching to deal with physical restrictions at the moving boundary. A convergence result for the numerical algorithm is shown. Numerical solutions to etched profiles in a single and double material configuration are presented.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. D. S. Ross. Ion etching: An application of the mathematical theory of hyperbolic conservation laws. Journal of Electrochemical Society, 135:1235, 1988.

    Article  Google Scholar 

  2. D. S. Ross. Evolution of material boundaries under ion bombardment. Journal of Electrochemical Society, 135:1260, 1988.

    Article  Google Scholar 

  3. A. Harten, B. Engquist, S. Osher and S.R. Chakravathy. Uniformly high order accurate essentially non-oscillatory schemes,iii. Journal Of Computational Physics, 71:231, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Shu and S. Osher. Efficient implementation of essentially non-oscillatory shock capturing schemes,ii. Journal of Computational Physics, 83:32, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  5. E.M. Ronquist and A.T. Patera. A legendre spectral element method for the stefan problem. International Journal for Numerical Methods in Engineering, 24:2273, 1987.

    Article  MathSciNet  Google Scholar 

  6. E. S. G. Shaqfeh and C. W. Jurgensen. Simulation of reactive ion etching pattern transfer. Journal of Applied Physics, 66:4664, 1989.

    Article  Google Scholar 

  7. S.J. Sherwin. Numerical simulation of the ion etching process. Master’s thesis, Princeton University, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrea Donato Francesco Oliveri

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

About this chapter

Cite this chapter

Sherwin, S.J., Orszag, S.A., Barouch, E., Karniadakis, G.E. (1993). Application of an E.N.O. Scheme to Simulate the Ion Etching Process. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_65

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-87871-7_65

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07643-6

  • Online ISBN: 978-3-322-87871-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics