Modelling silicon etching using inverse methods

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    This paper considers a real-world application of a recently presented alternative form of the Gelfand-Levitan equation. Here is considered the case of potential in the plasma above silicon during the etching process. It is shown that although standard methods have significant challenges, the alternative form of the Gelfand-Levitan equation gives a straightforward way to determine the reflection coefficient from an assumed potential.

     

     


  • Keywords


    Inverse Scattering; Gelfand-Levitan Equation; Reflection Coefficient; One-Dimensional Scattering.

  • References


      [1] D.G. Retzloff and J.W. Cobern, American Vacuum Society Monograph, 1982, private communication.

      [2] K. Chadan and P. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer-Verlag, (1977). https://doi.org/10.1007/978-3-662-12125-2.

      [3] I. Kay and H.E. Moses, Inverse Scattering Papers: 1955-1963, Math Sci Press, (1982).

      [4] K. Budden, Radio Waves in the Ionosphere, Cambridge University Press (1961).

      [5] A.K. Jordan and S. Ahn, “Inverse Scattering Theory and Profile Reconstruction”, IEE,126, (1979),945-962. https://doi.org/10.1049/piee.1979.0175.

      [6] C.S. Morawetz, “Computations with the nonlinear Helmholtz equation”, Comp. and Math. Appl.,7, (1981),319-333.

      [7] B. Defacio and J.H. Rose, “Inverse-scattering theory for the non-spherically-symmetric three-dimensional plasma wave equation”, Phys. Rev.,31, (1985), 897-912. https://doi.org/10.1103/PhysRevA.31.897.

      [8] R.G. Newton, “High frequency analysis of the Marchenko equation”, J. Math. Phys., 23, (1982), 594-613. https://doi.org/10.1063/1.525396.

      [9] J.H. Rose, M. Cheney and B. Defacio, “A perturbation method for inverse scattering”, J. Math. Phys., 25, (1984), 2995-3006. https://doi.org/10.1063/1.526015.

      [10] J.H. Rose, M. Cheney and B. Defacio,” “Three-dimensional inverse scattering: plasma and variable velocity wave equations,” J. Math. Phys., 26, (1985), 345-353. https://doi.org/10.1063/1.526705.

      [11] L.D. Faddeev, “The inverse problem in the quantum theory of scattering”, J. Math. Phys., 4, (1963), 72-85.

      [12] R.G. Newton, “Inverse scattering. II. Three dimensions”, J. Math. Phys., 25, (1980), 493-515.

      [13] P. Deift and E. Trubowitz, “Inverse scattering on the line”, Comm. Pure Appl. Math 32 (1979), 121-251. https://doi.org/10.1002/cpa.3160320202.

      [14] P.C. Sabatier, “Rational reflection coefficients and inverse scattering on the line”, Nuovo Cimento, 78, (1983), 1971-1996. https://doi.org/10.1007/BF02721099.

      [15] E. Kincanon, “Alternative Form of the Gelfand-Levitan Equation”, IJAMR, 10, (2021), 28-31. https://doi.org/10.14419/ijamr.v10i2.31842.


 

View

Download

Article ID: 31930
 
DOI: 10.14419/ijamr.v11i1.31930




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.