Advertisement

Journal of Computational Electronics

, Volume 6, Issue 4, pp 409–420 | Cite as

Inverse dopant profiling from transient measurements

  • M.-T. Wolfram
Article

Abstract

In this work we investigate inverse problems related to the transient semiconductor device models. Our main focus is the identification of the doping profile from indirect transient measurements of electrical currents and capacitances. We present the underlying analysis and discuss the applied regularization methods. Furthermore we discuss the identifiability of doping profiles and present uniqueness and non-uniqueness results for regularized solutions.

Keywords

Inverse Problem Diffusion Equation Current Measurement Semiconductor Device Capacitance Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    van Roosbroeck, W.R.: Theory of the flow of electrons and holes in germanium and other semiconductors. Bell Syst. Tech. J. 29, 560–607 (1950) Google Scholar
  2. 2.
    Markowich, P.A.: The Stationary Semiconductor Device Equations. Computational Microelectronics. Springer, Vienna (1986) Google Scholar
  3. 3.
    Markowich, P.A., Ringhofer, C.A., Schmeiser, C.: Semiconductor Equations. Springer, Vienna (1990) MATHGoogle Scholar
  4. 4.
    Hinze, M., Pinnau, R.: An optimal control approach to semiconductor design. Math. Model. Method. Appl. Sci. 12(1), 89–107 (2002) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Burger, M., Pinnau, R.: Fast optimal design of semiconductor devices. SIAM J. Appl. Math. 64(1), 108–126 (2003) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Burger, M., Engl, H.W., Markowich, P.A.: Inverse doping problems for semiconductor devices. In: Recent Progress in Computational and Applied PDEs, Zhangjiajie, 2001, pp. 39–53. Kluwer–Plenum, New York (2002) Google Scholar
  7. 7.
    Burger, M., Engl, H.W., Markowich, P.A., Pietra, P.: Identification of doping profiles in semiconductor devices. Inverse Probl. 17(6), 1765–1795 (2001) MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Burger, M., Engl, H.W., Leitao, A., Markowich, P.A.: On inverse problems for semiconductor equations. Milan J. Math. 72, 273–313 (2004) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Fang, W., Ito, K.: Reconstruction of semiconductor doping profile from laser-beam-induced current image. SIAM J. Appl. Math. 54(4), 1067–1082 (1994) MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gajewski, H.: On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors. Z. Angew. Math. Mech. 65(2), 101–108 (1985) MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Wolfram, M.-T.: Semiconductor inverse dopant profiling from transient measurements. Master’s thesis, Johannes Kepler University Linz (2005) Google Scholar
  12. 12.
    Markowich, P.A., Ringhofer, Ch.A.: Stability of the linearized transient semiconductor device equations. Z. Angew. Math. Mech. 67(7), 319–332 (1987) MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Schroder, D.K.: Semiconductor Material and Device Charcterization, 2nd edn. Wiley, New York (1998) Google Scholar
  14. 14.
    Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Mathematics and its Applications, vol. 375. Kluwer Academic, Dordrecht (1996) MATHGoogle Scholar
  15. 15.
    Isakov, V.: Inverse Problems for Partial Differential Equations. Applied Mathematical Sciences, 2nd edn., vol. 127. Springer, New York (2006) MATHGoogle Scholar
  16. 16.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D: Nonlinear Phenom. 11(60), 259–268 (1992) CrossRefGoogle Scholar
  17. 17.
    Dobson, D., Scherzer, O.: Analysis of regularized total variation penalty methods for denoising. Inverse Probl. 12(5), 601–617 (1996) MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Acar, R., Vogel, C.R.: Analysis of bounded variation penalty methods for ill-posed problems. Inverse Probl. 10(6), 1217–1229 (1994) MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Giles, M.B., Pierce, N.A.: An introduction to the adjoint approach to design. Flow Turbul. Combust. 65, 393–415 (2000) MATHCrossRefGoogle Scholar
  20. 20.
    Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1981) MATHGoogle Scholar
  21. 21.
    Fletcher, R.: Practical Methods of Optimization, 2nd edn. Wiley, New York (2001) MATHGoogle Scholar
  22. 22.
    Hinze, M., Pinnau, R.: Multiple solutions to a semiconductor design problem. Technical Report Preprint MATH-NM-14-2003, TU Dresden (2005) Google Scholar

Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.RICAMUniversity LinzLinzAustria

Personalised recommendations