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Part of the book series: Computational Microelectronics ((COMPUTATIONAL))

Abstract

The MC method is a stochastic method for the solution of integrals [3.1–3.4]. By formal integration the BTE is transformed into an integral equation, which can be solved with the MC method [3.5–3.12].

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References

  1. J. M. Hammarsley and D. C. HandscombMonte Carlo MethodsMethuen/Chapman and Hall, London, 1964.

    Book  Google Scholar 

  2. F. James, “Monte Carlo theory and practice”Rep. Prog. Phys. vol. 43, pp. 1144–1189, 1980.

    Article  Google Scholar 

  3. R. Y. Rubinstein, Simulation and the Monte Carlo method Wiley series in probability and mathematical statistics. John Wiley & Sons, New York, 1981.

    Google Scholar 

  4. M. H. Kalos and P. A. WhitlockMonte Carlo Methods, Basics vol. 1, John Wiley & Sons, New York, 1986.

    Book  Google Scholar 

  5. T. Kurosawa, “Monte Carlo calculation of hot electron problems”J. Phys. Soc. Jap. vol. 21, pp. 424–426, 1966.

    Google Scholar 

  6. W. Fawcett, A. D. Boardman, and S. Swain, “Monte Carlo determination of electron transport properties in gallium arsenide”, J. Phys. Chem. Solids vol. 31, pp. 1963–1990, 1970.

    Article  Google Scholar 

  7. A. Reklaitis, “The calculation of electron transient response in semiconductors by the Monte Carlo technique”, Phys. Lett. vol. 13, pp. 367–370, 1982.

    Google Scholar 

  8. L. ReggianiHot-Electron Transport in Semiconductors Springer, Berlin, 1985.

    Book  Google Scholar 

  9. C. Jacoboni and P. LugliThe Monte Carlo Method for Semiconductor Device Simulation Springer, Wien, 1989.

    Book  Google Scholar 

  10. M. Nedjalkov and P. Vitanov, “Iteration approach for solving the Boltzmann equation with the Monte Carlo method”Solid-State Electron. vol. 32, pp. 893896, 1989.

    Google Scholar 

  11. H.-J. Peifer, “Monte-Carlo Simulation des Hochenergietransports von Elektronen in submikron MOS-Strukturen”, Doctor thesis, RWTH Aachen, Aachen, 1992, Augustinus Buchhandlung.

    Google Scholar 

  12. C. MoglestueMonte Carlo Simulation of Semiconductor Devices Chapman & Hall, London, 1993.

    Google Scholar 

  13. S. K. Park and K. W. Miller, “Random number generators: Good ones are hard to find”Transactions of the ACM Nov. 1988.

    Google Scholar 

  14. S. BrandtDatenanalyse BI Wissenschaftsverlag, 1992.

    Google Scholar 

  15. P. J. Price, “Monte Carlo calculation of electron transport in solids”Semiconductors and Semimetals vol. 14, pp. 249–309, 1979.

    Article  Google Scholar 

  16. C. Jacoboni and L. Reggiani, “The Monte Carlo method for the solution of charge transport in semiconductors with application to covalent materials”Rev. Mod. Phys. vol. 55, pp. 645–705, 1983.

    Article  Google Scholar 

  17. A. PapoulisProbability,Random Variables and Stochastic Processes Mc GrawHill, 3rd edition, 1991.

    Google Scholar 

  18. H. D. Rees, “Calculation of steady state distribution functions by exploiting stabiblity”Phys. Lett. A vol. 26, pp. 416–417, 1968.

    Article  Google Scholar 

  19. H. Kosina, M. Nedjalkov, and S. Selberherr, “Theory of the Monte Carlo method for semiconductor device simulation”IEEE Trans. Electron Devices vol. 47, no. 10, pp. 1898–1908, 2000.

    Article  Google Scholar 

  20. C. Jacoboni, P. Poli, and L. Rota, “A new Monte Carlo technique for the solution of the Boltzmann transport equation”Solid-State Electron. vol. 31, pp. 523–526, 1988.

    Article  Google Scholar 

  21. M. Nedjalkov and P. Vitanov, “Application of the iteration approach to the ensemble Monte Carlo technique”Solid-State Electron. vol. 33, pp. 407–410, 1990.

    Article  Google Scholar 

  22. E. Sangiorgi, B. Riccò, and F. Venturi, “MOS2: An efficient Monte Carlo simulator for MOS devices”IEEE Trans. Computer-Aided Des. vol. 7, no. 2, pp. 259–271, 1988.

    Article  Google Scholar 

  23. R. Brunetti, C. Jacoboni, A. Matulionis, and V. Dienys, “Effect of interparticle collisions on energy relaxation of carriers in semiconductors”Physica vol. 134B, pp. 369–373, 1985.

    Google Scholar 

  24. P. Konijn, T. G. van de Roer, and F. P. Widdershoven, “An efficient Monte Carlo device simulation code based on rigorous application of internal scattering”Solid-State Electron. vol. 36, pp. 1579–1581, 1993.

    Article  Google Scholar 

  25. W. Shockley, John A. Copeland, and R. P. James “The impedance field method of noise calculation in active semiconductor devices”, in Quantum theory of atoms, molecules and solid state P. O. Lowdin, Ed., pp. 537–563. Academic Press, 1966.

    Google Scholar 

  26. S. M. ErmakowDie Monte-Carlo-Methode und verwandte Fragen R. Oldenbourg, München, Wien, 1975.

    Google Scholar 

  27. C. Jungemann, S Yamaguchi, and H. Goto, “Convergence estimation for stationary ensemble Monte Carlo simulations”IEEE J. Tech. Comp. Aided Design no. 10, 1998.

    Google Scholar 

  28. R.W. Hockney and J.W. EastwoodComputer Simulation Using Particles Institute of Physics Publishing, Bristol, Philadelphia, 1988.

    Book  Google Scholar 

  29. M. V. Fischetti and S. E. Laux, “Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects”Phys. Rev. B vol. 38, pp. 9721–9745, 1988.

    Article  Google Scholar 

  30. C. Jungemann, S. Decker, R. Thoma, W.-L. Engl, and H. Goto “Phase space multiple refresh: A general purpose statistical enhancement technique for Monte Carlo device simulation”IEEE J. Tech. Comp. Aided Design no. 2, 1997.

    Google Scholar 

  31. A. Pacelli and U. Ravaioli, “Analysis of variance-reduction schemes for ensemble Monte-Carlo simulation of semiconductor devices”Solid-State Electron. vol. 41, pp. 599–605, 1997.

    Article  Google Scholar 

  32. M. G. Gray, T. E. Booth, T. J. T. Kwan, and C. M. Snell, “A multi-comb variance reduction scheme for Monte Carlo semiconductor simulators”IEEE Trans. Electron Devices vol. 45, no. 4, pp. 918–924, 1998.

    Article  Google Scholar 

  33. N. G. van KampenStochastic Process in Physics and Chemistry North-Holland Publishing, Amsterdam, 1981.

    Google Scholar 

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© 2003 Springer-Verlag Wien

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Jungemann, C., Meinerzhagen, B. (2003). The Monte-Carlo Method. In: Hierarchical Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6086-2_3

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  • DOI: https://doi.org/10.1007/978-3-7091-6086-2_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7226-1

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