Skip to main content

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

  • 315 Accesses

Abstract

In the case of a device simulation the BTE has to be solved self-consistently with the Poisson equation for the electric field [6.1]. To this end the RS is discretized with a tensor-product grid as described in the first section of this chapter. The material parameters, like the germanium concentration, doping, etc, are defined on this grid together with the boundary conditions. The germanium-dependent band edges are given in the next section. The discrete Poisson equation is presented next and in the fourth section the self-consistent solution of the BTE and Poisson is discussed. The extension to a nonlinear Poisson equation based on the zero-current approximation for one carrier type is given in the following section. Nonself-consistent MC simulations, where the electric field is calculated with a momentum-based method, are introduced in the sixth section. A method for the enhancement of rare events (e.g. impact ionization) is discussed in the next section. In the following two sections methods for the evaluation of terminal currents and inclusion of contact resistances are presented. Finally, the normalization of physical quantities is discussed in the last section of this chapter.

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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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.

References

  1. R.W. Hockney and J.W. Eastwood, Computer Simulation Using Particles Institute of Physics Publishing, Bristol, Philadelphia, 1988.

    Book  Google Scholar 

  2. J. D. Cressler, “Re-engineering silicon: Si-Ge heterojunction bipolar technology”, IEEE Spectrum vol. 3, pp. 49–55, 1995.

    Article  Google Scholar 

  3. A. Schuppen, “SiGe-HBTs for mobile communication”, Solid-State Electron. vol. 43, pp. 1373–1381, 1999.

    Article  Google Scholar 

  4. C. K. Maiti and G. A. Armstrong, Applications of Silicon-Germanium Heterostructure Devices Series in Optics and Optoelectronics. Institute of Physics Publishing, Bristol, Philadelphia, 2001.

    Book  Google Scholar 

  5. L. Risch, H. Schäfer, B. Lustig, F. Hofmann, U. Scheler, M. Franosch, W. Roesner, T. Aeugle, and H. Fischer, “Channel engineering using RP-CVD epitaxy for high performance CMOS transistors”, in Proc. ESSDERC Bologna, 1996, vol. 26, pp. 321–324.

    Google Scholar 

  6. P. Bouillon, T. Skotnicki, S. Bodnar, C. Morin, J.-L. Regolini, P. Gouagout, and P. Dollfus, “Experiments with 0.18µm SiGe channel pMOSFETs and p+ polySiGe gate”, in Proc. ESSDERC Bologna, 1996, vol. 26, pp. 473–476.

    Google Scholar 

  7. T. Takagi, A. Inoue, Y. Hara, Y. Kanzawa, and M. Kubo, “A novel high performance SiGe channel heterostructure dynamic threshold pMOSFET (HDTMOS)”IEEE Electron Device Lett. vol. 22, no. 5, pp. 206–208, 2001.

    Article  Google Scholar 

  8. J. L. Hoyt, H. M. Nayfeh, S. Eguchi, I. Aberg, G. Xia, T. Drake, E. A. Fitzgerald, and D. A. Antoniadis, “Strained silicon MOSFET technology”, IEDM Tech. Dig. pp. 23–26, 2002.

    Google Scholar 

  9. K. Rim, J. L. Hoyt, and J. F. Gibbons, “Fabrication and analysis of deep sub-micron strained-Si N-MOSFET’s”, IEEE Trans. Electron Devices vol. 47, no. 7, pp. 1406–1415, 2000.

    Article  Google Scholar 

  10. C. Jungemann, S. Keith, and B. Meinerzhagen, “Full-band Monte Carlo device simulation of a Si/SiGe-HBT with a realistic Ge profile”IEICE Trans. on Electronics vol. E83-C, no. 8, pp. 1228–1234, 2000.

    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. F. Schäffier, “High-mobility Si and Ge structures”Semicond. Sci. Technol. vol. 12, pp. 1515–1549, 1997.

    Article  Google Scholar 

  13. D.Nuernbergk,“Simulation des Transportverhaltens in Si/Sir-Gex/Si-Heterobipolartransistoren”,Dissertation, Technische Universität Ilmenau, Ilmenau,1999,(H. Utz Verlag Wissenschaft,München: 1999).

    Google Scholar 

  14. J. W. Slotboom and H. C. de Graaf, “Measurements of bandgap narrowing in Si bipolar transistors”, Solid-State Electron. vol. 19, pp. 857–862, 1976.

    Article  Google Scholar 

  15. D. B. M. Klaassen, J. W. Slotboom, and H. C. de Graaf, “Unified apparent bandgap narrowing in n-and p-type silicon”Solid-State Electron vol. 35, pp. 125–129, 1992.

    Article  Google Scholar 

  16. R. J. E. Hueting, J. W. Slotboom, A. Pruijmboom, W. B. de Boer, C E Timmering, and N. E. B. Cowern, “On the optimization of SiGe-base bipolar transistors”IEEE Trans. Electron Devices vol. 43, no. 9, pp. 1518–1524, 1996.

    Article  Google Scholar 

  17. M. A. Green, “Intrinsic concentration, effective densities of states, and effective mass in silicon”J. Appl. Phys. vol. 67, pp. 2944–2954, 1990.

    Article  Google Scholar 

  18. H. K. Dirks, “Kapazitätskoeffizienten nichtlinearer dissipativer Systeme”, Habilitationsschrift, RWTH Aachen, 1988.

    Google Scholar 

  19. J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, New York, 2nd edition, 1975.

    MATH  Google Scholar 

  20. S. M. Sze, Physics of Semiconductors Devices, Wiley, New York, 1981.

    Google Scholar 

  21. R. S. Varga, Matrix Iterative Analysis, Series in Automatic Computation. Prentice-Hall, Englewood Cliffs, New Jersey, 1962.

    Google Scholar 

  22. 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 

  23. M. Saraniti, A. Rein, G. Zandler, P. Vogl, and P. Lugli, “An efficient multigrid poisson solver for device simulations”IEEE Trans. Computer-Aided Des. vol. 15, pp. 141–150, 1996.

    Article  Google Scholar 

  24. J. Stoer and R. Bulirsch, Einführung in die Numerische Mathematik, vol. 2, Springer, Berlin Heidelberg New York, 2nd edition, 1978.

    MATH  Google Scholar 

  25. P. W. Rambo and J. Denavit, “Time stability of Monte Carlo device simulation”IEEE Trans. Computer-Aided Des. vol. 12, pp. 1734–1741, 1993.

    Article  Google Scholar 

  26. A. Ghetti, X. Wang, F. Venturi, and F. A. Leon, “Stability issues in self-consistent Monte Carlo simulations”, in Proc. SISDEP, Erlangen, 1995, vol. 6, pp. 388–391.

    Google Scholar 

  27. P.W. Rambo and J. Denavit, “Time-step stability for self-consistent Monte Carlo device simulations”, inProc. IWCE, Portland, Oregon (USA), May 1994, pp. 33–36.

    Google Scholar 

  28. F. Liebig, A. Abou Elnour, and K. Schünemann, “An implicit coupling scheme for the use of long time steps in stable self-consistent particle simulation of semiconductor devices with high doping levels”, in Proc. SISPAD Tokyo, 1996, pp. 45–46.

    Google Scholar 

  29. A. Papoulis, Probability,Random Variables and Stochastic Processes Mc GrawHill, 3rd edition, 1991.

    Google Scholar 

  30. S. E. Laux, “On particle-mesh coupling in Monte Carlo semiconductor device simulation”IEEE Trans. Computer-Aided Des. vol. 15, pp. 1266–1277, 1996.

    Article  Google Scholar 

  31. S. Selberherr, Analysis and Simulation of Semiconductor Devices Springer, Wien,1984

    Book  Google Scholar 

  32. J. Stoer, Einführung in die Numerische Mathematik, vol. 1, Springer, Berlin Heidelberg New York, 2nd edition, 1978.

    MATH  Google Scholar 

  33. E. Sangiorgi, B. Riccó, 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 

  34. J. M. Higman, K. Hess, C. G. Hwang, and R. W. Dutton, “Coupled Monte Carlo-drift diffusion analysis of hot-electron effects in MOSFET’s”IEEE Trans. Electron Devices vol. 36, no. 5, pp. 930–937, 1989.

    Article  Google Scholar 

  35. D. Y. Cheng, C. G. Hwang, and R. W. Dutton, “PISCES-MC: A multiwindow and multimethod 2-D device simulator”IEEE Trans. Computer-Aided Des. vol. 7, pp. 1017–1026, 1988.

    Article  Google Scholar 

  36. J. D. Bude and M. Mastrapasqua, “Impact ionization and distribution functions in sub-micron nMOSFET technologies” IEEE Electron Device Lett. vol. 16, no. 10, pp. 439–441, 1995.

    Article  Google Scholar 

  37. C. Jungemann, S. Yamaguchi, and H. Goto, “On the accuracy and efficiency of substrate current calculations for sub-pm n-MOSFET’s”IEEE Electron Device Lett. vol. 17, no. 10, pp. 464–466, 1996.

    Article  Google Scholar 

  38. J. D. Bude,“Monte Carlo simulation of impact ionization feedback in sub-micron MOSFET technologies”, in Este. Abst. of the 1995 kite. Conf. on Solid State Devices and Materials, Osaka1995.

    Google Scholar 

  39. J. Bude, T. Iizuka, and Y. Kamakura, “Determination of threshold energy for hot electron interface state generation”IEDM Tech. Dig. pp. 865–868, 1996.

    Google Scholar 

  40. C. Jungemann, S. Yamaguchi, and H. Goto, “Accurate prediction of hot-carrier effects for a deep sub-pm CMOS technology based on inverse modeling and full band Monte Carlo device simulation”, in Proc. SISPAD 1996, vol. 1, pp. 59–60.

    Google Scholar 

  41. C. Jungemann, S. Yamaguchi, and H. Goto, “Investigation of the influence of impact ionization feedback on the spatial distribution of hot carriers in an NMOSFET”,in Proc. ESSDERC, Stuttgart, 1997, vol. 27, pp. 336–339.

    Google Scholar 

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

    Google Scholar 

  43. H.-J. Schlebusch, “Importance Sampling Techniken zur effizienten Simulation von Kommunikationssystemen”, Doctor thesis, RWTH Aachen, 1991.

    Google Scholar 

  44. 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 Designno 2, 1997.

    Google Scholar 

  45. 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”, IEEETrans. Electron Devices vol. 45, no. 4, pp. 918–924, 1998.

    Article  Google Scholar 

  46. A. M. Kriman and R. P. Joshi, “Scaled ensemble Monte Carlo studies of impact ionization”, in Proc. IWCE Portland, Oregon, May 1994, pp. 57–60.

    Google Scholar 

  47. A. Phillips Jr. and P. J. Price, “Monte Carlo calculations on hot electron energy tails”, Appl. Phys. Lett vol. 30, pp. 528–530, 1977.

    Article  Google Scholar 

  48. S. E. Laux, M. V. Fischetti, and D. J. Frank, “Monte Carlo analysis of semiconductor devices: The DAMOCLES program ”IBM J. Res. Develop. vol. 34, pp. 466–494, 1990.

    Article  Google Scholar 

  49. F. Venturi, R. K. Smith, E. C. Sangiorgi, M. R. Pinto, and B. RiccÒ, “A general purpose device simulation coupling Poisson and Monte Carlo transport with application to deep submicron MOSFET’s” IEEE Trans. Computer-Aided Des. vol. 8, no. 4, pp. 360–369, 1989.

    Article  Google Scholar 

  50. R. Thoma, H. J. Peifer, W. L. Engl, W. Quade, R. Brunetti, and C. Jacoboni, “An improved impact-ionization model for high-energy electron transport in Si with Monte Carlo simulation”J. Appl. Phys. vol. 69, pp. 2300–2311, 1991.

    Article  Google Scholar 

  51. 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 

  52. P. Graf, S. Keith, and B. Meinerzhagen, “Evaluation of solenoidal and statistically enhanced total current densities”Proc. SISPADCambridge, MA (USA), 1997.

    Google Scholar 

  53. P. D. Yoder, K. Gärtner, and W. Fichtner, “A generalized Ramo-Shockley theorem for classical to quantum transport at arbitrary frequencies”J. Appl. Phys. vol. 79, pp. 1951–1954, 1996.

    Article  Google Scholar 

  54. H. Kim, H. S. Min, T. W. Tang, and Y. J. Park, “An extended proof of the Ramo-Shockley theorem” Solid-State Electron. vol. 34, pp. 1251–1253, 1991.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Wien

About this chapter

Cite this chapter

Jungemann, C., Meinerzhagen, B. (2003). Device Simulation. In: Hierarchical Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6086-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6086-2_6

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7226-1

  • Online ISBN: 978-3-7091-6086-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics