A deterministic approach to RF noise in silicon devices based on the Langevin-Boltzmann equation

IEEE Transactions on Electron Devices

Volumn 54, Issue 5, 2007, Pages 1185-1192

  Jungemann, Christoph ^a  

^a BUNDESWEHR UNIVERSITY MUNICH   (Germany)

Author keywords

Boltzmann Equation (BE); Electron noise; RF; Small signal

Indexed keywords

BIPOLAR TRANSISTORS; BOLTZMANN EQUATION; COMPUTER SIMULATION; MONTE CARLO METHODS; NANOSTRUCTURES; SEMICONDUCTING SILICON; SPURIOUS SIGNAL NOISE;

ELECTRON NOISE; LANGEVIN-BOLTZMANN EQUATION; SILICON DEVICES; SPHERICAL HARMONICS EXPANSION;

SEMICONDUCTOR DEVICES;

EID: 34247874735     PISSN: 00189383     EISSN: None     Source Type: Journal    
DOI: 10.1109/TED.2007.893210     Document Type: Article

References (41)

1. T = 350/300 GHz and gate delay below 3.3 ps," in IEDM Tech. Dig., 2004, pp. 247-250.
2. A. J. Scholten, L. F. Tiemeijer, R. van Langevelde, R. J. Havens, A. T. A. Z. van Duijnhoven, and V. C. Venezia, "Noise modeling for RF CMOS circuit simulation," IEEE Trans. Electron Devices, vol. 50, no. 3, pp. 618-632, Mar. 2003.
3. T. H. Lee, The Design of CMOS Radio Frequency Integrated Circuits, 1st ed. Cambridge, U.K.: Cambridge Univ. Press, 1998.
4. S. E. Laux and M. V. Fischetti, "Monte-Carlo simulation of submicrometer Si n-MOSFET's at 77 and 300 K," IEEE Electron Device Lett., vol. 9, no. 9, pp. 467-469, Sep. 1988.
5. C. Jungemann, B. Neinhüs, and B. Meinerzhagen, "Comparative study of electron transit times evaluated by DD, HD, and MC device simulation for a SiGe HBT," IEEE Trans. Electron Devices, vol. 48, no. 10, pp. 2216-2220, Oct. 2001.
6. S. Kogan, Electronic Noise and Fluctuations in Solids. Cambridge, U.K.: Cambridge Univ. Press, 1996.
7. S. V. Gantsevich, V. L. Gurevich, and R. Katilius, "Theory of fluctuations in nonequilibrium electron gas," Nuovo Cim., vol. 2, no. 5, p. 5, 1979.
8. C. Moglestue, "Monte-Carlo particle modelling of noise in semiconductors," in Proc. Int. Conf. Noise Phys. Syst. and 1/f Fluctuations, 1983, pp. 23-25.
9. L. Varani, L. Reggiani, T. Kuhn, T. González, and D. Pardo, "Microscopic simulation of electronic noise in semiconductor materials and devices," IEEE Trans. Electron Devices, vol. 41, no. 11, pp. 1916-1925, Nov. 1994.
10. C. Jungemann, B. Neinhüs, S. Decker, and B. Meinerzhagen, "Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices - Part II: Results," IEEE Trans. Electron Devices, vol. 49, no. 7, pp. 1258-1264, Jul. 2002.
11. T. Gonzalez, J. Mateos, M. J. Martin-Martinez, S. Perez, R. Rengel, B. G. Vasallo, and D. Pardo, "Monte Carlo simulation of noise in electronic devices: Limitations and perspectives," in Proc. 3rd Int. Conf. Unsolved Problems Noise, 2003, pp. 496-503.
12. C. E. Korman and I. D. Mayergoyz, "Semiconductor noise in the framework of semiclassical transport," Phys. Rev. B, Condens. Matter, vol. 54, no. 24, pp. 17 620-17 627, Dec. 1996.
13. C. Jungemann and B. Meinerzhagen, "A Legendre polynomial solver for the Langevin-Boltzmann equation," J. Comput. Electron., vol. 3, no. 3/4, pp. 157-160, Oct. 2004.
14. C. Jungemann, A.-T. Pham, B. Meinerzhagen, C. Ringhofer, and M. Bollhöfer, "Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle," J. Appl. Phys., vol. 100, no. 2, pp. 024 502.1-024 502.13, Jul. 2006.
15. A. J. Piazza, C. E. Korman, and A. M. Jaradeh, "A physics-based semiconductor noise model suitable for efficient numerical implementation," IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 18, no. 12, pp. 1730-1740, Dec. 1999.
16. C. Jungemann and B. Meinerzhagen, "A frequency domain spherical harmonics solver for the Langevin-Boltzmann equation," in Proc. Int. Conf. Noise Phys. Syst. and 1/f Fluctuations, AIP, 2005, vol. 780, pp. 777-782.
17. F. Bonani, S. D. Guerrieri, and G. Ghione, "Physics-based simulation techniques for small-signal and large-signal device noise analysis in RF applications," IEEE Trans. Electron Devices, vol. 50, no. 3, pp. 633-644, Mar. 2003.
18. C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation. Wien, Austria: Springer-Verlag, 1989.
19. R. Brunetti, C. Jacoboni, F. Nava, L. Reggiani, G. Bosman, and R. J. J. Zijlstra, "Diffusion coefficient of electrons in silicon," J. Appl. Phys., vol. 52, no. 11, pp. 6713-6722, Nov. 1981.
20. A. H. Marshak and K. M. van Vliet, "Electrical current in solids with position-dependent band structure," Solid State Electron., vol. 21, no. 4, pp. 417-427, 1978.
21. 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, no. 2, pp. 125-129, Feb. 1992.
22. J. D. Jackson, Classical Electrodynamics, 2nd ed. New York: Wiley, 1975.
23. H. K. Gummel, "A self-consistent iterative scheme for one-dimensional steady state transistor calculations," IEEE Trans. Electron Devices vol. ED-11, no. 10, pp. 455-465, Oct. 1964.
24. A. Papoulis, Probability, Random Variables, and Stochastic Processes 3rd ed. New York: McGraw-Hill, 1991.
25. C. Jungemann and B. Meinerzhagen, Hierarchical Device Simulation: The Monte-Carlo Perspective, S. Selberherr, Ed. New York: Springer-Verlag, 2003.
26. W. Shockley, "Currents to conductors induced by a moving point charge," J. Appl. Phys., vol. 9, no. 10, pp. 635-636, Oct. 1938.
27. S. Ramo, "Currents induced by electron motion," Proc. IRE, vol. 27, no. 9, pp. 584-585, Sep. 1939.
28. B. Pellegrini, "Electric charge motion, induced current, energy balance, and noise," Phys. Rev. B, Condens. Matter, vol. 34, no. 8, pp. 5921-5924, Oct. 1986.
29. 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, no. 11, pp. 1251-1253, Nov. 1991.
30. C. Herring and E. Vogt, "Transport and deformation-potential theory for many-valley semiconductors with anisotropic scattering," Phys. Rev. vol. 101, no. 3, pp. 944-962, Feb. 1956.
31. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions New York: Dover, 1972.
32. W. Liang, N. Goldsman, I. Mayergoyz, and P. Oldiges, "2-D MOSFET modeling including surface effects and impact ionization by self-consistent solution of the Boltzmann, Poisson, and hole-continuity equations," IEEE Trans. Electron Devices, vol. 44, no. 2, pp. 257-267, Feb. 1997.
33. F. H. Branin, "Network sensitivity and noise analysis simplified," IEEE Trans. Circuit Theory, vol. CT-20, no. 3, pp. 285-288, May 1973.
34. F. Bonani, G. Ghione, M. R. Pinto, and R. K. Smith, "An efficient approach to noise analysis through multidimentional physics-based models," IEEE Trans. Electron Devices, vol. 45, no. 1, pp. 261-269, Jan. 1998.
35. C. Ringhofer, "Space-time discretization of series expansion methods for the Boltzmann transport equation," SIAM J. Numer. Anal., vol. 38, no. 2, pp. 442-465, 2000.
36. O. Madelung, Introduction to Solid State Theory. Berlin, Germany: Springer-Verlag, 1978.
37. T. Gonzalez, D. Pardo, L. Varani, and L. Reggiani, "Spatial analysis of electronic noise in semiconductor structures," Appl. Phys. Lett., vol. 63, no. 1, pp. 84-86, Jul. 1993.
38. C. Jungemann and B. Meinerzhagen, "Do hot electrons cause excess noise?" Solid State Electron., vol. 50, no. 4, pp. 674-679, Apr. 2006.
39. A. van der Ziel, Noise in Solid State Devices and Circuits. Etobicoke, ON, Canada: Wiley, 1986.
40. D. O. North, "Fluctuations in space-charge-limited currents at moderately high frequencies - Part II: Diodes and negative-grid triodes," RCA Rev., vol. 4, pp. 441-472, 1940.
41. C. Jungemann and B. Meinerzhagen, "In-advance CPU time analysis for stationary Monte Carlo device simulations," IEICE Trans. Electron. vol. E86-C, no. 3, pp. 314-319, 2003.