Abstract
The complicated dependence of the energy on the wave vector makes it impossible to capture all details of the band structure by analytical approximations and the full details of the band structure (full-band) are included in the MC model based on a numerical representation of the band structure [5.1]. The basic properties and symmetries of the band structure of RSi are discussed in the first section of this chapter. The more general case of strained SiGe follows in the next section. The grid and the interpolation method for the energy in the KS are developed in the third section. Based on this grid efficient methods for the calculation of the density of states are discussed in the fourth section and a formulation of the mass tensor consistent with an unstructured tetrahedral grid is given in the fifth section. Methods for the motion of particles in the KS are presented in the sixth section and CPU efficient methods for the selection of the final state are given in the seventh section.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Hess, Ed., Monte Carlo Device Simulation: Full Band and Beyond, Kluwer, Boston, 1991.
S. M. Sze, Physics of Semiconductors Devices, Wiley, New York, 1981.
O. Madelung, Introduction to Solid State Theory, Springer, Berlin, 1978.
E. Klingbeil, Tensorrechnung für Ingenieure, vol. 197 of Hochschultaschenbücher, Bibliographisches Institut, Mannheim, 1966.
M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1_xGex alloys on Si1_yGey substrates”, Phys. Rev. B, vol. 48, pp. 14276–14287, 1993.
M. M. Rieger and P. Vogl, “Electronic-band parameters in strained Si1_xGex alloys on Sil_yGey substrates”, Phys. Rev. B, vol. 50, pp. 8138, 1994, Erratum.
M. L. Cohen and J. R. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors, Springer, New York, 2nd edition, 1989.
G. Lehmann and M. Taut, “On the numerical calculation of the density of states and related properties”, Phys. Status Solidi B, vol. 54, pp. 469–477, 1972.
J. Y. Tang, H. Shichijo, K. Hess, and G. J. Iafrate, “Band-structure dependent impact ionization in silicon and gallium arsenide”, Journal de Physique, vol. 42, pp. 63–69, 1981.
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.
G. Wiesenekker and E. J. Baerends, “Quadratic integration over the three-dimensional Brillouin zone”, J. Phys.: Condens. Matter, vol. 3, pp. 6721–6742, 1991.
R. K. Smith and J. Bude, “Highly efficient full band Monte Carlo simulations”, in Proceedings of the International Workshop on Computational Electronics, Leeds, Aug. 1993, pp. 224–230.
J. Bude and R. K. Smith, “Phase-space simplex Monte Carlo for semiconductor transport”, Semicond. Sci. Technol., vol. 9, pp. 840–843, 1994.
T. Kunikiyo, M. Takenaka, Y. Kamakura, M. Yamaji, H. Mizuno, M. Morifuji, K. Taniguchi, and C. Hamaguchi, “A Monte Carlo simulation of anisotropic electron transport in silicon including full band structure and anisotropic impact—ionization model”, J. Appl. Phys., vol. 75, pp. 297–312, 1994.
E. X. Wang, M. D. Giles, S. Yu, F. A. Leon, A. Hiroki, and S. Odanaka, “Recursive M—tree method for 3—D adaptive tetrahedral mesh refinement and its application to Brillouin zone discretization”, in Proc. SISPAD, Tokyo, Sept. 1996, pp. 67–68.
M. Yamaji, K. Taniguchi, and C. Hamaguchi, “Multi-band Monte Carlo method using anisotropic-analytical multi-band model”, in Proc. SISPAD, Tokyo, Sept. 1996, pp. 63–64.
C. Jungemann, M. Bartels, S. Keith, and B. Meinerzhagen, “Efficient methods for Hall factor and transport coefficient evaluation for electrons and holes in Si and SiGe based on a full-band structure”, in Proc. IWCE, Osaka (Japan), 1998, pp. 104–107.
B. Fischer and K. R. Hofmann, “Discretization of the Brillouin zone by an Octree/Delaunay method with application to full-band Monte Carlo transport simulation”, in Proc. SISPAD, Leuven (Belgium), 1998, pp. 181–184.
C. Jungemann, S. Keith, M. Bartels, and B. Meinerzhagen, “Efficient full-band Monte Carlo simulation of silicon devices”, IEICE Trans. on Electronics, vol. E82-C, no. 6, pp. 870–879, 1999.
B. Fischer, “A full-band Monte Carlo charge transport model for nanoscale silicon devices including strain”, Doctor thesis, University Hannover, Hannover, 1999.
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 Elec¬tronics, vol. E83-C, no. 8, pp. 1228–1234, 2000.
G. Gilat and L. J. Raubenheimer, “Accurate numerical method for calculation frequency-distribution functions in solids”, Phys. Rev., vol. 144, pp. 390–395, 1966.
I. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathematik, B. G. Teubner, Stuttgart, 1991.
C. Jungemann, S. Keith, and B. Meinerzhagen, “Full-band Monte Carlo simulation of a 0.12µm-Si-PMOSFET with and without a strained SiGe-channel”, in IEDM Tech. Dig., San Francisco (USA), 1998, pp. 897–900.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Wien
About this chapter
Cite this chapter
Jungemann, C., Meinerzhagen, B. (2003). Full-Band Structure. In: Hierarchical Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6086-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6086-2_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-7226-1
Online ISBN: 978-3-7091-6086-2
eBook Packages: Springer Book Archive