Improved algorithm for modeling collision broadening through a sequence of scattering events in semiclassical Monte Carlo

Journal of Applied Physics

Volumn 87, Issue 1, 2000, Pages 303-311

  Register, Leonard F ^a   Hess, Karl ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012616748     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.371861     Document Type: Article

References (18)

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3. Capasso et al., J. Appl. Phys. 53, 3324 (1982).
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6. L. Reggiani, H.-J. Fitting, Th. Hingst, J. Köhn, S. Beauvivre, and L. Varani, Phys. Status Solidi B 194, 667 (1996).
7. Throughout the text as here, this distinction between "bare" and "nominal" carrier energies is made for conceptual accuracy, as a practical matter the real self-energy is typically relatively small compared to the bare energy.
8. J. R. Barker, Physica C 6, 2663 (1973).
9. E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970), pp. 480-486.
10. L. F. Register, in Selected Topics in Electronics and Systems, Vol. 14: Quantum-Based Electronic Devices and Systems, vol. edited by M. Dutta and M. A. Stroscio. series edited by P. K. Tien (World Scientific, Singapore, 1998), pp. 251-279, or L. F. Register, Int. J. High Speed Electron. Syst. 9, 251 (1998).
11. L. F. Register, in Selected Topics in Electronics and Systems, Vol. 14: Quantum-Based Electronic Devices and Systems, vol. edited by M. Dutta and M. A. Stroscio. series edited by P. K. Tien (World Scientific, Singapore, 1998), pp. 251-279, or L. F. Register, Int. J. High Speed Electron. Syst. 9, 251 (1998).
12. While a single carrier is considered for conceptual simplicity in this section, there is nothing in this theoretical discussion that prevents consideration of a multicarrier system coupled to the phonon bath, such as required for consideration of CB effects on impact ionization: simply let the coordinate k represent the multicarrier system, as n represents the multiphonon mode system.
13. f may still be zero.
14. More generally, the basic SEMC method also can be used for time-dependent calculations, and with potential structures that vary in multiple dimensions. See the preliminary work, L. F. Register and K. Hess, Phys. Rev. B 49, 1900 (1994).
15. In Ref. 10, the source term, whether it is a boundary source in real space or a known state, is referred to simply as the "source" while what is called the "intermediate" state here is there referred to as the "initial" state, but this is only a matter of semantics, not physics. 15 The basic SEMC procedure can be repeated sequentially to trace carriers through an unlimited number of scattering "events" - the old intermediate state becomes the new "known" initial state, a new intermediate state is selected stochastically from the old final states, and a new set of final states is generated to replace the complex potential function, each with its own complex potential function, as detailed in Ref. 10 - but this procedure which takes advantage of the lack of accumulating CB is not required for the simulations of this work.
16. L. F. Register and K. Hess, Appl. Phys. Lett. 71, 1222 (1997).
17. The use of approximate but analytically tractable distributions - e.g., purely Lorentzian - corrected via self-scattering events allows complicated distribution functions to be both accurately and easily sampled.
18. J. Bude, K. Hess, and G. J. Iafrate, Phys. Rev. B 45, 10958 (1992).