Simulation of semiconductor devices using a galerkin/spherical harmonic expansion approach to solving the coupled poisson-boltzmann system

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 15, Issue 10, 1996, Pages 1181-1196

  Rahmat, Khalid ^a   White, Jacob ^a   Antoniadis, Dimitri A ^b  

^a USA   (United States)

^b HEWLETT PACKARD LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; HARMONIC ANALYSIS; HARMONIC GENERATION; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING;

ELECTRON DISTRIBUTION FUNCTION; GALERKIN APPROACH; SPHERICAL HARMONIC EXPANSION APPROACH;

SEMICONDUCTOR DEVICES;

EID: 0030263753     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/43.541439     Document Type: Article

References (22)

1. H. D. Rees, "Numerical solution of electron motion in solids," J. Phys. C: Solid State Phys., vol. 5, pp. 641-656, 1972.
2. R. W. Hockney, R. A. Warriner, and M. Reiser. "Two-dimensional particle models in semiconductor-device analysis,Electron. Lett, vol. 10, pp. 484-4486, 1974.
3. [31 Y. L. Le Coz, "Semiconductor device simulation: A spectral method for solution of the Boltzmann Transport Equation," Ph.D. dissertation. Mass. Inst. Technol., 1988.
4. E. M. Conwell and M. O. Vassell, "High-field transport in u-type GaAs,Phys. Rev., vol. 166, no. 3, pp. 797-821. 1968.
5. T. lizuka and M. Fukuma, "Carrier transport simulator for silicon based on carrier distribution function evolutions,Solid Stale Electron, vol. 33, pp. 27-34, 1990.
6. N. Goldsman, L. Hendrickson, and J. Frey. "A physics-based analytical/numerical solution to the Boltzmann transport equation for use in device simulation,Solid Slate Electron., vol. 34, pp. 389-396, 1991.
7. A. Gnudi, D. Ventura, and G. Baccarani, "One-dimensional simulation of a bipolar transistor by means of spherical harmonics expansion of the Boltzmann equation," in Pmc. SJSDF.P Conj, 1991, pp. 205-208.
8. K. A. Hennacy, Y.-J. Yu. N. Goldsman, and I. D. Mayergoyz. "Deterministic MOSFET simulation using a generalized spherical harmonic expansion of the Boltzmann equation,Solid Stale Electron., vol. 38, pp. 1485-1495. 1995.
9. D. Ventura, A. Gnudi, G. Baccarani, and F. Odeh. "Multidimensional spherical harmonics expansion of Boltzmann Equation for transport in semiconductors,Appl. Math. Lets, vol. 5, no. 3, pp. 85, 1992.
10. G. Sansone. Orthogonal Functions. New York: Intersci., 1959.
11. C. Jacoboni and L. Reggiani, "The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials.Rev. Modern Phys., vol. 55, no. 3, pp. 645-704, 1983.
12. K. Rahmat, J. White, and D. A. Antoniadis, "A Galerkin method for the arbitrary order expansion in momentum space of the Boltzmann equation using spherical harmonics," in Proc. NUPAD V, 1994, pp. 133-136.
13. R. D. Richtmcyer and K. W. Motion, Difference Methods for InitialValue Problems. New York: Tntersci., 1967.
14. E. Fatemi and F. Odeh, "Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices," J. Computat. Phys., vol. 108, pp. 209-217, 1993.
15. P. L. Roe, "Approximate Kiemann solvers, parameter vectors, and difference schemes," J. Computat. Phys., vol. 43, pp. 357 372, 1981.
16. [16[ M. Y. Hussaini, A. Kumar, and M. D. Salas, Eds., Algorithmic Trends in Computational Fluid Dynamics. New York: Springer-Verlag, 1991, pp. 341-395,
17. J. M. Onega and W. C. Rheinholdt, Iterative solution of Nonlinear Equations in Several Variables. New York: Academic, 1970.
18. H. Lin, N. Goldsman, and I. D. Mayergoyz, "Device modeling by deterministic self-consistent solution of Poisson and Boltzmann transport equations,Solid State Electron., vol. 35, pp. 769-778, 1992.
19. K. Ralnnat, J. White, and D. A. Antoniadis, "Solution of the Boltzmann Transport Equation in two real space dimensions using a spherical harmonic expansion in momentum space," in IEDM Tech. Dig., 1994. pp. 359-362.
20. A. Gnudi, D. Ventura, and G. Baccarani. "Modeling impact ionization in a BIT by means of a spherical harmonic expansion of the Boltzmann Transport Equation,IEFF. Trans. Computer-Aided Design, vol. 12, pp. 1706-1713. 1993.
21. A. Henning, private communication.
22. K. Rahmat, J. White, and D. A. Antoniadis, "Computation of drain and substrate currents in ultra-short NMOSFET's using the hydrodynamic model.IEEE Trans. Computer-Aided Design, vol. 12, pp. 817-824, 1993.