[1] I. Babuška and T. Strouboulis. The Finite Element Method and its Reliability. Numerical Mathematics and Scientific Computation. Oxford University Press, 2001.
[2] N. Ben Abdallah and P. Degond. On a Hierarchy of Macroscopic Models for Semiconductors. Journal of Mathematical Physics, 37:3306–3333, 1996.
[3] N. Ben Abdallah, P. Degond, P. Markowich, and C. Schmeiser. High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors. Zeitschrift für angewandte Mathematik und Physik, 52(2):201–230, 2001.
[4] J. Bey. Finite-Volumen- und Mehrgitter-Verfahren für elliptische Randwertprobleme. B. G. Teubner, 1998.
[5] K. Blotekjaer. Transport Equations for Electrons in Two-Valley Semiconductors. IEEE Transactions on Electron Devices, 17(1):38–47, 1970.
[6] Boost C++ Libraries. http://www.boost.org/.
[7] R. Bordawekar, U. Bondhugula, and R. Rao. Can CPUs Match GPUs on Performance with Productivity? Experiences with Optimizing a FLOP-intensive Application on CPUs and GPU. Technical report, IBM T. J. Watson Research Center, 2010.
[8] D. Braess. Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, 1997.
[9] A. Bravaix, C. Guerin, V. Huard, D. Roy, J.M. Roux, and E. Vincent. Hot-Carrier Acceleration Factors for Low Power Management in DC-AC Stressed 40nm NMOS Node at High Temperature. In IEEE International Reliability Physics Symposium, pages 531–548, 2009.
[10] H. Brooks. Scattering by Ionized Impurities in Semiconductors. Physical Review, 83:879–887, 1951.
[11] R. Brunetti. A Many-Band Silicon Model for Hot-Electron Transport at High Energies. Solid State Electronics, 32:1663–1667, 1989.
[12] J. D. Bude. Gate Current by Impact Ionization Feedback in Sub-Micron MOSFET Technologies. IEEE Symposium on VLSI Technology, pages 101–102, 1995.
[13] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods. Springer, 2006.
[14] J. A. Carrillo, I. M. Gamba, A. Majorana, and C. W. Shu. 2D Semiconductor Device Simulations by WENO-Boltzmann Schemes: Efficiency, Boundary Conditions and Comparison to Monte Carlo Methods. Journal of Computational Physics, 214(1):55–80, 2006.
[15] D. M. Caughey and R. E. Thomas. Carrier Mobilities in Silicon Empirically Related to Doping and Field. In Proceedings of the IEEE, volume 55, pages 2192–2193, 1967.
[16] C. Fischer. Bauelementsimulation in einer computergestützten Entwurfsumgebung. PhD thesis, Institute for Microelectronics, TU Wien, 1994.
[17] P. Fleischmann. Mesh Generation for Technology CAD in Three Dimensions. PhD thesis, Institute for Microelectronics, TU Wien, 1999.
[18] W. Freeden, T. Gervens, and M. Schreiner. Constructive Approximation on the Sphere. Numerical Mathematics and Scientific Computation. Clarendon Press, Oxford, 1998.
[19] M. Galler. Multigroup Equations for the Description of the Particle Transport in Semiconductors. Series on Advances in Mathematics for Applied Sciences. World Scientific, 2005.
[20] W. Gautschi. Orthogonal Polynomials. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, 2004.
[21] A. Gnudi, D. Ventura, and G. Baccarani. One-Dimensional Simulation of a Bipolar Transistor by means of Spherical Harmonics Expansion of the Boltzmann Transport Equation. In Proceedings of SISDEP, volume 4, pages 205–213, 1991.
[22] A. Gnudi, D. Ventura, and G. Baccarani. Modeling Impact Ionization in a BJT by Means of Spherical Harmonics Expansion of the Boltzmann Transport Equation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 12(11):1706–1713, 1993.
[23] A. Gnudi, D. Ventura, G. Baccarani, and F. Odeh. Two-Dimensional MOSFET Simulation by Means of a Multidimensional Spherical Harmonics Expansion of the Boltzmann Transport Equation. Solid-State Electronics, 36(4):575–581, 1993.
[24] N. Goldsman. Modeling Electron Transport and Degradation Mechanisms in Semiconductor Submicron Devices. PhD thesis, Cornell University, 1989.
[25] N. Goldsman, L. Hendrickson, and J. Frey. A Physics-Based Analytical/Numerical Solution to the Boltzmann Transport Equation for the Use in Device Simulation. Solid-State Electronics, 34:389–396, 1991.
[26] N. Goldsman, C.-K. Lin, Z. Han, and C.-K. Huang. Advances in the Spherical Harmonic–Boltzmann–Wigner Approach to Device Simulation. Superlattices and Microstructures, 27(2-3):159–175, 2000.
[27] G. H. Golub and C. F. Van Loan. Matrix Computations. John Hopkins University Press, 1996.
[28] L. Grafakos. Classical-Fourier-Analysis. Springer, 2008.
[29] T. Grasser, H. Kosina, M. Gritsch, and S. Selberherr. Using Six Moments of Boltzmann’s Transport Equation for Device Simulation. Journal of Applied Physics, 90(5):2389–2396, 2001.
[30] T. Grasser, Tang T. W., H. Kosina, and S. Selberherr. A Review of Hydrodynamic and Energy-Transport Models for Semiconductor Device Simulation. Proceedings of the IEEE, 91(2):251–274, 2003.
[31] H. Groemer. Geometric Applications of Fourier Series and Spherical Harmonics. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1996.
[32] H.K. Gummel. A Self-Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculations. IEEE Transactions on Electron Devices, 11(10):455–465, 1964.
[33] G. Haase, M. Liebmann, C. Douglas, and G. Plank. A Parallel Algebraic Multigrid Solver on Graphics Processing Units. In High Performance Computing Applications, volume 5938 of LNCS, pages 38–47. Springer, 2009.
[34] R. N. Hall. Electron-Hole Recombination in Germanium. Physical Review, 87(2):387, 1952.
[35] Z. Han, N. Goldsman, and C.-K. Lin. Incorporation of Quantum Corrections to Semiclassical Two-Dimensional Device Modeling with the Wigner–Boltzmann Equation. Solid-State Electronics, 49(2):145–154, 2005.
[36] O. Hansen and A. Jüngel. Analysis of a Spherical Harmonics Expansion Model of Plasma Physics. Mathematical Models and Methods in Applied Sciences, 14:759–774, 2004.
[37] K. A. Hennacy, N. Goldsman, and I. D. Mayergoyz. 2-Dimensional Solution to the Boltzmann Transport Equation to Arbitrarily High-Order Accuracy. In Proceedings of IWCE, pages 118–122, 1993.
[38] K. A. Hennacy, Y. J. Wu, N. Goldsman, and I. D. Mayergoyz. Deterministic MOSFET Simulation Using a Generalized Spherical Harmonic Expansion of the Boltzmann Equation. Solid-State Electronics, 38(8):1485–1495, 1995.
[39] J. S. Hesthaven and T. Warburton. Nodal Discontinuous Galerkin Methods. Springer, 2008.
[40] V. Heuveline, D. Lukarski, and J. P. Weiss. Enhanced Parallel ILU(p)-based Preconditioners for Multi-core CPUs and GPUs – The Power(q)-pattern Method. EMCL Preprint 2011-08, EMCL, 2011.
[41] E. W. Hobson. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, 1955.
[42] S.-M. Hong and C. Jungemann. A Fully Coupled Scheme for a Boltzmann-Poisson Equation Solver Based on a Spherical Harmonics Expansion. Journal of Computational Electronics, 8:225–241, 2009.
[43] S.-M. Hong and C. Jungemann. Inclusion of the Pauli Principle in a Deterministic Boltzmann Equation Solver for Semiconductor Devices. In Proceedings of SISPAD, pages 135–138, 2010.
[44] S.-M. Hong, C. Jungemann, and M. Bollhofer. A Deterministic Boltzmann Equation Solver for Two-Dimensional Semiconductor Devices. In Proceedings of SISPAD, pages 293–296, 2008.
[45] S.-M. Hong, G. Matz, and C. Jungemann. A Deterministic Boltzmann Equation Solver Based on a Higher Order Spherical Harmonics Expansion With Full-Band Effects. IEEE Transactions on Electron Devices, 57(10):2390–2397, 2010.
[46] S.-M. Hong, A.-T. Pham, and C. Jungemann. Deterministic Solvers for the Boltzmann Transport Equation. Springer, 2011.
[47] C. Jacoboni and P. Lugli. The Monte Carlo Method for Semiconductor Device Simulation. Springer, 1989.
[48] S. Jin, S.-M. Hong, and C. Jungemann. An Efficient Approach to Include Full-Band Effects in Deterministic Boltzmann Equation Solver Based on High-Order Spherical Harmonics Expansion. IEEE Transactions on Electron Devices, 58(5):1287 –1294, 2011.
[49] A. Jüngel. Quasi-hydrodynamic Semiconductor Equations. Birkhäuser, 2001.
[50] A. Jüngel. Transport Equations for Semiconductors. Lecture Notes in Physics No. 773. Springer, Berlin, 2009.
[51] C. Jungemann, T. Grasser, B. Neinhüs, and B. Meinerzhagen. Failure of Moments-Based Transport Models in Nanoscale Devices Near Equilibrium. IEEE Transactions on Electron Devices, 52:2404–2408, 2005.
[52] C. Jungemann and B. Meinerzhagen. Hierarchical Device Simulation. Computational Microelectronics. Springer, 2003.
[53] 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. Journal of Applied Physics, 100(2):024502, 2006.
[54] C. Jungemann, S. Yamaguchi, and H. Goto. Investigation of the Influence of Impact Ionization Feedback on Spatial Distribution of Hot Carriers in an NMOSFET. In Proceedings of ESSDERC, pages 336–339, 1997.
[55] E. O. Kane. Band Structure of Indium Antimonide. Journal of Physics and Chemistry of Solids, 1(4):249–261, 1957.
[56] G. E. Karniadakis and S. Sherwin. Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press, 2005.
[57] Khronos Group: OpenCL. http://www.khronos.org/opencl/.
[58] Kitware Inc. ParaView. http://www.paraview.org/.
[59] Kitware Inc. Visualization Toolkit (VTK). http://www.vtk.org/.
[60] H. Kosina, M. Harrer, P. Vogl, and S. Selberherr. A Monte Carlo Transport Model Based on Spherical Harmonics Expansion of the Valence Bands. In Proceedings of SISDEP, pages 396–399, 1995.
[61] T. Kurosawa. Monte Carlo Calculation of Hot Electron Problems. Journal of the Physical Society of Japan, 21:424–426, 1966.
[62] P. W. Lagger. Scattering Operators for the Spherical Harmonics Expansion of the Boltzmann Transport Equation. Master’s thesis, Institute for Microelectronics, TU Wien, 2011.
[63] S.-C. Lee and T.-W Tang. Transport Coefficients for a Silicon Hydrodynamic Model extracted from Inhomogeneous Monte-Carlo Calculations. Solid-State Electronics, 35(4):561 – 569, 1992.
[64] R. J. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, 2002.
[65] H. Lin, N. Goldsman, and I. D. Mayergoyz. Improved Self-Consistent Device Modeling by Direct Solution to Boltzmann and Poisson Equations. In Proceedings of IWCE, pages 143–146, 1992.
[66] H. Lin, N. Goldsman, and I. D. Mayergoyz. Deterministic BJT Modeling by Self-Consistent Solution to the Boltzmann, Poisson and Hole-Continuity Equations. In Proceedings of IWCE, pages 55–59, 1993.
[67] M. Lundstrom. Fundamentals of Carrier Transport. Cambridge University Press, 2000.
[68] P. A. Markowich, C. A. Ringhofer, and C. Schmeiser. Semiconductor Equations. Springer, Wien, New York, 1990.
[69] G. Matz, S.-M. Hong, and C. Jungemann. Spherical Harmonics Expansion of the Conduction Band for Deterministic Simulation of SiGe HBTs with Full Band Effects. In Proceedings of SISPAD, pages 167–170, 2010.
[70] Nath, R. and Tomov, S. and Dongarra, J. An Improved MAGMA GEMM For Fermi Graphics Processing Units. International Journal of High Performance Computing Applications, 24(4):511–515, 2010.
[71] A. Okabe, B. Boots, and K. Sugihara. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley, 1992.
[72] V. Peikert and A. Schenk. A Wavelet Method to Solve High-dimensional Transport Equations in Semiconductor Devices. In Proceedings of SISPAD, pages 299–302, 2011.
[73] A.-T. Pham, C. Jungemann, and B. Meinerzhagen. A Full-Band Spherical Harmonics Expansion of the Valence Bands up to High Energies. In Proceedings of SISPAD, pages 361 –364, 2006.
[74] A.-T. Pham, C. Jungemann, and B. Meinerzhagen. Deterministic Multisubband Device Simulations for Strained Double Gate PMOSFETs including Magnetotransport. In IEDM 2008, pages 1 –4, 2008.
[75] A.-T. Pham, C. Jungemann, and B. Meinerzhagen. A Convergence Enhancement Method for Deterministic Multisubband Device Simulations of Double Gate PMOSFET. In Proceedings of SISPAD, pages 115–118, 2009.
[76] A.-T. Pham, C. Jungemann, and B. Meinerzhagen. On the Numerical Aspects of Deterministic Multisubband Device Simulations for Strained Double Gate PMOSFETs. Journal of Computational Electronics, 8:242–266, 2009.
[77] A. Pierantoni, A. Gnudi, and G. Baccarani. Hot-electron Injection in MOS Devices by Means of the Spherical Harmonics Expansion of the Boltzmann Equation. In Proceeding of ESSDERC, pages 320–323, 1998.
[78] K. Rahmat, J. White, and D. A. Antoniadis. 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, 15(10):1181–1195, 1996.
[79] S. E. Rauch, G. La Rosa, and F. J. Guarin. Role of E-E Scattering in the Enhancement of Channel Hot Carrier Degradation of Deep-Submicron NMOSFETs at High VGS Conditions . IEEE Transactions on Device and Materials Reliability, 1(2):113 –119, 2001.
[80] C. Ringhofer. Space-Time Discretization of Series Expansion Methods for the Boltzmann Transport Equation. SIAM Journal of Numerical Analysis, 38(2):442–465, 2000.
[81] C. Ringhofer. Dissipative Discretization Methods for Approximations to the Boltzmann Equation. Mathematical Models and Methods in Applied Sciences, 11:133–149, 2001.
[82] C. Ringhofer. Numerical Methods for the Semiconductor Boltzmann Equation Based on Spherical Harmonics Expansions and Entropy Discretizations. Transport Theory and Statistical Physics, 31:431–452, 2002.
[83] C. Ringhofer. A Mixed Spectral-Difference Method for the Steady State Boltzmann-Poisson System. SIAM Journal of Numerical Analysis, 41(1):64–89, 2003.
[84] C. Ringhofer, C. Schmeiser, and A. Zwirchmayr. Moment Methods for the Semiconductor Boltzmann Equation on Bounded Position Domains. SIAM Journal of Numerical Analysis, 39(3):1078–1095, 2001.
[85] B. Rivière. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations. SIAM, 2008.
[86] K. Rupp. Numerical Solution of the Boltzmann Transport Equation using Spherical Harmonics Expansions. Master’s thesis, Institute for Analysis and Scientific Computing, TU Wien, 2009.
[87] K. Rupp, A. Jüngel, and T. Grasser. Matrix Compression for Spherical Harmonics Expansions of the Boltzmann Transport Equation for Semiconductors. Journal of Computational Physics, 229(23):8750–8765, 2010.
[88] Y. Saad. Iterative Methods for Sparse Linear Systems, Second Edition. SIAM, 2003.
[89] Y. Saad and M. H. Schultz. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing, 7(3):856–869, 1986.
[90] D. L. Scharfetter and H. K. Gummel. Large-Signal Analysis of a Silicon Read Diode Oscillator. IEEE Transactions on Electron Devices, 16:64–77, 1969.
[91] J. Schöberl. Netgen Mesh Generator. http://sourceforge.net/projects/netgen-mesher/.
[92] D. Schroeder, D. Ventura, A. Gnudi, and G. Baccarani. Boundary Conditions for Spherical Harmonics Expansion of Boltzmann Equation. Electronics Letters, 28(11):995–996, 1992.
[93] S. Selberherr. Analysis and Simulation of Semiconductor Devices. Springer, 1984.
[94] J. R. Shewchuk. Delaunay Refinement Mesh Generation. PhD thesis, School of Computer Science, Carnegie Mellon University, 1997.
[95] W. Shockley and W. T. Read. Statistics of the Recombinations of Holes and Electrons. Physical Review, 87(5):835–842, 1952.
[96] J. Singh. Electronic and Optoelectronic Properties of Semiconductor Structures. Cambridge University Press, 2003.
[97] S. P. Singh. Modeling Multi-Band Effects of Hot-Electron Transport in Simulation of Small Silicon Devices by a Deterministic Solution of the Boltzmann Transport Equation Using Spherical Harmonic Expansion. PhD thesis, Department of Electrical Engineering, University of Maryland, 1998.
[98] K. Sonoda, M. Yamaji, K. Taniguchi, C. Hamaguchi, and S. T. Dunham. Moment Expansion Approach to Calculate Impact Ionization Rate in Submicron Silicon Devices. Journal of Applied Physics, 80(9):5444–5448, 1996.
[99] K. Tomizawa. Numerical Simulation of Submicron Semiconductor Devices. Artech House Inc, 1993.
[100] U. Trottenberg, C. W. Oosterlee, and A. Schuller. Multigrid. Academic Press, 2000.
[101] S.E. Tyaginov, I.A. Starkov, O. Triebl, J. Cervenka, C. Jungemann, S. Carniello, J.M. Park, H. Enichlmair, M. Karner, C. Kernstock, E. Seebacher, R. Minixhofer, H. Ceric, and T. Grasser. Hot-carrier Degradation Modeling Using Full-Band Monte-Carlo Simulations. In Proceedings of IPFA, pages 1 –5, 2010.
[102] H. A. van der Vorst. Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Non-Symmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing, 12:631–644, 1992.
[103] W. V. Van Roosbroeck. Theory of Flow of Electrons and Holes in Germanium and other Semiconductors. Bell System Technical Journal, 29:560–607, 1950.
[104] P. S. Vassilevski. Multilevel Block Factorization Preconditioners. Springer, 2008.
[105] M. C. Vecchi, J. Mohring, and M. Rudan. An Efficient Solution Scheme for the Spherical-Harmonics Expansion of the Boltzmann Transport Equation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 16(4):353–361, 1997.
[106] M. C. Vecchi and M. Rudan. Modeling Electron and Hole Transport with Full-Band Structure Effects by Means of the Spherical-Harmonics Expansion of the BTE. IEEE Transactions on Electron Devices, 45:230–238, 1998.
[107] M. C. Vecchi, D. Ventura, A. Gnudi, and G. Baccarani. Incorporating Full Band-Structure Effects in the Spherical Harmonics Expansion of the Boltzmann Transport Equation. In Proceedings of NUPAD, pages 55–58, 1994.
[108] A. Ventura, D. Gnudi, , and G. Baccarani. Inclusion of Electron-Electron Scattering in the Spherical Harmonics Expansion Treatment of the Boltzmann Transport Equation. In Proceedings of SISDEP, pages 161–164, 1993.
[109] D. Ventura, A. Gnudi, and G. Baccarani. A Deterministic Approach to the Solution of the BTE in Semiconductors. La Rivista del Nuovo Cimento, 18:1–33, 1995.
[110] D. Ventura, A. Gnudi, G. Baccarani, and F. Odeh. Multidimensional Spherical Harmonics Expansion of Boltzmann Equation for Transport in Semiconductors. Applied Mathematics Letters, 5(3):85–90, 1992.
[111] Vienna Computing Library (ViennaCL). http://viennacl.sourceforge.net/.
[112] H. F. Walker and L. Zhou. A Simpler GMRES. Numerical Linear Algebra with Applications, 1(6):571–581, 1994.
[113] W. Wessner. Mesh Refinement Techniques for TCAD Tools. PhD thesis, Institute for Microelectronics, TU Wien, 2006.
[114] W. Zhang, G. Du, Q. Li, A. Zhang, Z. Mo, X. Liu, and P. Zhang. A 3D Parallel Monte Carlo Simulator for Semiconductor Devices. In Proceedings of IWCE, pages 1–4, 2009.