Bibliography

[1]

International Technology Roadmap for Semiconductors (ITRS). 2015. url: http://www.itrs2.net.

[2]

C. Tavernier, F. Pereira, O. Nier, D. Rideau, F. Monsieur, G. Torrente, M. Haond, et al. “TCAD Modeling Challenges for 14nm Fully-Depleted SOI Technology Performance Assessment”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2015, pp. 4–7. doi: 10.1109/SISPAD.2015.7292244.

[3]

V. Moroz, L. Smith, J. Huang, M. Choi, T. Ma, J. Liu, Y. Zhang, et al. “Modeling and Optimization of Group IV and III FinFETs and Nano-Wires”. In: Electron Devices Meeting (IEDM), IEEE International. 2014, pp. 7.4.1–7.4.4. doi: 10.1109/IEDM.2014.7047004.

[4]

M. Lundstrom. “Drift-Diffusion and Computational Electronics - Still Going Strong After 40 Years!” In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2015, pp. 1–3. doi: 10.1109/SISPAD.2015.7292243.

[5]

E. Pop. “Energy Dissipation and Transport in Nanoscale Devices”. In: Nano Research 3.3 (2010), pp. 147–169. doi: 10.1007/s12274-010-1019-z.

[6]

D. K. Ferry and C. Jacoboni, eds. Quantum Transport in Semiconductors. Physics of Solids and Liquids. Plenum Press, 1992. isbn: 0306438534.

[7]

C. Jacoboni. Theory of Electron Transport in Semiconductors; a Pathway from Elementary Physics to Nonequilibrium Green Functions. Solid-State Sciences; 165. Springer, 2010. isbn: 9783642105852.

[8]

A. Jüngel. Transport Equations for Semiconductors. Lecture Notes in Physics ; 773. Springer, 2009. isbn: 3540895256. doi: 10.1007/978-3-540-89526-8.

[9]

S. Datta. Electronic Transport in Mesoscopic Systems. 1. paperback ed. (with corr.), reprint. Cambridge Studies in Semiconductor Physics and Microelectronic Engineering. Cambridge University Press, 2002. isbn: 0521416043.

[10]

D. Dolgos. “Full-Band Monte Carlo Simulation of Single Photon Avalanche Diodes”. PhD thesis. Eidgenössische Technische Hochschule Zürich, 2011. url: https://iis.ee.ethz.ch/~schenk/theses/dolgos.pdf.

[11]

M. V. Fischetti and S. E. Laux. “Monte Carlo Analysis of Electron Transport in Small Semiconductor Devices including Band-Structure and Space-Charge Effects”. In: Physical Review B 38.14 (1988), pp. 9721–9745. doi: 10.1103/PhysRevB.38.9721.

[12]

T. Ouisse. Electron Transport in Nanostructures and Mesoscopic Devices: an Introduction. John Wiley & Sons, 2013. isbn: 9781848210509.

[13]

E. Schöll. Theory of Transport Properties of Semiconductor Nanostructures. Vol. 4. Springer Science & Business Media, 2013. isbn: 9780412731006.

[14]

A. Gehring and S. Selberherr. “Evolution of Current Transport Models for Engineering Applications”. In: Journal of Computational Electronics 3.3-4 (2004), pp. 149–155. doi: 10.1007/s10825-004-7035-z.

[15]

U. Mishra and J. Singh. Semiconductor Device Physics and Design. Springer Science & Business Media, 2007. isbn: 9781402064814.

[16]

S. Selberherr. Analysis and Simulation of Semiconductor Devices. Springer, 1984. isbn: 3211818006.

[17]

M. Lundstrom. Fundamentals of Carrier Transport. Cambridge University Press, 2009. isbn: 9780521637244.

[18]

T. Grasser, H. Kosina, M. Gritsch, and S. Selberherr. “Using Six Moments of Boltzmann’s Transport Equation for Device Simulation”. In: Journal of Applied Physics 90.5 (2001), pp. 2389–2396. doi: 10.1063/1.1389757.

[19]

A. Jüngel, S. Krause, and P. Pietra. “A Hierarchy of Diffusive Higher-Order Moment Equations for Semiconductors”. In: SIAM Journal on Applied Mathematics 68.1 (2007), pp. 171–198. doi: 10.1137/070683313.

[20]

D. Vasileska and S. Goodnick. Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling. SpringerLink. Springer, 2011. isbn: 9781441988409.

[21]

W. Van Roosbroeck. “Theory of the Flow of Electrons and Holes in Germanium and other Semiconductors”. In: Bell System Technical Journal 29.4 (1950), pp. 560–607. doi: 10.1002/j.1538-7305.1950.tb03653.x.

[22]

R. Stratton. “Diffusion of Hot and Cold Electrons in Semiconductor Barriers”. In: Physical Review 126 (6 1962), pp. 2002–2014. doi: 10.1103/PhysRev.126.2002.

[23]

N. B. Abdallah, P. Degond, and S. Génieys. “An Energy-Transport Model for Semiconductors Derived from the Boltzmann Equation”. In: Journal of Statistical Physics 84.1-2 (1996), pp. 205–231. doi: 10.1007/BF02179583.

[24]

K. Blotekjaer. “Transport Equations for Electrons in Two-Valley Semiconductors”. In: Electron Devices, IEEE Transactions on 17.1 (1970), pp. 38–47. doi: 10.1109/T-ED.1970.16921.

[25]

R. Kosik. “Numerical Challenges on the Road to NanoTCAD”. PhD thesis. Technische Universität Wien, 2004. url: http://www.iue.tuwien.ac.at/phd/kosik/.

[26]

C. S. Lent and D. J. Kirkner. “The Quantum Transmitting Boundary Method”. In: Journal of Applied Physics 67.10 (1990), pp. 6353–6359. doi: 10.1063/1.345156.

[27]

F. Rossi and T. Kuhn. “Theory of Ultrafast Phenomena in Photoexcited Semiconductors”. In: Reviews of Modern Physics 74.3 (2002), pp. 895–950. doi: 10.1103/RevModPhys.74.895.

[28]

M. Pourfath. The Non-Equilibrium Green’s Function Method for Nanoscale Device Simulation. Springer, 2014. isbn: 9783709117996.

[29]

B. Gaury, J. Weston, M. Santin, M. Houzet, C. Groth, and X. Waintal. “Numerical Simulations of Time-Resolved Quantum Electronics”. In: Physics Reports 534.1 (2014), pp. 1–37. doi: 10.1016/j.physrep.2013.09.001.

[30]

B. Novakovic and G. Klimeck. “Atomistic Quantum Transport Approach to Time-Resolved Device Simulations”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2015, pp. 8–11. doi: 10.1109/SISPAD.2015.7292245.

[31]

V. Sverdlov, E. Ungersboeck, H. Kosina, and S. Selberherr. “Current Transport Models for Nanoscale Semiconductor Devices”. In: Materials Science and Engineering: Reports 58.6 (2008), pp. 228–270. doi: 10.1016/j.mser.2007.11.001.

[32]

M. Wagner, M. Karner, and K.-T. Grasser. “Quantum Correction Models for Modern Semiconductor Devices”. In: Proceedings of the 13th International Workshop on Semiconductor Devices. Vol. 1. 2005, pp. 458–461.

[33]

D. Ferry, R. Akis, and D. Vasileska. “Quantum Effects in MOSFETs: Use of an Effective Potential in 3D Monte Carlo Simulation of Ultra-Short Channel Devices”. In: Electron Devices Meeting (IEDM), IEEE International. 2000, pp. 287–290. doi: 10.1109/IEDM.2000.904313.

[34]

D. Ferry, S. Ramey, L. Shifren, and R. Akis. “The Effective Potential in Device Modeling: The good, the Bad and the Ugly”. In: Journal of Computational Electronics 1.1-2 (2002), pp. 59–65. doi: 10.1023/A:1020763710906.

[35]

Y. Li, T.-w. Tang, and X. Wang. “Modeling of Quantum Effects for Ultrathin Oxide MOS Structures with an Effective Potential”. In: Nanotechnology, IEEE Transactions on 1.4 (2002), pp. 238–242. doi: 10.1109/TNANO.2002.807386.

[36]

A. Asenov, A. Brown, and J. Watling. “Quantum Corrections in the Simulation of Decanano MOSFETs”. In: Solid-State Electronics 47.7 (2003), pp. 1141–1145. doi: 10.1016/S0038-1101(03)00030-3.

[37]

M. Ancona. “Multi-dimensional Semiconductor Tunneling in Density-Gradient Theory”. In: Book of Abstracts of the 17th International Workshop on Computational Electronics (IWCE). 2006, pp. 9–10. isbn: 3901578161.

[38]

O. Baumgartner, L. Filipovic, H. Kosina, M. Karner, Z. Stanojevic, and H. Cheng-Karner. “Efficient Modeling of Source/Drain Tunneling in Ultra-Scaled Transistors”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2015, pp. 202–205. doi: 10.1109/SISPAD.2015.7292294.

[39]

O. Badami, N. Kumar, D. Saha, and S. Ganguly. “Quantum Drift-Diffusion and Quantum Energy Balance Simulation of Nanowire Junctionless Transistors”. In: Silicon Nanoelectronics Workshop (SNW), IEEE. 2012, pp. 1–2. doi: 10.1109/SNW.2012.6243303.

[40]

M. Vasicek. “Advanced Macroscopic Transport Models”. PhD thesis. Technische Universität Wien, 2009. url: http://www.iue.tuwien.ac.at/phd/vasicek/.

[41]

M. Nedjalkov. “Book Chapter: Wigner Transport in Presence of Phonons: Particle Models of the Electron Kinetics”. In: From Nanostructures to Nanosensing Applications, Proceedings of the International School of Physics Enrico Fermi. Ed. by A. Paoletti, A. D’Amico, and G. Ballestrino. Vol. 160. IOS Press, 2005, pp. 55–103. isbn: 1586035274. doi: 10.3254/1-58603-527-4-55.

[42]

F. A. Buot. Nonequilibrium Quantum Transport Physics in Nanosystems; Foundation of Computational Nonequilibrium Physics in Nanoscience and Nanotechnology. World Scientific, 2009. isbn: 9812566791.

[43]

V. I. Tatarskii. “The Wigner Representation of Quantum Mechanics”. In: Sov. Phys. Usp. 26 (1983), pp. 311–327. doi: 10.1070/PU1983v026n04ABEH004345.

[44]

D. Leibfried, T. Pfau, and C. Monroe. “Shadows and Mirrors: Reconstructing Quantum States of Atom Motion”. In: Print edition 51.4 (1998), pp. 22–28. doi: 10.1063/1.882256.

[45]

E. Colomés, Z. Zhan, and X. Oriols. “Comparing Wigner, Husimi and Bohmian Distributions: Which One is a True Probability Distribution in Phase Space?” In: Journal of Computational Electronics 14.4 (2015), pp. 894–906. doi: 10.1007/s10825-015-0737-6.

[46]

D. Querlioz and P. Dollfus. The Wigner Monte Carlo Method for Nanoelectronic Devices - A Particle Description of Quantum Transport and Decoherence. ISTE-Wiley, 2010. isbn: 9781848211506.

[47]

M. Nedjalkov, D. Vasileska, D. K. Ferry, C. Jacoboni, C. Ringhofer, I. Dimov, and V. Palankovski. “Wigner Transport Models of the Electron-Phonon Kinetics in Quantum Wires”. In: Physical Review B 74 (3 2006), p. 035311. doi: 10.1103/PhysRevB.74.035311.

[48]

M. Nedjalkov, D. Querlioz, P. Dollfus, and H. Kosina. “Review Chapter: Wigner Function Approach”. In: Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling. Ed. by D. Vasileska and S. Goodnick. Springer, 2011, pp. 289–358. isbn: 9781441988393. doi: 10.1007/978-1-4419-8840-9˙5.

[49]

M. Nedjalkov, S. Selberherr, D. Ferry, D. Vasileska, P. Dollfus, D. Querlioz, I. Dimov, et al. “Physical Scales in the Wigner-Boltzmann Equation”. In: Annals of Physics 328 (2012), pp. 220–237. doi: 10.1016/j.aop.2012.10.001.

[50]

S. Barraud. “Dissipative Quantum Transport in Silicon Nanowires based on Wigner Transport Equation”. In: Journal of Applied Physics 110.9 (2011), p. 093710. doi: 10.1063/1.3654143.

[51]

I. Knezevic. Personal Communication and Presentation at Internal Meeting of Wigner Initiave, Vienna (Austria). http://www.iue.tuwien.ac.at/wigner-wiki. 22-24 July 2015.

[52]

E. Wigner. “On the Quantum Correction For Thermodynamic Equilibrium”. In: Physical Review 40 (5 1932), pp. 749–759. doi: 10.1103/PhysRev.40.749.

[53]

J. E. Moyal. “Quantum Mechanics as a Statistical Theory”. In: Mathematical Proceedings of the Cambridge Philosophical Society 45 (01 1949), pp. 99–124. doi: 10.1017/S0305004100000487.

[54]

N. C. Dias and J. N. Prata. “Admissible States in Quantum Phase Space”. In: Annals of Physics 313.1 (2004), pp. 110–146. doi: 10.1016/j.aop.2004.03.008.

[55]

H. Weyl. “Quantenmechanik und Gruppentheorie”. In: Zeitschrift für Physik 46.1-2 (1927), pp. 1–46. doi: 10.1007/BF02055756.

[56]

K.-Y. Kim and B. Lee. “Wigner Function Formulation in Nonparabolic Semiconductors using Power Series Dispersion Relation”. In: Journal of Applied Physics 86.9 (1999), pp. 5085–5093. doi: 10.1063/1.371484.

[57]

L. Demeio, P. Bordone, and C. Jacoboni. “Multiband, Non-Parabolic Wigner-Function Approach to Electron Transport in Semiconductors”. In: Transport Theory and Statistical Physics 34.7 (2005), pp. 499–522. doi: 10.1080/00411450508951151.

[58]

R. Hudson. “When is the Wigner Quasi-Probability Density Non-negative?” In: Reports on Mathematical Physics 6.2 (1974), pp. 249–252. doi: 10.1016/0034-4877(74)90007-X.

[59]

M. Nedjalkov, I. Dimov, P. Bordone, R. Brunetti, and C. Jacoboni. “Using the Wigner Function for Quantum Transport in Device Simulation”. In: Mathematical and Computer Modelling 25.12 (1997), pp. 33–53. doi: 10.1016/S0895-7177(97)00093-9.

[60]

M. Nedjalkov, I. Dimov, F. Rossi, and C. Jacoboni. “Convergency of the Monte Carlo Algorithm for the Solution of the Wigner Quantum-Transport Equation”. In: Mathematical and Computer Modelling 23.8–9 (1996), pp. 159–166. doi: 10.1016/0895-7177(96)00047-7.

[61]

N. Kluksdahl, A. Kriman, C. Ringhofer, and D. Ferry. “Quantum Tunneling Properties from a Wigner Function Study”. In: Solid-State Electronics 31.3 (1988), pp. 743–746. doi: 10.1137/S0036142901388366.

[62]

W. Frensley. “Boundary Conditions for Open Quantum Systems Driven far from Equilibrium”. In: Reviews of Modern Physics 62.3 (1990), pp. 745–789. doi: 10.1103/RevModPhys.62.745.

[63]

M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. Ferry. “Unified Particle Approach to Wigner-Boltzmann Transport in Small Semiconductor Devices”. In: Physical Review B 70.11 (2004), p. 115319. doi: 10.1103/PhysRevB.70.115319.

[64]

D. Querlioz and P. Dollfus. The Wigner Monte Carlo Method for Nanoelectronic Devices - A Particle Description of Quantum Transport and Decoherence. ISTE-Wiley, 2010. isbn: 9781848211506.

[65]

S. Barraud, P. Dollfus, S. Galdin, and P. Hesto. “Short-range and Long-range Coulomb Interactions for 3D Monte Carlo Device Simulation with Discrete Impurity Distribution”. In: Solid-State Electronics 46.7 (2002), pp. 1061–1067. doi: 10.1016/S0038-1101(02)00042-4.

[66]

A. Arnold, H. Lange, and P. F. Zweifel. “A Discrete-Velocity, Stationary Wigner Equation”. In: Journal of Mathematical Physics 41.11 (2000), pp. 7167–7180. doi: 10.1063/1.1318732.

[67]

T. Goudon. “Analysis of a Semidiscrete Version of the Wigner Equation”. In: SIAM Journal on Numerical Analysis 40.6 (2002), pp. 2007–2025. doi: 10.1137/S0036142901388366.

[68]

P. Bordone, M. Pascoli, R. Brunetti, A. Bertoni, C. Jacoboni, and A. Abramo. “Quantum Transport of Electrons in Open Nanostructures with the Wigner-Function Formalism”. In: Physical Review B 59.4 (1999), pp. 3060–3069. doi: 10.1103/PhysRevB.59.3060.

[69]

A. Baute, I. Egusquiza, and J. Muga. “Sources of Quantum Waves”. In: Journal of Physics A: Mathematical and General 34.20 (2001), pp. 4289–4299. doi: 10.1088/0305-4470/34/20/303.

[70]

A. Arnold. “Mathematical Concepts of Open Quantum Boundary Conditions”. In: Transport Theory and Statistical Physics 30.4-6 (2001), pp. 561–584. doi: 10.1081/TT-100105939.

[71]

T. González and D. Pardo. “Physical Models of Ohmic Contact for Monte Carlo Device Simulation”. In: Solid-State Electronics 39.4 (1996), pp. 555–562. doi: 10.1016/0038-1101(95)00188-3.

[72]

H. Jiang, W. Cai, and R. Tsu. “Accuracy of the Frensley Inflow Boundary Condition for Wigner Equations in Simulating Resonant Tunneling Diodes”. In: Journal of Computational Physics 230.5 (2011), pp. 2031–2044. doi: 10.1016/j.jcp.2010.12.002.

[73]

A. Savio and A. Poncet. “Study of the Wigner Function at the Device Boundaries in One-Dimensional Single-and Double-Barrier Structures”. In: Journal of Applied Physics 109.3 (2011), p. 033713. doi: 10.1063/1.3526969.

[74]

H. Jiang, T. Lu, and W. Cai. “A Device Adaptive Inflow Boundary Condition for Wigner Equations of Quantum Transport”. In: Journal of Computational Physics 258 (2014), pp. 773–786. doi: 10.1016/j.jcp.2013.11.007.

[75]

I. Dimov, M. Nedjalkov, J.-M. Sellier, and S. Selberherr. “Boundary Conditions and the Wigner Equation Solution”. In: Journal of Computational Electronics 14.4 (2015), pp. 859–863. doi: 10.1007/s10825-015-0720-2.

[76]

R. Rosati, F. Dolcini, R. C. Iotti, and F. Rossi. “Wigner-Function Formalism Applied to Semiconductor Quantum Devices: Failure of the Conventional Boundary Condition Scheme”. In: Physical Review B 88.3 (2013), p. 035401. doi: 10.1103/PhysRevB.88.035401.

[77]

N. C. Kluksdahl, A. M. Kriman, D. K. Ferry, and C. Ringhofer. “Self-Consistent Study of the Resonant-Tunneling Diode”. In: Physical Review B 39.11 (1989), pp. 7720–7735. doi: 10.1103/PhysRevB.39.7720.

[78]

C. Ringhofer, D. Ferry, and N. Kluksdahl. “Absorbing Boundary Conditions for the Simulation of Quantum Transport Phenomena”. In: Transport Theory and Statistical Physics 18.3-4 (1989), pp. 331–346. doi: 10.1080/00411458908204692.

[79]

A. Arnold. “On Absorbing Boundary Conditions for Quantum Transport Equations”. In: RAIRO - Modélisation Mathématique et Analyse Numérique 28.7 (1994), pp. 853–872.

[80]

W. R. Frensley. “Wigner-function Model of a Resonant-Tunneling Semiconductor Device”. In: Physical Review B 36.3 (1987), pp. 1570–1580. doi: 10.1103/PhysRevB.36.1570.

[81]

I. Knezevic. “Decoherence due to Contacts in Callistic Nanostructures”. In: Physical Review B 77 (12 2008), p. 125301. doi: 10.1103/PhysRevB.77.125301.

[82]

J. Sellier and I. Dimov. “Wigner Functions, Signed Particles, and the Harmonic Oscillator”. In: Journal of Computational Electronics 14.4 (2015), pp. 907–915. doi: 10.1007/s10825-015-0722-0.

[83]

U. Ravaioli, M. A. Osman, W. Pötz, N. Kluksdahl, and D. K. Ferry. “Investigation of Ballistic Transport through Resonant-Tunnelling Quantum Wells using Wigner Function Approach”. In: Physica B+C 134.1-3 (1985), pp. 36–40. doi: 10.1016/0378-4363(85)90317-1.

[84]

N. Kluksdahl, W. Pötz, U. Ravaioli, and D. Ferry. “Wigner Function Study of a Double Quantum Barrier Resonant Tunnelling Diode”. In: Superlattices and Microstructures 3.1 (1987), pp. 41–45. doi: 10.1016/0749-6036(87)90175-3.

[85]

K.-Y. Kim and B. Lee. “On the High Order Numerical Calculation Schemes for the Wigner Transport Equation”. In: Solid-State Electronics 43.12 (1999), pp. 2243–2245. doi: 10.1016/S0038-1101(99)00168-9.

[86]

C. Ringhofer. “A Spectral Method for the Numerical Simulation of Quantum Tunneling Phenomena”. In: SIAM Journal on Numerical Analysis 27.1 (1990), pp. 32–50. doi: 10.1137/0727003.

[87]

A. Arnold and C. Ringhofer. “Operator Splitting Methods Applied to Spectral Discretizations of Quantum Transport Equations”. In: SIAM Journal on Numerical Analysis 32.6 (1995), pp. 1876–1894. doi: 10.1137/0732084.

[88]

S. Shao, T. Lu, and W. Cai. “Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport”. In: Communications of Computational Physics 9 (2011), pp. 711–739. doi: 10.4208/cicp.080509.310310s.

[89]

A. Dorda and F. Schürrer. “A WENO-Solver Combined with Adaptive Momentum Discretization for the Wigner Transport Equation and its Application to Resonant Tunneling Diodes”. In: Journal of Computational Physics 284 (2015), pp. 95–116. doi: 10.1016/j.jcp.2014.12.026.

[90]

J. Cervenka, P. Ellinghaus, and M. Nedjalkov. “Deterministic Solution of the Discrete Wigner Equation”. In: Numerical Methods and Applications. Ed. by I. Dimov, S. Fidanova, and I. Lirkov. Springer International Publishing, 2015, pp. 149–156. isbn: 9783319155845. doi: 10.1007/978-3-319-15585-2˙17.

[91]

V. Peikert and A. Schenk. “A Wavelet Method to Solve High-Dimensional Transport Equations in Semiconductor Devices”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2011, pp. 299–302. doi: 10.1109/SISPAD.2011.6035029.

[92]

S.-M. Hong, A.-T. Pham, and C. Jungemann. Deterministic Solvers for the Boltzmann Transport Equation. Springer Science & Business Media, 2011. isbn: 9783709107775.

[93]

K. Rupp. “Deterministic Numerical Solution of the Boltzmann Transport Equation”. PhD thesis. Technische Universität Wien, 2011. url: http://www.iue.tuwien.ac.at/phd/rupp/.

[94]

N. Goldsman, C.-K. Lin, Z. Han, and C.-K. Huang. “Advances in the Spherical Harmonic-Boltzmann-Wigner Approach to Device Simulation”. In: Superlattices and Microstructures 27.2 (2000), pp. 159–175. doi: 10.1006/spmi.1999.0810.

[95]

P. Vitanov, M. Nedjalkov, C. Jacoboni, F. Rossi, and A. Abramo. “Unified Monte Carlo Approach to the Boltzmann and Wigner Equations”. In: Advances in Parallel Algorithms. Ed. by B. Sendov and I. Dimov. IOS Press, 1994, pp. 117–128.

[96]

F. Rossi, C. Jacoboni, and M. Nedjalkov. “A Monte Carlo Solution of the Wigner Transport Equation”. In: Semiconductor Science Technology 9 (1994), pp. 934–936. doi: 10.1088/0268-1242/9/5S/143.

[97]

R. Sala, S. Brouard, and J. G. Muga. “Wigner Trajectories and Liouville’s Theorem”. In: The Journal of Chemical Physics 99.4 (1993), pp. 2708–2714. doi: 10.1063/1.465232.

[98]

P. Bordone, A. Bertoni, R. Brunetti, and C. Jacoboni. “Monte Carlo Simulation of Quantum Electron Transport based on Wigner Paths”. In: Mathematics and Computers in Simulation 62.3-6 (2003), pp. 307–314. doi: 10.1016/S0378-4754(02)00241-0.

[99]

L. Shifren and D. Ferry. “A Wigner Function Based Ensemble Monte Carlo Approach for Accurate Incorporation of Quantum Effects in Device Simulation”. In: Journal of Computational Electronics 1.1-2 (2002), pp. 55–58. doi: 10.1023/A:1020711726836.

[100]

L. Shifren, C. Ringhofer, and D. Ferry. “A Wigner Function-based Quantum Ensemble Monte Carlo Study of a Resonant Tunneling Diode”. In: Electron Devices, IEEE Transactions on 50.3 (2003), pp. 769–773. doi: 10.1109/TED.2003.809434.

[101]

D. Querlioz, P. Dollfus, V.-N. Do, A. Bournel, and V. L. Nguyen. “An Improved Wigner Monte Carlo Technique for the Self-Consistent Simulation of RTDs”. In: Journal of Computational Electronics 5.4 (2006), pp. 443–446. doi: 10.1007/s10825-006-0044-3.

[102]

ViennaWD - Wigner Ensemble Monte Carlo Simulator. url: http://viennawd.sourceforge.net/.

[103]

R. Eckhardt. “Stan Ulam, John von Neumann, and the Monte Carlo Method”. In: Los Alamos Science 15 (1987), pp. 131–136.

[104]

T. Kurosawa. “Monte Carlo calculation of Hot Electron Problems”. In: Journal of the Physical Society of Japan 21 (1966), p. 424.

[105]

I. Dimov. Monte Carlo Methods for Applied Scientists. World Scientific, 2008. isbn: 9810223293.

[106]

I. Dimov. “Optimal Monte Carlo Algorithms”. In: Modern Computing, John Vincent Atanasoff International Symposium on. 2006, pp. 125–131. doi: 10.1109/JVA.2006.37.

[107]

I. Dimov and R. Georgieva. “Complexity of Monte Carlo Algorithms for a Class of Integral Equations”. In: International Conference on Computational Science (ICCS), Proceedings of the 7th. Ed. by Y. Shi, G. D. Albada, J. Dongarra, and P. M. A. Sloot. Springer, 2007, pp. 731–738. doi: 10.1007/978-3-540-72584-8˙97.

[108]

C. Jacoboni and L. Reggiani. “The Monte Carlo Method for the Solution of Charge Transport in Semiconductors with Applications to Covalent Materials”. In: Reviews of Modern Physics 55.3 (1983), p. 645. doi: 10.1103/RevModPhys.55.645.

[109]

K. Tomizawa. Numerical Simulation of Submicron Semiconductor Devices. Artech House, 1993. isbn: 0890066205.

[110]

C. Jacoboni and P. Lugli. The Monte Carlo Method for Semiconductor Device Simulation. Springer Science & Business Media, 2012. isbn: 9783709174531.

[111]

P. Poli, L. Rota, and C. Jacoboni. “Weighted Monte Carlo for Electron Transport in Semiconductors”. In: Applied Physics Letters 55.10 (1989), pp. 1026–1028. doi: 10.1063/1.101723.

[112]

C. Jacoboni, P. Poli, and L. Rota. “A New Monte Carlo Technique for the Solution of the Boltzmann Transport Equation”. In: Solid-State Electronics 31.3 (1988), pp. 523–526. doi: 10.1016/0038-1101(88)90332-2.

[113]

M. Nedjalkov and P. Vitanov. “Iteration Approach for Solving the Boltzmann Equation with the Monte Carlo Method”. In: Solid-State Electronics 32.10 (1989), pp. 893–896. doi: 10.1016/0038-1101(89)90067-1.

[114]

H. Kosina, M. Nedjalkov, and S. Selberherr. “The Stationary Monte Carlo Method for Device Simulation. I. Theory”. In: Journal of Applied Physics 93.6 (2003), pp. 3553–3563. doi: 10.1063/1.1544654.

[115]

R. Chambers. “The Kinetic Formulation of Conduction Problems”. In: Proceedings of the Physical Society. Section A 65.6 (1952), pp. 458–468. doi: 10.1088/0370-1298/65/6/114.

[116]

H. ZhiMin, Y. ZaiZai, and C. JianRui. “Monte Carlo Method for Solving the Fredholm Integral Equations of the Second Kind”. In: Transport Theory and Statistical Physics 41.7 (2012), pp. 513–528. doi: 10.1080/00411450.2012.695317.

[117]

I. Dimov and T. Gurov. “Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-linearity: Parallel Implementation”. In: Pliska Studia Mathematica Bulgarica 13.1 (2000), pp. 117–132.

[118]

I. Dimov and T. Gurov. “Estimates of the Computational Complexity of Iterative Monte Carlo Algorithm Based on Green’s Function Approach”. In: Mathematics and Computers in Simulation 47.2–5 (1998), pp. 183–199. doi: 10.1016/S0378-4754(98)00102-5.

[119]

T. Gurov, P. Whitlock, and I. Dimov. “A Grid Free Monte Carlo Algorithm for Solving Elliptic Boundary Value Problems”. In: Numerical Analysis and Its Applications (NAA), Second International Conference on. Ed. by L. Vulkov, P. Yalamov, and J. Waśniewski. Springer, 2001, pp. 359–367. doi: 10.1007/3-540-45262-1˙42.

[120]

I. Dimov and R. Papancheva. “Green’s Function Monte Carlo Algorithms for Elliptic Problems”. In: Mathematics and Computers in Simulation 63.6 (2003), pp. 587–604. doi: 10.1016/S0378-4754(03)00094-6.

[121]

K. Chatterjee, J. R. Roadcap, and S. Singh. “A New Green’s Function Monte Carlo Algorithm for the Solution of the Two-Dimensional Nonlinear Poisson–Boltzmann Equation: Application to the Modeling of the Communication Breakdown Problem in Space Vehicles during Re-Entry”. In: Journal of Computational Physics 276 (2014), pp. 479–485. doi: 10.1016/j.jcp.2014.07.042.

[122]

I. Dimov. “Monte Carlo Algorithms for Linear Problems”. In: Pliska Studia Mathematica Bulgarica 13.1 (2000), pp. 55–77.

[123]

H. Kosina, M. Nedjalkov, and S. Selberherr. “Theory of the Monte Carlo Method for Semiconductor Device Simulation”. In: IEEE Transactions on Electron Devices 47.10 (2000), pp. 1898–1908. doi: 10.1109/16.870569.

[124]

F. W. Byron and W. Fuller. Mathematics of Quantum and Classical Physics. Dover, 1992. isbn: 9780486671642.

[125]

Y. Fu and M. Willander. “Electron Wave-Packet Transport through Nanoscale Semiconductor Device in Time Domain”. In: Journal of Applied Physics 97.9 (2005), p. 094311. doi: 10.1063/1.1890452.

[126]

H. Rees. “Calculation of Distribution Functions by Exploiting the Stability of the Steady State”. In: Journal of Physics and Chemistry of Solids 30.3 (1969), pp. 643–655. doi: 10.1016/0022-3697(69)90018-3.

[127]

Lua Scripting Language. url: http://www.lua.org/.

[128]

P. Ellinghaus, M. Nedjalkov, and S. Selberherr. “Efficient Calculation of the Two-Dimensional Wigner Potential”. In: Computational Electronics (IWCE), International Workshop on. 2014, pp. 1–3. doi: 10.1109/IWCE.2014.6865812.

[129]

M. Frigo and S. Johnson. “The Design and Implementation of FFTW3”. In: Proceedings of the IEEE 93.2 (2005), pp. 216–231. doi: 10.1109/JPROC.2004.840301.

[130]

H.-Y. Huang, Y.-Y. Lee, and P.-C. Lo. “A Novel Algorithm for Computing the 2D Split-Vector-Radix FFT”. In: Signal Processing 84.3 (2004), pp. 561–570. doi: 10.1016/j.sigpro.2003.11.018.

[131]

Z. Chen and L. Zhang. “Vector Coding Algorithms for Multidimensional Discrete Fourier Transform”. In: Journal of Computational and Applied Mathematics 212.1 (2008), pp. 63–74. doi: 10.1016/j.cam.2006.11.025.

[132]

E. Jacobsen and R. Lyons. “The Sliding DFT”. In: Signal Processing Magazine, IEEE 20.2 (2003), pp. 74–80. doi: 10.1109/MSP.2003.1184347.

[133]

E. Jacobsen and R. Lyons. “An Update to the Sliding DFT”. In: Signal Processing Magazine, IEEE 21.1 (2004), pp. 110–111. doi: 10.1109/MSP.2004.1516381.

[134]

D. Ferry and S. M. Goodnick. Transport in Nanostructures. 6. Cambridge University Press, 1997. isbn: 9780521663656.

[135]

C. Jacoboni and P. Bordone. “Wigner Transport Equation with Finite Coherence Length”. In: Journal of Computational Electronics 13.1 (2014), pp. 257–263. doi: 10.1007/s10825-013-0510-7.

[136]

F. Harris. “On the use of Windows for Harmonic Analysis with the Discrete Fourier Transform”. In: Proceedings of the IEEE 66.1 (1978), pp. 51–83. doi: 10.1109/PROC.1978.10837.

[137]

P. Ellinghaus, M. Nedjalkov, and S. Selberherr. “Implications of the Coherence Length on the Discrete Wigner Potential”. In: Computational Electronics (IWCE), International Workshop on. 2014, pp. 1–3. doi: 10.1109/IWCE.2014.6865852.

[138]

J. W. Tukey. “An Introduction to the Calculation of Numerical Spectrum Analysis”. In: Spectral Analysis of Time Series (1967). Ed. by B. Harris, pp. 22–46.

[139]

P. Ellinghaus, M. Nedjalkov, and S. Selberherr. “Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method”. In: Lecture Notes in Computer Science. Ed. by I. Dimov, S. Fidanova, and I. Lirkov. Vol. 8962. Springer International Publishing, 2015, pp. 27–33. isbn: 9783319155845. doi: 10.1007/978-3-319-15585-2˙3.

[140]

N. Akhiezer. The Classical Moment Problem: and Some Related Questions in Analysis. University Mathematical Monographs. Out of Print. Oliver & Boyd, 1965.

[141]

C. A. R. Hoare. “Algorithm 64: Quicksort”. In: Communications of the ACM 4.7 (1961), pp. 321–322. doi: 10.1145/366622.366644.

[142]

V. Los and N. Los. “Exact Solution of the One-Dimensional Time-Dependent Schrödinger Equation with a Rectangular Well/Barrier Potential and its Applications”. In: Theoretical and Mathematical Physics 177.3 (2013), pp. 1706–1721. doi: 10.1007/s11232-013-0128-8.

[143]

J. M. Sellier, M. Nedjalkov, I. Dimov, and S. Selberherr. “A Benchmark Study of the Wigner Monte Carlo Method”. In: Monte Carlo Methods and Applications 20.1 (2014), pp. 43–51. doi: 10.1515/mcma-2013-0018.

[144]

P. Ellinghaus, M. Nedjalkov, and S. Selberherr. “The Wigner Monte Carlo Method for Accurate Semiconductor Device Simulation”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2014, pp. 113–116. doi: 10.1109/SISPAD.2014.6931576.

[145]

C. Moore. “Data Processing in Exascale-Class Computer Systems”. In: The Salishan Conference on High Speed Computing. 2011. url: http://www.lanl.gov/conferences/salishan/.

[146]

L. Dagum and R. Enon. “OpenMP: an Industry Standard API for Shared-Memory Programming”. In: Computational Science & Engineering 5.1 (1998), pp. 46–55. doi: 10.1109/99.660313.

[147]

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, and J. Dongarra. MPI-The Complete Reference, Volume 1: The MPI Core. 2nd. (Revised). MIT Press, 1998. isbn: 0262692155.

[148]

P. Ellinghaus, J. Weinbub, M. Nedjalkov, S. Selberherr, and I. Dimov. “Distributed-Memory Parallelization of the Wigner Monte Carlo Method using Spatial Domain Decomposition”. In: Journal of Computational Electronics 14.1 (2015), pp. 151–162. doi: 10.1007/s10825-014-0635-3.

[149]

J. Weinbub, P. Ellinghaus, and S. Selberherr. “Parallelization of the Two-Dimensional Wigner Monte Carlo Method”. In: Large-Scale Scientific Computing. Ed. by I. Lirkov, S. D. Margenov, and J. Waśniewski. Vol. 9374. Lecture Notes in Computer Science. Springer International Publishing, 2015, pp. 309–316. isbn: 9783319265193. doi: 10.1007/978-3-319-26520-9˙34.

[150]

J. Weinbub, P. Ellinghaus, and M. Nedjalkov. “Domain Decomposition Strategies for the Two-Dimensional Wigner Monte Carlo Method”. In: Journal of Computational Electronics 14.4 (2015), pp. 922–929. doi: 10.1007/s10825-015-0730-0.

[151]

Vienna Scientific Cluster - VSC-3. url: http://vsc.ac.at/.

[152]

U. Sivan, M. Heiblum, C. P. Umbach, and H. Shtrikman. “Electrostatic Electron Lens in the Ballistic Regime”. In: Physical Review B 41 (11 1990), pp. 7937–7940. doi: 10.1103/PhysRevB.41.7937.

[153]

J. Spector, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, and K. W. West. “Electron Focusing in Two-Dimensional Systems by means of an Electrostatic Lens”. In: Applied Physics Letters 56.13 (1990), pp. 1290–1292. doi: 10.1063/1.102538.

[154]

R. Wang, H. Liu, R. Huang, J. Zhuge, L. Zhang, D.-W. Kim, X. Zhang, et al. “Experimental Investigations on Carrier Transport in Si Nanowire Transistors: Ballistic Efficiency and Apparent Mobility”. In: Electron Devices, IEEE Transactions on 55 (2008), pp. 2960–2967. doi: 10.1109/TED.2008.2005152.

[155]

M. Muraguchi and T. Endoh. “Size Dependence of Electrostatic Lens Effect in Vertical MOSFETs”. In: Japanese Journal of Applied Physics 53.4S (2014), 04EJ09. doi: 10.7567/JJAP.53.04EJ09.

[156]

P. Ellinghaus, M. Nedjalkov, and S. Selberherr. “Improved Drive-Current into Nanoscaled Channels using Electrostatic Lenses”. In: Simulation of Semiconductor Processes and Devices (SISPAD), International Conference on. 2015, pp. 24–27. doi: 10.1109/SISPAD.2015.7292249.

[157]

A. Dixit, A. Kottantharayil, N. Collaert, M. Goodwin, M. Jurczak, and K. De Meyer. “Analysis of the Parasitic S/D Resistance in Multiple-Gate FETs”. In: Electron Devices, IEEE Transactions on 52.6 (2005), pp. 1132–1140. doi: 10.1109/TED.2005.848098.

[158]

A. Villalon, C. Le Royer, S. Cristoloveanu, M. Casse, D. Cooper, J. Mazurier, B. Previtali, et al. “High-Performance Ultrathin Body c-SiGe Channel FD-SOI pMOSFETs Featuring SiGe Source and Drain: Vth tuning, variability, access resistance, and mobility issues”. In: Electron Devices, IEEE Transactions on 60.5 (2013), pp. 1568–1574. doi: 10.1109/TED.2013.2255055.

[159]

S. Berrada, M. Bescond, N. Cavassilas, L. Raymond, and M. Lannoo. “Carrier Injection Engineering in Nanowire Transistors via Dopant and Shape Monitoring of the Access Regions”. In: Applied Physics Letters 107.15 (2015), p. 153508. doi: 10.1063/1.4933392.

[160]

Y. Jiang, T. Liow, N. Singh, L. Tan, G. Lo, D. Chan, and D. Kwong. “Performance Breakthrough in 8 nm Gate Length Gate-All-Around Nanowire Transistors using Metallic Nanowire Contacts”. In: VLSI Technology, Symposium on. 2008, pp. 34–35. doi: 10.1109/VLSIT.2008.4588553.

[161]

H. Kim, H. Min, T. Tang, and Y. Park. “An Extended Proof of the Ramo-Shockley Theorem”. In: Solid-State Electronics 34.11 (1991), pp. 1251–1253. doi: 10.1016/0038-1101(91)90065-7.

[162]

S. Smirnov. “Physical Modeling of Electron Transport in Strained Silicon and Silicon-Germanium”. PhD thesis. Technische Universität Wien, 2004. url: http://www.iue.tuwien.ac.at/phd/smirnov/.

[163]

M. V. Fischetti. “Monte Carlo Simulation of Transport in Technologically Significant Semiconductors of the Diamond and Zinc-Blende Structures. I. Homogeneous transport”. In: Electron Devices, IEEE Transactions on 38.3 (1991), pp. 634–649. doi: 10.1109/16.75176.

[164]

D. Ferry. Semiconductors. Macmillan Publishing Company, 1991. isbn: 9780023371301.

[165]

S. M. Goodnick, D. K. Ferry, C. W. Wilmsen, Z. Liliental, D. Fathy, and O. L. Krivanek. “Surface Roughness at the Si(100)-SiO2 Interface”. In: Physical Review B 32 (12 1985), pp. 8171–8186. doi: 10.1103/PhysRevB.32.8171.

[166]

D. Vasileska and D. K. Ferry. “Scaled Silicon MOSFETs: Universal Mobility Behavior”. In: Electron Devices, IEEE Transactions on 44.4 (1997), pp. 577–583. doi: 10.1109/16.563361.