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- AES03
-
A. Arnold, M. Ehrhardt, and I. Sofronov.
Approximation, stability and fast calculation of non-local boundary
conditions for the Schrödinger equation.
Commun. Mathematical Sciences, 1(3):501-556, 2003.
- Akt99
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T. Aktosun.
On the Schrödinger equation with steplike potentials.
Journal of Mathematical Physics, 40(11):5289-5305, 1999.
- App00
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D. M. Appleby.
Husimi transform of an operator product.
J.Phys.A, 33(21):3903-3915, 2000.
- Arn01
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A. Arnold.
Mathematical concepts of open quantum boundary conditions.
Transp. Theory Stat. Phys., 30(4-6):561-584, 2001.
- ARR00
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A. M. Anile, V. Romano, and G. Russo.
Extended hydrodynamical model of carrier transport in semiconductors.
SIAM Journal on Applied Mathematics, 61(1):74-101, February
2000.
- BA00
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N. Ben-Abdallah.
On a multidimensional Schrödinger-Poisson scattering model for
semiconductors.
Journal of Mathematical Physics, 41(7):4241-4261, 2000.
- BAD96
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N. Ben-Abdallah and P. Degond.
On a hierarchy of macroscopic models for semiconductors.
J. Math. Phys., 37(7):3306-333, 1996.
- BADM97
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N. Ben-Abdallah, P. Degond, and P. A. Markowich.
On a one-dimensional Schrödinger-Poisson scattering model.
ZAMP, 48:135-155, 1997.
- BAM+03
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M. Bescond, J. L. Autran, D. Munteanu, N. Cavassilas, and M. Lannoo.
Atomic-scale modeling of source-to-drain tunneling in ultimate
Schottky barrier double-gate MOSFET's.
ESSDERC 2003, pages 395-398, 2003.
- BAPGR02
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N. Ben-Abdallah, O. Pinaud, C. L. Gardner, and C. Ringhofer.
A comparison of resonant tunneling based on Schrödinger's equation
and quantum hydrodynamics.
VLSI Design, 15:695-700, 2002.
- BAR86
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D. Ben-Avraham and S. Redner.
Kinetics of -species annihilation: Mean-field and
diffusion-controlled limits.
Physical Review A, 34(1):501-509, 1986.
- BBB00
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K. Bandyopadhyay, K. Bhattacharyya, and A. K. Bhattacharya.
On some problems of the maximum entropy ansatz.
Pramana - journal of physics, 54(3):365-375, March 2000.
- BCJP03
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K. Bernstein, Ch.-T. Chuang, R. Joshi, and R. Puri.
Design and CAD challenges in sub-90nm CMOS technologies.
Proceedings of the International Conference on Computer Aided
Design 2003 (San Jose, California, USA), pages 129-136, 2003.
- BD01
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M. Bohner and O. Dosly.
The discrete Prüfer Transformation.
Proceedings of the American Mathematical Society,
129(9):2715-2726, 2001.
- BFV01
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G. Bonneau, J. Faraut, and G. Valent.
Self-adjoint extensions of operators and the teaching of quantum
mechanics.
Am.J.Phys, 69:322, 2001.
- Bie97
-
B. A. Biegel.
Quantum electronic device simulation, PhD thesis.
Stanford University, 1997.
- Bie98
-
B. A. Biegel.
Wigner function simulation of intrinsic oscillations, hysteresis, and
bistability in resonant tunneling structures.
In SPIE Proceedings Vol. 3277: Ultrafast Phenomena in
Semiconductors II, pages 159-169, San Jose, CA, USA, 1998.
- Bit00
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E. R. Bittner.
Quantum tunneling dynamics using hydrodynamic trajectories.
Journal of Chemical Physics, 112(22):9703-9710, 2000.
- BJSS04
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F. Boeuf, X. Jehl, M. Sanquer, and T. Skotnicki.
Experimental study of transport in nanoscale planar MOSFETs near the
ballistic limit.
IEEE Transactions on Nanotechnology, 3(1):105-109, 2004.
- BM98
-
S. Blinnikov and R. Moessner.
Expansions for nearly Gaussian distributions.
Astron. Astophys. Suppl. Ser., 130:193-205, 1998.
- BM02
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I. Burghardt and K. B. Moller.
Quantum dynamics for dissipative systems: A hydrodynamic perspective.
Journal of Chemical Physics, 117(16):7409-7425, 2002.
- BMP+00
-
A. D. Baute, R. S. Mayato, J. P. Palao, J. G. Muga, and I. L. Egusquiza.
Time-of-arrival distribution for arbitrary potentials and Wigner's
time-energy uncertainty relation.
Physical Review A, 61:022118(5), 2000.
- CAP+94
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W.-S. Choi, J.-G. Ahn, Y.-J. Park, H.-S. Min, and C.-G. Hwang.
A time dependent hydrodynamic device simulator.
IEEE Trans.Computer-Aided Design, 13(7):899-908, 1994.
- CK85
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A. Cohen and T. Kappeler.
Scattering and inverse scattering for steplike potentials in the
Schrödinger equation.
Indiana University Mathematics Journal, 34(1):127-180, 1985.
- CMP03
-
R. Compano, L. Molenkamp, and D. J. Paul.
Technology roadmap for nanoelectronics, 2003.
see http://public.itrs.net/Files/
2003ITRS/LinkedFiles/ERD/NanoeletronicsRdmp.pdf.
- Coh89
-
L. Cohen.
Time-frequency distributions - a review.
Proc. IEEE, 77(7):941-981, 1989.
- Com01
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R. Compañó.
Trends in nanoelectronics.
Nanotechnology, 12(22):85-88, 2001.
- Dal03
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J. Daligault.
Non-Hamiltonian dynamics and trajectory methods in quantum phase
spaces.
Physical Review A, 68(4), 2003.
- DGS00
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L. Diosi, N. Gisin, and W. T. Strunz.
Quantum approach to coupling classical and quantum dynamics.
Physical Review A, 61(2), 2000.
- DGW81
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P. D. Drummond, C. W. Gardiner, and D. F. Wallis.
Quasiprobability methods for nonlinear chemical and optical systems.
Physical Review A, 24(2):914-926, 1981.
- dPC97
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G. Garcia de Polavieja and M. S. Child.
Quantum instability of the flux lines in the coherent state
representation.
Physical Review E, 55(2):1451-1456, 1997.
- FG01
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D. K. Ferry and S. M. Goodnick.
Transport in nanostructures.
Cambridge University Press, 2001.
- FJP03
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A. Fannjiang, S. Jin, and G. Papanicolaou.
High frequency behavior of the focusing nonlinear Schrödinger
equation with random inhomogeneities.
SIAM Journal on Applied Mathematics, 63(4):1328-1358, 2003.
- Fre87
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W. R. Frensley.
Wigner-function model of a resonant-tunneling semiconductor device.
Physical Review B, 36(3):1570-1580, 1987.
- Fre90
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W. R. Frensley.
Boundary conditions for open quantum systems driven far from
equilibrium.
Reviews of Modern Physics, 62(3):745-791, 1990.
- Geh03
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A. Gehring.
Simulation of tunneling in semiconductor devices, PhD thesis.
Institut für Mikroelektronik, TU Wien, Vienna, 2003.
- GHLL+98
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W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, and
M. Snir.
MPI: The complete reference (Vol. 1+2).
The MIT Press, 1998.
- GHT79
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H. Grabert, P. Haenggi, and P. Talkner.
Is quantum mechanics equivalent to a classical stochastic process?
Physical Review A, 19(6):2440-2445, 1979.
- GJK+04
-
T. Grasser, C. Jungemann, H. Kosina, B. Meinerzhagen, and S. Selberherr.
Advanced transport models for sub-micrometer devices.
To appear, 2004.
- GKGS01
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T. Grasser, H. Kosina, M. Gritsch, and S. Selberherr.
Using six moments of Boltzmann's transport equation for device
simulation.
J.Appl.Phys., 90(5):2389-2396, 2001.
- GKHS02
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T. Grasser, H. Kosina, C. Heitzinger, and S. Selberherr.
Accurate impact ionization model which accounts for hot and cold
carrier populations.
Appl.Phys.Lett., 80(4):613-615, 2002.
- GKS01
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T. Grasser, H. Kosina, and S. Selberherr.
Investigation of spurious velocity overshoot using Monte Carlo
data.
Appl.Phys.Lett., 79(12):1900-1903, 2001.
- GMN93
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K. K. Gullapalli, D. R. Miller, and D. P. Neikirk.
Wigner-Poisson simulation of memory switching heterostructure
tunneling diodes.
In IEEE International Electron Devices Meeting, Washington, DC,
Dec. 5-8, 1993, pages 109-112, 1993.
- GP79
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C. George and I. Prigogine.
Coherence and randomness in quantum theory.
Phys. A, 99(3):369-382, 1979.
- Gri02
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M. Gritsch.
Numerical modeling of silicon-on-insulator MOSFETs, PhD thesis.
Institut für Mikroelektronik, TU Wien, TU Wien, 2002.
- GTKS03
-
T. Grasser, T.-W. Tang, H. Kosina, and S. Selberherr.
A review of hydrodynamic and energy-transport models for
semiconductor device simulation.
Proc.IEEE, 91(2):251-274, 2003.
- Gum64
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H. K. Gummel.
A self-consistent iterative scheme for one-dimensional steady state
transistor calculations.
IEEE Trans.Electron Devices, ED-11:455-465, 1964.
- Hal92
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P. Hall.
The bootstrap and Edgeworth expansion.
Springer-Verlag, 1992.
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A. Hald.
A history of mathematical statistics.
Wiley Series in Probability and Statistics, 1998.
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R. J. Harvey.
Navier-Stokes analog of quantum mechanics.
Physical Review, 152(4):1115, 1966.
- HBZB02
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J. A. Hutchby, G. I. Bourianoff, V. V. Zhirnov, and J. E. Brewer.
Extending the road beyond CMOS.
IEEE Circuits & Devices Magazine, pages 28-41, 2002.
- HWL04
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S. Hasan, J. Wang, and M. Lundstrom.
Device design and manufacturing issues for 10 nm-scale MOSFETs: a
computational study.
Solid-State Electronics, 48:867-875, 2004.
- IP95
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G. Iannaccone and B. Pellegrini.
Unified approach for electron transport in resonant tunneling
structures.
Physical Review B, 52:17406, 1995.
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K. L. Jensen and F. A. Buot.
Numerical simulation of intrinsic bistability and high-frequency
current oscillations in resonant tunneling structures.
Physical Review Letters, 66(8):1078-1081, 1991.
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M. Junk and A. Unterreiter.
Maximum entropy for reduced moment problems.
Mathematical Models and Methods in Applied Sciences,
10:1001-1025, 2000.
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H. B. Keller.
Lectures on numerical methods in bifurcation problems.
Springer Verlag, 1986.
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C. T. Kelley.
Iterative methods for linear and nonlinear equations, volume 16
of Frontiers in Applied Mathematics.
SIAM, 1995.
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T. D. Kieu and C. J. Griffin.
Monte Carlo simulations with indefinite and complex-valued measures.
Physical Review E, 49:3855-3859, 1994.
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N. C. Kluksdahl, A. M. Kriman, D. K. Ferry, and C. Ringhofer.
Self-consistent study of the resonant-tunneling diode.
Physical Review B, 39(11):7720-7735, 1989.
- KKNS03
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H. Kosina, G. Klimeck, M. Nedjalkov, and S. Selberherr.
Comparison of numerical quantum device models.
2003 Intl. Conf. on Simulation of Semiconductor Processes and
Devices (SISPAD), pages 171 - 174, 2003.
- KNR02
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H.-C. Kaiser, H. Neidhardt, and J. Rehberg.
Density and current of a dissipative Schrödinger operator.
Journal of Mathematical Physics, 43(11):5325-5350, 2002.
- KNRS03
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H. Kosina, M. Nedjalkov, C. Ringhofer, and S. Selberherr.
Semi-classical approximation of electron-phonon scattering beyond
Fermi's Golden Rule.
Submitted, 2003.
- KNS01
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H. Kosina, M. Nedjalkov, and S. Selberherr.
Variance reduction in Monte Carlo device simulation by means of
event biasing.
In M. Laudon and B. Romanowicz, editors, Proc. Modeling and
Simulation of Microsystems, MSM 2001, pages 11-14. Computational
Publications, March 2001.
- KNS03
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H. Kosina, M. Nedjalkov, and S. Selberherr.
A weight decomposition approach to the sign problem in Wigner
transport simulations.
Large-Scale Scientific Computing, 4th International Conference,
LSSC 2003, Sozopol, Bulgaria, June 4-8, 2003, Revised Papers. Lecture Notes
in Computer Science 2907 Springer 2004, ISBN 3-540-21090-3, pages 178-184,
2003.
- Kol00
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V. N. Kolokoltsov.
Semiclassical analysis for diffusions and stochastic processes,
volume 1724 of Lecture Notes in Mathematics.
Springer, 2000.
- KR85
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K. Kang and S. Redner.
Fluctuation-dominated kinetics in diffusion-controlled reactions.
Physical Review A, 32(1):435-447, 1985.
- Lev96
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C. D. Levermore.
Moment closure hierarchies for kinetic theories.
J.Stat.Phys., 83(1):1021-1065, 1996.
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C. S. Lent and D. J. Kirkner.
The quantum transmitting boundary method.
J.Appl.Phys., 67(10):6353-6359, 1990.
- LK90b
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C. S. Lent and D. J. Kirkner.
The quantum transmitting boundary method.
J.Appl.Phys., 67(10):6353-6359, 1990.
- LKF02
-
S. E. Laux, A. Kumar, and M. V. Fischetti.
Ballistic FET modeling using QDAME: quantum device analysis by modal
evaluation.
IEEE Transactions on Nanotechnology, 1(4):255-259, 2002.
- LSR95
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P. L'Eplattenier, E. Suraud, and P. G. Reinhard.
The Husimi representation and the Vlasov equation.
Ann. Physics, 244(2):426-444, 1995.
- Lun00
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M. Lundstrom.
Fundamentals of carrier transport.
Cambridge University Press, 2000.
- Lun02
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M. Lundstrom.
Is nanoelectronics the future of microelectronics.
Proceedings of the 2002 international symposium on low power
electronics and design (Monterey, California, USA), pages 172-177, 2002.
- LW99
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C. L. Lopreore and R. E. Wyatt.
Quantum wave packet dynamics with trajectories.
Physical Review Letters, 82(26):5190-5193, 1999.
- Mad27
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E. Madelung.
Quantentheorie in hydrodynamischer Form.
Z.Phys., 40:322, 1927.
- Mar91
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M. S. Marinov.
A new type of phase-space path integral.
Physics Letters A, 153(1):5-11, 1991.
- Mat99
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L. Mattner.
What are cumulants?
Doc. Math., 4:601-622, 1999.
- ME88
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B. Meinerzhagen and W. L. Engl.
The influence of the thermal equilibrium approximation on the
accuracy of classical two-dimensional numerical modeling of silicon
submicrometer MOS transistors.
IEEE Trans.Computer-Aided Design, 35(5):689-697, 1988.
- MH94
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R. K. Mains and G. I. Haddad.
An accurate re-formulation of the Wigner function method for quantum
transport modeling.
J.Comput.Phys., 112:149-161, 1994.
- Moy49
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J. E. Moyal.
Quantum mechanics as a statistical theory.
Proc. Cambridge Philos. Soc., 45:99, 1949.
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M. McClendon and H. Rabitz.
Numerical simulations in stochastic mechanics.
Physical Review A, 37(9):3479-3492, 1988.
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B. Mielnik and M. A. Reyes.
The classical Schrödinger equation.
J.Phys.A, 29:6009-6025, 1996.
- MRS84
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P. Markowich, C. Ringhofer, and A. Steindl.
Computation of current-voltage characteristics in a semiconductor
device using arc-length continuation.
IMA J. Appl. Math., 33(2):178-187, 1984.
- MT95
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H. Mizuta and T. Tanoue.
The physics and applications of resonant tunneling diodes.
Cambridge University Press, 1995.
- Nag00
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M. Nagasawa.
Stochastic processes in quantum physics.
Birkhaeuser, 2000.
- NDB+97
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M. Nedjalkov, I. Dimov, P. Bordone, R. Brunetti, and C. Jacoboni.
Using the Wigner function for quantum transport in device simulation.
Mathematical and Computer Modelling, 25:33-53, 1997.
- NDRJ96
-
M. Nedjalkov, I. Dimov, F. Rossi, and C. Jacoboni.
Convergency of the Monte Carlo algorithm for the Wigner quantum
transport equation.
Journal of Mathematical and Computer Modelling,
23(8/9):159-166, 1996.
- Nel66
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E. Nelson.
Derivation of Schrödinger equation from Newtonian mechanics.
Physical Review, 150(4):1079-1085, 1966.
- Nie93
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F. Nier.
A variational formulation of Schrödinger-Poisson systems in
dimensions .
Commun. in Partial Differential Equations, 18:1125-1147, 1993.
- NKKS01
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M. Nedjalkov, R. Kosik, H. Kosina, and S. Selberherr.
A Wigner equation for nanometer and femtosecond transport regime.
Proceedings of the 2001 First IEEE Conference on Nanotechnology,
(Maui, Hawaii), pages 277-281, October 2001.
- NKKS02
-
M. Nedjalkov, R. Kosik, H. Kosina, and S. Selberherr.
Wigner transport through tunneling structures - scattering
interpretation of the potential operator.
2002 Intl. Conf. on Simulation of Semiconductor Processes and
Devices (SISPAD), pages 187-190, 2002.
- OFW99
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J. C. O'Neill, P. Flandrin, and W. J. Williams.
On the existence of discrete-time Wigner distributions.
IEEE Sig. Proc. Lett., 6(12):304-306, 1999.
- OW98
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J. C. O'Neill and W. J. Willams.
Distributions in the discrete Cohen classes.
In Proceedings of the IEEE International Conference on
Acoustics, Speech and Signal Processing, ICASSP, volume 3, pages 1581-1584,
Seattle, WA, 12-15 May 1998.
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E. Prugovecki.
Stochastic quantum mechanics and quantum spacetime.
Reidel, 1984.
- PW02
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L. Praxmeyer and K. Wodkiewicz.
Quantum interference in the Kirkwood-Rihaczek representation.
2002.
available as http://www.arxiv.org/quant-ph/0207127.
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C. Ringhofer, D. Ferry, and N. Kluksdahl.
Absorbing boundary conditions for the simulation of quantum transport
phenomena.
Trans. Theo. Stat. Phys., pages 331-346, 1989.
- Rin00
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C. Ringhofer.
Space - time discretization of series expansion methods for the
Boltzmann transport equation.
SIAM J. Numerical Analysis, 38:442-465, 2000.
- Rin01
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C. Ringhofer.
Dissipative discretization methods for approximations to the
Boltzmann equation.
M3AS, 11:133-149, 2001.
- RJ02
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M. Rockinger and E. Jondeau.
Entropy densities with an application to autoregressive conditional
skewness and kurtosis.
J. Econometrics, 106(1):119-142, 2002.
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International technology roadmap for semiconductors - 2001 edition, 2001.
see http://public.itrs.net.
- RO003
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International technology roadmap for semiconductors - 2003 edition, 2003.
see http://public.itrs.net.
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G.-C. Rota.
Twelve problems in probability no one likes to bring up.
In Algebraic combinatorics and computer science, pages 57-93.
Springer Italia, Milan, 2001.
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A. Royer.
Wigner function in Liouville space: A canonical formalism.
Physical Review A, 43(1):44-56, 1991.
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M. S. Richman, T. W. Parks, and R. G. Shenoy.
Discrete-time, discrete-frequency, time-frequency Analysis.
IEEE Transactons on Signal Processing, 46(6):1517-1527, 1998.
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C. Ringhofer, C. Schmeiser, and A. Zwirchmayr.
Moment methods for the semiconductor Boltzmann equation on bounded
position domains.
SIAM J. Numer. Anal., 39:1078-1095, 2001.
- RVG+03
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Z. Ren, R. Venugopal, S. Goasguen, Supriyo Datta, and Mark S. Lundstrom.
nanoMOS 2.0: A two-dimensional simulator for quantum transport in
double-gate MOSFETs.
IEEE Trans.Electron Devices, 50:1914-1925, 2003.
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R. Sala, S. Brouard, and J. G. Muga.
Wigner trajectories and Liouville's theorem.
J.Chem.Phys., 99(4):2708-2714, 1993.
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J. F. Schipper.
Wigner quantum density function in the classical limit. Development
of a three-dimensional WKBJ-type solution.
Physical Review, 184(5):1283-1302, 1969.
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Semiconductor industry association.
The National Technology Roadmap for Semiconductors, 1997.
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L. Shifren and D.K. Ferry.
Particle Monte Carlo simulation of Wigner function tunneling.
Physics Letters, A285:217-221, 2001.
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S. Seeger and K. H. Hoffmann.
The cumulant method for computational kinetic theory.
Continuum Mech. Thermodyn., 12:403-421, 2000.
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Y. M. Shirokov.
Quantum and classical mechanics in the phase space representation.
Sov.J.Part.Nucl., 10(1):1-18, 1979.
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J. P. Sun, G. I. Haddad, P. Mazumder, and J. N. Schulman.
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K. E. Schmidt and M. H. Kalos.
Applications of the Monte Carlo Method in statistical physics.
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T. C. Schmidt and K. Möhring.
Stochastic path-integral simulation of quantum scattering.
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J. L. Spouge.
Exact solutions for a diffusion-reaction process in one dimension.
Physical Review Letters, 60(10):871-874, 1988.
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R. T. Skodje, H. W. Rohrs, and J. VanBuskirk.
Flux analysis, the correspondence principle, and the structure of
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G. A. Skorobogatov and S. I. Svertilov.
Quantum mechanics can be formulated as a non-Markovian stochastic
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H. Struchtrup.
Extended moment method for electrons in semiconductors.
Physica A, 275:229-255, 2000.
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K.-I. Sonoda, M. Yamaji, K. Taniguchi, C. Hamaguchi, and S. T. Dunham.
Moment expansion approach to calculate impact ionization rate in
submicron silicon devices.
J.Appl.Phys., 80(9):5444-5448, 1996.
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C. Schmeiser and A. Zwirchmayr.
Convergence of moment methods for linear kinetic equations.
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A. Tagliani.
Maximum entropy solutions and moment problem in unbounded domains.
Applied Mathematics Letters, 16(4):519-524, May 2003.
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T.-W. Tang.
Extension of the Scharfetter-Gummel algorithm to the energy balance
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V. I. Tatarski.
The Wigner representation of quantum mechanics.
Sov. Phys. Usp., 26:311-327, 1983.
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Discretization of flux densities in device simulations using optimum
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IEEE Trans.Computer-Aided Design, 14(11):1309-1315, 1995.
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T.-W. Tang and M.-K. Ieong.
Why are there so many different hydrodynamic transport models in
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H. Tsuchiya and T. Miyoshi.
Simulation of dynamic particle trajectories through
resonant-tunneling structures based upon Wigner distribution function.
Proc. 6th Int. Workshop on Computational Electronics IWCE6,
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H. Tsuchiya, M. Ogawa, and T. Miyoshi.
Simulation of quantum transport in quantum devices with spatially
varying effective mass.
IEEE Trans.Electron Devices, 38(6):1246-1252, 1991.
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G. Torres-Vega and J. H. Frederick.
Quantum mechanics in phase space: New approaches to the
correspondence principle.
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G. Torres-Vega and J. H. Frederick.
A quantum mechanical representation in phase space.
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J. C. Vink.
Quantum mechanics in terms of discrete beables.
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O. von Roos.
Boltzmann-Vlasov equation for a quantum plasma.
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T. C. Wallstrom.
Inequivalence between the Schrödinger equation and the Madelung
hydrodynamic equations.
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E. Wigner.
On the quantum correction for thermodynamic equilibrium.
Physical Review E, 40:749-759, 1932.
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J. Wang and M. Lundstrom.
Does source-to-drain tunneling limit the ultimate scaling of MOSFETs.
IEDM 2002, pages 707-710, 2002.
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J. J. Wlodarz.
On quantum mechanical phase-space wave functions.
J. Chem. Phys., 100(10):7474-7480, 1994.
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J. J. Wlodarz.
On marginalization of phase-space distribution functions.
Phys.Lett.A, 264(1):18-21, 1999.
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E.X. Wang, M. Stettler, S. Yu, and C. Maziar.
Application of cumulant expansion to the modeling of non-local
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