REFERENCES

• Ando, T., A. B. Fowler, and F. Stern, 1982, Rev. Mod. Phys. 54, 437.

• Apostol, T. M., 1969, Calculus, Vol. II, Multi-Variable Calculus and Linear Algebra (Blaisdell, Waltham, MA) ch. 1.

• Aubert, J. P., J. C. Vaissiere, and J. P. Nougier, 1984, J. Appl. Phys. 56, 1128.

• Baranger, H. U., and J. W. Wilkins, 1987, Phys. Rev. B 36, 1487.

• Bardeen, J., 1949, Bell Syst. Tech. J. 28, 428.

• Barker, J. R., D. W. Lowe and S. Murray, 1984, in The Physics of Submicron Structures, edited by H. L. Grubin, K. Hess, and D. K. Ferry (Plenum, New York), p. 277.

• Bedeaux, D., K. Lakatos-Lindenberg, and K. E. Shuler, 1971, J. Math. Phys. 12, 2116.

• Berry, M. V., 1977, Philos. Trans. R. Soc. London 287, 237.

• Bjorken, J. D., and S. D. Drell, 1964, Relativistic Quantum Mechanics (McGraw-Hill, New York), sec 6.3.

• Blakemore, J. S., 1982, Solid-State Electron. 25, 1067.

• Broekaert, T. P. E., W. Lee, and C. G. Fonstad, 1988, Appl. Phys. Lett. 53, 1545.

• Büttiker, M., Y. Imry, R. Landauer, and S. Pinhas, 1985, Phys. Rev. B 31, 6207.

• Cahay, M., M. McLennan, S. Datta, and M. S. Lundstrom, 1987, Appl. Phys. Lett. 50, 612.

• Caldeira, A. O., and A. J. Leggett, 1983, Physica A121, 587.

• Carruthers, P., and F. Zachariasen, 1983, Rev. Mod. Phys. 55, 245.

• Castagné, R., 1985, Physica 134B, 55.

• Champlin, K. S., D. B. Armstrong, and P. D. Gunderson, 1964, Proc. IEEE 52, 677.

• Chang, L. L., L. Esaki, and R. Tsu, 1974, Appl. Phys. Lett. 24, 593.

• Chester, G. V., 1963, Rep. Prog. Phys. 26, 411.

• Conwell, E M., 1967, High Field Transport in Semiconductors, Solid State Phys., Suppl. 9 (Academic, New York).

• Claasen, T. A. C. M., and W. F. G. Mecklenbräuker, 1980, (in three parts) Philips J. Res. 35, 217; 35, 276; 35, 372.

• Claasen, T. A. C. M., and W. F. G. Mecklenbräuker, 1983, IEEE Trans. Acoust. Speech Signal Process., ASSP-31, 1067.

• Constant, E., 1985, in Hot-Electron Transport in Semiconductors, edited by L. Reggiani, Topics in Applied Physics, Vol. 58 (Springer, Berlin), p. 227.

• Dahl, J. P., 1981, ``Dynamical Equations for the Wigner Functions,'' Technical University of Denmark preprint.

• Davies, E. B., 1976, Quantum Theory of Open Systems (Academic, London) and references therein.

• Dickinson, H. W., 1938, A Short History of the Steam Engine (Cambridge University Press, Cambridge), ch. 6.

• Dingle, R., W. Wiegmann, and C. H. Henry, 1974, Phys. Rev. Lett. 33, 827.

• Dresden, M., 1961, Rev. Mod. Phys. 33, 265.

• Duke, C. B., 1969, Tunneling in Solids, Solid State Phys., Suppl. 10 (Academic, New York).

• Duderstadt, J. J., and W. R. Martin, 1979, Transport Theory (Wiley, New York) sec. 8.1.2.

• Eastman, A. V., 1949, Fundamentals of Vacuum Tubes, (McGraw-Hill, New York).

• Fawcett, W., A. D. Boardman, and S. Swain, 1970, J. Phys. Chem. Solids 31, 1963.

• Ferry, D. K., 1980, in Physics of Nonlinear Transport in Semiconductors, edited by D. K. Ferry, J. R. Barker, and C. Jacoboni (Plenum, New York), p. 117.

• Fetter, A. L., and J. D. Walecka, 1971, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York), pp. 59-61.

• Feynman, R. P., 1972, Statistical Mechanics, A Set of Lectures (Benjamin, Reading, MA), ch. 2.

• Frensley, W. R., 1985, J. Vac. Sci. Technol. B 3, 1261.

• Frensley, W. R., 1986, Phys. Rev. Lett. 57, 2853; 60, 1589(E).

• Frensley, W. R., 1987a, Phys. Rev. B 36, 1570; 37, 10379(E).

• Frensley, W. R., 1987b, Appl. Phys. Lett. 51, 448.

• Frensley, W. R., 1988a, Superlatttices and Microstructures 4 497.

• Frensley, W. R., 1988b, Solid-State Electron. 31, 739.

• Frensley, W. R., 1989a, in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, eds. (Academic, Boston), p. 219.

• Frensley, W. R., 1989b, Solid-State Electron. 32, 1235.

• Frensley, W. R., and J. H. Luscombe, 1990, unpublished.

• Frölich, H., 1967, Physica 37, 215.

• Gordon, J. P., 1967, Phys. Rev. 161 367.

• Grinberg, A. A., and S. Luryi, 1989, Phys. Rev. B 39, 7466.

• Groenewold, H. J, 1946, Physica 12, 405.

• Haken, H., 1975, Rev. Mod. Phys. 47, 67.

• Heller, E. J., 1976, J. Chem. Phys. 65, 1289.

• Heinrich, H., G. Bauer, and F. Kuchar, 1988, Eds., Physics and Technology of Submicron Structures, Springer Series in Solid-State Sciences No. 83 (Springer, Berlin).

• Hillery, M., R. F. O'Connell, M. O. Scully, and E. P. Wigner, 1984, Phys. Rep. 106, 121.

• Hockney, R. W., and J. W. Eastwood, 1981, Computer Simulation Using Particles (McGraw-Hill, New York), ch. 10.

• Horowitz, P., and W. Hill, 1980, The Art of Electronics (Cambridge University Press, Cambridge).

• Hu, G. Y., and R. F. O'Connell, 1987, Phys. Rev. B 36, 5798.

• Iafrate, G. J., H. L. Grubin, and D. K. Ferry, 1981, J. Phys. (Paris) Colloque C7, Suppl. 10, 42, 307.

• Jacoboni, C., and L. Reggiani, 1983, Rev. Mod. Phys. 55, 645.

• Jauho, A.-P., 1989, Solid-State Electron. 32, 1265.

• Jensen, K. L., and F. A. Buot, 1989a, J. Appl. Phys. 65, 5248.

• Jensen, K. L., and F. A. Buot, 1989b, Appl. Phys. Lett. 55, 669.

• Jensen, K. L., and F. A. Buot, 1990, unpublished.

• Kadanoff, L. P., and G. Baym, 1962, Quantum Statistical Mechanics (Benjamin/Cummings, Reading, MA).

• Keldysh, L. V., 1964, Zh. Eksp. Teor. Fiz. 47, 1515 [Sov. Phys. JETP 20, 1018 (1965).]

• Kluksdahl, N. C., A. M. Kriman, D. K. Ferry, and C. Ringhofer, 1988, IEEE Electron Device Lett. 9, 457.

• Kluksdahl, N. C., A. M. Kriman, D. K. Ferry, and C. Ringhofer, 1989, Phys. Rev. B 39, 7720.

• Kohn, W., and J. M. Luttinger, 1957, Phys. Rev. 108, 590.

• Kreuzer, H. J., 1981, Nonequilibrium Thermodynamics and its Statistical Foundations, (Oxford University Press, Oxford, New York).

• Krieger, J. B., and G. J. Iafrate, 1986, Phys. Rev. B 33, 5494.

• Kubo, R., 1957, J. Phys. Soc. Japan 12, 570.

• Kubo, R., M. Toda, and N. Hashitsume, 1985, Statistical Physics II, Nonequilibrium Statistical Physics (Springer, Berlin, 1985), ch. 2.

• Lapidus, L., and G. F. Pinder, 1982, Numerical Solution of Partial Differential Equations in Science and Engineering (Wiley, New York), ch. 2.

• Lanczos, C., 1961, Linear Differential Operators (van Nostrand, London), sec. 3.6, sec. 3.8, and sec. 4.16.

• Landau, L. D., and E. M. Lifshitz, 1959, Fluid Mechanics, translated by J. B. Sykes and W. H. Reid (Pergamon, London), ch. 1.

• Landauer, R., 1957, IBM J. Res. Develop. 1, 233.

• Landauer, R., 1970, Philos. Mag. 21, 863.

• Langmuir I., and K. T. Compton, 1931, Rev. Mod. Phys. 2, 123.

• Langreth, D. C., 1976, in Linear and Nonlinear Electron Transport in Solids, edited by J. T. Devreese and V. E. van Doren (Plenum, New York) p. 3.

• Lebowitz, J. L., 1959, Phys. Rev. 114, 1192.

• Lebwohl, P. A., and P. J. Price, 1971, Appl. Phys. Lett. 19, 530.

• Lei, X. L., and C. S. Ting, 1985, Phys. Rev. B 32, 1112.

• Lent, C. S., and D. J. Kirkner, 1990, J. Appl. Phys. (in press).

• Levinson, I. B., 1969, Zh. Eksp. Teor. Fiz. 57, 660 [Sov. Phys. JETP 30, 362 (1970)].

• Louisell, W. H., 1973, Quantum Statistical Properties of Radiation (Wiley, New York).

• Luryi, S., 1985, Appl. Phys. Lett. 47, 490.

• Luttinger, J. M., and W. Kohn, 1955, Phys. Rev. 97, 869.

• Mahan, G. D., 1987, Phys. Rep. 145 251.

• Mains, R. K., and G. I. Haddad, 1988a, J. Appl. Phys. 64, 3564.

• Mains, R. K., and G. I. Haddad, 1988b, J. Appl. Phys. 64, 5041.

• Mains, R. K., and G. I. Haddad, 1988c, ``Numerical Considerations in the Wigner Function Modeling of Resonant-Tunneling Diodes,'' University of Michigan preprint.

• Mains, R. K., and G. I. Haddad, 1989, ``A New Formulation of the Wigner Function Method for Quantum Transport Modeling,'' University of Michigan preprint.

• Mains, R. K., I. Mehdi, and G. I. Haddad, 1989, Appl. Phys. Lett. 55, 2631.

• Makhoul, J., 1975, Proc. IEEE 63, 561.

• Marland, E. A., 1964, Early Electrical Communication (Abelard-Schuman Ltd., London).

• Mehdi, I, and G. I. Haddad, 1989, in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, eds. (Academic, Boston), p. 207.

• Messiah, A., 1962, Quantum Mechanics (Wiley, New York), vol. 1, p. 120.

• Miller, D. R., and D. P. Neikirk, 1990, unpublished.

• Milnes, A. G., and D. L. Feucht, 1972, Heterojunctions and Metal-Semiconductor Junctions (Academic, New York), sec. 9.9.

• Morrow, R. A., and K. R. Brownstein, 1984, Phys. Rev. B 30, 678.

• Moyal, J. E., 1949, Proc. Cambridge Philos. Soc. 45, 99.

• Narcowich, F. J., 1986, and R. F. O'Connell, Phys. Rev. A 34, 1.

• Oppenheim, A. V., and R. W. Schafer, 1975, Digital Signal Processing, (Prentice-Hall, Englewood Cliffs, NJ).

• Oppenheim, I., K. E. Shuler, and G. H. Weiss, 1977, Stochastic Processes in Chemical Physics: The Master Equation (MIT, Cambridge, Mass.) and reprints included therein.

• Peierls, R., 1974, in Transport Phenomena, edited by G. Kirczenow and J. Marro, Lecture Notes in Physics, Vol. 31 (Springer, Berlin), p. 1.

• Poletti, M. A., 1988, J. Acoust. Soc. Am. 84, 238.

• Pötz, W., 1989, J. Appl. Phys. 66, 2458.

• Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1986, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, Cambridge), sec. 17.1.

• Prigogine, I., 1980, From Being to Becoming. Time and Complexity in the Physical Sciences, (Freeman, San Francisco).

• Putterman, S. J., 1974, Superfluid Hydrodynamics, (North-Holland, Amsterdam), sec. 50.

• Ramo, S., 1939, Proc. IRE 27, 584.

• Ravaioli, U., M. A. Osman, W. Pötz, N. Kluksdahl, and D. K. Ferry, 1985, Physica 134B, 36.

• Reed, M. A., W. R. Frensley, W. M. Duncan, R. J. Matyi, A. C. Seabaugh, and H.-L. Tsai, 1989, Appl. Phys. Lett. 54, 1256.

• Reed, M. A., and W. P. Kirk, 1989, Eds., Nanostructure Physics and Fabrication (Academic, Boston).

• Reggiani, L., 1985, in Hot-Electron Transport in Semiconductors, edited by L. Reggiani, Topics in Applied Physics, Vol. 58 (Springer, Berlin), p. 7.

• Reichl, L. E., 1980, A Modern Course in Statistical Physics (University of Texas Press, Austin, TX).

• Reynolds, T. S., 1983, Stronger than a Hundred Men, A History of the Vertical Water Wheel (Johns Hopkins University Press, Baltimore), ch. 4.

• Ringhofer, C., D. K. Ferry, and N. C. Kluksdahl, 1989, Transport Theor. Stat. Phys. 18, 331.

• Roache, P. J., 1976, Computational Fluid Dynamics (Hermosa, Albuquerque, NM).

• Scully, M. O., and W. E. Lamb, Jr., 1967, Phys. Rev. 159, 208.

• Selberherr, S., 1984, Analysis and Simulation of Semiconductor Devices (Springer, Wien).

• Shockley, W., 1938, J. Appl. Phys. 9, 635.

• Shockley, W., 1949, Bell Syst. Tech. J. 28, 435.

• Slater, J. C., 1949, Phys. Rev. 76, 1592.

• Sollner, T. C. L. G., W. D. Goodhue, P. E. Tannenwald, C. D. Parker, and D. D. Peck, 1983, Appl. Phys. Lett. 43, 588.

• Stone, A. D., and A. Szafer, 1988, IBM J. Res. Develop. 32, 384.

• Szafer, A., and A. D. Stone, 1989, Phys. Rev. Lett. 62, 300.

• Tolman, R. C., 1938, The Principles of Statistical Mechanics (Oxford University Press, Oxford), (republished by Dover, New York, 1979).

• Tsu, R., and L. Esaki, 1973, Appl. Phys. Lett. 22, 562.

• Visscher, P. B., 1988, Fields and Electrodynamics, A Computer-Compatible Introduction, (Wiley, New York).

• Visscher, P. B., 1989, Computers in Physics 3 (#2), 42.

• Webb, R. A., 1989, in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, eds. (Academic, Boston), p. 43.

• Wilkinson, J. H., 1965, The Algebraic Eigenvalue Problem (Oxford University Press, London), ch. 2, sec. 13.

• Wigner, E., 1932, Phys. Rev. 40, 749.

• Wigner, E. P., 1971, in Perspectives in Quantum Theory, edited by W. Yourgrau and A. van der Merwe (MIT, Cambridge, MA), p.25.

• Wingreen, N. S., and J. W. Wilkins, 1987, Bull. Am. Phys. Soc. Ser. II 32, 833.

• Wolf, E. L., 1985, Principles of Electron Tunneling Spectroscopy (Oxford University Press, New York).

• Woolf, H. B., 1981, Editor in Chief, Webster's New Collegiate Dictionary (G. & C. Merriam, Springfield, MA), p. 200.

• Yennie, D. R., 1987, Rev. Mod. Phys. 59, 781.

• Zwanzig, R., 1964, Physica , 1109.