Thornber, K. K. and Feynman, Richard P. (1970) Velocity acquired by an electron in a finite electric field in a polar crystal. Physical Review B, 1 (10). pp. 4099-4114. ISSN 0556-2805. http://resolver.caltech.edu/CaltechAUTHORS:THOprb70
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The expectation value of the steady-state velocity acquired by an electron interacting with the longitudinal, optical phonons of a polar crystal in a finite electric field is analyzed quantum mechanically for arbitrary coupling strength, field strength, and temperature. The rate of loss of momentum by an electron drifting through the crystal in the applied field is expressed in a form in which the lattice coordinates (the phonons) have been eliminated exactly by path-integral methods. This expression is then evaluated by a path-integral approach similar to that used to calculate the impedance of electrons in polar crystals. We present numerical calculations of field (loss of energy per unit distance) versus velocity for three coupling strengths using the Fröhlich polaron model. In a single curve, all the expected phenomena appear, including a threshold field for producing hot electrons and a decreasing rate of energy loss with velocity for very fast electrons. Using only the experimentally measured values of the reststrahlen energy and the static and optical dielectric constants, we find an energy loss of 0.025 eV/Å for electrons near the threshold in Al2O3, which compares favorably with the experimental value of about 0.03 eV/Å. We conclude that optical-phonon scattering can indeed produce the high rate of energy loss that is present in tunnel-cathode structures.
|Additional Information:||©1970 The American Physical Society. Received 24 November 1969. We wish to express our sincerest appreciation to C.A. Mead for calling this problem to our attention. We thank Robert V. Langmuir for arranging the necessary computer financing and Thomas C. McGill, Jr., for help with the basic computer program. For a critical reading of the manuscript we thank J.R. Brews and P.M. Platzman. Thanks are also due to our many friends at the California Institute of Technology and Stanford University for their continuing support and encouragement throughout this project. One of us (K.K.T.) acknowledges the kind support of the National Science Foundation and the Air Force Office of Scientific Research fellowships, parts of the tenures of which were devoted to this project. [K.K.T. was a] National Science Foundation Cooperative Graduate Fellow 1963-1966, National Academy of Sciences-National Research Council-Air Force Office of Scientific Research Postdoctoral Fellow 1966-1967.|
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|Deposited By:||Tony Diaz|
|Deposited On:||12 Mar 2008|
|Last Modified:||26 Dec 2012 09:52|
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