Abstract
We derive the stationary tunneling solution for charged particles moving in a spherical, 3-dimensional zero-range potential plus a constant electric field. From the analytic expression for the wave function we calculate the distribution of the current inside and outside the vacuum barrier. At low field strengths there is a constant spreading of the tunnel current orthogonal to the direction of the applied field. At intermediate field strengths the exact results for the current distribution behave different from the semiclassical predictions.
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References
Mang, H.J.: Ann. Rev. Nucl. Sci.14, 1 (1964)
Wolf, E.L.: Principles of electron tunneling spectroscopy. New York: Oxford Press 1985
Binnig, G., Rohrer, H., Gerber, Ch., Weibel, E.: Appl. Phys. Lett.40, 178 (1982); Phys. Rev. Lett.49, 57 (1982)
Feuchtwang, T.E., Cutler, P.H.: Phys. Scr.35, 132 (1987)
Hansma, P.K., Tersoff, J.: J. Appl. Phys.61, R1 (1987)
Lang, N.D.: Comm. Condens. Matter Phys.14, 253 (1989)
Chen, C.J.: Phys. Rev. B42, 8841 (1990)
Ciraci, S., Baratoff, A., Batra, I.P.: Phys. Rev.B41, 2763 (1990)
Demkov, Yu.N., Drukarev, G.F.: Zh. Eksp. Teor. Fiz.47, 918 (1964)
Demkov, Yu.N., Ostrovskii, V.N.: Zero-range potentials and their applications in atomic physics. New York: Plenum Press 1988
Garcia-Calderon, G., Peierls, R.: Nucl. Phys. A265, 443 (1976)
Landau, L.D., Lifshitz, E.M.: Quantenmechanik. Berlin: Akademie-Verlag 1979
Elberfeld, W., Kleber, M.: Z. Phys. B — Condensed Matter73, 23 (1988)
Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions. New York: Dover 1970
Fermi, E.: Ric. Sci.7, 13 (1936)
[10], page 5
[12], page 127
Kapur, P.L., Peierls, R.: Proc. R. Soc. London Ser. A163, 606 (1937)
Das, B., Mahanty, J.: Phys. Rev. B36, 898 (1987)
Huang, Z.H., Feuchtwang, T.E., Cutler, P.H., Kazes, E.: Phys. Rev. A41, 32 (1990)
Ring, P., Rasmussen, J.O., Massmann, H.: Sov. J. Part. Nucl.7, 366 (1976)
Schutte, C.J.H.: The theory of molecular spectroscopy. Vol. 1. Amsterdam: North-Holland Publishing Company 1976
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Dedicated to Prof. Dr. H.-J. Mang on the occasion of his 60th birthday
We acknowledge discussions with Dr. W. Elberfeld and Professor R. Gomer. The work was supported by Deutsche Forschungsgemeinschaft initially through contract number Kl 315/3-2 and later on by means of the SFB 338.
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Gottlieb, B., Kleber, M. & Krause, J. Tunneling from a 3-dimensional quantum well in an electric field: an analytic solution. Z. Physik A - Hadrons and Nuclei 339, 201–206 (1991). https://doi.org/10.1007/BF01282950
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DOI: https://doi.org/10.1007/BF01282950