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The Escape of Particles from a Confining Potential well

Published online by Cambridge University Press:  15 February 2011

James P. Lavine ,
Edmund K. Banghart  and
Joseph M. Pimbley
James P. Lavine
Affiliation:
Microelectronics Technology Division, Eastman Kodak Company, Rochester, NY 14650-2008
Edmund K. Banghart
Affiliation:
Microelectronics Technology Division, Eastman Kodak Company, Rochester, NY 14650-2008
Joseph M. Pimbley
Affiliation:
Department of Mathematical Sciences, Renssalaer Polytechnic Institute, Troy, NY 12180-3590
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Abstract

Many electron devices and chemical reactions depend on the escape rate of particles confined by potential wells. When the diffusion coefficient of the particle is small, the carrier continuity or the Smoluchowski equation is used to study the escape rate. This equation includes diffusion and field-aided drift. In this work solutions to the Smoluchowski equation are probed to show how the escape rate depends on the potential well shape and well depth. It is found that the escape rate varies by up to two orders of magnitude when the potential shape differs for a fixed well depth.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 249
Copyright
Copyright © Materials Research Society 1993

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References

1. Kramers, H.A., Physica 7, 284 (1940).Google Scholar
2. Banghart, E.K., Lavine, J.P., Pimbley, J.M., and Burkey, B.C., COMPEL 1 0, 205 (1991).Google Scholar
3. Cavaillès, J.A., Miller, D.A.B., Cunningham, J.E., Wa, P. Li Kam, and Miller, A., Appl. Phys. Lett. 6 1, 426 (1992).Google Scholar
4. van Kampen, N.G., Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), Ch. 6.Google Scholar
5. Schuss, Z., Theory and Applications of Stochastic Differential Equations (John Wiley, New York, 1980), Ch. 8.Google Scholar
6. Hänggi, P., Talkner, P., and Borkovec, M., Rev. Mod. Phys. 6 2, 251 (1990).Google Scholar
7. Larson, R.S. and Lightfoot, E.J., Physica 149A, 296 (1988).Google Scholar
8. Lavine, J.P. and Burkey, B.C., Solid-State Electronics 2 3, 75 (1980).Google Scholar
9. Lavine, J. P., Chang, W.-C., Anagnostopoulos, C.N., Burkey, B.C., and Nelson, E.T., IEEE Trans. Electron Devices ED–3 2, 2087 (1985).Google Scholar
10. Subroutines D02KAF and D02KDF from the NAG FORTRAN Library, Numerical Algorithms Group, Inc., Downers Grove, Illinois.Google Scholar
11. Hong, K.M. and Noolandi, J., Surf. Sci. 7 5, 561 (1978).Google Scholar
12. Parzen, E., Stochastic Processes (Holden-Day, San Francisco, 1962), Chs. 6 and 7.Google Scholar
13. Goel, N.S. and Richter-Dyn, N., Stochastic Models in Biology (Academic Press, New York, 1974), Chs. 2 and 3 and the appendices.Google Scholar
14. Gillespie, D.T., Markov Processes: An Introduction for Physical Scientists (Academic Press, Boston, 1992), Chs. 3 and 6.Google Scholar
15. Weaver, D.L., Phys. Rev. B 2 0, 2558 (1979).Google Scholar
16. Weaver, D.L., J. Chem. Phys. 7 2, 3483 (1980).Google Scholar
17. Deutch, J.M., J. Chem. Phys. 7 3, 4700 (1980).Google Scholar
18. Weiss, G.H., Adv. Chem. Phys. 1 3, 1 (1967).Google Scholar
19. Weaver, D.L., Surf. Sci. 9 0, 197 (1979).Google Scholar