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Verifications of Schottky's Conjecture
- Source :
- Journal of Applied Physics. 125:215306
- Publication Year :
- 2019
- Publisher :
- AIP Publishing, 2019.
-
Abstract
- Schottky's Conjecture posits that the geometric field enhancement produced by a hybrid shape formed from a small perturbation on a larger base is the product of the individual field enhancement factors of the base and perturbation in isolation. This is a powerful concept with practical applications to understanding field emitter design and operation, as actual field emitters have complicated surface shapes with structure and, therefore, contributions to field enhancement, occurring simultaneously on many length scales. Recent studies of the Conjecture imply that the degree to which it accurately predicts a hybrid structure's total field enhancement depends on the degree of self-similarity between the base and perturbation shapes. To explore these aspects of the Conjecture, we have used the zero-potential surface produced by simple charge distributions to produce compound shapes with small perturbations on larger base structures. In the limit of small perturbation strength, these simple models adequately approximate idealized compound shapes, such a hemisphere-on-hemisphere geometry. Changing the base shape and the location of the perturbation allows us to selectively degrade the self-similarity present in the problem geometry. Proofs of the Schottky Conjecture in the limit of small perturbation strength will be provided, using these techniques, for hemisphere-on-hemisphere and half-cylinder-on-half-cylinder systems—the latter being the geometry considered by Schottky and for which the Conjecture was first proposed, but not proven.
- Subjects :
- 010302 applied physics
Physics
Conjecture
Mathematical analysis
Schottky effect
General Physics and Astronomy
Perturbation (astronomy)
Schottky diode
02 engineering and technology
Total field
021001 nanoscience & nanotechnology
Mathematical proof
01 natural sciences
Field electron emission
0103 physical sciences
0210 nano-technology
Common emitter
Subjects
Details
- ISSN :
- 10897550 and 00218979
- Volume :
- 125
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Physics
- Accession number :
- edsair.doi...........dd03573b9171f5a9d15ff02b69c4b5c5
- Full Text :
- https://doi.org/10.1063/1.5091712