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Stimulated emission of surface plasmons by electron tunneling in metal‐barrier‐metal structures
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5.In the present work the plasmon momentum is small compared to that of electrons; this is true except very close to a resonance and can thus be neglected in the more complete plasmon potential Furthermore, since the wavelength of the plasmon is much larger than the gap width the vector potential in the Coulomb gauge can be neglected. The average plasmon potential is then given by where is the magnitude of the component of electric field directed across the barrier.
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9.A finite lifetime necessitates a summation over a distribution of possible transistions For typical metals, however, this is sufficiently narrow so that the tunneling probability is essentially constant and can be replaced by a δ function.
10.There are contributions from the diagram associated with emission‐absorption interactions as well as terms associated with the zero frequency density operator and which correspond to the modulation of the dc tunneling current by the ac potential: where This is identical with the expression obtained from the current in the WKB approximation, such as that obtained by J. G. Simmons [J. Appl. Phys. 34, 1793 (1963);
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