PERTURBATION APPROACH FOR QUANTUM TRANSMISSION

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Abstract
In scanning tunneling microscopy (STM), the potential barriers are often close to or lower than the Fermi level, where both semiclassical tunneling theory and Bardeen’s tunneling theory are no longer valid. We present a new perturbation approach for general quantum transmission phenomena. For thick, positive potential barriers, it reduces to Bardeen’s tunneling theory. For potential barriers lower than the energy level, it is valid as long as the barrier thickness is smaller than one half of the de Broglie wavelength, a condition which is always satisfied in STM. An immediate application is shown.

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