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The Wentzel-Kramers-Brillouin approximation is extended to consider tunneling through three-dimensional potential barriers. The formalism is used to obtain the tunnel-current density in a scanning-tunneling microscope with a realistic model of the potential barrier. It is shown that the tunnel-current density has a sharp peak under the tip, and that explains the high lateral resolution of the instrument.
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Das et al. (1987) studied this question.
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