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Systematic general expressions of the tunnel current in the STM are derived by the use of the Green's functions of the protrusion of the tip and the sample surface. Tersoff and Hamann's result is discussed in the light of the general theory. Improved definition of the sampling point of the surface DOS is given and the inevitable coarse graining is concluded. Effect of the electron-phonon coupling on the tunneling spectroscopy is clarified.
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Tsukada et al. (1987) studied this question.
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