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We have found an asymptotically exact solution of the Schrodinger equation for electrons tunneling into surface states through an inhomogeneous barrier of large amplitude. Assuming an elliptic dispersion law for the charge carriers, the “standing wave” pattern in the conductance of the system resulting from the electron scattering by a single defect in the vicinity of the surface is analyzed.

Electron tunneling into surface states through an inhomogeneous barrier: Asymptotically exact solution of the problem, and STM theory