[01] N. V. Khotkevych, B.I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkiv, Ukraine. [02] Yu. A. Kolesnichenko, B.I. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.

This paper is dedicated to further development of the theory of the current states in small size tunnel contacts. We have consistently investigated the problem of electron tunneling through an inhomogeneous barrier, which is described by Dirac delta function, between a conducting half-space, and a three-dimensional quantum well. The electron tunneling from the states with the continuous energy spectrum into the quantized states of the three-dimensional potential well is considered as well as the tunneling in the opposite direction. In order to solve the above problem we develop an original method based on the asymptotical expansion of the electron wave function in small parameter, could be defined by means of characteristic radius of the transmission region and an amplitude of the tunnel barrier. The key advantage of our method is in its ability to determine the system properties in the asymptotically explicit way. Following our approach we describe the tunnel current in such systems as a function of the system parameters. The results can be used for interpretation of experiments in scanning tunneling microscopy.

Electron Tunneling, Tunnel Current, Conductance, STM, Inhomogeneous Barrier

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