Deconvolution of the density of states of tip and sample through constant-current tunneling spectroscopy

We introduce a scheme to obtain the deconvolved density of states (DOS) of the tip and sample, from scanning tunneling spectra determined in the constant-current mode (z-V spectroscopy). The scheme is based on the validity of the Wentzel-Kramers-Brillouin (WKB) approximation and the trapezoidal approximation of the electron potential within the tunneling barrier. In a numerical treatment of z-V spectroscopy, we first analyze how the position and amplitude of characteristic DOS features change depending on parameters such as the energy position, width, barrier height, and the tip-sample separation. Then it is shown that the deconvolution scheme is capable of recovering the original DOS of tip and sample with an accuracy of better than 97% within the one-dimensional WKB approximation. Application of the deconvolution scheme to experimental data obtained on Nb(110) reveals a convergent behavior, providing separately the DOS of both sample and tip. In detail, however, there are systematic quantitative deviations between the DOS results based on z-V data and those based on I-V data. This points to an inconsistency between the assumed and the actual transmission probability function. Indeed, the experimentally determined differential barrier height still clearly deviates from that derived from the deconvolved DOS. Thus, the present progress in developing a reliable deconvolution scheme shifts the focus towards how to access the actual transmission probability function.