Recovery of local density of states using scanning tunneling spectroscopy

Abstract

Scanning tunneling spectroscopy (STS) provides a unique method for the investigation of the local surface-projected electron density of states (DOS), mostly for its capability of reaching atomic resolution. Such information is contained in a nonobvious way in STS data, and a proper understanding of the overall features of the system $(\text{sample}+\text{tip})$ is mandatory in order to obtain quantitative information. Several approaches have been proposed in the literature to tackle this problem. A common feature of these methods is that they are mostly based on a one-dimensional (1D) WKB description of the tunneling current. We present a critical analysis and an extension of the methods so far proposed, with the main goal of applying the results to STS experimental data. This study has been conducted by modeling the tip-sample system within the frame of 1D-WKB theory, investigating key open issues, such as the estimation of required but usually experimentally unknown parameters such as the tip-sample distance and the role played by the presence of a nonconstant tip local DOS on STS data. This investigation allows us to ascertain strengths and weaknesses of the existing methods and leads to an optimized and improved strategy which we propose for the analysis of STS data. We tested our conclusions on STS measurements of the $\text{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ and Au(111) surfaces, acquired with W and Cr tips.