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

Abstract

SummaryWe 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.

Engineering the electronic structure of surface dangling bond nanowires of different size and dimensionality

“…In all spectroscopic data presented here the surface and probe combined local density of states (LDOS s,t ) was recovered [15] from the simultaneously measured dI/dV(V) and I(V) spectra. The use of the combined LDOS for the surface characterization is a good approximation to the actual surface density of states since the electronic structure of the metallic tip is larger in magnitude and less corrugated in comparison with that of semiconductor surface [17]. Moreover, even if the probe LDOS becomes corrugated due to uncontrolled hydrogen adsorption, it was demonstrated previously [17] that this will only significantly impact the filled states bias region below −1 V. We will now provide a detailed description of the four types of DBs wires shown in figure 1.…”

Enhanced conductance of molecular states at interstitial sites

“…Schemes have been designed to extract the LDOS from subsets of I(V, x, y, z), e.g. 'spectra' of I(V) or its derivative dI(V)/dV [14][15][16][17][18][19][20][21][22][23][24][25]. Laterally resolved maps recorded under experimental conditions such as constant height, constant current, or constant conductance have also been evaluated [17,18,26,27].Here we present STM data from artificial molecular clusters.…”

4,4′-Dithiodipyridine on Au(111): A Combined STM, STS, and DFT Study

“…∂ V I is still a measure of the change of tunneling probability with sample bias and, therefore, a measure of the LDOS. 42,43 This spectroscopy mode leads to a gentler treatment of the sample because an increasing tunneling bias causes an increasing tip−sample separation. To refine the method a bit, we multiply ∂I/∂V by V to obtain a better measure of the LDOS, ρ.…”

“…Here, the topographic feedback-loop of the STM is left on while scanning the sample bias, V , and acquiring the tip–sample separation, z , together with the conductivity, ∂ V I , that is, at constant tunneling current, I . ∂ V I is still a measure of the change of tunneling probability with sample bias and, therefore, a measure of the LDOS. , This spectroscopy mode leads to a gentler treatment of the sample because an increasing tunneling bias causes an increasing tip–sample separation. To refine the method a bit, we multiply ∂ I /∂ V by V to obtain a better measure of the LDOS, ρ.…”