We demonstrate how a single scanning voltage probe can be used to map the local conductivity and current density in a thin film with no a priori knowledge of the geometry of the electrical contacts. With state-of-the-art scanning voltage probes, unde
r appropriate conditions such mapping should be possible down to nanometer scales. The technique requires two non-colinear voltage scans. When only one voltage map is available, determination of the conductivity is not possible because the solution to the governing equation is not unique. The only restriction on the technique is that the sheet conductivity is a local function of position.
Specific contact resistivity measurements have conventionally been heavy in both fabrication and simulation/calculation in order to account for complicated geometries and other effects such as parasitic resistance. We propose a simpler geometry to de
liver current, and the use of a scanning voltage probe to sense the potential variation along the sample surface, from which the specific contact resistivity can be straightforwardly deduced. We demonstrate an analytical example in the case where both materials are thin films. Experimental data with a scanning Kelvin probe measurement on graphene from the literature corroborates our model calculation.
Under mesoscopic conditions, the transport potential on a thin film with current is theoretically expected to bear spatial variation due to quantum interference. Scanning tunneling potentiometry is the ideal tool to investigate such variation, by vir
tue of its high spatial resolution. We report in this {it Letter} the first detailed measurement of transport potential under mesoscopic conditions. Epitaxial graphene at a temperature of 17K was chosen as the initial system for study because the characteristic transport length scales in this material are relatively large. Tip jumping artifacts are a major possible contribution to systematic errors; and we mitigate such problems by using custom-made slender and sharp tips manufactured by focussed ion beam. In our data, we observe residual resistivity dipoles associated with topoographical defects, and local peaks and dips in the potential that are not associated with topographical defects.
A theoretical description of scanning tunneling potentoimetry (STP) measurement is presented to address the increasing need for a basis to interpret experiments on macrscopic samples. Based on a heuristic understanding of STP provided to facilitate t
heoretical understanding, the total tunneling current related to the density matrix of the sample is derived within the general framework of quantum transport. The measured potentiometric voltage is determined implicitly as the voltage necessary to null the tunneling current. Explicit expressions of measured voltages are presented under certain assumptions, and limiting cases are discussed to connect to previous results. The need to go forward and formulate the theory in terms of a local density matrix is also discussed.
