Two-probe scanning tunneling spectroscopy: determination of transconductance in planar atomic structures

Abstract

Due to unprecedented precision reaching picometers scanning probe microscopy (SPM) methods are currently the most popular and reliable tools for local characterization of atomic and single-molecule systems supported on surfaces of solids. However, direct determination of many functional properties, including especially electronic transport in prototypical planar atomic-scale devices, lies beyond the single-probe SPM approach. Recent technical advances provide multi-probe SPM instruments, which are able to operate on the same surface simultaneously with stability comparable to best cryogenic single-probe SPMs. In this work, we describe the full methodology behind atomically defined two-probe scanning tunneling microscopy/spectroscopy (2P-STM/STS) experiments performed on model systems on the germanium (001) surface. Firstly, we discuss our methodology for fine relative positioning of two STM probes on Ge(001) and Ge(001):H surfaces with exact atomic precision and lateral probe to probe distances below 50 nm. That technical results opens possibility of direct testing of on-surface electron transport in atomic-scale systems. Here, it is realized by a novel 2P-STS methodology, in which both STM tips are kept in tunneling conditions above a grounded sample. By applying a small AC component to a varied DC bias voltage on one of the probes and by demodulation of resulting current signals on the second probe, we extract corresponding transconductance dI2/dV1 2P-STS signal. In the case of the Ge(001) surface we show that the detection of transconductance is related to coherent hot-electron transport through quasi one-dimensional π* states of Ge dimer-rows located within bulk bang gap of the surface. Our two-probe experimental results are corroborated by first-principles calculations combining the non-equilibrium Green’s function (NEGF) formalism with density function theory (DFT) in a four-terminal setup.