Surface conductivity of Si(100) and Ge(100) surfaces determined from four-point transport measurements using an analyticalN-layer conductance model

Abstract

An analytical N-layer model for charge transport close to a surface is derived from the solution of Poisson's equation and used to describe distance-dependent electrical four-point measurements on the microscale. As the N-layer model comprises a surface channel, multiple intermediate layers and a semi-infinite bulk, it can be applied to semiconductors in combination with a calculation of the near-surface band-bending to model very precisely the measured four-point resistance on the surface of a specific sample and to extract a value for the surface conductivity. For describing four-point measurements on sample geometries with mixed 2D-3D conduction channels often a very simple parallel-circuit model has so far been used in the literature, but the application of this model is limited, as there are already significant deviations, when it is compared to the lowest possible case of the N-layer model, i.e. the 3-layer model. Furthermore, the N-layer model is applied to published distance-dependent four-point resistance measurements obtained with a multi-tip scanning tunneling microscope (STM) on Germanium(100) and Silicon(100) with different bulk doping concentrations resulting in the determination of values for the surface conductivities of these materials.

Detection of the Spin-Chemical Potential in Topological Insulators Using Spin-Polarized Four-Probe STM

“…A more realistic model requires the consideration of the coupling between these two channels and should allow a cross channel current at every point along the interface. Such a quantitative differentiation has only recently been available with the development of the four-probe spectroscopy technique [29,37]. In these measurements, four STM tips are used as probes aligned in a collinear configuration.…”

Surface sensitivity of four-probe STM resistivity measurements of bulk ZnO correlated to XPS

“…[44,45] For micro four-point probe measurements (4pp) on a bulk substrate with the probes far away from any boundaries the sample may be approximated by a semi-infinite volume of uniform resistivity material. The floating potential in the material at a distance from a point contact current probe is given by [14]:…”

“…Some notable results have refined our knowledge of defects in topological insulators using scanning tunnelling potentiometry, [4] contacting and manipulating single atoms at 4K, [5] tuning of atomic chains by chemisorption, [6] conductance measurements of self-assembled single layer molecules, [7] identification of metallic twin grain boundaries on monolayers, [8] charge transport in nanowires, [9][10][11][12][13] and using four-probe measurements to separate surface and atomic step conductivity from bulk conductivity. [14,15] In the area of sensors, where surface modification is typically used to induce a change in the electrical conductivity of a device, for example via adsorption, [16] covalent attachment or bio-functionalisation [17], understanding the details of surface modification and correlating these details with the changes in surface conductivity due to band bending and the influence of surface states is a crucial step in realising the potential of such devices. These devices depend on changes in channel conductivity, typically this necessitates that one of the dimensions of the channel is reduced to the nanoscale at which the Debye length becomes a significant fraction of the relevant dimension.…”

Four-point probe measurements using current probes with voltage feedback to measure electric potentials

“…The transport properties of this surface have been under recent discussion because earlier results on its surface conductivity varied largely as a result of numerous different measurement and sample preparation procedures [4]. One way to measure the surface conductivity is to determine the two-dimensional contribution in distance-dependent four-probe measurements [5,9,11,26]. measurements.…”