Green's function modeling of response of two-dimensional materials to point probes for scanning probe microscopy

Abstract

A Green’s function (GF) method is developed for interpreting scanning probe microscopy (SPM) measurements on new two-dimensional (2D) materials. GFs for the Laplace/Poisson equations are calculated by using a virtual source method for two separate cases of a finite material containing a rectangular defect and a hexagonal defect. The prescribed boundary values are reproduced almost exactly by the calculated GFs. It is suggested that the GF is not just a mathematical artefact but a basic physical characteristic of material systems, which can be measured directly by SPM for 2D solids. This should make SPM an even more powerful technique for characterization of 2D materials.

Ullmann-like reactions for the synthesis of complex two-dimensional materials

“…Multi-probe measurements using STM would provide information on longer-range charge and thermal transport properties [25,26]. These results can be interpreted by using a Green's function (GF) technique that accounts for surface geometry and includes long range effects [27]. The GF, which, by definition, gives the total response of a material to a point probe, can be directly measured by STM for 2D materials [27].…”

“…These results can be interpreted by using a Green's function (GF) technique that accounts for surface geometry and includes long range effects [27]. The GF, which, by definition, gives the total response of a material to a point probe, can be directly measured by STM for 2D materials [27]. Thus multiprobe STM measurements combined with GF can be a valuable tool for investigating the surface effects on charge and thermal transport.…”