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Green’s function modeling of response of two-dimensional materials to point probes for Scanning Probe Microscopy



Vinod K. Tewary, Rebecca C. Quardokus, Frank W. DelRio


A Green’s function based mathematical model is developed for interpreting the scanning probe microscopy (SPM) measurements on the new two-dimensional materials. The Green’s functions for the Laplace/Poisson nist-equations subject to the Dirichlet boundary conditions are calculated by using a virtual source method and applied to two separate cases of a material containing a rectangular antidot and another one containing a hexagonal antidot. It is shown that the boundary values are reproduced almost exactly in the virtual source method. It is suggested that SPM can directly yield the values of the Green’s function, which should make the SPM an even more powerful technique for electrostatic and thermal characterization of two-dimensional materials.
Physics Letters


antidots, boundary value problems, graphene and two-dimensional materials, Green’s function, Laplace and Poisson equation, scanning probe microscopy
Created April 29, 2016, Updated November 10, 2018