Greens 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 Greens function based mathematical model is developed for interpreting the scanning probe microscopy (SPM) measurements on the new two-dimensional materials. The Greens 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 Greens function, which should make the SPM an even more powerful technique for electrostatic and thermal characterization of two-dimensional materials.