Nanoscale adaptive meshing for rapid STM imaging

The numerical evaluation of individual tunnel currents (pixels) constitutes the bottleneck of fast scanning tunneling microscopy (STM) imaging. The number and the position of grid points where the current is punctually evaluated have to be judiciously chosen to reveal the most important contrasts. In this note, we present an adaptive meshing approach that significantly accelerates the computation time to produce STM images by reducing the number of pixels to evaluate without affecting the final image resolution. This method iteratively reveals the STM image by selecting new probing locations that improves the image quality at each step. A straightforward method to compute a STM image is to send a high resolution square grid to a solver that will return a pixel color intensity for each node [1,2]. Since pixel calculation is the most time consuming step but is independent of the grid quality, redefining the surface discretization will reduce the amount of computed pixels and thus the time required to compute an image. This process is a step by step image analysis in which zones of interest, such as contrasts related to adsorbed molecules or structural defects, are identified. Contrarily to mesh modeling where one creates an optimized mesh from a high resolution solution, here we want to iteratively build an optimized mesh from a coarse and previous solution. A Delaunay triangulation has been used to efficiently generate optimized meshes from high resolution images [3], and a similar discretization scheme is used in the present work. During mesh generation, standard point insertion algorithms [4] are favored over methods that enable coarsening and smoothing operations [5], since displacing or removing already computed pixels will results in undesirable exclusion of already computed data.