Bias electric field distribution analysis based on finite difference method with non-uniform grids for a non-contact tunneling current probe

During proposal and development of a new non-contact nano-probe based on tunneling effect, analysis of the bias electric field (BEF) distribution is a key step for modeling and characterization of the probe. However, the BEF between the spherical electrode serving as the probing ball and the surface to be measured has combined features of macro-and micro-dimensions, which makes the modeling of it a far tricky problem. In this paper, a modeling finite difference method (FDM) based on non-uniform grids generation according to the structural features of the BEF is proposed, and the field distribution is solved with high accuracy. The maximum relative calculation error is within 15% compared with calculation results for a bias electric field with regular boundary with analytical electric image method.