Two-dimensional electrostatic model for the Van der Pauw method

We use a two-dimensional electrostatic model to explore Van der Pauw (VdP) method on samples with holes. Results of electrostatic simulation based on the model are consistent with the experimental results. The quantitative investigation of VdP method on sample with one hole indicate the value of f, i.e. the right hand side of VdP equation, is depend on the position of contacts and the size of holes. We also quantitatively explore the VdP method used on sample with two holes in special position of contacts and sample geometry. According to the guidance of simulation and experiment, we find proper position of contacts, which make VdP equation f=1 valid again on sample with holes. It is helpful for the optimization of VdP method and measuring the resistivity of sample with holes.