Finite element analysis of resistivity measurement with four point probe in a diamond anvil cell

Using finite element analysis, we studied the steady current field distribution under the configuration of four point probe method for resistivity measurement in a diamond anvil cell (DAC). Based on the theoretical analysis, we made a correction to the formula by Valdes [L. B. Valdes, Proc IRE, 42, 420 (1958)]. The results show that our formula provides more accurate determination of sample resistivity, especially when the sample thickness is less than the probe spacing. We found that finite size of the electrode could lead to significant errors in resistivity measurement for semiconducting samples. We also found that the probe spacing is a key factor in the resistivity measurement accuracy for samples in DAC. When the sample thickness t is close to the probe spacing s, the error becomes larger and reaches a maximum.