Finite-Element Analysis Of Resistivity Measurement With Four Probe Method In A Diamond Anvil Cell

Resistivity is a very important property for matter. It is a groundwork to full and scientific study of material properties that accurately determining its resistivity. With the development of science and technology, more and more in situ experiments can be performed in diamond anvil cells (DAC). These increasingly mature techniques have led to a great improvement in the research of high pressure physics. Four probe method (Four-point probe method and Van der Pauw method) being introduced makes it impossible that we study material electrical properties under high pressure. However, it is still a problem that how to accurately determine resistivity under high pressure in DAC. In this thesis, for solving above technical problems, we perform Finite-element analysis (FEA). Based on theoretical results, we find that pressure, the geometries of sample and probe and the difference between sample and probe, and so on, all can affect the measurement accuracy using four probe method in DAC.To have a better understanding, we build two models: one whose electrodes have point contacts, and another with finite electrode size which simulates experimental condition. Our analyses indicate that it is more reasonable to use t/s=1 instead of t/s=0.5 as a dividing point for different definitions of correction factor B0. To improve the accuracy of the resisitvity determination, we modify the definitions for the correction factor B0 according to our theoretical analysis as described in the following sections. to summarize, we modified the correction factors as: for t/s<1, B0=1.50646s/t for t/s≥1, B0=1+0.605/(t/s)1.9 Apparently, the accuracy has improved significantly. Result shows that the error becomes larger when the thickness t is close to the spacing s. And the error reaches a maximum value at the dividing point, i.e., when t/s=c and c is the dividing point of different correction formulae. We find that it is caused by the different theory hypothesis for B0.The results show that there is a larger error for thin sample. We think there is an electrode effect which may lead to large error. This finding is contrary to the general viewpoint that the thinner the sample, the more accurate the result is. We believe such outcome is caused by the electric field gradient. In fact, the effect of probe size on accuracy becomes larger, when the sample becomes thin under high pressure. So, we can achieve better results by decreasing the contact area or the resistivity difference between the electrodes and the sample. For some samples, we can achieve accurate results using these electrodes are with larger resistivities.We used the FEA to analyze the accuracy of the resistivity measurement of van der Pauw method in a DAC. Based on the theoretical analyses, we obtained the theoretical accuracy curve of the van der Pauw method. The results show that this method provides accurate determination of sample resistivity when the ratio of sample thickness to its diameter is less than 0.45, especially when the ratio is less than 0.4. Contrary to general belief that thinner sample gives more accurate resistivity result, we found that this is not true for semiconducting samples with finite electrode sizes. In fact, when the ratio decreases to some value, the electrode size effect becomes dominant and leads to significant error for samples of large resistivity. Furthermore, the contact area between electrode and sample is another key factor in the resistivity measurement accuracy for samples in DAC. When the contact area increases under pressure, it could also lead to significant errors in resistivity measurements for semiconducting samples. If we hypothesize that the contact area is square and the side is a. there exits a simple relation between sample diameter D and the side a: We found that for a given measurement accuracy, the size of contact area is dependent on the sample diameter.In conclusion, FEA is an important way to investigate how to making accurate resistivity determinations in a diamond anvil cell. This thesis offers possibilities for determining resistivity quantitatively. The result will be a significant benefit to those interested in electrical measurements in extreme environments where sample configurations are controlled by experimental limitations. Using finite element analysis (FEA), many potential sources of error such as the effects of changing sample dimensions and electrode geometry are addressed.