| The structure and characteristics of many materials changes with pressure. High pressure physics has become an important branch of condensed mater physics. To obtain high pressure in laboratory, people developed all kinds of equipments to generate high pressure, from early piston-cylinder device to diamond anvil cell(DAC) that can generate high pressure of several GPa. In-situ X-Ray diffraction, Raman spectrum, Brillouin scattering, inferred spectrum and Mossbauer spectrum can be conducted in a DAC. Earlier electrical measurement in a DAC was performed by introducing metal threads in a DAC, the resistance of the sample was measured by 2-probe or 4-probe method. This method demands that the metal thread must be well insulated from the metal gasket. With the pressure increasing, the shearing force that the diamond anvil gives to the metal electrode increases, thus the metal electrodes tends to break. On the other hand, the geometry of sample chamber changes with pressure, usually the sample thickness is about tens to one or two hundred microns at standard atmosphere while about only ten microns at high pressure to scores of GPa. Under the circumstances, even the resistivity of the sample is the same, we get different resistances at different pressure. This will lead to the wrong estimation of the sample characteristics. Later, thin film electrode were fabricated on diamond anvil by sputtering or epitaxial growth. This has overcome the shortage of the metal thread electrode that is fragile to the diamond anvil sheering force, and the difficulty of being introduced into the DAC chamber, but has no contribution to reduce the effect of sample distortion.In this thesis, we discussed how the electrode distribution and the electrode size affects the results in Van der Pauw method measurement. the result showed that the more the electrode locate to the edge of the sample, the smaller the relative error is. If the sample and the gasket are well insulated, Van der Pauw method is applicable. For 4-prode resistivity measurement in a DAC, only when the electrode area is small enough, can the relative error be small. With the electrode area increasing, the error increases fast. To fabricate small area electrode (relative to the sample in a DAC) is not easy, this means the limitation of this method.While performing high pressure resistivity measurement in a DAC using traditional Van der Pauw method and 4-probe method, if the sample is not well insulated from the metal gasket, there will be great error in the measurement result. Since the sample chamber is quite small, and it is difficult to well insulate the sample from the metal gasket. The sample is to some extent electrical shorted to the metal gasket, thus obvious error occurs. In this thesis we discussed to what extent does the electrical short affects the measurement result. The error increases with the electrical shorted area, only when the poor insulated area is less then 20%, can the error be less then 10%. If the poor insulated area exceeds 25%, the error increases very fast.In this thesis we studied that when the sample and the gasket are not well insulated, the error correspond to the distance between electrode and the center of the sample in Van der Pauw method. To make the electrode close to the sample edge, measurement error can be diminished. When 25% of the side wall of the gasket is poor insulated, the relative error can be reduced from 34% to 19% by making the electrode as close as possible to the sample edge.To avoid the error caused by the poor insulation between the sample and the gasket, we established a new method to measure the sample resistivity in a DAC, as we called a bi-electrode model. A circular electrode thin film is fabricated on the diamond anvil, the gasket is considered as another electrode. To work out the MAXWEL EQUATIONs in the DAC, by means of FINITE DEFFERENCE, can give the sample resistivity. By this means, the error caused by the poor insulation between the sample and the gasket can be totally eliminated. The result shows that the error can be restrained below 7%. We also compared the result of our bi-electrode model to that of Van der Pauw method. When the sample was pressed from 150 microns thick to 20 microns, the error of bi-electrode model was-0.94% to-6.71%, and these errors were caused by the numerical method which can be diminished by improving the program. This indicates that our bi-electrode model can carry out precise resistivity measurement in a DAC. For Van der Pauw method, when the sample thickness exceeded 100 microns, a biggish error appeared. When the sample thickness reached 150 microns, the error was about 37.5%. The result also tells that in our bi-electrode model, even the electrode size varies from a considerable scale, the measurement can be quite accurate.To overcome the inconvenience of accurately measuring the sample thickness, we developed a tri-electrode model based on the bi-electrode one. By distributing electrodes properly and some electrical and mathematical method, the sample resistivity, thickness can be calculated automatic. Two thin film electrodes fabricated on the diamond anvil, gasket as the third one, this is our tri-electrode model.In this thesis, we also brought forward a method to measure the permittivity of the sample in a DAC, by means of the same FINITE DEFFERENCE method and calculated that only sample with large permittivity like titanium dioxide and barium titanate can be measured in a DAC.All the FINITE DEFFERENCE program was wrote in Visual Basic.
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