| In the large-scale integrated circuit production,the size of silicon-based chips has gradually decreased and the degree of integration has continued to increase.In order to ensure the stability of integrated circuit performance,silicon wafers need to have good electrical characteristics.The micro-area resistivity of the thin-layer silicon wafer can directly affect the electrical properties.Therefore,it is necessary to study the method of measuring the resistivity of the silicon wafer to obtain a more accurate resistivity value.The conventional four-probe measurement method needs to be performed in a constant temperature experimental environment.It has the disadvantage that the probe is easy to contaminate the measurement sample,and the measurement results show that it is not intuitive enough.The instrument with high measurement accuracy is very expensive.In view of these existing problems,this paper mainly researches from two aspects of the method and system of measuring the resistivity of silicon wafers.First,the problems that need to be solved for the positive measurement of silicon resistivity are analyzed and the solution steps of the finite element method are deduced.The model is establishing to obtain the calculated voltage of the boundary.Then,the solution steps of the boundary element method of single connected domain are summarized,and the boundary element method of two connected domains is used to solve the positive problem to obtain the boundary node voltage of the silicon wafer.Furthermore,a positive problem model combining finite element and boundary element is constructed to solve the positive problem,which can reduce the calculation amount while ensuring accuracy.Finally,the method of solving nonlinear and ill-conditioned inverse problems is summarized.Because Newton-type iterative algorithms have high imaging accuracy and a wide range of applications,this algorithm is used.At the same time,the regularization method is added to the inverse problem of silicon resistivity.The single-step iteration result is used as the initial value and the regularization parameter is selected.The specific model is simulated and the solution method with high precision is selected.Based on the principle and functional requirements of the silicon resistivity measurement method used in this paper,the measurement device and system is designed.The measuring device is designed with an electrode pad that can automatically switch between 8 electrodes and 16 electrodes.At the same time,it is equipped with a groove test bench that can be moved up and down to complete the electrode voltage measurement.The measurement system includes: a constant current source module that provides a constant current for measuring silicon,a voltage detection module that measures the voltage between two electrodes,a channel selection module that gates any two electrodes,a motor control module that controls the number and position of electrodes,a touch screen module that directly inputs and displays the measurement results,a temperature control module that regulates the temperature of the measurement system,and a WIFI module that communicates with a remote host computer.In order to complete the functions of each module,the software system is developed.The lower computer program for measuring voltage and the upper computer MATLAB program for image reconstruction are written.According to the measurement system,the method of this paper can be used to complete the resistivity measurement of silicon wafers and generate intuitive color reconstructed images.The reconstructed results can accurately reflect the resistivity distribution of In the case of the silicon wafer.Thus,the correctness and practicability of the method in this paper are verified. |
