Arrangement optimization of fiber Bragg grating temperature sensor network for wafer surface temperature field reconstruction with grey wolf optimization-Kriging algorithm based on K-medoids

Temperature is a significant control parameter in the silicon-based MEMS fabrication process, and the uneven distribution of the temperature on the surface of a silicon wafer can have a huge impact on the entire process. In this study, an FBG temperature sensing network was used to monitor temperature trends and abnormal temperature regions during the manufacturing process. The measurement of wafer surface temperature using FBG arrays often only records limited spatio-temporal temperature data, rather than the temperature distribution across the entire surface. Therefore, a reconstruction algorithm is needed to reconstruct the temperature field on the wafer surface. In order to find the optimal FBG sensor arrangement while improving the reconstruction accuracy of the wafer surface temperature field, this paper discusses the influence of the number of sensors and the sensors' placement. COMSOL is used to simulate the process of wafer heating. Sparse temperature data are obtained by numerical calculations to reconstruct the temperature field with both linear and fan-shaped sensor position arrangements. The RMSE between the temperature field obtained by the optimized layout and the simulation results is smaller than 2.5°C. The FBG network layout proposed in this paper can provide an application basis for temperature field reconstruction in the MEMS manufacturing process.