Research On Inverse Heat Conduction Problem Of Czochralski Silicon Single Crystal Growth Process

Silicon single crystals are the basic material for manufacturing semiconductor products.However,the healthy development of China’s semiconductor industry is hampered by international problems such as turbulent international relations,the prevalence of unilateralism and related technological blockades,as well as the complexity of the scientific theory.Therefore,it is important to produce large size and high quality silicon single crystals independently.In the production of silicon single crystal by Czochraski method,the heat fluxes influence temperature distributionthe.When the heat flux varies drastically or is too large,the temperature field becomes unsuitable for crystal growth,resulting in a large number of defects and affecting the quality of the silicon single crystal.Therefore,research into the process of heat flux changes in key areas related to crystal quality,enabling a full understanding of the crystal growth principle.It is important to product large size,high quality silicon single crystals.This thesis first describes the inverse heat conduction problem in the crystal growth process in the background of producing silicon single crystal by Czochralski method.The heat flux at the solid-liquid interface was taken as the main research object.The mathematical model of the thermal field of silicon single crystal is established by combining the heat conduction theory and technical approach,and solved by the finite difference method.It also provides data support and algorithm validation.The main research of this thesis is as follows:(1)For the one-dimensional unsteady inverse heat conduction problem,this thesis proposes a real-time solution based on Parameter-Adaptive PID with improved whale optimization algorithm.The model takes the deviation between the predicted temperature and the actual temperature of the measuring point as the input of the PID algorithm,and outputs the increment of the estimated heat flux,and the estimated value is taken as the boundary condition to get estimated temperature at measurement point and feedback to the PID module.The improved whale optimization algorithm is used to select PID parameters adaptively,so as to improve the stability and robustness of the system,and compared with EMM and WOA-PID,the effectiveness of the algorithm is verified.(2)To solve the problem that the IWOA-PID inverse heat transfer algorithm cannot invert multiple boundary heat fluxes simultaneously,this thesis proposes a real-time solution strategy based on dynamic matrix control.The algorithm uses the dynamic step response coefficient of the heat conduction model to build the temperature prediction model,which can predict temperature of measuring points.Based on the sensitivity coefficient,the rolling optimization model is established to optimize the boundary heat flux until the objective function reached the minimum value.Compared with SFSM algorithm,the proposed algorithm is proved to be effective.Experimental analysis of the influence of the location of the measurement points,the number of measurement points and the future time step on the accuracy of the inversion.The algorithm is applied to solve the heat flux at the solid-liquid interface,and the correctness of the inversion results is verified by silicon crystal temperature reconstruction experiments and the convergence of measurement point errors.(3)For the location of measuring point and number of measuring point problems,improved fuzzy c-means clustering is proposed to select the best location of measuring points under the limited number of measuring points,so as to improve the inversion accuracy.The algorithm combines with the basic theory of clustering technology,randomly selectes multiple temperature measuring points from the heat conduction system,takes the sensitivity coefficient vector of each measuring point in the next time step as the feature vector,and takes the clustering center of each category as the best temperature measuring point location.By comparing the inversion results of random selection of measuring points and clustering selection of optimal measuring points,the effectiveness of the algorithm is verified.