Uncertainty Quantification Analysis on Silicon Electrodeposition Process Via Numerical Simulation Methods

Silicon is one of the commonly used semiconductors for various industrial applications. Traditional silicon synthesis methods are often expensive and cannot meet the continuously growing demands for high-purity Si; electrodeposition is a promising and simple alternative. However, the electrodeposited products often possess nonuniform thicknesses due to various sources of uncertainty inherited from the fabrication process; to improve the quality of the coating products, it is crucial to better understand the influences of the sources of uncertainty. In this paper, uncertainty quantification (UQ) analysis is performed on the silicon electrodeposition process to evaluate the impacts of various experimental operation parameters on the thickness variation of the coated silicon layer and to find the optimal experimental conditions. To mitigate the high experimental and computational cost issues, a Gaussian process (GP) based surrogate model is constructed to conduct the UQ study with finite element (FE) simulation results as training data. It is found that the GP surrogate model can efficiently and accurately estimate the performance of the electrodeposition given certain experimental operation parameters. The results show that the electrodeposition process is sensitive to the geometric settings of the experiments, i.e., distance and area ratio between the counter and working electrodes; whereas other conditions, such as the potential of the counter electrode, temperature, and ion concentration in the electrolyte bath are less important. Furthermore, the optimal operating condition to deposit silicon is proposed to minimize the thickness variation of the coated silicon layer and to enhance the reliability of the electrodeposition experiment.