Etching Rate Analysis Model Based on Quartz Bond Angle Characteristics

This paper proposes a method for classifying crystal planes based on the bond angle characteristics of quartz unit cells and constructs an etch rate model for quartz crystal planes at both macro and micro scales. By omitting oxygen atoms from the quartz cell structure, a method based on bond angle characteristics was established to partition the atomic arrangement of the crystal surface. This approach was used to analyze the etching processes of typical quartz crystal planes (R, r, m, and (0001)), approximating the etching process of crystals as a cyclic removal of certain bond angle characteristics on the crystal planes. This led to the development of an etch rate model based on micro-geometric parameters of crystal planes. Additionally, using the proposed bond angle classification method, the common characteristics of atomic configurations on the crystal plane surfaces within the X_cut type were extracted and classified into seven regions, further expanding and applying the etch rate model. The computational results of this model showed good agreement with experimental data, indicating the rationality and feasibility of the proposed method. These also provide a theoretical basis for understanding the microstructural changes during quartz-based MEMS etching processes.