The role of localized rotational imbalance in drive level dependence phenomena

The motivation for this study comes from mode shape measurements made of a thickness shear quartz plate with a splatter accidentally attached during Cu deposition. The results show distinct flexural motions extending out to the blank edges in narrow bands. These flexural motions are not present for a clean blank. Finite element analysis calculations are performed for the motion of a contoured quartz thickness shear blank with a small amount of mass attached to the top surface. A 2-dimensional model of the blank is used to facilitate calculation. The added mass causes a localized perturbation of rotational motion that excites a small flexural component extending to the blank edge. This flexural component is similar to a nearby overtone flexural resonant mode. The magnitude of the induced flexural motion varies strongly as the location of the particle moves a few microns from a node to an antinode of the flexural component. This would explain why high level drive can cure a crystal exhibiting drive level dependence (DLD) without the particles being removed and cause others with particles originally not exhibiting DLD to become DLD. It also explains why some blanks with particle contamination function well without showing DLD.