Crystallographic Effects on Energy Dissipation in High- $Q$ Silicon Bulk-Mode Resonators

This letter reports measured results of quality factor (Q ) for single-crystal silicon square-plate resonators in relation to their crystal orientation within the (100) plane. Results from both the Lamé and extensional modes oriented in the 〈110〉 and 〈100〉 axes are presented. Q appears to be dependent on orientation for the Lamé mode. In the extensional mode, there is no significant difference in Q between the two axes due to the dominance of anchor loss. These trends agree well with the brief theoretical analysis that we have described here to provide a quantitative basis for interpreting the trends between Q and orientation observed in our measurements.