On-Chip Precision Residual Strain Diagnostic Based on Gap-Dependent Electrical Stiffness

An on-chip strain measurement device is demonstrated that harnesses precision frequency measurement to precisely extract sub-nm displacements, allowing it to determine the residual strain in a given structural film with best-in-class accuracy, where stress as small as 15MPa corresponds to 2.9nm of displacement. The approach specifically harnesses a spoke-supported ring structure (cf. Fig. 1) surrounded both inside and outside by balanced capacitive-gap transducers that pull its resonance frequency according to strain-induced changes in inner and outer electrode-to-structure gap spacing. The use of a ring structure with balanced electrodes further eliminates uncertainty in the starting gap spacing, which in turn enhances accuracy. The importance of attaining such accuracy manifests in the fact that knowledge of residual strain might be the single most important constraint on the complexity of large mechanical circuits, such as the mechanical filter of [1].