Tunable Three-Dimensional Vibrational Structures for Concurrent Determination of Thin Film Modulus and Density

The real-time characterization of thin film properties can provide insights into the behavior of film material during process such as phase-transition, hydration, and chemical reaction. The shift of reasonant frequency in structural vibration serves as the basis of an effective approach to determine film properties, but encounters the difficulty that multiple to-be-determined quantites (e.g., film modulus and density) are often related to the resonant frequency simultaneously and therefore cannot be determined by a structure with fixed shape and vibration mode. Determinsitic mechanical buckling provides an effective route for the vibrational structure to rapidly switch between designed shapes and vibration modes. Here, we adopt a ribbon structure in the flat state and buckled state to yield two distinct vibration modes. Theoretical models of the natural frequencies are established for first-order out-of-plane modes of the ribbon with patterned thin films in these two states, respectively. The model suggests that with optimized film pattern the sensitivity of the natural frequencies to the film modulus and density can be partially decoupled. The results lead to a simple and effective method based on tunable vibration to characterize the thin film modulus and density at small scale.