Optical Detection of Coefficient of Thermal Expansion via Frequency Tracking at Cryogenic Temperatures

Abstract

Accurate characterization of the coefficient of thermal expansion (CTE) in nanoscale thin films is critical for predicting residual stress and ensuring the reliability of modern micro-electromechanical systems and advanced semiconductor architectures. The primary limitation is that traditional methods depend on precise thickness measurements or are restricted to crystalline materials. In this work, we present an in-situ, non-destructive optical methodology to determine the CTE of suspended nanofilms by tracking the temperature-dependence of their vibrational frequency. This approach eliminates thickness measurements entirely and works for amorphous films where X-ray diffraction (XRD) fails. We experimentally validate this technique across a broad temperature range, evaluating membranes in their native microstructure state without requiring additional destructive patterning or complex sample preparation. This non-contact optical method achieves uncertainty below 5.3 * 10-8 K-1, substantially improving upon conventional thin-film CTE metrology.