Model-based thickness estimation of multilayer films in picosecond ultrasonics metrology with aliased echoes

Picosecond ultrasonics (PU) combines the advantages of optical and acoustic measurements, and also provides nanoscale longitudinal resolution, making it the workhorse technique for in-line thickness measurement of opaque submicron films. In PU measurements of multilayer films, echo aliasing often occurs and leads to inaccurate thickness estimation based on straightforward time-domain analysis. This work proposes a model-based thickness estimation method for cases where some echoes are aliased, forming discrete echo-signal regions. The model used is lightweight and does not rely on reference signals obtained from standard specimens. Specifically, a theoretical model is developed to reflect the spectrum relationship between different echo-signal regions in one measurement curve, and is then used to fit the measured spectrum relationship to inversely extract thicknesses. Simulations are conducted and yield ways to reduce noise impact. Eventually, the proposed method is validated through PU measurements of submicron W/Al bilayer films, with estimation errors within 2.3%.