Simultaneous Thin-Film Stress and Mass-Change Measurements Using Quartz Resonators

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Abstract
It is shown theoretically and experimentally that stresses in a thin film on a quartz resonator surface can set up sufficient static mechanical bias in the resonator to cause measurable shifts in the resonant frequency through finite strain effects. In particular, it is found that if a 5‐MHz AT‐cut fundamental mode and a 6.19‐MHz BT‐cut fundamental mode are subjected to the same combination of thin‐film stress and mass/cm2 changes on their surfaces, the sum of the observed frequency shifts is proportional to the mass/cm2 change alone, and the difference of the frequency shifts is proportional to the integral through the film thickness of the change in the thin‐film stress alone. This ``double‐resonator'' technique is demonstrated with implantation studies of 220‐keV 84Kr implants into Si films deposited on the flat electrodes of planoconvex 5‐MHz AT‐cut and 6.19‐MHz BT‐cut resonators. The double‐resonator technique stress results were verified quantitatively by implanting ions into a Si film on one surface of a quartz cantilever beam and monitoring the movement of the free end of the cantilever beam by the changes in capacitance between the free end and a fixed electrode. The sensitivity of the double‐resonator technique is 125 dyn/cm and 6 × 1014 amu/cm2 for a 0.1‐Hz frequency shift. The technique is suited best to thin‐film stress studies with small mass changes.