Abstract

Mechanical loss of the coating materials, and hence thermal noise from the mirror coatings, is a limiting factor for the sensitivity of the laser interferometer gravitational waves detector at its most sensitive frequency range. Mechanical loss of the thin films are often measured using the cantilever ring-down method. But when the thin film is under stress, the regular ring-down method gives incorrect results. We report a method to obtain the mechanical loss of stressed thin film using the cantilever ring-down technique. A proof-of-concept example is given to demonstrate and verify our method. The method can also be applied to obtain the mechanical loss angle of a rough interface; an example showed that loss angle of the interface between silicon nitride film deposited by plasma enhanced chemical vapor deposition method and silicon substrate is highly frequency dependent.

Highlights

  • Sensitivity of the current laser interference gravitational waves detector at its most sensitive frequency region ~100 Hz is limited by the thermal noise of the mirror coatings[1]

  • Thermal noise is related to the mechanical loss angle through the fluctuation-dissipation theorem[2]

  • Er is the energy stored in the rough interface, Yr is the effective Young's modulus of the interface, we assume Yr can be taken as the average of the Young's modulus of the film and the substrate

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Summary

Introduction

Sensitivity of the current laser interference gravitational waves detector at its most sensitive frequency region ~100 Hz is limited by the thermal noise of the mirror coatings[1]. Cantilever ring-down is a common method for measuring the mechanical loss of coatings[3]. A cantilever, usually silicon, with a thicker clamping pad is fabricated and the coating is deposited on one side of the thinner cantilever. The loss angle of the film can be deduced from the difference between coated and un-coated cantilevers[4]. To fabricate the cantilever one starts with a double-side polished thick silicon wafer, using a lithographic method and KOH etching on one-side to form the cantilever of the desired thickness[7]. When the coating is stressed, the coated cantilever warps as shown, which may lead to inaccurate ring-down measurement. We developed a method to separate the loss angle of the film on the smooth surface from that of the double-side coatings. Examples are given to demonstrate the validity of our methods

Sample Configuration
Loss Angle Calculation
Loss angle of the rough interface
Conclusion
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