Simultaneous determination of the residual stress, elastic modulus, density and thickness of ultrathin film utilizing vibrating doubly clamped micro-/nanobeams

Ivo Stachiv,Vincent Mortet,Te-Hua Fang,Chih-Yun Kuo

doi:10.1063/1.4947031

Abstract

Measurement of ultrathin film thickness and its basic properties can be highly challenging and time consuming due to necessity of using several very sophisticated devices. Here, we report an easy accessible resonant based method capable to simultaneously determinate the residual stress, elastic modulus, density and thickness of ultrathin film coated on doubly clamped micro-/nanobeam. We show that a general dependency of the resonant frequencies on the axial load is also valid for in-plane vibrations, and the one depends only on the considered vibrational mode. As a result, we found that the film elastic modulus, density and thickness can be evaluated from two measured in-plane and out-plane fundamental resonant frequencies of micro-/nanobeam with and without film under different prestress forces. Whereas, the residual stress can be determined from two out-plane (in-plane) measured consecutive resonant frequencies of beam with film under different prestress forces without necessity of knowing film and substrate properties and dimensions. Moreover, we also reveal that the common uncertainties in force (and thickness) determination have a negligible (and minor) impact on the determined film properties. The application potential of the present method is illustrated on the beam made of silicon and SiO2 with deposited 20 nm thick AlN and 40 nm thick Au thin films, respectively.

Highlights

Functional polymer and solid ultrathin films are of emerging interest for variety applications including solar cell panes, biosensors, sensors for the environmental monitoring and food quality control, corrosion and wear protection.[1,2,3,4] In order the application these films is successful, it is essential to precisely know their elastic modulus, thickness and mass density
We show that a general dependency of the resonant frequencies on the axial load is valid for in-plane vibrations, and the one depends only on the considered vibrational mode
We found that the film elastic modulus, density and thickness can be evaluated from two measured in-plane and out-plane fundamental resonant frequencies of micro-/nanobeam with and without film under different prestress forces

Summary

INTRODUCTION

The resonant based method developed by Ma et al.[26] is generally capable to simultaneously measure film elastic modulus and the created residual stress. It is of practical importance to develop an easy accessible method enabling simultaneous determination of the film elastic modulus, density, thickness and created residual stress on structures with rectangular or squared cross-sectional areas. Based on the obtained results, we found that the film elastic modulus, density and thickness can be calculated from two in- and out-plane fundamental resonant frequencies of beam under different intentionally applied prestress forces before and after film deposition. To determine the residual stress require measurement of two out-plane (in-plane) consecutive resonant frequencies of doubly clamped beam with deposited ultrathin film vibrating again under intentionally applied prestress force(s). IV, we present a method capable to simultaneously determine elastic modulus, density and thickness of the polymer and solid ultrathin films

BACKGROUND

RESIDUAL STRESS DETERMINATION

CONCLUSIONS