Abstract
The purpose of this study is to utilize average X-ray strain (AXS) method combined with nano-indentation to accurately measure the residual stress of ZrN thin film and to find out the limit thickness of our method. The goal is to verify that AXS method could overcome the problem of anisotropy by increasing the sampling volume. Based on the equation of AXS (σ = (AXS) E/(1+ν)), it is known that stress value can be obtained by incorporating the elastic constant and strain value AXS. The elastic constant incorporated into the AXS equation to obtain the X-ray stress of the samples was measured by nano-indentation. In order to have sufficient sampling volume, multiple φ angles were chosen to carry out the X-ray diffraction measurement, and the accuracy of the X-ray stress was confirmed by comparing with the optical stress. By incorporating reliable elastic constant and accurate AXS value, the stress value of X-ray diffraction method turns out to be very close to the optical residual stress. The largest deviation was about 4％ for the X-ray stress obtained by incorporated the elastic constant of the thickest sample. It is found that the limit for nano-indentation to accurately measure the elastic constant of ZrN thin film is 500 nm, and the accuracy of AXS can reach to 200 nm with enough sampling volume. It is found that the fluctuation of the strain values measured by the φ angles increases as film thickness decreases from the distribution of strain value in respect of φ angles. It is thus recommended to utilize 7 or more φ angles to carry out the X-ray diffraction measurement to obtain accurate AXS value for the film thinner than 500 nm. The limit thickness of ZrN thin film for AXS method to carry out turns out to be 200 nm. The X-ray stress of ZrN thin film of 304SS substrate was also successfully measured, and it is about 4 GPa larger than the one of Si substrate.