Methods of piezo-spectroscopic calibration of thin-film materials: I. Ball-on-ring biaxial flexure

A ball-on-ring flexure jig has been developed for applying a controlled biaxial stress to thin-film materials and its reliability is validated by measuring the biaxial piezo-spectroscopic coefficients (namely the wavelength shift rate upon stress) of selected bands from the fluorescence or Raman spectrum of two technically important materials, silicon and sapphire films. Due to the small thickness of the investigated samples, measurement conditions had to be adjusted according to the transparency characteristics of the material for laser probe to gain meaningful stress information upon loading the plate. Two different procedures have been developed: (i) a surface scan along an arbitrary diameter of the flexure plate was found to be appropriate only for opaque materials, in which the penetration depth of the laser probe was negligible in comparison with the stress gradient developed along the sample thickness; and (ii) a 'through-focus' scan along the plate thickness (coupled with an analytical deconvolution of the optical probe) at a selected point of the sample was found to be the most reliable method for assessing highly transparent materials with an acceptable calculation time (i.e. by ignoring the stress distribution and probe function in the x – y plane). The workable defocus distance in the 'through-focus' scan method, which is available for very thin films and large probe sizes, was discussed accordingly. These calibration procedures may be useful in piezo-spectroscopic stress assessments of semiconductor materials for which bulk specimens may not be available.