Evaluation of crack-tip stress in titanium oxide film using piezo-spectroscopy methods

The biaxial piezo-spectroscopic coefficient of 530 nm cathodoluminescence band of polycrystalline anatase titanium oxide film was measured using a local calibration procedure. Firstly, the crack-tip stress intensity factor in titanium oxide was measured from the crack opening displacement of a Vickers indentation crack using both Irwin's formula and Fett's formula, and the validity of these two formulas was evaluated. The obtained value was about K_tip=1 Mpa√m. In such a brittle material, the fracture toughness can be considered to be very close to the stress intensity factor measured in an equilibrium indentation crack (K_tip=K_C). From the K_tip value, we calculated the stress distribution ahead of the crack tip using principles of linear elastic fracture mechanics. An important finding was that the cathodoluminescence 530 nm band that originated from excitons self-trapped on TiO₆ octahedra, is sensitive to stress. Using the shift of this peak and the calculated stress from linear elastic fracture mechanics, the biaxial piezo-spectroscopic coefficient of this band was determined (40 nm/GPa with a 20% error rate). Using this piezo-spectroscopic coefficient, approximate stress maps can be collected of unknown stress fields within thin films with high spatial resolution into the scanning electron microscope. The present experiments provide a vivid example of quantitative micromechanical stress analysis by piezo-spectroscopic techniques.