Estimation of bowing in hetero-epitaxial GaN-on-sapphire substrate at elevated temperatures by X-ray diffraction rocking curve measurement

A new approach to estimate bowing in hetero-epitaxial films-on-single crystalline substrate at elevated temperatures using X-ray diffraction (XRD) rocking curve measurement is proposed. To demonstrate the new approach, GaN-on-sapphire substrate was subjected to XRD rocking curve measurements for sapphire (0 0 0 6) reflections with various incident X-ray slit widths and temperatures ranging from 25 to 800 °C. It was found that the FWHM increased linearly with the slit width of the incident X-ray when substrates exhibited bowing, and the degree of the broadening effect of the FWHM with slit width reflected the extent of substrate bowing. An accurate estimation of the bowing was demonstrated with every measurement up to 800 °C, quantifying not only the extent of bowing but also the change in its direction from convex to concave with increasing ambient temperature. This approach is theoretically applicable for all types of single crystalline substrates with hetero-epitaxial films, and would enable us to provide useful feedback on the optimization of epitaxial growth process conditions.