Quantitative analysis of in situ wafer bowing measurements for III-nitride growth on sapphire

Wafer bowing measurements have been recently developed into an efficient tool for MOVPE and MBE process optimization. In combination with temperature and reflectance measurements they are applied for direct but mostly qualitative evaluation of III-nitride epitaxial growth processes. In this work, applying a quantitative analysis of wafer bowing throughout the full epitaxial process, we are able to trace the lattice constant mismatch between substrate and every single layer of the growing structures.Starting from the basic models of compressive/tensile film stress causing convex/concave wafer bowing we will describe the physical effects and models to be included for a quantitative analysis. The contributions of vertical temperature gradients, composition dependent lattice constants and thermal expansion coefficients will be separated.It is shown that for (Al,In,Ga)N growth on sapphire the lattice-mismatch induced stress can be described accurately by combining the well-known Stoney equation with the concept of a GaN–sapphire effective substrate. This enables an accurate determination of AlGaN and InGaN lattice constants already during growth.