Wafer curvature in the nonlinear deformation range

In situ curvature measurements during hetereoepitaxial growth of silicon-doped GaN on silicon substrates reveal a strong bending of the substrate, which cannot be described by the Stoney formula usually applied for the interpretation of such measurements. Instead, large bending including in-plane deformation is necessary for the interpretation of the curvature measurements. General expressions for the curvature-strain relationship in the case of large bending and arbitrary thickness ratios between film and substrate are developed which can be solved quasi-analytically. It will be shown that the mismatch strains are underestimated by up to 100% when using the Stoney formula instead of the full nonlinear approach. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)