Automatic x-ray diffraction measurement of the lattice curvature of substrate wafers for the determination of linear strain patterns

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Abstract
An x‐ray diffraction topography goniometer (Lang camera) under computer control has been used to measure localized bending of silicon wafers. The wafer, mounted free from external stresses, is set for Bragg reflection in transmission by lattice planes perpendicular to the surface (Laue case) and it traverses across the x‐ray beam in steps of 0.01 mm or multiples thereof. At each step the angular position and the intensity of the peak of the Bragg reflection is determined by least‐squares methods from the peak profile with a precision better than the minimum angular step of 0.001°. The lattice curvature obtained from the peak shift is a direct measure of the magnitude of the strains imposed on the wafer by oxide layers, thin films, implantation, and other manufacturing processes. Therefore linear strain maps, showing, for instance, strain gradients occurring at film edges, can be measured quantitatively with high resolution, fully automatically and nondestructively in several direction across a substrate wafer. Measuring substrates of high crystalline perfection and controlling the ambient temperature, the radius of curvature R (in meters) of a uniformly curved substrate can be measured with a probable relative error ΔR/R=R/(1700 m).