Metrology of Warpage in Silicon Wafers Using X-Ray Diffraction Mapping

X-ray diffraction (XRD) mapping is a nondestructive metrology technique that enables the reconstruction of warpage induced on a silicon wafer through thermomechanical stress. Here, we mapped the wafer’s warpage using a methodology based on a series of line scans in the x- and y-directions and at different 90◦ rotations of the same sample. These line scans collect rocking curves (RCs) from the wafer’s surface, recording the diffraction angle (ω) deviated from the Bragg angle due to surface misorientation. The surface warpage reflects in XRD measurements by inducing a difference between the measured diffraction angle and the reference Bragg angle (ω − ω₀) and RC broadening full-width at half-maximum (FWHM). By collecting and integrating the RCs and FWHM broadening from the whole surface and multiple rotations of the wafer, we could generate 3-D maps of the surface function f(x) and the angular misorientation (warpage). The warpage exhibits a convex shape, aligning with optical profilometry measurements reported in the literature. The lab-based XRD imaging (XRDI) has the potential to be developed to map the wafer’s warpage in a shorter time and in situ, as can be perfectly performed in synchrotron radiation source.