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

Abstract

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 ( $\omega $ ) 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 ( $\omega - \omega _{0}$ ) 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.