Measurement of Flexure in Silicon Wafers by the Lang X-ray Diffraction Technique†

Abstract

The Lang x-ray diffraction technique provides a simple non-destructive method for measuring flexure in single-crystal silicon wafers at different stages of integrated circuit fabrication. A molybdenum target provides Kα₁ and Kα₂ x-radiation which is diffracted from the set of {110} normal to the surface parallel {111}. The widths of the diffracting regions and their separation are simply related to the flexure, which may be expressed as a radius of curvature (p). This method is limited to wafers which do not diffract from the entire region irradiated, i.e. p 1590 in. for a substrate to 203 in. after several processing stages. Non-uniformity in individual wafers is much greater after the material has been through several processing stages.