Precise X-ray relative measurement of lattice parameters of silicon wafers by multiple-crystal Bragg-case diffractometry. Computer simulation of the experiment

Abstract

A feasibility study of an X-ray experiment is presented by which the lattice parameter of a silicon wafer relative to that of a perfect reference silicon crystal can be measured with a precision of 10−7. A multicrystal geometry in the symmetric Bragg case is proposed, using a monolithic monochromator as a beam splitter. Sample and analyser crystals are aligned with respect to the monochromator and the rotation of the analyser around its Bragg position produces two diffraction peaks. Their separation is related to the difference between the lattice parameters of monochromator and sample. The sample can be a piece of any commercial slice, generally cut from the ingot with an angle between the surface normal and the nominal crystallographic orientation and bent due to the mirror finishing on only one side. Moreover, the bending can be induced by layers grown on the surface by the processes of planar technology. Miscutting angle and curvature influence the diffraction peak position. The X-ray tracing and the procedure chosen for measurement eliminate these effects.