ABSTRACT
Measurements of the orientation and spacing of a crystal plane are the most fundamental x-ray diffraction measurement, stemming directly from the Bragg law (
n
λ
= 2
d
sin
θ
). Differentiating the latter, we obtain
(4.1)
The higher the Bragg angle,
θ
, the greater the sensitivity to strain,
δ
d/d
. It is fairly straightforward to detect peak shifts (in the scattering angle, 2
θ
) in polycrystalline materials to 0.01˚ by x-ray diffraction (XRD). At an intermediate Bragg angle (45˚) this corresponds to a strain of 200 ppm. In epitaxial structures one can do at least 10 times better by high-resolution x-ray diffraction (HRXRD). With special methods (not suitable for fabrication line tools) another order of magnitude sensitivity is possible. With topographic methods, changes in strain of this order can be mapped across the whole wafer.
