A high-resolution diffuse X-ray scattering study of defects in dislocation-free silicon crystals grown by the float-zone method and comparison with Czochralski-grown crystals

Point-defect aggregates in (111) dislocation-free silicon single crystals grown by the float-zone (FZ) method have been studied by diffuse X-ray scattering (DXS) and compared with those in the Czochralski-grown (CZ) crystals. A two-axis X-ray diffractometer was used. It employs three monochromators in (+, −, −) setting to obtain a highly collimated and monochromatic Mo Kα₁ beam. DXS measurements were made around the 111 reciprocal-lattice point (r.l.p.) with K* along ±[111] and ±[01]; K is the vector which joins the elemental volume of the reciprocal space under investigation to the nearest r.l.p. For FZ crystals for a given K* the DXS intensity was higher for θ < θ_B in comparison with that for θ > θ_B showing that the anisotropy (DXS I_{θ > θB} − DXS I_{θ < θB}) is negative, as expected for vacancy clusters. For CZ crystals the anisotropy was positive, owing to the presence of interstitial clusters. The magnitude of anisotropy in the FZ crystals was smaller than that observed in the CZ crystals. The DXS intensity varies approximately as K⁻² near Bragg peaks (Huang scattering) and as K^*−4 (Stokes–Wilson scattering) away from it. From the K* values where the changeover from Huang to Stokes–Wilson scattering takes place the size of the clusters assumed to be the origin of the observed DXS is estimated as ~ 2 × 10⁻⁴ and 2.6 × 10⁻³ mm for FZ and ~ 5.5 × 10⁻⁴ and 3 × 10⁻³ mm for CZ crystals. The experimental data were compared with theoretically calculated DXS distributions assuming the defects to be dislocation loops. The number of point defects in a loop has been estimated.