Distribution of SiO2 precipitates in large, oxygen rich Czochralski-grown silicon single crystals after annealing at 750 °C

Abstract

The defects due to oxygen precipitation in Czochralski grown silicon single crystals annealed for 216 h at 750 °C and with oxygen concentration varying between 18 and 12×10¹⁷ atoms per cm³ (according to DIN 50438) were studied by means of small angle neutron scattering and γ‐ray diffractometry probing the same volume elements in the sample. The size and the shape of the SiO₂ precipitates were determined by means of small angle neutron scattering. In the center of the disk‐shaped sample of 10 cm diameter one finds spherical precipitates with a radius of ≊20 Å, at the border the precipitates are of plate‐like shape, ≊146×146×41 Å in dimension. The k‐space distribution of the diffuse scattering caused by the strain field of the SiO₂ precipitates has been determined by means of a double‐crystal diffractometer and 316 keV γ radiation. Modeling with Huang and Stokes–Wilson theory suggests that the relatively small SiO₂ precipitates are loosely bound in larger clusters with a radius of ≊2000 Å in which the crystal matrix is strongly distorted. With the γ‐ray diffractometer operated in the single‐crystal mode the thickness dependence of the integrated reflecting power was measured from which the static Debye–Waller factor for the 2 2 0 reflection is determined using statistical dynamical theory. The results confirm qualitatively the cluster model. In the center of the sample the size of the precipitates could be calculated by additional measurement of the static Debye–Waller factor of the 4 4 0 reflection. The result is in excellent agreement with the small angle neutron scattering data. Combining all the experimental data taken in the oxygen rich center of the annealed silicon crystal the average distance between the centers of the SiO₂ precipitates in the clusters is ≊80 Å and the distance between the large clusters is ≊40 000 Å.