Possible causes of electrical resistivity distribution inhomogeneity in Czochralski grown single crystal silicon

Abstract

Electrical resistivity distribution maps have been constructed for single crystal silicon wafers cut out of different parts of Czochralski grown ingots. The general inhomogeneity of the wafers has proven to be relatively high, the resistivity scatter reaching 1–3 %. Two electrical resistivity distribution inhomogeneity types have been revealed: azimuthal and radial. Experiments have been carried out for crystal growth from transparent simulating fluids with hydrodynamic and thermophysical parameters close to those for Czochralski growth of silicon single crystals. We show that a possible cause of azimuthal electrical resistivity distribution inhomogeneity is the swirl-like structure of the melt under the crystallization front (CF), while a possible cause of radial electrical resistivity distribution inhomogeneity is the CF curvature. In a specific range of the Grashof, Marangoni and Reynolds numbers which depend on the ratio of melt height and growing crystal radius, a system of well-developed radially oriented swirls may emerge under the rotating CF. In the absence of such swirls the melt is displaced from under the crystallization front in a homogeneous manner to form thermal and concentration boundary layers which are homogeneous in azimuthal direction but have clear radial inhomogeneity. Once swirls emerge the melt is displaced from the center to the periphery, and simultaneous fluid motion in azimuthal direction occurs. The overall melt motion becomes helical as a result. The number of swirls (two to ten) agrees with the number of azimuthally directed electrical resistivity distribution inhomogeneities observed in the experiments. Comparison of numerical simulation results in a wide range of Prandtl numbers with the experimental data suggests that the phenomena observed in transparent fluids are universal and can be used for theoretical interpretation of imperfections in silicon single crystals.