Characterization of Dislocation Densities in Germanium and Silicon Single Crystals by High Resolution X-Ray Diffraction

Abstract

The dislocation density of silicon and germanium single crystals are determined by the combined measurements of etch pits densities (EPD) and of the full width at half maximum (FWHM) of X-ray rocking curves. The crystals investigated were grown by either a floating zone or Czochralski technique. The conventional X-ray rocking curve technique normally used to measure dislocation densities in the range from 10 5 to 10 9 cm -2 is extended by a high resolution X-ray diffraction technique (HRXRD) to a range of 0 to 10 5 cm -2 . This extension was achieved by careful and accurate measurements of (111) rocking curves and elimination of several disturbing effects. The well-known effects causing broadening of rocking curves like the dislocation density itself, the instrumental wavelength dispersion, the beam divergence, the surface distortion and the sample miscut were carefully determined experimentally and separated such that their effects on the rocking curves could be corrected. Especially the instrumental broadening, i.e. the resolution of the monochromator and the divergence of the X-ray beam is exactly measured. A quadratic relationship between the dislocation density as measured by EPD and HRXRD and the FWHM is experimentally established.