Use of dynamical diffraction effects on x-ray fluorescence to determine the polarity of GaP single crystals

Abstract

The dynamical theory of x-ray diffraction, which predicts a highly structured internal field intensity during symmetric Bragg reflection from large single crystals, was applied to the \ifmmode\pm\else\textpm\fi{} (111) and \ifmmode\pm\else\textpm\fi{} (222) Bragg reflections from noncentrosymmetric GaP crystals. It was shown that theory predicts an internal field intensity with maximal and minimal surfaces. At the low-angle side of the region of total reflection, the surface of maximal field intensity is positioned to sense the least amount of charge density. The field intensity moves into the crystal during the scan of the total reflection range until it senses the maximum amount of charge density at the high-angle limit of total reflection. During scans of the (111) and (\ifmmode\bar\else\textasciimacron\fi{} 1 \ifmmode\bar\else\textasciimacron\fi{} 1 \ifmmode\bar\else\textasciimacron\fi{} 1) reflections, the field intensity moves across the atomic planes in different sequences so that the polarity of the crystal may be determined by monitoring the x-ray fluorescence from the phosphorus or gallium atoms. This polarity determination does not reguire an anomalously scattered component in the diffracted beam as have all previous determinations. Experimental phosphorus fluorescence profiles were obtained during diffraction of $\mathrm{Cu} K\ensuremath{\alpha}$ radiation from the \ifmmode\pm\else\textpm\fi{} (111) and \ifmmode\pm\else\textpm\fi{} (222) reflections. The long-wavelength phosphorus $K\ensuremath{\alpha}$ radiation provided distinct advantages in detecting the internal field motion, and the \ifmmode\pm\else\textpm\fi{} (222) reflection profiles provided internal checks on the \ifmmode\pm\else\textpm\fi{} (111) results. The experimental profiles agreed with theoretical predictions and determined the GaP crystal polarity. The polarity was also determined by the traditional anomalous dispersion method using $\mathrm{Mo} K\ensuremath{\alpha}$ radiation. The two methods gave consistent results providing experimental confirmation of the predictions of dynamical and kinematic theories of x-ray diffraction. The fluorescence technique also provides a means for determining the arrangement of atoms in crystals in a new and direct way.