Determination of the atomic geometries of the (110) surfaces of CuCl and CuBr by dynamical low-energy electron diffraction intensity analysis.

Abstract

The atomic geometries of the nonpolar (110) surfaces of CuCl and CuBr are determined by dynamical analysis of the intensities of 13 diffracted beams for CuCl and 16 beams for CuBr associated with normally incident electrons at T=125 and 100 K, respectively. The structural model is specified by six independent variables consisting of the tilt angles (${\mathrm{\ensuremath{\omega}}}_{\mathit{i}}$) of the top two layers, the three independent bond lengths (${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$) associated with atoms in the top two layers, and the inner potential. The focus of our analysis is the accuracy and precision with which these six structural parameters can be extracted from the measured intensities. A six-dimensional statistical error analysis was performed for two electron-solid scattering models: one model in which all nonstructural parameters assumed the values used in a family of previous structural analyses for the (110) surface of CuCl and other binary zinc-blende structure materials, and one in which these parameters were treated as adjustable parameters to fit the measured intensities. The structural parameters emanating from these two analyses differ by \ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\le}4\ifmmode^\circ\else\textdegree\fi{} and \ensuremath{\Delta}(${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$)\ensuremath{\le}0.3 \AA{}. Statistical analysis of uncertainties in the structural parameters resulting only from uncertainties in the measured intensities yields \ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\le}1.3\ifmmode^\circ\else\textdegree\fi{}, \ensuremath{\Delta}(${\mathit{c}}_{\mathit{i}}$-${\mathit{a}}_{\mathit{j}}$)\ensuremath{\le}0.02 \AA{}. Thus, the uncertainties in the structural parameters associated with the selection of the nonstructural parameters, especially the model of the electron exchange interaction, dominate those associated with the uncertainties in the experimental intensity data. Within these uncertainties we find the top-layer bond lengths are contracted by 0.3 \AA{} for CuCl(110) and 0.1 \AA{} or less for CuBr(110). Changes in the backbonds from the anion and cation cannot be established for CuCl using the existing intensity data in our analysis. For CuBr(110) the backbond from the top-layer cation is contracted by 0.35\ifmmode\pm\else\textpm\fi{}0.2 \AA{}. The tilt angles are ${\mathrm{\ensuremath{\omega}}}_{1}$=(53\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{} for CuCl and (35\ifmmode\pm\else\textpm\fi{}2)\ifmmode^\circ\else\textdegree\fi{} for CuBr with ${\mathrm{\ensuremath{\omega}}}_{2}$=(-5\ifmmode\pm\else\textpm\fi{}1)\ifmmode^\circ\else\textdegree\fi{} for both. These results are compatible with previously identified structural systematics that the most ionic zinc-blende structures exhibit top-layer bond-length contractions which increase their tilt angles relative to the value of (29\ifmmode\pm\else\textpm\fi{}3)\ifmmode^\circ\else\textdegree\fi{} characteristic of bond-length-conserving rotational relaxations of covalent III-V and II-VI (110) surfaces. \textcopyright{} 1996 The American Physical Society.