Unit-cell determination of epitaxial thin films based on reciprocal-space vectors by high-resolution X-ray diffractometry

A new approach, based on reciprocal-space vectors (RSVs), is developed to determine Bravais lattice types and accurate lattice parameters of epitaxial thin films by high-resolution X-ray diffractometry. The lattice parameters of single-crystal substrates are employed as references to correct the systematic experimental errors of RSVs of thin films. The general procedure is summarized, involving correction of RSVs, derivation of the raw unit cell, and subsequent conversion to the Niggli unit cell and the Bravais unit cell by matrix calculation. Two methods of this procedure are described: in three-dimensional reciprocal space and in six-dimensional G⁶ space. The estimation of standard error in the lattice parameters derived by this new approach is discussed. The whole approach is illustrated by examples of experimental data. The error of the best result is 0.0006 Å for the lattice parameter of indium tin oxide film. This new RSV method provides a practical and concise route to the crystal structure study of epitaxial thin films and could also be applied to the investigation of surface and interface structures.