The atomic and electronic structure of the ͓0001͔/(1 2 3 0) ⌺ϭ7 symmetric tilt boundary in ZnO has been investigated by an ab initio plane-wave pseudopotential method within the local-density approximation. Two types of equilibrium geometries are obtained with similar boundary energies. Atomic arrangement is largely reconstructed to vanish dangling bonds in one configuration, whereas the other shows small bond distortion but has dangling bonds at the boundary core. The balance between the energies for deforming atomic arrangements and vanishing dangling bonds should be significant in determining the boundary energies. The electronic structure of the grain boundaries is discussed with a special interest in the relationship with the bond disorder. Owing to the bond distortion and/or the presence of the dangling bonds, localized states form mainly at the lower valence band and the bottom of the upper valence band. On the other hand, the electronic states in the vicinity of the band gap are not significantly affected by the bond disorder. Deep electronic states are not generated in the band gap even for the configuration with dangling bonds. This behavior can be generally explained by the band structure intrinsic to ZnO.

A method of improving the resolution and reliability of a laser interferometer which is used for measuring displacement is proposed. By giving code numbers to the divided segments of the interference fringe interval, the theoretical resolution is improved up to 1/170 of the light wave length. As the error caused by environmental noise is not integrated, the reliability is improved.