Lattice parameter determination of a strained area of an InAs layer on a GaAs substrate using CBED

All the six lattice parameters (a, b, c, alpha, beta and gamma) of a strained area of an InAs layer grown on a GaAs substrate were determined without any assumption of the crystal lattice symmetry from the higher-order Laue zone (HOLZ) lines appearing in one convergent-beam electron diffraction (CBED) pattern. The analysis was performed with three steps. Firstly, the parameters alpha and beta were determined from the deviations of the HOLZ lines from the mirror symmetry perpendicular to the [001] direction. Secondly, the parameter c was determined from the distance between the intersections of the HOLZ lines, which have the same h and k indices but different l indices. Finally, the parameters a, b and gamma were determined simultaneously from several distances between the intersections of the HOLZ lines. The lattice parameters determined for the strained area were a = 0.611(2) nm, b = 0.615(1) nm, c = 0.6119(7) nm, alpha = 89.5(1) degrees, beta = 89.0(2) degrees and gamma = 89.1(2) degrees. This result implies that the cubic lattice of InAs is elongated approximately in the [111] direction and the exact lattice symmetry is triclinic. The same analysis procedure was applied to another two specimen areas. It was found that the areas have orthorhombic distortions with lattice parameters a = 0.607(2) nm, b = 0.604(1) nm and c = 0.6085(7) nm for one area, and with a = 0.607(2) nm, b = 0.605(1) nm and c = 0.6065(7) nm for the other area. It is should be emphasized that the present analysis of lattice distortions is immediately applicable to the other semiconductors, such as Si, SiGe or GaAs layers, without assuming any crystal system.