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Local lattice strains of semiconductor devices have been so far examined using higher order Laue zone (HOLZ) line patterns of convergent-beam electron diffraction (CBED). Recently, strain analyses in highly strained regions near interfaces have been reported using split HOLZ line patterns. In the present paper, it is demonstrated for arsenic-doped silicon that the use of CBED rocking curves of low-order reflections provides a promising new tool for the determination of strain distributions of highly strained specimen areas. That is, the anomalous intensity increase in the CBED rocking curves of low-order reflections is explained using a model structure with a strain gradient in the electron beam direction, which is similar to the models used for the split HOLZ line patterns.

All the six lattice parameters (a, b, c, alpha, beta and gamma) of a Si (001) layer grown on a sapphire (1102) substrate were determined by convergent-beam electron diffraction with no assumption of crystal lattice symmetry. A lattice compression in the Si (001) plane and an elongation in the [001] direction were revealed. An anisotropic lattice compression in the (001) plane was clearly detected for the first time. That is, the lattice compression in the Si [100] direction, which is parallel to the sapphire [1101] direction, was larger than that of the Si [010] direction, which is parallel to the sapphire [1120] direction. It was also revealed that the lattice parameters of the Si-layer depend on the distance from the interface. Anisotropy of carrier mobility was reasonably explained in terms of the anisotropy of the lattice parameters determined.

The six lattice parameters (a, b, c, alpha, beta and gamma) of Si(1-x)Ge(x), which was grown epitaxially on a Si (001) substrate with a varying Ge concentration, were determined by convergent-beam electron diffraction (CBED) without any assumption of crystal lattice symmetry. It was revealed that the lattice parameter c of Si(1-x)Ge(x) varies linearly with the Ge concentration and that the lattice symmetry is lowered from cubic to tetragonal, excluding an artifact due to the thinning of the specimen. The effect of strain relaxation that is caused by thinning specimens is discussed. Ge concentrations of examined specimen areas are evaluated using the obtained lattice parameters.

Characteristic signals were detected from As-doped (< 1 at.%) regions of silicon by dark-field transmission electron microscopy and convergent-beam electron diffraction. A slight intensity increase was observed in 220 dark-field images, which may be explained by an increase of scattering amplitude due to the As doping. The doped region showed a much higher intensity in 004 dark-field images. The characteristic high intensity was observed for specimens with As concentrations of about 0.09-0.8 at.%. Convergent-beam electron diffraction patterns obtained from the As-doped region showed a characteristic rocking curve for 004 reflection. These characteristics should originate from incoherent elastically scattered electrons due to a static lattice distortion around the doped As atoms. The observed characteristics in dark-field images and rocking curves of the 004 reflection should be a good probe not only for investigating the concentration of doped atoms in Si lattice, but also for the amount of impurity and/or point defects in other crystalline materials.

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.

Inelastic scattering of fast transmission electrons from a perfect crystal is investigated using the Bloch wave theory. A comprehensive expression for the scattering of electrons is given, which includes both elastic and inelastic multiple scatterings. This expression is an extended form of Fujimoto's expression for elastic scattering (J. Phys. Soc. Japan 14: 1558 (1959)). For the approximation of single inelastic scattering, the expression becomes equivalent to the formula of Rez et al. (Phil. Mag. 35: 81 (1977)). When thermal diffuse scattering (TDS) is considered using the Einstein model or the scattering factor for TDS given by Hall and Hirsch (Proc. R. Soc. A 286: 158 (1965)), Rossouw and Bursill's expression (Acta Cryst. A 41: 320 (1985)) is derived. This expression has been used in computer simulations of TDS intensity distribution (Kikuchi pattern). It is shown that the simulations for magnesium oxide (MgO) using 357 beams agree quite well with the experimental ones.

Energy filtered CBED patterns of the Cr-stabilized L1(2) phase of a titanium tri-aluminide alloy reveal deficit higher order Laue zone (HOLZ) lines in the zeroth order diffraction disk, for which the expected 4-mm symmetry is significantly broken in the projection. This apparent break of symmetry may be explained by the presence of lattice strains of order 10(-3). Effects of strain-induced lattice distortions on HOLZ line symmetries are calculated by an introduction of rhombohedral, tetragonal or monoclinic distortions to the cubic unit cell. It is shown how tensile and shear components of strain affect the overall HOLZ line symmetries in different ways.