Lattice distortions perpendicular to the surface in thin surface layers of ion-implanted (111) silicon crystals have been mapped as a function of depth and lateral position with resolutions of 0.05 and 0.65gm, respectively. X-ray triple-crystal diffractometry data were collected near the fundamental 111 and satellite reflections from samples with periodic superstructure modulations in the lateral direction. 300 keV B + ions implanted through surface mask windows are found to produce lattice distortions in a very thin layer of 0.15 gm thickness at 1.05 gm depth below the surface, with interplanar lattice spacings normal to the surface increased by several parts in 104 . The distortions are appreciably extended in the lateral direction, suggesting diffusion of the ions. A 0.5 gm-thick thermaloxide strip is found to contract the interplanar spacing of substrate silicon crystal under the strip region by a few parts in 104, while the strain field created by the parallel oxide edges extends beyond a depth of 3 Bm. A practical procedure is also described for arriving at a solution of the phase problem in the case of a strain field involving heavily distorted layers.

The dynamical problem of X-ray Bragg diffraction from a thick (semi-infinite) crystal deformed by a uniform strain gradient (USG) is treated on the basis of the Green-Riemann function formalism. The rigorous solution of the problem is formulated by means of the Huygens-Fresnel principle. The exact Green functions are obtained in the form of the Laplace integrals suitable in physical applications. The quasi-classical and the Born (kinematical) asymptotic expansions of the Green functions are constructed as functions of the effective USG parameter B. Special attention is paid to the analysis of the wave-field propagation in a crystal with USG. The spatial harmonics Re(q) of the diffracted Green function, when Re(qB) < 0, as is shown, propagate within the proper 'waveguides', while the ones with Re(qB) > 0 are damped exponentially in the bulk of the crystal. The Taupin problem of the Bragg dynamical diffraction of the X-ray incident plane wave from a thick crystal, the lattice spacing being a linear function of the coordinate z (along the inward normal to the entrance surface) only is solved exactly in analytical form. In the latter case the waveguide nature of the propagation of the spatial harmonics inside such a crystal, provided that Re(qB) < 0, is clearly revealed.

General properties of the rigorous solution of the problem of the X-ray dynamical Laue diffraction from a bent crystal are discussed. The solution based on the Takagi equations is formulated in the form of the Huygens-Fresnel principle. Special attention is paid to the behaviour of the quasi-classical asymptotic expansion of the exact dynamical wave fields and to the comparison of the results with those obtained by the eikonal theory. The eikonal theory is developed as a result of the application of the stationary-phase method for the evaluation of the Kirchhoff integral in accordance with the Huygens-Fresnel principle. The focusing of X-rays (the intersection of the ray trajectories and the formation of a caustic) is analysed. The generalized eikonal theory when elaborated yields that the integrated diffracted intensity from a bent crystal tends to the correct kinematical value as the strain gradient increases. For practical purposes, a simple numerical method of calculation of the integrated intensity applied in a general case of asymmetric Laue diffraction is proposed.

A rapid numerical method of the calculation of X‐ray rocking curves (RC) from crystals with thin surface damaged layers is developed on the basis of a semi‐kinematical approach. The determination of the strain profile in the layer from experimental RC's by a „best correspondence”︁ fitting procedure is demonstrated. Strain profiles in Si crystals doped with boron ions with energy from 40 to 100 keV are obtained and discussed in comparison with the distributions of impurity atoms and radiation defects found by other experimental techniques.

A new method for unambiguous reconstruction of crystal-lattice strains in epitaxially grown layers from high-resolution x-ray diffraction data is proposed. The technique uses x-ray diffracted intensity profiles collected for two different radiation wavelengths. We enhance the theory for the previously developed algorithm for model-independent determination of crystal-lattice strain profiles in single crystals with epitaxially grown top-surface layers. The method relies on the retrieval of the scattered x-ray wave phase from its intensity profile via a logarithmic Hilbert transform. This phase-retrieval technique is always associated with the problem of complex polynomial root finding. A practical procedure for the mapping of complex polynomial roots is proposed to distinguish true and virtual zeros. This allows the phase of the diffracted x-ray wave to be retrieved unambiguously. The method was applied to determine physical dimensions and concentration composition of a Si/Si1−xGex/Si alloy multilayer structure typical for SiGe heterobipolar transistor device.