Theoretical investigations of secondary emission yield and standing waves in curved crystals under dynamical Bragg diffraction of X-rays (Taupin problem)

Abstract

The first results of the theory of the behaviour of standing waves in curved crystals are presented. The proposed theory is based on the Taupin theory of dynamical X-ray diffraction in curved crystals and the theory of the secondary radiation yield in deformed crystals. This theory is applied for calculation of the angular dependence of the secondary emission yield in a cylindrically bent Si(400) monocrystal, Cu Kalpha radiation. Processes with different depth of secondary emission yield, i.e. photoemission (Lyi=0.1 mu m) and fluorescence (Lyi=70 mu m) are considered. The behaviour of the reflection coefficient and standing waves in the bulk of the curved crystal is investigated. The standing wave intensities in the depth of the curved crystal show much more sensitivity to the phaseshift than in the perfect one. This fact can be used for the investigation of thin layers of impurity atoms embedded in the crystal matrix.

Theory and applications of x-ray standing waves in real crystals

“…Theory of x-ray standing wave behavior in crystals with USG and as a special case bent crystals was for the first time developed in papers [89,90,91]. Later similar theoretical approach for the analysis of the crystals with USG was performed in [92].…”

“…implanted crystals, heterostructures) are often curved. Below we will present results obtained in [89,90,91].…”

“…The problem of x-ray Bragg diffraction and standing wave determination in a bent crystal can be effectively solved with numerical methods. In the papers [89,90] the modified layer model described in the previous Section was used (see Fig. 35).…”

X-ray standing waves on the surface of the crystal with the uniform strain gradient

“…The angular position of this oscillations depend not only from the value of deformation (determined in our case by the constant B) but also by the phase shift A p . The origin of this oscillations is the waveguide character of the X-ray propagation in the crystal with the USG [10,14,9].…”

“…In previous papers [8,9] results of the theoretical treatment of the XSW method and the secondary radiation yield (fluorescence and photoemission yield) in a bent crystal were presented. This results were obtained in the frame of Taupin approach [10].…”