Bragg and diffuse components of X-ray reflection measured using acoustic excitation of an Si crystal with oxide precipitates

Abstract

Bragg and diffuse scattering contributions to a reflection can be separated using the intensity dependence on the amplitude of transverse ultrasound excited in the crystal. The method is based on the fact that a weak ultrasound with wavelength equal to the extinction length suppresses almost completely the anomalous transmission of the coherent (Bragg) beam in a sufficiently thick absorbing crystal and does not affect diffuse scattering. Both parameters characterizing diffraction in a slightly imperfect crystal, the static Debye-Waller factor and the coefficient of additional absorption due to diffuse scattering, have been determined for a silicon crystal containing oxide precipitates after heat treatment.

Structure Perfection Study of Crystals Containing Micro- and Macrodistortions by X-Ray Acoustic Method

“…The characteristic size R and the concentration N of microdefects were estimated from the values of L and μd, using the following expressions [17]:…”

Structure Perfection Diagnostics of Single Crystals by Means of Diffractometry Measurements Using X-Ray Continuous Spectrum

“…The dislocation density was also determined by such methods in another Si crystal. The procedure of intensity measurements and conditions of ultrasound excitation were similar to those in the previous paper [6].…”

“…Now we have suggested to choose a specific wavelength λ 0 of the continuous spectrum for wlich the intensities of a real and perfect crystal coincide (Id = Ιp ) due to equality of scattering and absorption contribution to total reflectivity of a sample with structural defects [3]. Under this condition one can use only one dependence Id(W) measured in a real crystal as distinguished from [6] where such a graph was plotted fora sample with perfect stucture, too.…”

“…The value L for a Ge sample with Nd 2.4 x 105 cm-2 happened to be 4.1 x 10 -2 which is in agreement with results of independent measurements. One should note that L can be also calculated using data of the metallographical dislocation density N m d a c c o r d i n g t o [ 6 ] :…”

Integral Structure Perfection Diagnostics of Single Crystals Using Two Wavelengths of X-Ray Spectrum

“…a concentration n and characteristic radius r, entering the corresponding expressions for the Debye-Waller factor L [1][2][3] and the coefficient of pd, additional energy losses of X-rays due to diffuse scattering on defects, determine finally the value of the integral reflectivity Ri of a dislocation-free real crystal. There are several experimental methods basing on the Ri measurements which permit to obtain the integral characteristics of structure perfection of a crystal (L, pd) [3][4][5][6][7]. Also several combinations of these methods exist [8,9].…”