High-resolution X-ray Bragg diffraction in Al thermomigrated Si channels

Abstract

Si(111) wafers patterned with an array of vertical 120 µm-wide Al-doped (1 × 1019 cm−3) p-channels extending through the whole wafer were studied with the X-ray double- and triple-crystal diffraction technique in Bragg geometry with copper radiation. Reciprocal space maps (RSMs) of diffraction intensity far from the channels and near them were measured, and their non-trivial shape was observed. The obtained experimental RSMs demonstrate high sensitivity to the structural distortions of the crystal in the subsurface layer owing to the influence of the surface on the elastic strain field in the channel. These features result from the small difference of the ionic radii of Si and Al, leading to the absence of misfit dislocations on the borders of the channel. Simulations of RSMs using the Takagi–Taupin dynamical diffraction theory taking into account the influence of the surface on the elastic strain field in the channel and the effect of the instrumental function were carried out. Finally, numerical RSM calculations showed that the proposed model of the surface effect on the elastic strain field in a semi-infinite crystal with a vertical Si(Al) channel can be used to retrieve the information on the concentration of aluminium in the thermomigrated Si(Al) channel from the diffraction data obtained in the Bragg geometry.

Dynamical and kinematical X-ray diffraction in a bent crystal

“…Calculations of dynamical X-ray diffraction from a bent crystal were performed on the basis of the T-T equations ( 2) in an oblique coordinate system using the half-step derivative algorithm (Epelboin, 1985;Gronkowski, 1991;Lomov et al, 2022;Kohn, 2023). We also performed calculations using the T-T equations (4) in a rectangular coordinate system using the Runge-Kutta method (Kolosov & Punegov, 2005).…”

“…To calculate X-ray diffraction in crystals, different methods of integrating the T-T equations can be used. In particular, these include the above-mentioned half-step derivative algorithm in an oblique coordinate system (Authier et al, 1968;Epelboin, 1985;Gronkowski, 1991;Lomov et al, 2022;Kohn, 2023), the finite-element approach (Honkanen et al, 2017(Honkanen et al, , 2018, the Runge-Kutta method in a rectangular coordinate system (Kolosov & Punegov, 2005) and a finite difference scheme on an arbitrary orthogonal network using Fourier interpolation (Carlsen & Simons, 2022).…”