A computationally efficient method to solve the Takagi-Taupin equations for a large deformed crystal

TL;DR

This paper introduces a computationally efficient method for solving the Takagi-Taupin equations in large deformed crystals, accounting for slowly varying strain fields, and validates it through comparison with experimental data on bent silicon wafers.

Contribution

The paper develops a new efficient computational approach for the Takagi-Taupin equations that simplifies calculations for large deformed crystals with slowly varying strain fields.

Findings

Reflectivity curves are shifted by strain but retain shape.

The method accurately predicts experimental reflectivity for bent silicon wafers.

Good agreement between computed and experimental results.

Abstract

We present a treatise on solving the Takagi-Taupin equations in the case of a strain field with an additional, spatially slowly varying component (owing to \emph{e.g.}~heat expansion or angular compression). We show that the presence of such a component in a typical case merely shifts the reflectivity curve as a function of wavelength or incidence angle, while having a negligible effect on its shape. On the basis of the derived result, we develop a computationally efficient method to calculate the reflectivity curve of a large deformed crystal. The validity of the method is demonstrated by comparing computed reflectivity curves with experimental ones for bent silicon wafers. A good agreement is observed.