XRD fitting analysis of semiconductor heterostructures [Puolijohderakenteiden r\"ontgendiffraktion sovitusanalyysi] (in Finnish)

TL;DR

This paper presents a software tool for analyzing X-ray diffraction data from semiconductor heterostructures, using fitting analysis and dynamical diffraction theory to accurately model and interpret measured data.

Contribution

A novel software implementation combining dynamical diffraction calculations with differential evolution fitting for XRD analysis of heterostructures, accessible via Java/Matlab and GNU Octave.

Findings

Software produces results similar to existing tools.

Fitting algorithm effectively analyzes measured XRD data.

Operability tested with InGaAs, GaAs, and GaAsN structures.

Abstract

Analysis of measured X-ray diffraction (XRD) data from heterostructures with fitting analysis is discussed, for which computer program was written. Lattice constant and Poisson's ratio of a multi-compound layer is calculated from Vegard's law. Layers are strained in in-plane direction causing additional strain in out-of-plane direction and may be only partially strained. For crystals, wavelength-dependent electric susceptibility is represented as Fourier series, components of which are calculated from atomic scattering factors, H\"onl anomalous dispersion correction terms and Debye-Waller factor. XRD intensity from heterostructures as a function of angle is calculated with dynamical diffraction theory using Takagi-Taupin differential equation solution in form of recursive equations. XRD measurements are analyzed by fitting a simulated XRD curve to the measured XRD curve. Inverse problem related to curve fitting is solved with differential evolution where principal component analysis is used to reduce interparameter dependencies. For measurement analysis a software was written with Java/Matlab, user interface (UI) of which was designed by taking into account feedback from users. With UI, it is really easy to build a layer model, parameters of which are obtained by fitting a simulation to measurement. Software is also able to use GNU Octave and therefore works without requiring any commercial components. Operability of simulation code of XRD curves was tested by comparing the curves simulated by it with curves simulated by 2 other software using single/multilayer InGaAs, GaAs and GaAsN structures. Software was tested by analyzing a measurement series having been published previously. Software was observed to produce results similar to other software and the fitting algorithm was observed to work efficiently.