Crystal Size and Stress Account in Reciprocal Space Map

Abstract

In this study, five periodic InGaN / GaN LED (light emitting diode) structures grown by the Metal Organic Vapor Deposition (MOCVD) at different active layer growth temperatures were studied. These structures were grown as InGaN / GaN multiple quantum wells (MQW) between c-oriented sapphire substrate and n-GaN and p-AlGaN + GaN contacts. These constructions were characterized by the high-resolution X-ray diffraction (HR-XRD) system. HRXRD patterns obtained by X-ray diffraction and Reciprocal space maps were performed from the same data. One of the most effective ways of studying the crystal lattice is reciprocal space mapping with HR-XRD technique. This technique does not damage the sample. Information can be obtained from the internal system of the sample or from the intermediate layer including substrate. Using the FWHM (β_hkl) values and the elastic coefficients of the structures obtained for each of the three samples separately with the inverse mesh technique, D (nm) particle size, σ (GPa) uniform stress, ε strain, u (kJm^-3) anisotropic energy density parameters were calculated. These calculations were done in a  Scherrer method and Uniform Deformation Model (UDM) which is the Williamson Hall method, modified uniform Williamson stresses model (USDM) and Uniform Deformation Energy Density Model (UDEDM). The results show that the stretching in the crystal size is very little. Line expansion in HR-XRD is due to small crystal size and lattice strain. UDEDM, one of the W-H methods, has emerged as the most suitable model for stretching.. 

Keywords

• Strain,particle size,Williamson-Hall,reciprocal space mapping

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