Crystal Size and Stress Account in Reciprocal Space Map

Year 2019, Volume: 22 Issue: 1, 1 - 9, 01.03.2019

İlknur Kars Durukan , Mustafa Kemal Öztürk Süleyman Özçelik Ekmel Özbay

https://doi.org/10.2339/politeknik.417752

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

References

• [1]. Morkoç, H., “Hand book of Nitride Semiconductors and Devices”, Wiley-VCH, 16. Berlin, (2008).
• [2]. Kapolnek, D., Wu, X. H., Heying,B., Keller, S., Keller, B. P., Mishra, U. K., Den Baars, S. P. and Speck, J. S. “Structural evolution in epitaxial metalorganic chemical vapor deposition grown GaN films on sapphire”, Applied Physics Letters, 67(11): 1541-1543, (1995).
• [3]. Ponce, F. A., Krusor, B. S., Jr, J. S. M., Plano, W. E. and Welch, J. “Microstructure of GaN epitaxy on SiC using AlN buffer layers”, Applied Physics Letters, 67(3): 410-412, (1995).
• [4]. Chichibu, S., Azuhata, T., Sota, T., Nakamura, S. “Spontaneous emission of localized excitons in InGaN single and multiquantum well structures”, Applied Physics Letters, 69(27): 4188-4190, (1996).
• [5]. Lester, S. D., Ponce, F. A., Crawford, M. G., Steigerwald, D. A. “High Dislocation Densities in High-Efficiency Gan-Based Light-Emitting-Diodes”, Applied Physics Letters, 66(10): 1249-1251, (1995).
• [6]. Baş, Y. “InxGa1-xN (x= 0,075; 0,090; 0,100) “Mavi LED’lerin Mikroyapısal Kusurlarının Ters Örgü Uzay Haritası İle İncelenmesi”, Doktora Tezi, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara, (2015).
• [7]. Baş, Y., Demirel, P., Akın, N., Başköse, C., Özen, Y., Kınacı B., Öztürk, M.K., Özçelik, S., Özbay, E. “Microstructural defect properties of InGaN/GaN blue light emitting diode structures”, Journal of Materials Science: Materials in Electronics, 25(9): 3924-393, (2014).
• [8]. Moram, M. A.,Vickers, M. E. “X-ray diffraction of III-nitrides”, Reports on Progress in Physics, 72(3): 036502-036541, (2009).
• [9]. Öztürk, M. K., Yu, H., Sarıkavak, B., Korçak, S., Özçelik, S., Özbay, E. “Structural analysis of an InGaN/GaN based light emitting diode by X-ray diffraction”, Journal of Materials Science: Materials in Electronic, 21(2): 185-191, (2010).
• [10]. Öztürk, M. K., Altuntaş, H., Çörekçi, S., Hongbo, Y., Özçelik, S. and Özbay E. “Strain-Stress analysis of AlGaN/GaN heterostructures with and without an AlN suffer and Interlayer”, Strain, 47(2): 19-27, (2011).
• [11]. Kisielowski, C. “Strain in GaN thin films and heterostructures”, Semiconductors and Semimetals, 57(GaN II): 275-317, (1999).
• [12]. Çetin, S. S., Öztürk, M. K., Özçelik, S., Özbay, E. “Strain analysis of InGaN/GaN multi quantum well LED structures”, Crystal Research and Technology, 47(8): 824-833, (2012).
• [13]. Yıldız, A., Öztürk, M. K., Bosi, M., Özçelik, S., Kasap, M. “Structural, electrical and optical characterization of InGaN layers grown by MOVPE”, Chinese Physics B, 18(9): 4007-4012, (2009).
• [14] Öztürk, M. K., Çörekçi, S., Tamer, M., Çetin, S. Ş., Özçelik, S., Özbay E. “Microstructural properties of InGaN/GaN light-emitting diode structures with different In content grown by MOCVD”, Applied Physics A-Materials Science&Processing, 114(4): 1215-1221, (2014).
• [15]. Singla, G., Singh, K., Pandey, O. P. “Williamson–Hall study on synthesized nanocrystalline tungsten carbide (WC)”, Applied Physics A, 113(1): 237–242, (2013).
• [16]. Khorsand Zak, A., Majid, W.H.A., Abrishami, M.E., Yousefi, R. “X-ray analysis of ZnO nanoparticles by Williamson-Hall and size-strain plot methods”, Solid State Sci., 13: 251, (2011).
• [17]. Prabhu, Y. T., Rao, K. V., Kumar, V. S. S., Bandla Siva Kumari, “X-Ray Analysis by Williamson-Hall and Size-Strain Plot Methods of ZnO Nanoparticles with Fuel Variation”,World Journal of Nano Science and Engineering, 4: 21-28, (2014).
• [18]. Rosenberg, Y., Machavariant, V.S., Voronel, A., Garber, S., Rubshtein, A., Frenkel, A.I., Stern, E.A. “Strain energy density in the x-ray powder diffraction from mixed crystals and alloys”, J. Phys. Condens. Matter, 12: 8081, (2000).
• [19]. Warren, B.E., Averbach, B.L.” The Effect of Cold‐Work Distortion on X‐Ray Patterns”, J. Appl. Phys., 21: 595, (1950).
• [20]. Zang, J., Zhang, Y., Xu, K.W., Ji, V. “General compliance transformation relation and applications for anisotropic hexagonal metals”, Solid State Commun., 139: 87, (2006).
• [21]. Balzar, D., Ledbetter, H. J. “Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks”, Appl. Crystallogr., 26: 97,(1993).