Hybrid Multiple diffraction

E. de Prado¹, J. Kub¹, O. Pacherova¹, A. Hospodková², V. Novák², M. Cukr²

¹Institute of Physics of the Czech Academy of Sciences, v. v. i., Na Slovance 1999/2, 182 21 Praha 8, Czech Republic

²Institute of Physics of the Czech Academy of Sciences, v. v. i., Cukrovarnická 10, 16200 Praha 6, Czech Republic

prado@fzu.cz

The analysis of multiple diffraction (MD) processes could provide an alternative method for the structural characterization of samples. One of the first studies reported on this topic was made by Renninger in 1937 [1] and used for the 222 reflection of diamond, obtaining accurately its lattice parameters [2]. MD takes place inside a material when more than one set of planes fulfills simultaneously the Bragg condition in the path of the incident beam. In the real space it means that a specific diffraction (called primary) can be produced by the combined diffracting effects from two or more different set of planes (Fig. 1). This is possible because the sum of two or more diffraction vectors always end up at a reciprocal-lattice point of their corresponding space. Experimentally, since it is not possible to discriminate the different contributions to diffraction between conventional two-beam diffraction and MD, this phenomenon is generally studied for forbidden or very weak reflections, in which changes in intensity may be more easily observed.

Figure 1 Geometry of a three-beam MD in real and reciprocal space.

Hybrid Multiple Diffraction (HMD) is a particular and poorly studied kind of multiple diffraction that can happen in heteroepitaxial systems. In these systems two different materials are involved in the generation of MD in such a way that the participant planes belong to different reciprocal lattices. In this respect, the final beam is not diffracted exactly towards the outgoing primary direction (q) but in a direction very close to it (q_H). Thus HMD phenomenon can be observed also for allowed reflections unlike as happens with MD. One of the first studies in this frame was performed by Isherwood et al.[3] , who investigated cubic Ga1-xAlxAs epitaxially grown on (001) GaAs substrates. Later, it was studied by Morelhao et al. [4]–[8] and Domagala and coworkers for different cubic and, ultimately, for wurtzite c-oriented materials [9] and by E. de Prado et al [10] for r-oriented wurtzite structures.

The three-beam X-Ray diffraction condition can be fulfilled by rotating the sample around the primary diffraction vector P of the reflection whose intensity is monitored, generally a symmetric one. That is, participant planes are excited only at some specific azimuthal angles of the incident direction. This makes that this type of diffraction could be observed only for some particular azimuthal angles.

In this work we show some additional conditions that must been satisfied in order to achieve HMD. To illustrate it we present our study on an InGaN thin layer grown by Metal Organic Vapor Phase Epitaxy (MOVPE) on a thick GaN buffered c-Al2O3 substrate (Fig 2).

Figure 2: Diffractogram showing the (006) InGaN and GaN reflections and an hybrid peak

We present also an easy procedure for identify the participant planes in the HMD process using for that a thick MnGaAs layer grown by Molecular Beam Epitaxy on GaAs c-oriented substrate. In this sample all the hybrid reflections (Fig 3) were identified.

Figure 3 Azimuthal scan around (006) symmetric reflection showing the signal from the layer, the substrate and the hybrid points

[1]         M. Renninger, “‘Detour-excitation’ a hitherto unobserved interaction effect in space-lattice interference,” Zeitschrift für Phys., vol. 106, no. November, pp. 141–76, 1937.

[2]         M. Renninger, “Beitrag zur Kenntnis der röntgenographischen Unterschiede zwischen den beiden Diamant-Typen,” Acta Crystallogr., vol. 8, no. 10, pp. 606–610, 1955.

[3]         B. J. Isherwood, B. R. Brown, and M. A. G. Halliwell, “X-ray multiple diffraction as a tool for studying heteroepitaxial layers. I. Coherent, on-axis layers,” J. Cryst. Growth, vol. 54, no. 3, pp. 449–460, 1981.

[4]         S. L. Morelhão and L. P. Cardoso, “Simulation of hybrid reflections in X-ray multiple diffraction experiments,” J. Cryst. Growth, vol. 110, no. 3, pp. 543–552, 1991.

[5]         S. L. Morelhão, L. P. Cardoso, J. M. Sasaki, and M. M. G. De Carvalho, “Hybrid multiple diffraction in Renninger scan for heteroepitaxial layers,” J. Appl. Phys., vol. 70, no. 5, pp. 2589–2593, 1991.

[6]         S. L. Morelhão and L. P. Cardoso, “Structural properties of heteroepitaxial systems using hybrid multiple diffraction in Renninger scans,” J. Appl. Phys., vol. 73, no. 9, pp. 4218–4226, 1993.

[7]         S. L. Morelhão, A. A. Quivy, and J. Härtwig, “Hybrid and effective satellites for studying superlattices,” Microelectronics J., vol. 34, no. 5–8, pp. 695–699, 2003.

[8]         S. L. Morelhão and J. Z. Domagala, “Hybrid reciprocal space for X-ray diffraction in epitaxic layers,” J. Appl. Crystallogr., vol. 40, no. 3, pp. 546–551, 2007.

[9]         J. Z. Domagała, S. L. Morelhão, M. Sarzyński, M. Maździarz, P. Dłużewski, and M. Leszczyński, “Hybrid reciprocal lattice: application to layer stress appointment in GaAlN/GaN(0001) systems with patterned substrates,” J. Appl. Crystallogr., vol. 49, no. June, pp. 798–805, 2016.

[10]       E. De Prado, M. C. Martinez-Tomas, C. Deparis, V. Munoz-Sanjose, and J. Zuniga-Perezb, “Hybrid multiple diffraction in semipolar wurtzite materials: (0112)-oriented ZnMgO/ZnO heterostructures as an illustration,” J. Appl. Crystallogr., vol. 50, pp. 1165–1173, 2017.