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Modelling of X-Ray diffraction curves for GaN nanowires on Si(111)

Vasyl Kladko 1Andrian Kuchuk 1Hryhorii Stanchu 1Nadiia Safriuk 1Alexander Belyaev 1Aleksandra Wierzbicka 2Marta Sobanska 2Kamil Klosek Zbigniew R. Zytkiewicz 2

1. V. Lashkaryov Institute of Semiconductor Physics NASU (ISP), 41, pr. Nauki, Kiev 03028, Ukraine
2. Institute of Physics, Polish Academy of Sciences, Warsaw 02-668, Poland


   Recently the GaN nanowires (NWs) grown on various substrates have been extensively studied. At the same time many diagnostic methods are developed that allow analysis of NWs properties. For structural characterization the nondestructive X-ray diffraction (XRD) is mainly used.

   The structure of GaN NWs, as well as of planar layers, is described by mosaic model, which takes into account such parameters as tilt, twist and size of mosaic blocks. All these parameters cause broadening of the X-ray diffraction curves (XDC) for both types of epitaxial structures. However, there are a strong differences between the full width at half maximum (FWHM) of XDCs of nanowire and planar GaN layers. For GaN layers different types of dislocations contribute mainly to the XDC broadening, while for dislocation free GaN NWs broadening is cased by the their small size as well as by large values of tilt and twist (spatial orientation). Attempts to fit the XDC by Lorentzian and Gaussian functions, as well as their combinations, often do not describe experimental observations. Moreover, this approach doesn't give any information about physical parameters which affect the broadening of XDC. Only modeling of XDC and comparison of calculated and experimental curves allow obtaining real structure parameters of NWs.

  In this paper, we study the profiles of X-ray diffraction peaks from self-assembled GaN NWs grown by PAMBE (760oC) on Si(111) substrate. As the sizes of scattering objects (NWs) are small, the X-rays kinematic scattering theory is applied. The peak profile was calculated taking into account coherence of the x-ray beam, size and spatial orientation distributions of NWs. As it can be seen from Fig. 1a, the best fit of experimental and calculated ω-scan for 0002 reflection from NWs GaN/Si(111) was obtained considering both distributions of NW's tilt and diameter. Moreover, the diameter distributions obtained by calculation of XDC well correlate with distributions obtained by SEM (Fig. 1b). All results obtained by modeling of XDC from GaN NWs will be compared with results from other X-ray diffraction techniques (Williamson-Hall, reciprocal space mapping) as well as with complimentary methods (SEM, AFM etc.).

Fig.1. Calculated and experimental XRD ω-scan for 0002 reflection of GaN NWs (a); experimental and fitted diameter distributions (b).

This work was supported by the European Union within European Regional Development Fund, through grant Innovative Economy (POIG.01.01.02-00-008/08 NanoBiom).


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Submitted: 2013-04-15 15:49
Revised:   2013-08-09 16:06