High-resolution X-ray diffraction analysis of strain distribution in GaN nanowires on Si(111) substrate
© Stanchu et al.; licensee Springer. 2015
Received: 22 October 2014
Accepted: 19 January 2015
Published: 6 February 2015
In this work, the influence of micro- and macro-deformation profiles in GaN nanowires (NWs) on the angular intensity distribution of X-ray diffraction are studied theoretically. The calculations are performed by using kinematical theory of X-ray diffraction and assuming the deformation decays exponentially from the NW/substrate interface. Theoretical modeling of X-ray scattering from NWs with different deformation profiles are carried out. We show that the shape of the (002) 2θ/ω X-ray diffraction profile (XDP) is defined by initial deformation at the NW's bottom and its relaxation depth given by the decay depth of the exponential deformation profile. Also, we demonstrate that macro-deformation leads to XDP shift, whereas micro-deformations are the cause of XDP's asymmetry and its symmetrical broadening. A good correlation between calculated and experimental XDP from self-assembled GaN NWs on Si(111) substrate was achieved by taking into account all parameters of micro- and macro-deformation profiles.
The wide range of unique properties of semiconductor GaN nanowires (NWs), along with various techniques of NW's growth, makes them promising candidates for nano-sized optoelectronics . In recent years, a great deal of effort has been devoted to explore their optical, electrical, and structural properties. The main sources of deterioration of NW's properties are their crystalline imperfection and residual strain. Generally, NWs are considered almost strain-free crystalline-objects without extended defects that propagate into their structure [2-5]. In comparison with thick planar epilayers, where the mechanism of lattice accommodation is preferably plastic and where the formation of misfit dislocation networks takes place, NWs are considered to be predominantly free of dislocations [6,7]. At the same time, the process of deformation relaxation in NWs is not completely studied.
Over recent years, there have been only a few significant reports devoted to this subject. In , the assessment of macro- and micro-deformation in GaN NWs grown on Si(111) was performed with X-ray diffraction, where the NWs were found to be free of deformations on the macro scale but not on the micro scale. In comparison to self-assembled GaN NWs , an exponential relaxation of the macro-strain along the NW height was observed for top-down fabricated GaN NWs grown on silicon and sapphire substrates [3,4]. An exponential decay of the mean-squared micro-strain along the self-assembled GaN NW was considered to describe the X-ray diffraction peaks in . Moreover, theoretical analysis of the elastic energy relaxation in NWs of different geometries grown on lattice mismatched substrates was performed assuming an exponential decay of strain .
In this letter, we study the influence of macro- and micro-deformation along the GaN NW's growth axis on the X-ray diffraction peak profile. We show that macro-deformations lead to X-ray diffraction profile (XDP) shift, whereas micro-deformations are the cause of XDP's asymmetry and its symmetrical broadening. This allows distinguishing the influence of macro- and micro-deformation components on XDP and thereby to extract them separately.
Self-induced GaN NWs were grown by plasma-assisted molecular beam epitaxy (MBE) on a Si(111) substrate at approximately 760°C under highly nitrogen-rich conditions. Before the growth started, the substrate was exposed to a nitrogen flux for 30 min at the nitridation temperature of approximately 150°C. The procedure of plasma-assisted MBE growth of GaN NWs on Si(111) is described in [10,11]. The high-resolution X-ray diffraction measurements were performed by using PANalytical X'Pert Pro MRD diffractometer (PANalytical, Almelo, the Netherlands) equipped with a 1.6 kW X-ray tube (vertical line focus) with CuKα1 radiation (λ = 1.540598 Å), a symmetric 4 × Ge(220) monochromator and a channel-cut Ge(220) analyzer.
Results and discussion
In this work, the theoretical analysis of micro- and macro-deformation parameters that influence symmetrical (002) 2θ/ω XDP from GaN NWs is presented. It is demonstrated that the macro-deformation ε | of a whole NW leads to the angular position shift of XDP. Inhomogeneous micro-deformation ε ||(z) along the NW height leads to asymmetry of the XDP. The micro-deformation ε |||(z) fluctuation around the ε ||(z) causes only broadening of XDP. Thus, our theoretical approach of 2θ/ω XDP calculation can be used for quantitative analysis of GaN NWs with different shapes and deformation states.
This study was supported by the National Academy of Sciences of Ukraine within the framework of the scientific-technological program ‘Nanotechnology and Nanomaterials’ 2010 to 2014, project no. 22.214.171.124/19.
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