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High-resolution X-ray diffraction analysis of strain distribution in GaN nanowires on Si(111) substrate.

Stanchu H, Kladko V, Kuchuk AV, Safriuk N, Belyaev A, Wierzbicka A, Sobanska M, Klosek K, Zytkiewicz ZR - Nanoscale Res Lett (2015)

Bottom Line: The calculations are performed by using kinematical theory of X-ray diffraction and assuming the deformation decays exponentially from the NW/substrate interface.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.

View Article: PubMed Central - PubMed

Affiliation: V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Pr. Nauky 45, Kyiv, 03028 Ukraine.

ABSTRACT
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.

No MeSH data available.


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Experimental and calculated 2θ/ω XDPs of the (002) reflection for GaN NWs. The black dashed line indicates the peak position of bulk GaN. The inset NW's diameter distribution was estimated using top-view image of scanning electron microscopy (SEM).
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Fig5: Experimental and calculated 2θ/ω XDPs of the (002) reflection for GaN NWs. The black dashed line indicates the peak position of bulk GaN. The inset NW's diameter distribution was estimated using top-view image of scanning electron microscopy (SEM).

Mentions: Further, we calculated the XDP for a whole GaN nanowire ensemble taking into account the NW diameter distribution. We used the approach presented in [8], where the XDP of each NW is multiplied by D2 (where D is the NW's diameter) and the frequency of the corresponding nanowire diameter. Experimental and calculated (002) 2θ/ω XDPs of GaN NWs are shown in Figure 5. The simulated XDP (red line) is plotted along with the XDPs where either the ε///(z) or ε//(z) is taken into account individually (blue and green line, respectively). It is demonstrated that in order to achieve a good fitting of experimental 2θ/ω XDPs, both components of micro-deformation should be considered. Moreover, since no peak shift is observed, we conclude that the NWs are free of macro-deformation ε/, which well correlates with results obtained from RSM. The large asymmetry of the red XDP indicates significant ε//(z) tensile micro-deformation at the bottom of the GaN NWs. The calculation provides the value of deformation relaxation depth LR to be 1.4 times larger than the NW's diameter and the magnitude of ε//(z) of the order of 10−3, which are close to values obtained in [3,4,8]. Also, the fitting procedure gives the average NW's height z equal to 400 nm, which correlates well with values obtained from cross-sectional SEM image (not shown here). The average value of micro-deformation < ε///(z) > ~ 1.7 × 10− 4 is in good agreement with the values presented in [2,13] for GaN NWs grown also on Si(111). Thus, in comparison with standard WH analysis based on FWHM of 2θ/ω-scans (which gives the average value of VCL and micro-strain fluctuation), the calculation of the full XDP allows to evaluate the macro- and micro-deformation depth profiles and more accurate value of the NW's height.Figure 5


High-resolution X-ray diffraction analysis of strain distribution in GaN nanowires on Si(111) substrate.

Stanchu H, Kladko V, Kuchuk AV, Safriuk N, Belyaev A, Wierzbicka A, Sobanska M, Klosek K, Zytkiewicz ZR - Nanoscale Res Lett (2015)

Experimental and calculated 2θ/ω XDPs of the (002) reflection for GaN NWs. The black dashed line indicates the peak position of bulk GaN. The inset NW's diameter distribution was estimated using top-view image of scanning electron microscopy (SEM).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4385025&req=5

Fig5: Experimental and calculated 2θ/ω XDPs of the (002) reflection for GaN NWs. The black dashed line indicates the peak position of bulk GaN. The inset NW's diameter distribution was estimated using top-view image of scanning electron microscopy (SEM).
Mentions: Further, we calculated the XDP for a whole GaN nanowire ensemble taking into account the NW diameter distribution. We used the approach presented in [8], where the XDP of each NW is multiplied by D2 (where D is the NW's diameter) and the frequency of the corresponding nanowire diameter. Experimental and calculated (002) 2θ/ω XDPs of GaN NWs are shown in Figure 5. The simulated XDP (red line) is plotted along with the XDPs where either the ε///(z) or ε//(z) is taken into account individually (blue and green line, respectively). It is demonstrated that in order to achieve a good fitting of experimental 2θ/ω XDPs, both components of micro-deformation should be considered. Moreover, since no peak shift is observed, we conclude that the NWs are free of macro-deformation ε/, which well correlates with results obtained from RSM. The large asymmetry of the red XDP indicates significant ε//(z) tensile micro-deformation at the bottom of the GaN NWs. The calculation provides the value of deformation relaxation depth LR to be 1.4 times larger than the NW's diameter and the magnitude of ε//(z) of the order of 10−3, which are close to values obtained in [3,4,8]. Also, the fitting procedure gives the average NW's height z equal to 400 nm, which correlates well with values obtained from cross-sectional SEM image (not shown here). The average value of micro-deformation < ε///(z) > ~ 1.7 × 10− 4 is in good agreement with the values presented in [2,13] for GaN NWs grown also on Si(111). Thus, in comparison with standard WH analysis based on FWHM of 2θ/ω-scans (which gives the average value of VCL and micro-strain fluctuation), the calculation of the full XDP allows to evaluate the macro- and micro-deformation depth profiles and more accurate value of the NW's height.Figure 5

Bottom Line: The calculations are performed by using kinematical theory of X-ray diffraction and assuming the deformation decays exponentially from the NW/substrate interface.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.

View Article: PubMed Central - PubMed

Affiliation: V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Pr. Nauky 45, Kyiv, 03028 Ukraine.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus