Statistical Analysis of the Shape of One-Dimensional Nanostructures: Determining the Coalescence Degree of Spontaneously Formed GaN Nanowires

Single GaN nanowires formed spontaneously on a given substrate represent nanoscopic single crystals free of any extended defects. However, due to the high area density of thus formed GaN nanowire ensembles, individual nanowires coalesce with others in their immediate vicinity. This coalescence process may introduce strain and structural defects, foiling the idea of defect-free material due to the nanowire geometry. To investigate the consequences of this process, a quantitative measure of the coalescence of nanowire ensembles is required. We derive objective criteria to determine the coalescence degree of GaN nanowire ensembles. These criteria are based on the area–perimeter relationship of the cross-sectional shapes observed and in particular on their circularity. Employing these criteria, we distinguish single nanowires from coalesced aggregates in an ensemble, determine the diameter distribution of both, and finally analyze the coalescence degree of nanowire ensembles with increasing fill factor.

[1]  J. Klein-Wiele,et al.  Ga-polar GaN nanocolumn arrays with semipolar faceted tips , 2013 .

[2]  Kevin A. Grossklaus,et al.  Misorientation defects in coalesced self-catalyzed GaN nanowires , 2013 .

[3]  V. Consonni,et al.  Effects of nanowire coalescence on their structural and optical properties on a local scale , 2009 .

[4]  L. Geelhaar,et al.  Different growth rates for catalyst-induced and self-induced GaN nanowires , 2010 .

[5]  J. Neugebauer,et al.  Large anisotropic adatom kinetics on nonpolar GaN surfaces: Consequences for surface morphologies and nanowire growth , 2009 .

[6]  Igor Levin,et al.  Catalyst-free growth of GaN nanowires , 2006 .

[7]  A. Di Carlo,et al.  Strain evolution in GaN nanowires: From free-surface objects to coalesced templates , 2013, 1305.7115.

[8]  L. Schmidt‐Mende,et al.  ZnO - nanostructures, defects, and devices , 2007 .

[9]  O. Brandt,et al.  Spontaneous nucleation and growth of GaN nanowires: the fundamental role of crystal polarity. , 2012, Nano letters.

[10]  O. Brandt,et al.  Sub-meV linewidth of excitonic luminescence in single GaN nanowires: Direct evidence for surface excitons , 2010 .

[11]  S. Kret,et al.  Influence of substrate nitridation temperature on epitaxial alignment of GaN nanowires to Si(111) substrate , 2013, Nanotechnology.

[12]  K. Sabelfeld,et al.  Self-regulated radius of spontaneously formed GaN nanowires in molecular beam epitaxy. , 2013, Nano letters.

[13]  Morphology and optical properties of Mg doped GaN nanowires in dependence of growth temperature , 2010 .

[14]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[15]  Bruce M. Clemens,et al.  Crystallite coalescence: A mechanism for intrinsic tensile stresses in thin films , 1999 .

[16]  L. Largeau,et al.  Facet and in-plane crystallographic orientations of GaN nanowires grown on Si(111) , 2008, Nanotechnology.

[17]  H. Renevier,et al.  Polarity of GaN nanowires grown by plasma-assisted molecular beam epitaxy on Si(111) , 2011 .

[18]  Takashi Fukui,et al.  Control of InAs nanowire growth directions on Si. , 2008, Nano letters.

[19]  V. Consonni,et al.  Nucleation and coalescence effects on the density of self-induced GaN nanowires grown by molecular beam epitaxy , 2011 .

[20]  A. Waag,et al.  GaN based nanorods for solid state lighting , 2012 .

[21]  K. Bertness,et al.  Mechanism for spontaneous growth of GaN nanowires with molecular beam epitaxy , 2008 .

[22]  M. Hanke,et al.  Nucleation mechanisms of self-induced GaN nanowires grown on an amorphous interlayer , 2011 .

[23]  H. Lüth,et al.  Interface and wetting layer effect on the catalyst-free nucleation and growth of GaN nanowires. , 2008, Small.

[24]  O. Brandt,et al.  Inhomogeneous strain in GaN nanowires determined from x-ray diffraction peak profiles , 2012 .

[25]  O. Brandt,et al.  Raman spectroscopy as a probe for the coupling of light into ensembles of sub-wavelength-sized nanowires , 2012 .

[26]  Guy Feuillet,et al.  MOCVD growth mechanisms of ZnO nanorods , 2010, 1106.4291.

[27]  H. Im,et al.  Optical properties of GaN nanorods grown by molecular-beam epitaxy; dependence on growth time , 2006, Nanotechnology.

[28]  O. Brandt,et al.  Macro- and micro-strain in GaN nanowires on Si(111) , 2011, Nanotechnology.

[29]  V. Bright,et al.  Effect of AlN buffer layer properties on the morphology and polarity of GaN nanowires grown by molecular beam epitaxy , 2011 .

[30]  O. Brandt,et al.  Time-resolved photoluminescence spectroscopy of individual GaN nanowires , 2012 .

[31]  Kevin W Eliceiri,et al.  NIH Image to ImageJ: 25 years of image analysis , 2012, Nature Methods.

[32]  Oliver Brandt,et al.  Statistical analysis of excitonic transitions in single, free-standing GaN nanowires: Probing impurity incorporation in the poissonian limit , 2010 .

[33]  Jonathan J. Wierer,et al.  Spatial mapping of efficiency of GaN/InGaN nanowire array solar cells using scanning photocurrent microscopy. , 2013, Nano letters.

[34]  Richard L. Church,et al.  UC Office of the President Recent Work Title An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems Permalink , 2013 .

[35]  J. Grandal,et al.  A growth diagram for plasma-assisted molecular beam epitaxy of GaN nanocolumns on Si(111) , 2009, 2401.16328.

[36]  James S. Speck,et al.  Quasi-equilibrium crystal shapes and kinetic Wulff plots for gallium nitride grown by hydride vapor phase epitaxy , 2013 .

[37]  H. Lüth,et al.  Nucleation and growth of GaN nanowires on Si(111) performed by molecular beam epitaxy. , 2007, Nano letters.

[38]  S. Reitzenstein,et al.  Properties of GaN Nanowires Grown by Molecular Beam Epitaxy , 2011, IEEE Journal of Selected Topics in Quantum Electronics.

[39]  J. Devreese,et al.  Coexistence of the Meissner and Vortex States on a Nanoscale Superconducting Spherical Shell , 2009, 0903.2800.

[40]  R. Voss,et al.  Fractal (Scaling) Clusters in Thin Gold Films near the Percolation Threshold , 1982 .

[41]  J. Ristić,et al.  Wurtzite GaN nanocolumns grown on Si(001) by molecular beam epitaxy , 2006 .

[42]  R. Beresford,et al.  The effect of the III/V ratio and substrate temperature on the morphology and properties of GaN- and AlN-layers grown by molecular beam epitaxy on Si(1 1 1) , 1998 .

[43]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .