Analytical Description of Nanowires: Morphing Wurtzite Structure Cross Sections to Match Arbitrary Convex Shapes

Setting out from previous work, an analytic description of regular wurtzite- (w-) structure nanowires (NWires) is extended by introducing morphing terms to describe arbitrary convex cross sections featuring linear interfaces as encountered in experiment. Add-on terms to the existing number series of regular cross sections are provided with their respective running indices, yielding the required flexibility for cross section morphing. The main variables are the number of NWire atoms $N_{\mathrm{Wire}}$, bonds between NWire atoms $N_{\mathrm{bnd}}$ and interface bonds $N_{\mathrm{IF}}$ as a function of NWire size and shape, complemented by other basic geometric variables such as specific lengths of interface facets, as well as widths, heights, and total area of the cross section. Cross section morphing is demonstrated for the three high symmetry w-NWires with low-index faceting frequently occurring in NWire processing. The fundamental insights revealed here offer a universal gauge and thus enable major advancements in data interpretation and understanding of above-mentioned w-structure based NWires with arbitrary convex cross sections. As a corroborating example, a precise description of an irregular w-GaAs/w-Ge core/shell NWire cross section is given, whereby a radially changing lattice constant can be included.