Analytic description of nanowires II: morphing of regular cross sections for zincblende- and diamond-structures to match arbitrary shapes

Setting out from our recent publication [König & Smith (2021 ▸). Acta Cryst. B77, 861], we extend our analytic description of the regular cross sections of zincblende- and diamond-structure nanowires (NWires) by introducing cross section morphing to arbitrary convex shapes featuring linear interfaces as encountered in experiment. To this end, we provide add-on terms to the existing number series with their respective running indices for zinc-blende- (zb-) and diamond-structure NWire cross sections. Such add-on terms to all variables yield the required flexibility for cross section morphing, with main variables presented by the number of NWire atoms N (Wire)(d (Wire)[i]), bonds between NWire atoms N (bnd)(d (Wire)[i]) and interface bonds N (IF)(d (Wire)[i]). Other basic geometric variables, such as the specific length of interface facets, as well as widths, heights and total area of the cross section, are given as well. The cross sections refer to the six high-symmetry zb NWires with low-index faceting frequently occurring in the bottom-up and top-down approaches of NWire processing. The fundamental insights into NWire structures revealed here offer a universal gauge and thus enable major advancements in data interpretation and the understanding of all zb- and diamond-structure-based NWires with arbitrary convex cross sections. We corroborate this statement with an exact description of irregular Si NWire cross sections and irregular InGaAs/GaAs core-shell NWire cross sections, where a radially changing unit-cell parameter can be included.