Analytical description of nanowires. I. Regular cross sections for zincblende and diamond structures

Semiconductor nanowires (NWires) experience stress and charge transfer from their environment and impurity atoms. In response, the environment of a NWire experiences a NWire stress response which may lead to propagated strain and a change in the shape and size of the NWire cross section. Here, geometric number series are deduced for zincblende- (zb-) and diamond-structured NWires of diameter d_Wire to obtain the numbers 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]) for six high-symmetry zb NWires with the low-index faceting that occurs frequently in both bottom-up and top-down approaches of NWire processing. Along with these primary parameters, the specific lengths of interface facets, the cross-sectional widths and heights and the cross-sectional areas are presented. The fundamental insights into NWire structures revealed here offer a universal gauge and thus could enable major advancements in data interpretation and understanding of all zb- and diamond-structure-based NWires. This statement is underpinned with results from the literature on cross-section images from III-V core-shell NWire growth and on Si NWires undergoing self-limiting oxidation and etching. The massive breakdown of impurity doping due to self-purification is shown to occur for both Si NWires and Si nanocrystals (NCs) for a ratio of N_bnd/N_Wire = N_bnd/N_NC = 1.94 ± 0.01 using published experimental data.