Ionization energy of donor and acceptor impurities in semiconductor nanowires: Importance of dielectric confinement

Calculations of the electronic states of donor and acceptor impurities in nanowires show that the ionization energy of the impurities is strongly enhanced with respect to the bulk, above all when the wires are embedded in a material with a low dielectric constant. In free-standing nanowires with diameter below $10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the ionization of the impurities at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is strongly reduced and heavy doping is necessary to obtain conductive systems. These results imply that the critical density for metal-nonmetal transitions is not the same as in the bulk. Experiments are proposed to test the predictions.