Genomic design of strong direct-gap optical transition in Si/Ge core/multishell nanowires

Finding a Si-based material with strong optical activity at the band-edge remains a challenge despite decades of research. The interest lies in combining optical and electronic functions on the same wafer, while retaining the extraordinary know-how developed for Si. However, Si is an indirect-gap material. The conservation of crystal momentum mandates that optical activity at the band-edge includes a phonon, on top of an electron-hole pair, and hence photon absorption and emission remain fairly unlikely events requiring optically rather thick samples. A promising avenue to convert Si-based materials to a strong light-absorber/emitter is to combine the effects on the band-structure of both nanostructuring and alloying. The number of possible configurations, however, shows a combinatorial explosion. Furthermore, whereas it is possible to readily identify the configurations that are formally direct in the momentum space (due to band-folding) yet do not have a dipole-allowed transition at threshold, the problem becomes not just calculation of band structure but also calculation of absorption strength. Using a combination of a genetic algorithm and a semiempirical pseudopotential Hamiltonian for describing the electronic structures, we have explored hundreds of thousands of possible coaxial core/multishell Si/Ge nanowires with the orientation of [001], [110], and [111], discovering some "magic sequences" of core followed by specific Si/Ge multishells, which can offer both a direct bandgap and a strong oscillator strength. The search has revealed a few simple design principles: (i) the Ge core is superior to the Si core in producing strong bandgap transition; (ii) [001] and [110] orientations have direct bandgap, whereas the [111] orientation does not; (iii) multishell nanowires can allow for greater optical activity by as much as an order of magnitude over plain nanowires; (iv) the main motif of the winning configurations giving direct allowed transitions involves rather thin Si shell embedded within wide Ge shells. We discuss the physical origin of the enhanced optical activity, as well as the effect of possible experimental structural imperfections on optical activity in our candidate core/multishell nanowires.