Excitons and excitonic fine structures in Si nanowires: Prediction of an electronic state crossover with diameter changes

Abstract

Si nanowires have attracted considerable attention as promising candidates for electronic, thermoelectric, photonic, and photovoltaic devices, yet there appears to be only limited understanding of the underlying electronic and excitonic structures on all pertinent energy scales. Using atomistic pseudopotential calculations of single-particle as well as many-body states, we have identified remarkable properties of Si nanowires in three energy scales: (i) In the ``high-energy'' $\ensuremath{\sim}$1-eV scale, we find an unusual electronic state crossover whereby the nature of the lowest unoccupied molecular orbital (LUMO) state changes its symmetry with wire diameters for [001]-oriented wires but not for [011]-oriented wires. This change leads to orbitally allowed transitions becoming orbitally forbidden below a certain critical diameter for [001] wires. (ii) In the ``intermediate-energy'' $\ensuremath{\sim}$10${}^{\ensuremath{-}1}$-eV scale, we describe the excitonic binding, finding that in [001] wires the diameter ($D$) dependence of excitonic gap scales as $1/{D}^{1.9}$, not as $1/{D}^{1}$ as expected. The exciton binding energy increases from 52 meV at $D=7.6$ nm to 85 meV at $D=3.3$ nm and 128 meV at $D=2.2$ nm. (iii) In the ``low-energy'' $\ensuremath{\sim}$10${}^{\ensuremath{-}3}$-eV scale, we describe dark/bright excitonic states and predict how orbitally allowed transitions [in scale (i)] become spin-forbidden due to the electron-hole exchange interaction, whereas the spin-allowed states in the orbitally forbidden diameter region remain dark. The diameter dependence of the fine-structure splitting of excitonic states scales as $1/{D}^{2.3}$ in [001] wires and as $1/{D}^{2.6}$ in [011] wires. Surface-polarization effects are found to significantly enhance electron-hole Coulomb interaction, but have a small effect on the exchange fine-structure splitting. The present work provides a road map for a variety of electronic and optical effects in Si nanowires that can guide spectroscopic studies.