Giant excitonic exchange splitting in Si nanowires: First-principles calculations

The size and doping dependence of the electron-hole exchange interaction in Si nanowires is investigated from first principles. In pure Si nanowires we found excitonic exchange splittings in very good agreement with the experimental results for porous silicon. For $n$-doped Si nanowires a giant singlet-triplet splitting, three order of magnitude bigger than in bulk silicon, is predicted as due to the dramatic enhancement of the electron and the hole probability of being in the same place at the same time.

Figure 1

(Color online) Experimental ${\Delta }^{S-T}$ for PSi (Refs. 9, 12), as a function of the gap. Vertical and diagonal crosses: theoretical ${\Delta }^{S-T}$ for [100] and [110] Si-NWs, respectively. The dashed line is the fit of the experimental data, assuming an inverse power scaling behavior.

Figure 2

(Color online) Optical absorption spectra for light polarized along the NW axis, obtained including the e-h interaction. Black curve (top): for a pure, H-terminated, Si-NW oriented along the [110] direction and with $d=1.1\text{nm}$. Cyan curve(light gray; second from top): for the same Si-NW but doped with $P$ impurities and with the presence of surface dangling bonds. Red dashed curve (gray, second from bottom): as before but for $B$ impurities. Blue dot-dashed curve (bottom): for the same Si-NW but doped with both $P$ and $B$ impurities. The black arrows indicate the position of the lowest energy excitons.

Figure 3

(Color online) Geometrical structure of $d=1.1\text{nm}$ Si [110] wires with the same order from top to bottom of Fig. 2 Yellow/light grey spheres represent Si atoms, black (magenta/grey) spheres P (B) impurities, white spheres H atoms used to saturate the dangling bonds. The violet/grey isosurface gives the probability distribution ${\left|{\psi }_{exc}\left(r_e,r_h\right)\right|}^2$ for finding the electron when the hole is in a given position, indicated by the black crosses and by the dashed line. This position has been chosen in each case near the maximum of the charge distribution of the highest occupied state.