Designing small silicon quantum dots with low reorganization energy

A first-principles, excited-state analysis is carried out to identify ways of producing silicon quantum dots with low excitonic reorganization energy. These focus on the general strategy of either reducing or constraining exciton-phonon coupling, and four approaches are explored. The results can be implemented in quantum dot solids to mitigate polaronic effects and increase the lifetime of coherent excitonic superpositions. It is demonstrated that such designs can also be used to alter the shape of the spectral density for reorganization so as to reduce the rates of both decoherence and dissipation. The results suggest that it may be possible to design quantum dot solids that support partially coherent exciton transport.

Figure 1

Reorganization following QD excitation for ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$. Ground-state structure (left) relaxes into a new structure (right) when promoted into one of its degenerate first excited singlet states. As a result, the dot contracts along the vertical axis. The displacement is magnified five times in order to make this distortion clear.

Figure 2

(Left) Vertical excitation to an excited-state manifold, due to photon absorption, is followed by reorganization of the nuclei. The overall displacement can be spectrally resolved into that of individual phonon mode amplitudes, $q_{\xi }$. The excited-state manifold is assumed to be a displaced version of its ground-state counterpart. (Right) Excited-state surfaces depend on spin state as depicted for the pair of orbitals comprising an exciton.

Figure 3

Schematic of optimized shape of spectral density, $\mathcal{J}$, in which there exists a small slope for low-energy vibrations and small reorganization energies for vibrational modes in the vicinity of the dot-to-dot electronic coupling, $J$. Along with a low reorganization energy $\lambda$, high electronic coupling $J$, spectral densities with this character will lead to longer lifetimes for excitonic superpositions.

Figure 4

The reorganization energy of H-terminated SiQDs changing with number of Si atoms.

Figure 5

The linear dependence of reorganization energy on the inverse of the number of Si atoms per quantum dot, $N_{Si}$. An equivalent relation is also given in terms of the dot diameter, $D$, measured in nm using the bulk diamond Si volume per atom of 0.02 ${\text{nm}}^3$.

Figure 6

(a) HOMO distribution of H-terminated ${\mathrm{Si}}_{78}$. (b) HOMO distribution of Cl-terminated ${\mathrm{Si}}_{78}$.

Figure 7

(a) ${\mathrm{Si}}_{78}{\mathrm{H}}_{64}$ and (b) the same quantum dot after surface restructuring produces six ${\mathrm{H}}_2$ molecules leaving ${\mathrm{Si}}_{78}{\mathrm{H}}_{52}$.

Figure 8

The reorganization trend as ${\mathrm{Si}}_{35}$ becomes more rigid. The blue dots corresponds to H-terminated ${\mathrm{Si}}_{35}$; the green dot corresponds to ${\mathrm{Si}}_{35}$ within one oxidized Si shell; the red dot corresponds to H-terminated ${\mathrm{Si}}_{35}$ with H fixed to mimic ${\mathrm{Si}}_{35}$ within an infinite large matrix.

Figure 9

Plots of excitonic reorganization energy versus SiQD diameter for: standard H termination (red); surface reconstructed dots with lower H content (green); and electron-withdrawing Cl termination (blue). The connecting lines are a guide to the eye.

Figure 10

Spectral density of ${\mathrm{Si}}_{78}{\mathrm{H}}_{64}$ (red) compared with that of its surface-restructured counterpart, ${\mathrm{Si}}_{78}{\mathrm{H}}_{52}$ (green). Vertical lines indicate non-negligible contributions to the reorganization energy and have been normalized to the peak value of the fitted spectral density.