Supplemental Information
Elucidating the role of non-radiative processes in charge transfer of core-shell Si:SiO2
nanoparticles
Jeffery D. Mottishaw†, Dmitri Kilin†*, Hai-Ping Cheng‡, Valentin Karasev‡, Qi Hua Fan±,
Haoran Sun†*
† Department of Chemistry, University of South Dakota, Vermillion, SD 57069
*Dmitri.Kilin@usd.edu and *Haoran.Sun@usd.edu
‡ Quantum Theory Project, University of Florida, Gainesville, FL 32611
± Department of Electrical Engineering and Computer Science, South Dakota State University,
Brookings, SD 57007
Discussion of Relaxation Pathways
The physical meaning of the values listed in the table 1 includes a transition from the valence
band to the conduction band. When this excitation occurs, the electron-hole pair created can
either recombine and give off a photon (radiative recombination), or it can decay to a lower
energy level through thermal dissipation (non-radiative recombination). For an ideal solar cell,
suppressing both of these modes of recombination and having an asymmetry between electron
and hole relaxation is ideal so that the excitons only dissociate at the surface and the electrons
can then be utilized in an electric circuit. As mentioned above, Kohn-Sham orbitals are only
approximations of quasi-particles like excitons, and because of this, anything involving an
excited state will be under-bound inherently. However, by treating all of the orbitals and
transitions in the same manner, it is possible to make comparisons rather than to establish
“benchmark” results for electron and hole lifetimes. Our goal was to compare the pathways, and
Figure 6 does an excellent job of showing this.
Discussion of Challenges in Cooling Pathways.
For excitations of higher energy, the scenario of charge carrier cooling can be dramatic.
Specifically, there is no proof that decrement of average energy of a carrier will always have a
single exponential character, used in equations 14-18. A visual analysis of dynamics of charge
density distribution, shown in Fig. 6 and Fig. S1can serve as a qualitative test for validating
applicability of Eqs. 14-18. Present form of Fig. S1 illustrates trivial case with a purpose of
going from simple to complicated.
Discussion of Cooling Mechanism.
There are several factors responsible for the rate of carrier cooling. Specifically, the spatial
overlap of involved KS orbitals and spatial distribution of normal modes, a resonance condition
between electronic energy subgaps and normal mode frequencies – all affect the rate of cooling.
Discussion of Dephasing
Pure dephasing is important for the ultrashort time interval after the instantaneous
photoexcitation. Pure dephasing can be computed based on the autocorrelation function of
energies of Kohn-Sham orbitals, presented in Figure S2. Used method is able to address
dephasing, however this work focuses on depopulation process.
Discussion of Density of States and Partial Charge Density
It is possible that the bulk Si system studied in the DOS figure 2 does not have the quantum
confinement caused by being flanked by silica on the outside. This gives evidence that quantum
confinement is occurring in the model interface and is an important conclusion reached by the
manuscript. We have carefully inspected partial charge densities of the interface in a broad range
and can happily provide evidence that over 10 orbitals above LU and below HO are localized on
Si or have a nature of trap interfacial states. There are no bulk SiO2 states in this region. It is
known that SiO2 is a wide gap dielectric. Gap of SiO2 is several times wider than the gap of Si
(8.5eV vs. 1.12 eVs). Fermi energy undergoes modification upon bringing two materials in
contact. 1eV modification of Efermi is way less than the gap of SiO2 of 8.5 eVs.
Discussion of the Influence of Silica on Cooling Rates
Silicon dioxide provides (i) quantum confinement, (ii) interfacial states, and (iii) additional
rigidity. Due to presence of rigid dielectric, atomic motions of Silicon atoms in the
semiconductor part of the model have smaller amplitude of atomic motions in respect to thermal
motion of Si:H surface interfacing vacuum at the same conditions.
Figure S1. Electron and hole dynamics of low-energy initial excitations. (A) An initial excitation
HO-1LU+1 leads to the electron has a non-radiative electron relaxation rate of 6.4601
ps-1, and a hole relaxation rate of 0.1466 ps-1. This can be compared with (B) illustrating
initial excitation HO-3LU+3 leads to where the electron only relaxes at the rate of
0.4035 ps-1, and the hole relaxes at the rate of 1.1253 ps-1.
KSO energy, eV
5.5
5
4.5
4
3.5
3
0
50 100 150 200 250 300
time, fs
Figure S2. Energies of Kohn-Sham orbital as function of energy along microcanonical
trajectory. Orbitals with energies 4.8 eV and above correspond to CB. Orbitals with energies
below 4.2 eV and below correspond to VB. Fluctuation of each orbital shows amplitude of about
.1 eV and period of about 20fs. This corresponds to Si-O stretch characteristic motion of SiO2
modulates motion of semiconductor part of the model.