Communication: Biexciton generation rates in CdSe nanorods are length independent

Forces from Stochastic Density Functional Theory under Nonorthogonal Atom-Centered Basis Sets

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (fluctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and find that the systematic bias is of the order of 0.065 eV/Å (∼1.2 × 10-3Eh/a0) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is sufficiently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.

Electron-Hole Correlations Govern Auger Recombination in Nanostructures

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valence electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are two orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known "universal volume scaling law" for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

Efficient Carrier Multiplication in Colloidal Silicon Nanorods

Auger recombination lifetimes, absorption cross sections, and the quantum yields of carrier multiplication (CM), or multiexciton generation (MEG), were determined for solvent-dispersed silicon (Si) nanorods using transient absorption spectroscopy (TAS). Nanorods with an average diameter of 7.5 nm and aspect ratios of 6.1, 19.3, and 33.2 were examined. Colloidal Si nanocrystals of similar diameters were also studied for comparison. The nanocrystals and nanorods were passivated with organic ligands by hydrosilylation to prevent surface oxidation and limit the effects of surface trapping of photoexcited carriers. All samples used in the study exhibited relatively efficient photoluminescence. The Auger lifetimes increased with nanorod length, and the nanorods exhibited higher CM quantum yield and efficiency than the nanocrystals with a similar band gap energy E_g. Beyond a critical length, the CM quantum yield decreases. Nanorods with the aspect ratio of 19.3 had the highest CM quantum yield of 1.6 ± 0.2 at 2.9E_g, which corresponded to a multiexciton yield that was twice as high as observed for the spherical nanocrystals.

Theory of highly efficient multiexciton generation in type-II nanorods

Multiexciton generation, by which more than a single electron–hole pair is generated on optical excitation, is a promising paradigm for pushing the efficiency of solar cells beyond the Shockley–Queisser limit of 31%. Utilizing this paradigm, however, requires the onset energy of multiexciton generation to be close to twice the band gap energy and the efficiency to increase rapidly above this onset. This challenge remains unattainable even using confined nanocrystals, nanorods or nanowires. Here, we show how both goals can be achieved in a nanorod heterostructure with type-II band offsets. Using pseudopotential atomistic calculation on a model type-II semiconductor heterostructure we predict the optimal conditions for controlling multiexciton generation efficiencies at twice the band gap energy. For a finite band offset, this requires a sharp interface along with a reduction of the exciton cooling and may enable a route for breaking the Shockley–Queisser limit.

Multiple exciton generation could help limit thermalization losses in solar cells, but the efficiency of the process is still limited. Here, the authors show by atomistic calculations that type-II interfaces in nanostructures along with a change in exciton cooling rate favour multiple exciton generation.

Multiexciton Generation in Seeded Nanorods

The stochastic formulation of multiexciton generation (MEG) rates is extended to provide access to MEG efficiencies in nanostructures containing thousands of atoms. The formalism is applied to a series of CdSe/CdS seeded nanorod heterostructures with different core and shell dimensions. At energies above 3Eg (where Eg is the band gap), the MEG yield increases with decreasing core size, as expected for spherical nanocrystals. Surprisingly, this behavior is reversed for energies below this value, and is explained by the dependence of the density of states near the valence band edge, which increases with the core diameter. Our predictions indicate that the onset of MEG can be shifted to lower energies by manipulating the density of states in complex nanostructure geometries.