Hill and Whaley's 1995 two-particle tight-binding calculations quantitatively reproduced photoluminescence energies of hydrogen-passivated, ideal-surface silicon nanocrystals up to about 10 nm (100 Å) in diameter, but left open how nonideal surfaces — incomplete passivation, surface disorder, atomic reconstruction, and oxidation — modify exciton energies, exciton spatial distributions, optical absorption and emission spectra, and radiative efficiencies, and whether surface-related emission channels can dominate in poorly passivated samples. Later work substantially settled the qualitative picture: oxidizing species such as Si=O create states inside the band gap of small nanocrystals, and self-trapped excitons localized at Si–Si and Si–O surface motifs of the Si/SiO2 interface dominate emission in oxidized particles. What remains open is the general quantitative core of the original question: a predictive, atomistic, two-particle (or equivalent many-body) account connecting explicitly specified surface chemistry and morphology of realistic disordered nanocrystals across the experimentally relevant size range to exciton energies, distributions, spectra, and radiative efficiencies, including the crossover conditions at which surface channels override quantum-confined core-exciton recombination.

Background

When the diameter of a silicon (Si) crystallite approaches the exciton Bohr radius (about 4.9 nm in bulk Si), quantum confinement widens the band gap as the particle shrinks, so that nanocrystalline and porous silicon, which showed efficient visible and near-infrared photoluminescence in the early 1990s, were expected to emit at energies fixed mainly by crystallite size. An exciton is the bound electron–hole pair created by optical absorption; predicting its energy requires the quasiparticle gap of the confined structure minus the electron–hole Coulomb binding energy, and early single-particle band-structure calculations that estimated the Coulomb term perturbatively disagreed with measured photoluminescence by more than 1.5 eV for the smallest particles. In Hill and Whaley (1995), the authors performed two-particle calculations that include the electron–hole Coulomb interaction nonperturbatively: they propagated the two-particle wave function in time under a nearest-neighbor tight-binding Hamiltonian (a quantum-mechanical model in which electronic states are built from atomic orbitals on each Si site, with on-site energies and inter-site hopping parameters) using an expanded basis of five orbitals per Si atom, with on-site Coulomb integrals from Slater orbitals (analytic hydrogen-like orbital forms used to evaluate those integrals), intersite Coulomb terms from the Ohno interpolation formula (a standard semiempirical interpolation of the intersite electron–electron Coulomb integral between its on-site value and its long-range inverse-distance limit), and a distance-dependent dielectric screening. The nanocrystals modeled were hydrogen-passivated ideal-surface structures: hydrogen atoms terminate the surface dangling bonds (unsatisfied valences that would otherwise introduce states inside the gap), so that the calculated exciton energies could be compared directly with photoluminescence from size-selected, surface-passivated Si nanocrystals, with quantitative agreement up to about 10 nm (100 Å) diameter. The authors also found that, for these passivated structures, perturbative and nonperturbative treatments of the Coulomb interaction gave indistinguishable exciton energies, attributing the improvement over earlier work mainly to the more complete orbital basis. Immediately after publication, Delerue, Lannoo, and Allan commented on the screening and Coulomb treatment used, with a reply by the authors, which is the contemporaneous record of the quantitative debate over the screening model. The paper's own caveats concern the fact that experimentally realistic particles — porous silicon and nanocrystals with incompletely passivated, disordered, reconstructed, or oxidized surfaces — are not ideal hydrogen-terminated structures: how surface chemistry and morphology then alter the confinement trends, the exciton spatial distributions, the two-particle absorption and emission spectra, and the radiative efficiency was left unresolved, including whether emission from surface-related localized states becomes dominant in poorly passivated samples. Subsequent work introduced the key surface motifs involved: oxygen bridges and Si=O double bonds at the surface, which introduce electronic states inside the band gap of small nanocrystals; and self-trapped excitons, i.e. electron–hole pairs that localize at particular surface motifs (such as Si–Si dimers or Si–O configurations at the Si/SiO2 interface) by distorting the surrounding bonds, forming an emission channel distinct from recombination of the quantum-confined core exciton.

Problem Statement

Determine, by quantitative atomistic two-particle (excitonic) or equivalent many-body calculations validated against experiment, how nonideal surfaces of silicon nanocrystals — incomplete passivation leaving dangling bonds, surface disorder, atomic reconstruction, and oxidation (including partial oxide shells and Si–O surface species) — modify (i) exciton energies and the size-dependent quantum-confinement trends, (ii) exciton spatial (electron and hole charge) distributions, (iii) two-particle optical absorption and emission spectra, and (iv) radiative efficiencies together with the competing nonradiative channels, for nanocrystals in the experimentally relevant size range (from below ~1 nm up to roughly 10 nm diameter, including porous-silicon-type structures). The problem includes establishing the surface-chemistry and morphology conditions under which surface-related emission channels (localized gap states from oxidized species, and self-trapped excitons — electron–hole pairs localized at surface Si–Si or Si–O bonding motifs by distorting the surrounding lattice) dominate over quantum-confined core-exciton recombination, and whether the confinement trends established for hydrogen-passivated ideal-surface nanocrystals survive, and in what quantitative form, for realistically passivated, disordered, or oxidized samples. Quantitative agreement with experiment is required for the experimentally accessible observables — exciton energies, absorption and emission spectra, and radiative efficiencies — at the level of absolute values within the reported experimental uncertainty across the stated size range, together with reproduction of the measured size-dependent trends.

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