Introduction Sp3-hybridized semiconductors (including InP, GaAs, CdSe, and Si) are remarkable from the perspective of physical chemistry. A single electron created by HOMOLUMO promotion moves rapidly in response to an applied electric field, because there is little lattice distortion (i.e., small Franck-Condon factors) accompanying its creation. According to Marcus-Hush electron transfer theory, electron motion is resonant in the limit of vanishing reorganization energy. Franck-Condon factors are also small around an electron-hole pair, which is an electronically excited state. As a consequence, radiationless internal conversion (unimolecular decay converting electronic energy into heat) is extremely slow. Excited states decay radiatively in a defect-free, direct gap semiconductor such as CdSe. These simple spectroscopic facts have important practical consequences. Semiconductor lightemitting diodes have narrow emission bands and can show near 30% efficiency in converting electrical power into light. Semiconductor lasers and diodes also show excellent long-term stability against photochemical and current-induced degradation, when compared with many organic materials. All these properties reflect the strong chemical bonding, and the extremely delocalized nature of the electronic wave functions. Semiconductor nanocrystals lie between the traditional regimes of chemistry and solid-state physics.1 Nanocrystal research was initially motivated by an effort to understand the evolution of bulk structural and electronic properties from the molecular scale.2 Presently, technological interest in nanocrystals stems from the prospect of creating novel materials with distinct physical properties. Nanocrystals act like molecules as they interact with light via their electronic transition dipoles. Yet, their delocalized solid-state parentage causes them to display unusual photophysics relative to molecules. In many molecules vibronic interaction in the excited state is strong as the wave function is localized on just one or a few bonds. The molecular excited state has a different structure which promotes fast nonradiative deactivation into the ground state. Emission quantum yields can be low, and often sensitive to quenching by the local environment. The situation is different in nanocrystals. In a 23 A diameter nanocrystal, for example, the wave function is delocalized over ∼100 unit cells with little probability density at the surface. This suggests that, in the absence of defects, internal or surface, a nanocrystal should exhibit near unity fluorescence quantum yield, and partial protection from quenching. The emission spectrum should be sharp as the Franck-Condon factors are small. At room temperature nanocrystals can be better photoemitters than bulk semiconductors because in nanocrystals the electron and hole remain superimposed due to quantum confinement. Nanocrystals have the potential to serve as ideal chromophores if their surface chemistry can be understood and controlled. In this Account we describe nanocrystal photophysics and make comparisons between inorganic solid-state materials and organic dye molecules.

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Luminescence Photophysics in Semiconductor Nanocrystals

This Review summarizes advances in understanding the unique physical properties of hybrid perovskites that enable the fabrication of high-efficiency solar cells with high open-circuit voltages, which is crucial for their further development towards commercialization.

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Understanding the physical properties of hybrid perovskites for photovoltaic applications

An inconsistency between commonly used values of the silicon intrinsic carrier concentration, the effective densities of states in the conduction and valence bands, and the silicon band gap is resolved by critically assessing the relevant literature. As a result of this assessment, experimentally based values for the valence‐band ‘‘densities‐of‐states’’ effective mass are determined in the 300–500 K range and are shown to be in good agreement with recent theoretical calculations. At 300 K, experimentally based values of 3.1×1019 cm−3 for the valence‐band effective densities of states and 1.08×1010 cm−3 for the intrinsic carrier concentration are determined. Although in good agreement with theoretical calculations, these are significantly higher and lower, respectively, than commonly used values in the past. These results have important implications in the calculation of other silicon material and device parameters.

Intrinsic concentration, effective densities of states, and effective mass in silicon

The band‐gap energy Eg of silicon has been reevaluated with high precision between 2 and 300 K by the following method: the derivative of the absorption coefficient, resulting from free‐exciton absorption, has a well‐defined singularity, which can be detected unambiguously by wavelength‐modulation spectroscopy. The energy of this singularity yields the band gap. Our data deviated by more than 5 meV from the earlier results of MacFarlane et al. and Haynes et al. and fell between their Eg(T) curves. The approximation of Eg(T) = A + BT + CT2 gives A = 1.170 eV, B = 1.059×10−5 eV/K, and C = −6.05×10−7 eV/K2, for 0<T≤190 K, and A = 1.1785 eV, B = −9.025×10−5 eV/K, and C = −3.05×10−7 eV/K2, for 150≤T≤300 K, which fits our data within 0.2 meV. The major uncertainty of about 1 meV lies in the energies of exciton and TO phonon.

Temperature dependence of the band gap of silicon

The optical properties of luminescence centres in silicon

Measurements of the wavelength derivative of the indirect absorption edge in Si show features associated with the creation of free excitons in states $n=1 \mathrm{and} 2$ as well as in the exciton continuum. The spectrum shows no valley-orbit splitting of the excitons, contrary to previous suggestions, and it is shown theoretically that such splitting of free excitons cannot exist. It is found also that previous determinations of the energies of higher exciton states ($ng1$) were in error. Finally, LO phonon participation has been identified for the first time in the indirect edge of Si.

K. L. Shaklee

Papers

Valley-Orbit Splitting of Free Excitons? The Absorption Edge of Si