Topic

# Direct and indirect band gaps

About: Direct and indirect band gaps is a research topic. Over the lifetime, 10940 publications have been published within this topic receiving 327355 citations.

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TL;DR: The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy and the effect of quantum confinement on the material's electronic structure is traced.

Abstract: The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 06 eV This leads to a crossover to a direct-gap material in the limit of the single monolayer Unlike the bulk material, the MoS₂ monolayer emits light strongly The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 10⁴ compared with the bulk material

12,822 citations

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TL;DR: This observation shows that quantum confinement in layered d-electron materials like MoS(2), a prototypical metal dichalcogenide, provides new opportunities for engineering the electronic structure of matter at the nanoscale.

Abstract: Novel physical phenomena can emerge in low-dimensional nanomaterials. Bulk MoS2, a prototypical metal dichalcogenide, is an indirect bandgap semiconductor with negligible photoluminescence. When the MoS2 crystal is thinned to monolayer, however, a strong photoluminescence emerges, indicating an indirect to direct bandgap transition in this d-electron system. This observation shows that quantum confinement in layered d-electron materials like MoS2 provides new opportunities for engineering the electronic structure of matter at the nanoscale.

7,886 citations

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TL;DR: In this article, the absolute energy positions of conduction and valence band edges were compiled for about 50 each semiconducting metal oxide and metal sulfide minerals, and the relationship between energy levels at mineral semiconductor-electrolyte interfaces and the activities of these minerals as a catalyst or photocatalyst in aqueous redox reactions were reviewed.

Abstract: The absolute energy positions of conduction and valence band edges were compiled for about 50 each semiconducting metal oxide and metal sulfide minerals. The relationships between energy levels at mineral semiconductor-electrolyte interfaces and the activities of these minerals as a catalyst or photocatalyst in aqueous redox reactions are reviewed. The compilation of band edge energies is based on experimental flatband potential data and complementary empirical calculations from electronegativities of constituent elements. Whereas most metal oxide semiconductors have valence band edges 1 to 3 eV below the H2O oxidation potential (relative to absolute vacuum scale), energies for conduction band edges are close to, or lower than, the H2O reduction potential. These oxide minerals are strong photo-oxidation catalysts in aqueous solutions, but are limited in their reducing power. Non-transition metal sulfides generally have higher conduction and valence band edge energies than metal oxides; therefore, valence band holes in non-transition metal sulfides are less oxidizing, but conduction band electrons are exceedingly reducing. Most transition-metal sulfides, however, are characterized by small band gaps (<1 eV) and band edges situated within or close to the H2O stability potentials. Hence, both the oxidizing power of the valence band holes and the reducing power of the conduction band electrons are lower than those of non-transition metal sulfides.

3,145 citations

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General Electric

^{1}TL;DR: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0 as mentioned in this paper.

Abstract: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0. The small band gap requires an accurate treatment of conduction and valence band interactions while higher bands are treated by perturbation theory. A highly nonparabolic conduction band is found. The valence band is quite similar to germanium. Energy terms linear in k which cannot exist in germanium are estimated and found to be small, though possibly of importance at liquid-helium temperature. An absolute calculation of the fundamental optical absorption is made using the cyclotron resonance mass for n-type InSb. The agreement with experimental data for the fundamental absorption and its dependence on n-type impurity concentration is quite good. This evidence supports the assumptions made concerning the band structure.

2,905 citations

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TL;DR: In this article, a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator is presented.

Abstract: We present a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator. The full dielectric matrix is used to evaluate the self-energy operator in the GW approximation: the first term in an expansion of the self-energy operator in terms of the dynamically screened Coulomb interaction (W) and the dressed Green's function (G). Quasiparticle energies are calculated for the homopolar materials diamond, Si, and Ge as well as for the ionic compound LiCl. The results are in excellent agreement with available experimental data. In particular, the indirect band gap is calculated as 5.5, 1.29, and 0.75 eV as compared with experimental gaps of 5.48, 1.17, and 0.744 eV for diamond, Si, and Ge, respectively. The Ge results include relativistic effects. The calculated direct gap for LiCl is within 5% of experiment. Viewed as a correction to the density-functional eigenvalues calculated with the local-density approximation, the present results show a correction dominated by a large jump at the gap. It is found that because of the charge inhomogeneity, the full dielectric screening matrix must be included, i.e., local-field effects are essential. The dynamical effects are also found to be crucial. The required dielectric matrices are obtained within the density-functional approach for the static case and extended to finite frequency with use of a generalized plasmon-pole model based on sum rules. The model reproduces the \ensuremath{\omega} and ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}1}$ moments of the exact many-body response function. The qualitative features of the electron self-energy operator are discussed. Using the static Coulomb-hole--screened-exchange approximation for illustration, the role of local fields in the self-energy operator are explained. The role of dynamical renormalization is illustrated. The same qualitative features are observed in both the homopolar and ionic materials.

2,717 citations