Direct bandgap transition

Fluorescence Ufetimes were very similar for both reduction approaches. In both cases, fluorescence decays (Figure 6.5) required a three-exponential fit with average lifetimes of 6 ns when reducing with IiAlH4 and 4.7 ns when with NaBH4. These short lifetimes reveal a rapid recombination associated with direct bandgap transitions in silicon nanocrystals. 

Hot PL band From yellow to blue 425-630 ps range 0.01 % Quantum confinement in Si nanocrystals direct bandgap transitions observed only under high excitation redshifi upon size reduetion (de Boer etal. 2010)... 

Recent developments such as fast phonon-less transitions from carbon-terminated nanocrystals (Dohnalova et al. 2013), fast direct bandgap transitions (Prokofiev et al. 2009 de Boer et al. 2010), and very high values of luminescence quantum efficiencies of silicon nanocrystals in layers (in porous silicon, 23 % (Gelloz et al. 2005 Gelloz and Koshida 2005), and in other assemblies, 18-100 % (Ledoux et al. 2000) and 60 % (Jurbergs et al. 2006)) show that the luminescence of nanocrystalline silicon is progressively paving its way toward applications. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

The optical properties of a-Si H are of considerable importance, especially for solar-cell applications. Because of the absence of long-range order, the momentum k is not conserved in electronic transitions. Therefore, in contrast to crystalline silicon, a-Si H behaves as though it had a direct bandgap. Its absorption coefficient for visible light is about an order of magnitude higher than that of c-Si [74]. Consequently, the typical thickness (sub-micrometer) of an a-Si H solar cell is only a fraction of that of a c-Si cell. 

In Ref. 54, XRD showed the deposit to be hexagonal CuSe. Analysis of the absorption spectrum gave a direct bandgap of 2.02 eV. As commonly seen for these compounds, there was still strong absorption at lower energies (e.g., at 1.9 eV, the absorption coefficient was >7 X 10" cm ), possibly due to an indirect transition but likely due, at least in part, to free-carrier absorption. From Hall measurements, the doping (acceptor) density was ca. 10 cm (heavily degenerate) and the mobility ca. 1 cm V sec The dependence of film thickness and deposition rate on the deposition parameters has been studied in a separate paper [62]. 

The n parameter equals 1 for direct bandgap semiconductors or 4 for indirect bandgap semiconductors in the case of allowed fundamental transitions [22], Other values of n, 2 or 3, are valid only for forbidden transitions. The proper transformation allows estimation of the bandgap energy, Eg, for both types of crystalline semiconductors. Figure 7.7 presents the procedure of Eg evaluation. 

Luminescence can be generated in a semiconductor electrode either, (a) by exciting an electron from the valence band to the conduction band by light absorption, or (b) via injection of minority carriers in an electrochemical process. In general, it has been observed with solid state devices that the luminescence originates from a radiative transition in the bulk. In the case of semiconductors with a direct bandgap, for example, GaAs, InP and CdS (see Appendix D), the luminescence corresponds mostly to a... 

Recent developments in solid state solutions of AlN/SiC/InN/GaN open up the possibility of a new generation of heterostructure devices based on SiC. Single crystal epitaxial layers of AlN/SiC/InN have been recently demonstrated by Dmitriev [4]. A whole range of solid state solutions has been grown. Recently Dmitriev et al [5] reported on an (AlNx-SiC,.x)-(AlNySiC,.y) p-n junction. Solid state solutions of AlN-SiC [6,7] are also expected to lead to direct gap ternary materials for UV and deep blue optoelectronics, including the development of visible lasers. The direct to indirect bandgap transition is predicted to occur at between 70 and 80 % of AIN in SiC. 

Here, is a constant and m depends on the nature of the optical transition m = Vi for a direct bandgap, and ni = 2 for an indirect gap. From (2.6), extrapolation of a plot of (ahv) vs. hv plot gives the indirect bandgap, while a plot of (ahv) vs. hv yields the direct bandgap of the material. Such a plot is called a Tauc plot [7] and is often encoimtered in the photoelectrochemistry and photocatalysis literature. 

Figure 2 shows the energy band diagram of a direct bandgap semiconductor where is lower in energy than Ex, and spontaneous emission of a photon is the most likely path for recombination. In Fig. 2, the F valley of the conduction band is directly above the holes where the momentum change in the transition is nearly zero. Electrons in the X valley of the conduction band have a different momentum and thus cannot directly recombine with... 

Prokofiev AA, Moskalenko AS, Yassievich IN, de Boer WDAM, Timmerman D, Zhang H, Buma WJ, Gregorkiewicz T (2009) Direct bandgap optical transitions in Si nanocrystals. JETP Lett 90 758-762... 

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