Inter-band transitions

Unlike metals, semiconductors and insulators have bound valence electrons. This aspect gives rise to inter band transitions. The objective of this and the next section is... 

Electro-absorption (EA) spectroscopy, where optical absorption is observed under the application of an electric field to the sample, is another method that can distinguish between localised and inter-band excitations. The electric field produces a Stark shift of allowed optical absorptions and renders forbidden transitions allowed by mixing the wavefunctions of the excited states. Excitons show a quadratic Stark (Kerr) effect with a spectral profile that is the first derivative of the absorption spectrum for localised (Frenkel) excitons and the second derivative for charge transfer excitons, i.e. 

The excitation of the surface plasmon effect also induces strongly enhanced fluorescence properties of gold nanoparticles due to the enhanconent in the radiative rate of the inter-band electronic transitions relative to that in bulk metals. Metal nanoparticles, especially gold nanorods exhibit enhanced two-photon luminescence (TPL) and multi-photon luminescoice (MPL) [7, 8]. Strongly-enhanced TPL has been observed from individual particles [9, 10] and particle solutions [11] under femtosecond NIR laser excitation. This observation raises the possibility of nonlinear optical imaging in the NIR region, where water and biomolecules have... 

Optical properties [84,85] of interest for catalytic applications are particularly those that reveal contributions of the inter-band transitions of k-electrons ... 

Illumination of a semiconductor electrode generates excited electrons in the conduction band and holes in the valence band. Some of them recombine with each other radiatively, resulting in emission of luminescence called photoluminescence (PL). The radiative recombination may occur directly between the conduction and valence bands (inter-band transition) or via certain impurity or defect levels within the band gap at which either electrons or holes, or both are trapped, as schematically illustrated in Fig. 5(a). Also,... 

The luminescence mainly originates from the inter-band transitions, which are divided into direct and indirect transitions according to the transition modes. If the electrons jump at the same point between the VBM (valence band maximum) and the CBM (conduction band minimum), this transition is direct. In contrast, there is indirect transition. The semiconductors silicon (Si) and gallium arsenide (GaAs) are typical examples as shown in Fig. 6.6. They have an indirect and direct band gap with the values 1.95 and 0.17 eV, respectively. When the crystal size becomes smaller, e.g., forming quantum dots, the Si becomes a better self-activated luminescence material. 

They have analyzed Rl-dispersion data in more than a hundred different solids and liquids and established that the parameter Ed, which is a measure of the strength of inter-band optical transitions, obeys a simple empirical rule... 

The dielectric components Cj and Sj now correspond exactly to the constants observed in photon spectroscopy, but electron loss may give very different emphasis from an optical absorption or reflection experiment. If Ej is low, the dominant bulk feature will be a bulk plasmon (e = 0) loss, which for a free electron gas (electron density n) occurs at energy cOp = y/4nn. On the other hand if Ej is reasonably large (> 2) and not varying rapidly with A ,Im(—1/e) reflects structure in Ej. One-electron transitions, e.g., of inter band-type will then be emphasised. This is exactly what occurs for core losses where at high AE, Ej 1, Ej is small and Im( —1/e) Ej. This implies that the atomistic analysis discussed in section 2.3 is perfectly consistent with the dielectric formulation. In some cases Ej and 2 vary together leading to... 

The electromagnetic theory is based on the assumption that electrons are allowed to move freely being excited by an external field. Contrary to that, the positively charged ion cores are immobile. Thus, it is clear from this precondition that metals with free electrons exhibit the strongest optical effects and are best suited to study the electronic properties of resonant particle plasmons. These metals have partially filled conduction bands but completely filled valence bands. Ideally free electron metals response is based on the conduction electrons whereas in reality most metals exhibit various inter-band transitions. 

Noble or semi-noble metals colloids from copper, silver or gold exhibit both free electron and inter-band transition behavior. As a clear consequence from the band model of molecular and cluster excitation the deterioration is depending on the frequency range. Ofien the IR and red part of the spectrum exhibits ideal behavior whereas at the interband level (higher energy) spectra a dominated by inter-band excitation and plasmons are quenched rapidly. For theoretical studies alkali metals are ideal, but due to their instability in an ambient environment, only noble metal clusters are applicable in air and under aqueous solvents. 

However, at high frequencies in real metals, inter-band transitions (not included in the Drude model) contribute to the imaginary part of e [co] resulting in absorptive losses. 

In noble or coinage metals (Cu, Ag, Au), the optical response does not reduce to the response of the free electron gas. Noble metals consist of atoms with completely filled 3d, 4d, and 5d shells and just a single electron in the 4s, 5s, and 6s bands, respectively this last electron in not completely free to move and the dielectric response is essentially influenced by optical transitions of electrons in deeper (e.g. core) levels. These inter-band excitations alter the dielectric function considerably. This contribution can be described using a full quantum mechanical treatment, which is introduced in the next section. 

Figure 1.5 presents the experimentally observed dielectric function, refractive index and reflectance of bulk solid silver. Deviations from the Drude model are evident. Inter-band transitions drastically alter the dielectric function, with absorption losses in the range 5 — 9 eV. 

Inter-band transitions can be considered as well, directly from Eq. (1.139) [5]. 

Theoretical and experimental studies reveal that the optical peaks of AGNRs might be utilized as tools to determine the nature of their edges (Barone et al. 2006 Pimenta et al. 2007). The first calculations of the optical spectrum of GNRs was presented by Barone et al. (2006) by means of DFT using the screened-exchange hybrid HSE functional. As expected from an inter-band transitions framework, first optical excitations present the corresponding oscillations as a function of the width. Second-order transitions also exhibit these oscillations, as shown in O Fig- 24-8. 

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