Drude absorption

The first investigation of the phonon modes in binary InN was an extrapolation of the Gai-xInxN (0 < x < 1) alloy modes in reflection towards the binary compound [1], A typically high free carrier concentration in the mid 1020 cm 3 range controls the absorption (Drude absorption) in the infrared and must also account for the broadened Reststrahlen band in pure InN films (e.g. in [1]). In this case infrared active phonons couple to the plasma of the free electrons forming phonon-plasmon coupled modes [10,11], However, layers of low carrier concentration have been achieved and pure LO phonon energies have been derived in Raman spectroscopy. Resonant Raman spectroscopy at 514 nm has been performed, assigning five of the six Raman allowed zone centre phonon modes [8,9] (TABLE 1). 

The determination of the space-charge capacitance from free-carrier IR absorption is free from interference with the interface-state capacitance, which plagues the use of common capacitance measurements. The method in this respect is equivalent to what can be obtained from microwave reflectivity measurements (Drude absorption is nothing but ac Joule dissipation at an IR frequency). 

As a rule, the experimental (Section 3.2) frequency dependence of the free-carrier absorption (or the Drude absorption) disagrees with the law predicted by the Drude model [Eq. (1.43a)]. The actual dependence of the decay constant a follows the co p law [40, 42, 46], where is a constant over the range < p < A. The constant p depends on the semiconductor, the frequency range, the temperature, and the concentration of impurities and free carriers. The quantum-mechanical extension of the Drude theory [73] shows that... 

As discussed in Section 3.7, a smooth background that increases at lower wavenumbers is characteristic of free-carrier absorption, also termed Drude absorption (DA) (Figs. 3.44 and 3.47). The potential dependence of DA for the silicon-fluoride electrolyte interface is shown in Fig. 7.31. Free-carrier absorption is negligible at negative potentials, at which the silicon electrode is depleted. Since DA obeys the Schottky-Mott law (inset in Fig. 7.31), the flat-band potential was found to be - -0.4 V. Weak absorption by flee carriers... 

VeOi3, we observe a continuous decrease of the electrical conductivity, which is also recorded in the far-infrared spectrum by the disappearance of the Drude absorption [137]. 

My interest at that time revolved around evaluating optical rotary dispersion data [12]. The paired values of optical rotation vs. wavelength were used to fit a function called the Drude equation (later modified to the Moffitt equation for William Moffitt [Harvard University] who developed the theory) [13]. The coefficients of the evaluated equation were shown to be related to a significant ultraviolet absorption band of a protein and to the amount of alpha-helix conformation existing in the solution of it. 

By a careful inspection of Figure 4.17, we see how further transitions between bands below and above the Fermi level can also occur at energies higher than 1.5 eV. However, as these bands are not parallel, the density of states at these energies is lower than at 1.5 eV. In any case, the absorption probability is still significant, and it acconnts for the experimentally observed redaction in the reflectivity of Al in respect to the predictions from the Drude model (see Figure 4.5). 

We showed in the preceding section that for solids with strong vibrational bands the position of features in absorption spectra can be shifted appreciably in going from the bulk to particulate states. Metallic particles can deviate even more markedly from the behavior of the bulk parent material they can have absorption features over broad frequency regions where none appear in the bulk. For a simple metal—one that is well described by the Drude formula... 

The dielectric function of a metal can be decomposed into a free-electron term and an interband, or bound-electron term, as was done for silver in Fig. 9.12. This separation of terms is important in the mean free path limitation because only the free-electron term is modified. For metals such as gold and copper there is a large interband contribution near the Frohlich mode frequency, but for metals such as silver and aluminum the free-electron term dominates. A good discussion of the mean free path limitation has been given by Kreibig (1974), who applied his results to interpreting absorption by small silver particles. The basic idea is simple the damping constant in the Drude theory, which is the inverse of the collision time for conduction electrons, is increased because of additional collisions with the boundary of the particle. Under the assumption that the electrons are diffusely reflected at the boundary, y can be written... 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

Figure 12.6 Calculated absorption spectra of aluminum spheres, randomly oriented ellipsoids (geometrical factors 0.01, 0.3, and 0.69), and a continuous distribution of ellipsoidal shapes (CDE). Below this is the real part of the Drude dielectric function.

Extinction calculations for aluminum spheres and a continuous distribution of ellipsoids (CDE) are compared in Fig. 12.6 the dielectric function was approximated by the Drude formula. The sum rule (12.32) implies that integrated absorption by an aluminum particle in air is nearly independent of its shape a change of shape merely shifts the resonance to another frequency between 0 and 15 eV, the region over which e for aluminum is negative. Thus, a distribution of shapes causes the surface plasmon band to be broadened, the... 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

At a farther distance from the absorption region, the rotation of the molecular system is expressed as a sum of the one-term Drude formula ... 

We investigated the ultrafast dynamics in a Na-NaBr melt at 1073 K by fs pump probe absorption spectroscopy. A simple model was used to simulate the dynamics of polaron-, bipolaron- and Drude-type electrons. The relaxation times for polarons and bipolarons are 210 fs and 3 ps, respectively. The existence of an isosbestic point at 1.35 eV indicates an inter-conversion between bipolarons and Drude-type electrons. 

Within the pulse duration, polarons and bipolarons dissociate into Drude-type electrons and the subsequent bleach recovery at various probe wavelengths indicates the reformation of those species. On the other hand, the equilibrated absorption spectrum of Drude-type electrons is substantially red-shifted [7] compared to the F-centre absorption band. According to our mechanism polarons and bipolarons form Drude-type electrons after ultrafast excitation which leads to an increase of the transient absorption in the NIR region. 

Fig. 11.6 Absorption spectra K restored from diffuse reflection R by using the Kubelka-Munk equation. Spectra 1, 2, and 3 are initial nanostructures, hydrogenated and annealed at 700°C during 6 h, respectively, (a) Spectra of NFs, (b) SWNTs. Dashed curves are Drude approximation of the absorption spectra, K = A. v0 5...

Fig. 11.7 Optical density spectra of thin films of the initial, hydrogenated and outgassed SWNTs (spectra 1, 2 and 3, respectively). The dashed curves in the low-energy part of the spectra represent the Drude approximation of the absorption spectra. The inset in Fig. 11.7 shows the absorption lines of the C-H bonds in a thin film of the hydrogenated SWNTs...

Hamada et al. 1992 Saito et al. 1992), this increase of absorption is caused by high-frequency conductivity of the free carriers in metallic nanotubes. Relative intensities of the spectra of Fig. 11.7 we have found as a result of the diffuse reflection measurements of powders at low wavenumbers. The discussed above Drude approximations of the low-energy part of the absorption spectra are shown by dashed curves in Fig. 11.7. Comparison of the spectra 1 and 2 shows that hydrogenation decreases high-frequency conductivity of the SWNTs by one order of magnitude. 

Drude first proposed that the rotatory power of a dissymmetric substance could be understood if its absorption of light involved the motion of a charged particle along a helical path within the molecule [8]. This type of motion would result in the simultaneous production of an electric dipole from the translatory motion and a magnetic dipole from the rotatory motion. The model requires that the electric and dipole moments have at least some components which are collinear with each other, or else stereospecific interaction with circularly polarized light would not be possible. 

The first major absorption bands of alkyl halides lie in the vacuum ultraviolet (Table 6), outside the range of ordinary ORD and CD instruments. Measurements in the longer-wavelength regions of transparency often give rotations ([M] ) following a single-term Drude expression (equation 8),... 

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