Free-carrier Drude model

To describe the optical properties of the crystals over a wide temperature range and to derive the basic phenomenological parameters of the electronic transition, we fitted the R(co) and a(co) spectra using the Drude-Lorentz model. The Drude part describes the intraband transition of free carriers,... 

The simplest model of charge transport in delocalized bands is the Drude model, which assumes the carriers are free to move under the inhuence of an applied electric held, but subject to collisional damping forces. Note that the scattering centers are not the nuclei of the background material, but rather phonons (lattice vibrahons) or impurities. A statistical equahon for estimahng the mean drift velocity of the carriers in the direction of the electric held may be written as... 

However, the low frequency electrical response is not dominated by localized carriers for samples A-D near the IMT. Figure 15.22b shows e((o) for samples A-D. In addition to the dielectric response of localized electrons at 1 eV, a third zero crossing of s co) termed Wp is evident in the far-IR. For energies lower than Wp, s co) remains negative as expected for free carriers. If the carriers are free electrons, then their frequency response is described by the Drude model. At sufficiently high frequencies (t 1/w), the Drude dielectric function is given by... 

The early studied PAN-CSA [133] and PPy doped with perchlorate [165] both had ojc 100 S/cm, indicating that the carriers were reasonably localized. Therefore, the agreement of the optical properties with the localization-modified Drude model (with t 10 s) is expected. However, this model is unable to account for the free electron behavior observed in higher samples because Drude dispersion requires that fcpA 1. 

Metals are denoted as fi ee-electron metals if most of the electronic and optical properties are due to the conduction electrons alone. Examples are Al, Mg, and alkali metals. The dispersion of the optical constants of the fi ee-electron metals is described by the Drude model [72], which can be regarded as a special case of the Lorentz model (1.3.3°) when the restoring (bounding) force is equal to zero, and hence the resonance frequency of free carriers, a>o = -JWfm (here, m is electron mass), is also equal to zero, damping force y results... 

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... 

In eq. (5) the first term stands for the Drude free-carrier conductivity with plasma frequency 0>pD and scattering rate 1/r. The second term accounts for the additional contributions to the conductivity that are modeled with Lorentzian oscillators centered at frequency ft) with plasma frequency tOj, and damping yp. These additional contributions are assigned to two-magnon excitations, interband transitions, polarons and unpurity states. 

Although the overall low-frequenspectral response of all metallic conducting polymers, such as PANI-CSA, PPy-PF6, and PEDOT-PFg, can be attributed to free-carrier intraband excitations, their o like behavior below 0.2 eV [1160-1165]. The anomalous behavior of a(o)) and ei(oj) in the low energies (typically below 0.2-0.4 eV) can be attributed to disorder-induced localization, and can be analyzed in terms of the localization-modified Drude (LMD) model [1160-1165], This LMD model, originally proposed by Mott and co-workers [1125, 1156, 1157], has been modified by Lee et al. [1160] and successfully introduced into the analysis of optical spectra of metallic conducting polymers [1160-1165]. This model is a first-order correction of the Drude model in the regime of weak localization, as given by [1160]... 

One of the earliest models for charge transport in delocalized bands is the Drude model [12], which assumes the charge carriers as free to move under the influence of an applied electric field, but subject to damping forces due to collisions. This model is valid in semiconductors, where the density of carriers is much lower that the atomic density in metals, where the density of carriers is much higher, it leads to inconsistencies that were removed by taking quantum effects into account. 

Free-charge carriers in semiconductors form collective excitation modes, the so-called plasma mode (plasmon). The plasma modes will couple to the LO lattice modes and form the so-called coupled LO plasmon-phonon (LPP) modes. Depending on the strength of the coupling, the free carriers thereby influence the dielectric function. A possible contribution from free carriers to the dielectric functions is also accounted for by virtue of the classical Drude model [38] ... 

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