Free carrier plasma frequency

Infrared active modes couple to the free carrier plasma and the energy of the coupled phonon-plasmon mode is sensitive to the electron density [3,20-22], In the range 1 x 1017 cm 3 < n < 1019 cm 3 the following approximation can be used for the free electron density as a function of the Ai(LO) mode frequency vmax [21] ... 

Fig. VI-4 shows R(to) for samples (A-F) as measured at room temperature. For the most metallic sample (A), R(w) exhibits distinct metal-like signatures a free carrier plasma resonance as indicated by the minimum in R(w) around 1.5 x 10 cm and high R(a)) in the far-IR (R 90% for (o<20 cm ). As PPy-PF goes from the metallic to the insulating regime via the critical regime (Samples A"F), R(w) is gradually suppressed in the IR. In the insulating regime (F), R(o)) remains well below that of the metallic sample (A) throughout the IR (R = 65% at w = 50 cm ). Note that the R(t>)) spectra are in excellent correspondence with the transport results (this is especially clear at low frequencies in Fig.VI-4b) the...

In a heavily N-doped 6H sample (6xlOl9cm 3) Klein et al [34] observed an asymmetric broadening and a shift of the A,(LO) phonon which were attributed to the overdamped coupling between LO phonon and plasmon modes [35]. The interaction between these two excitations occurs via their macroscopic electric fields when the frequency of oscillation of a free-carrier plasma is close to that of the LO phonon. The dependence of the LO phonon-overdamped plasmon coupled modes on carrier concentration was reported by Yugami et al [36] in 3C-SiC films, where the carrier concentrations varied from 6.9 x 1016 to 2xl0,scm 3. They verified that the carrier concentrations obtained from RS were in fairly good agreement with the Hall measurement values, and that the Faust-Henry coefficient [35] for the 3C-SiC (C = + 0.35) was close to the value reported for 6H-SiC (C = + 0.39) [34]. 

FIGURE 15.25 Temperature dependence of the free carrier dielectric response for metallic PAN-CSA sample A. (a) Far-IR e(o)) plotted against 1 as a function of temperature, (b) Comparison of the temperature dependence of the free electron plasma frequency fip and o-dc- (From Kohlman, R.S. and Epstein, A.J., Handbook of conducting polymers, 2nd ed., eds. Skotheim, T.A., Elsenbaumer, R.L., and Reynolds, J.R., Marcel Dekker, New York, 1988, chap. 3. Reprinted from Routledge/Taylor Francis Group, LLC. With permission.)... 

Fig. 3.21 Temperature dependence of the free carrier dielectric response for metallic PAN-CSA sample A. (a) Far-infrared eiw) plotted against l/oj- as a function of temperature. (b) Comparison of the temperature dependence of the free electron plasma frequency /ip and...

At low temperatures a pure semiconductor is a perfect insulator with no free carriers. Upon laser irradiation at a frequency greater than the semiconducting band gap, a high density of electron-hole pairs can be excited which, at liquid-helium temperatures, condense into small droplets of electron-hole plasma. These electron-hole (e-h) droplets have been discussed thoroughly in a dedicated volume of Solid State Physics that contains reviews of theoretical aspects (Rice, 1977) and experiments (Hensel et al., 1977). 

Electrons in metals and semiconductors give rise to free-carrier absorption, the absorption coefficient being proportional to the square of the incident wavelength (hence high in the infrared region for most metals). The reflectivity of metals is related to the plasma frequency, cOp, by the relation... 

The transmittance and reflectance spectra of an undoped AP-CVD ZnO film and of a doped AP-CVD ZnO Al film are shown in Fig. 6.40. While the transmittance of the undoped film stays over 80% along the whole visible range, the transmittance of the doped film displays a pronounced drop in the near-infrared wavelength range. The drop corresponds to a minimum in the reflectance curve, as well as to a maximum (peak) in the absorbance curve. This occurs close to the so-called plasma frequency. These effects are due to free carrier absorption. When N is increased, the plasma frequency is shifted towards shorter wavelengths, and the drop in optical transmittance becomes more pronounced. This is illustrated for the case of LP-CVD ZnO.B films in... 

For PPY-PF6 and PAN-CSA the microwave dielectric constant remains negative in the far IR even at 10-3 K, which shows that there are free carriers even at these low temperatures. These values of the dielectric constants give small values of plasma frequency which shows that only a small fraction of conduction electrons participate in plasma response. Scattering times come out to be 2 orders of magnitude larger than the values for alkali and noble metals. It is predicted that if technology improves, the conductivity of the doped polymers may become larger than that of metals. 

The characteristic composite behavior of (t maM for medium consisting of spherical particles with volume fractions / of Drude conductor and 1 - / of insulator is shown in Figure 15.5. For a volume fraction / less than the percolation value (/ = 1/3 for spheres), (Tema (impurity band of localized plasmon-like excitations. As the system approaches the percolation threshold, the localized peak o-ema(w) shifts to lower frequency. Above the percolation threshold, a Drude peak corresponding to the carriers that have percolated through the composite structure occurs at low frequency. Only a fraction ( (3/— l)/2 [119]) of the full conduction electron plasma frequency appears in the Drude peak, depending on the proximity to the percolation threshold. The same percolating free electron behavior is observable in the dielectric response ema(w) for the system. 

The values obtained for fip are very small compared with the full conduction electron density (fipi 2 eV), suggesting that only a small fraction (Mfree/ cond) of the conduction electrons are delocalized macroscopically. This small fraction of delocalized carriers is consistent with the small number of percolation paths that occur close to the percolation threshold in composite systems. The fraction of the carriers that are delocalized can be estimated by comparing the plasma frequency of free electrons (fip) with the full conduction electron plasma frequency (fipi). 

The microwave frequency dielectric constant ( mw) is a key probe of the delocalization of charge carriers. For delocalized Drude electrons at frequencies less than their plasma frequency, the real part of the dielectric function s a>) is negative due to the inertia of the free electron in an alternating current field [40,103,130,164]. For a localized carrier, the charges can stay in phase with the field and s to) is positive at low frequencies. Thus, the sign of the microwave dielectric constant serves as a sensitive probe of the presence of free electrons and provides independent verification of the IR results. 

The simplest van der Waals forces involving free charge carriers occur where only a single substance has the free charges and no other substance in the system being considered can make an electrostatic contribution. For example, an electrolyte sphere coated with a nonpolar hydrocarbon near a pure water aerosol particle is such a system. In this case, the two-particle interaction force can be computed by use of local dielectric permeabilities whenever the charge carrier s plasma frequency is less than the lowest absorption frequency of the system [e.g., in (5.38)]. 

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