Free carrier absorption

The optical constants are very important because they describe the optical behavior of the materials. The absorption coefficient of the material is a very strong function of photon energy and band gap energy. 

Absorbance (A) is defined as the ratio between absorbed light intensity Ia) by material and the incident intensity of light (If) [71,72]. 

The transmittance (T) is given by reference to the intensity of the transmitting light from the film (I) to the intensity of the incident light on it (If) T = -, and can be calculated by  

The absorption coefficient (a) is defined as the ability of a material to absorb the light of a given wavelength 

The refractive index (n) of a material is the ratio of the velocity of the light in vacuum to that in the specimen  

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The interest of physicists in the conducting polymers, their properties and applications, has been focused on dry materials 93-94 Most of the discussions center on the conductivity of the polymers and the nature of the carriers. The current knowledge is not clear because the conducting polymers exhibit a number of metallic properties, i.e., temperature-independent behavior of a linear relation between thermopower and temperature, and a free carrier absorption typical of a metal. Nevertheless, the conductivity of these specimens is quite low (about 1 S cm"1), and increases when the temperature rises, as in semiconductors. However, polymers are not semiconductors because in inorganic semiconductors, the dopant substitutes for the host atomic sites. In conducting polymers, the dopants are not substitutional, they are part of a nonstoichiometric compound, the composition of which changes from zero up to 40-50% in... 

The decrease in free carriers (holes) after hydrogenation of p-type Si is also evidenced by the decrease in IR absorption at the longer wavelengths, where free-carrier absorption dominates, and by a decrease in the device capacitance of Schottky-barrier diodes, due to the increase in the depletion width (at a given reverse bias) as the effective acceptor concentration decreases. 

Another demonstration that hydrogenation neutralizes acceptors is the decrease in free-carrier absorption observed during infrared transmission experiments by Pankove et al. (1985). 

Characteristic infrared absorption lines have been identified for various hydrogen-acceptor and hydrogen-donor complexes (see Chapter 8), and the strength of such a line in any given specimen is a measure of the quantity of the complex present. However, depth resolution is crude, and masking by free-carrier absorption is sometimes a problem. Raman lines have also been seen (see Chapter 8) and in principle should be capable of detecting species that are not infrared active however, the sensitivity is low, and the most interesting and presumably abundant species, an H2 complex, has not yet been detected in this way. 

Fig. 5.12 The oxide thickness (broken line) and the free carrier absorption (dotted line, in arbitrary units) determined by FTIR spectroscopy for galvanostatic (top, 58 pA cm-2) and potentio-static (bottom, 7 V) conditions in buffered HF (0.1 M, pH=4.5). Redrawn from [Chi 2].

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]. 

Reference 59 provides a comprehensive explanation of the optical spectra and extracted bandgaps. The direct bandgap of ca. 2.36 eV is compared to the literature value of ca. 2.2 eV and explained by size quantization in the fairly small (20 nm) crystals. An indirect bandgap of 1.9 eV was measured (literature value < 1.4 eV), but it was stressed that this provided an upper limit only, since the absorption in this region was dominated by free-carrier absorption, which masked the indirect absorption. Annealing decreased the conductivity and the free-carrier absorption and changed the indirect gap to > 1.3 eV. 

Bandgap measurements for Cu sulphides and selenides are complicated by the fact that these semiconductors are normally degenerate, with high free-carrier absorption in the near-infrared and possible Moss-Burstein shifts (due to saturation of the top of the valence band by holes) in the optical gap. It is quite possible that variations in bandgaps in these materials are due to differences in stoichiometry, phase, and doping rather than to any quantum size effect. Only studies where crystal size can be estimated and are possibly in the quantum size range are given here. 

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... 

A theoretical description of the a.c. conductivity has not been given. At low frequencies one would expect free-carrier absorption corresponding to the enhanced effective mass. At a frequency co comparable to E /h, where E is the unenhanced Fermi energy, we should expect the mass to go over to the unenhanced value. An example of this behaviour, taken from the infrared reflectivity of the vanadium oxides, is shown in Figs. 6.8 and 6.9. 

The decrease of the free-carrier absorption upon hydrogenation can be associated with localization of free carries near C-H bonds in SWNTs, or increase in the rate of their scattering by these defects. The complete removal of hydrogen by vacuum annealing at 700°C only partly restored the intensity of the... 

For both AP-CVD and LP-CVD processes, the main observation concerning the variation of the transparency of the ZnO films is a reduction of transmittance in the near-infrared (N1R) range when the substrate temperature is increased. Indeed, N is usually increased with temperature, and this leads to a stronger free carrier absorption (FCA) effect for higher substrate temperatures. 

LP-CVD ZnO Optical total and diffuse transmittance spectra (TT and DT spectra) of a temperature series of undoped LP-CVD ZnO films are shown in Fig. 6.25 TT does not vary strongly with substrate temperature. Indeed, as Fig. 6.25 is related to a series of undoped samples, the values of carrier density N are too low to produce an observable free carrier absorption effect... 

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... 

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