Tauc plots

Calculate the absorption coeflicient (if thickness is known) and create Tauc plots... 

Fig. 5.4 (a) Absorbance data from a 1.7 [tm film of electrodeposited polycrystaUine CU2O plotted as (b) Normalized absorption coefficient vs. energy and in (c) Allowed direct (d) Allowed indirect (e) Forbidden direct, and (f) Forbidden indirect band gap Tauc plots [26]. Plot (c) Suggests an allowed direct transition with a band gap of approximately 2.4 eV, as reported by others [27-30]. Plots (d-f) suggest transitions near 2.0 eV. CU2O literature supports both allowed indirect [31, 32] and forbidden direct [33, 34] transitions. Allowed direct transitions near 2.0 eV have also been observed [35-37], and signal from an absorption tail below 2.0 eV has previously been attributed to copper ion vacancies and free carriers [23-25]... 

Table 5.1 Tauc plots and their respective transition types...

Fig. 7.4 Allowed direct band gap Tauc plot of a GaInP2 photoelectrode using the normalized photocurrent...

Here, is a constant and m depends on the nature of the optical transition m = Vi for a direct bandgap, and ni = 2 for an indirect gap. From (2.6), extrapolation of a plot of (ahv) vs. hv plot gives the indirect bandgap, while a plot of (ahv) vs. hv yields the direct bandgap of the material. Such a plot is called a Tauc plot [7] and is often encoimtered in the photoelectrochemistry and photocatalysis literature. 

Fig. 29 Crystal structures of (A) Ag2Si03 and (B) Ag9(Si04)2N03. Ag, Si, O, and N ions are represented as grey, blue, red, and pale violet spheres, respectively. (C) Tauc plots to determine the optical band gaps of Ag2Si03 and Ag9(Si04>2N03. Reprinted with permission from T.-G. Kim, D.-H. Yeon, T. Kim, J. Lee and S.-J. Im, Appl. Phys. Lett., 2013, 103, 043904. Copyright 2013, American Institute of Physics.

If the surface oxide is of a semiconducting composition (e.g., MoOj, V2O5, and WO3), its electronic band structure can be probed through optical absorption spectroscopy [78]. UV-visible (vis) diffuse reflectance measurement of powders enables experimental determination of the optical absorption gap most commonly estimated through Tauc s relation [33,79-81 ], although other methods exist [80-82]. A Tauc plot linearly extrapolates versus E to zero absorption to... 

These data can be reorganized with the AVqh data [29, 39] in Table 11.3 as a function of (or d ox) to reveal an underlying dependence on ps , not immediately evident in the as-published dataset. Similarly, Table 11.3 shows that UV-vis optical absorption gaps estimated as E p, , s from Tauc plots [78] on the same W0x/Zr02 dataset [39] also exhibit dependence. The dependence of AVoh and Eopt,meas on psurQ is another example of how surface density provides a useful basis for analyzing the structure and catalysis of SMOs. 

The optical band gap of a-C is determined by using a Tauc plot, a method common for amorphous material where the k selection rule is relaxed. A parabolic distribution of the density of states for both bands near the band edges is assumed, together with matrix elements for interband transitions being equal for all transitions ... 

As a limiting case, the tt and bands can be completely localized and an optical gap will still be obtained from the Tauc plot. 

Tauc plot [81], // is the number of benzoid rings that form the cluster, and /3 is the resonance integral (Hiickel theory gives jS = 2,9 eV). The fluence dependence of g for ion-implanted polymers can usually be fitted with an exponential function,... 

Fig. 17.5 a Reflection and b absorption spectra of p-Si of different particle sizes measured at ambient temperature. Epa is obtained with the Tauc plot fitting of the reflection and absorption data. Size dependence of c PL spectra in particle size range of R = 1.4-2.1 nm [31] (reprinted with permission from [30])... 

Fig. 14 Optical absorption spectrum of CdSe nanoparticles inset shows the Tauc plot for calculating energy band gap (Tiwari et al., ref [273]).

Figure 6. Tauc plots for Ti02 thin films of varying thicknesses...

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