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How To Correctly Determine the Band Gap Energy of Modified Semiconductor Photocatalysts Based on UV−Vis Spectra A misuse of the Tauc plot to determine the band gap energy of semiconductors may lead to erroneous estimates. Particularly large errors can be associated with characterization of modified semiconductors showing a significant absorption of sub-band gap energy photons. Taking the model methyl orange/titanium dioxide system, we address the problem and discuss how to apply the Tauc method correctly. The band gap energy of a semiconductor describes the energy needed to excite an electron from the valence band to the conduction band. An accurate determination of the band gap energy is crucial in predicting photophysical and photochemical properties of semiconductors. In particular, this parameter is often referred to when photocatalytic properties of semiconductors are discussed. In 1966 Tauc proposed a method of estimating the band gap energy of amorphous semiconductors using optical absorption spectra.1 His proposal was further developed by Davis and Mott.2,3 The Tauc method is based on the assumption that the energy-dependent absorption coefficient α can be expressed by the following equation (1): (α ·hν)1/ γ = B(hν − Eg )
Figure 1. Method of band gap energy (Eg) determination from the Tauc plot. The linear part of the plot is extrapolated to the x-axis.
absorbance at energies below Eg, the obtained results may be significantly distorted. It is the case for defected, doped, bulk, or surface modified materials. All these modifications may introduce intraband gap states that reflect in the absorption spectrum as an Urbach tail, i.e., an additional, broad absorption band. Its presence influences the Tauc plot and therefore must be taken into account to determine the band gap energy. In such cases, a direct application of the Tauc method results in an inaccurate estimation of Eg. This error appears frequently in several publications in which authors incorrectly interpret the shift of the x-axis intersection point (zero of the fitting function) to lower values as reducing the band gap energy. In fact, the apparent Eg reduction is due to the inapplicability of the Tauc method in such cases. Researchers are well aware of the problem, and therefore, various attempts to improve the band gap estimation, such as the Cody plot (compare Supporting Information) or others, have been developed and investigated.7−10 The Tauc plots presented in Figure 2A were used to determine the band gap energies (Table 1, column 1). All determined band gap energies are smaller than that found for the original TiO2 sample (3.22 eV). To verify the applicability of the Tauc method, another set of spectra was recorded. Barium sulfate mixtures, ground separately with titania and MO, were placed side by side in the holder (system denoted as MO|TiO2; Figure 2B, inset). Collected spectra were transformed into the Tauc plot, as presented in Figure 2B. The determined values of x-axis intersection points are presented in Table 1 (column 1). All spectra show a steep change of absorbance in the UV region, which is characteristic of wide band gap semiconductors. Comparing spectra of the MO|TiO2 system and MO + TiO2 sample reveals the distinct differences. Absorption spectra (or F(R∞)) of the MO|TiO2 system are the spectral sums of two components (MO and TiO2), while in the MO + TiO2 sample,
(1)
where h is the Planck constant, ν is the photon’s frequency, Eg is the band gap energy, and B is a constant. The γ factor depends on the nature of the electron transition and is equal to 1/2 or 2 for the direct and indirect transition band gaps, respectively.4 The band gap energy is usually determined from diffuse reflectance spectra. According to the theory of P. Kubelka and F. Munk presented in 1931,5 the measured reflectance spectra can be transformed to the corresponding absorption spectra by applying the Kubelka−Munk function (F(R∞), eq 2). F(R ∞) =
where R ∞ =
(1 − R ∞)2 K = S 2R ∞ R sample R standard
(2)
is the reflectance of an infinitely thick
specimen, while K and S are the absorption and scattering coefficients, respectively.6 Putting F(R∞) instead of α into eq 1 yields the form (3) (F(R ∞) ·hν)1/ γ = B(hν − Eg )
(3)
Figure 1 shows the reflectance spectrum of TiO2 (an indirect band gap semiconductor) transformed according to eq 1 plotted against the photon energy. The region showing a steep, linear increase of light absorption with increasing energy is characteristic of semiconductor materials. The x-axis intersection point of the linear fit of the Tauc plot gives an estimate of the band gap energy. This approach can be applied for all semiconducting materials that do not absorb light of the sub-band gap energy (or show a negligible absorbance), as exemplified in Figure 1. When it is applied to materials showing a considerable © 2018 American Chemical Society
Published: December 6, 2018 6814
DOI: 10.1021/acs.jpclett.8b02892 J. Phys. Chem. Lett. 2018, 9, 6814−6817
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Figure 2. Tauc plots of the bare TiO2, methyl orange, (A) MO + TiO2 sample, and (B) MO|TiO2 system (linear fit for measurement b (blue line) and c (green line) overlap). Numbered spectra were recorded for the same pellet differently placed in the holder. The insets show schematically the sample in the holder.
Table 1. Experimental Eg Values Obtained from the Direct Application of the Tauc Plot (Column no. 1), from the Tauc Plot Applied to the Differential Spectra (Column no. 2), and from the Simplified Analysis of the Tauc Plot (Column no. 3)
where a and b determine the contributions of the components (they depend on the components concentrations), while αs(hν) and αm(hν) are the absorption coefficients of the semiconductor and organic dye. The Tauc transformation (eq 1) should not be directly applied to the spectrum of both components together, but to the spectrum of the semiconductor alone (αs(hν)). Therefore, an appropriate approach to determine the band gap energy should involve the withdrawal of the semiconductor spectrum from the spectral sum. Figure 3A shows the Tauc plots of the semiconductor spectra obtained by subtracting the MO component from the recorded spectra (αs(hν) = α(hν) − c·αm(hν)). To account for different concentrations of MO component, the spectrum of MO needs to be normalized to the corresponding level of MO concentration in the sample (parameter c). The values of the band gap energy were determined as for a neat semiconductor (Table 1, column no. 2). An analogous analysis made for the MO + TiO2 sample (Figure 3B) revealed similar Eg values listed in column no. 2 (Table 1). All Eg values for both systems (MO|TiO2, MO + TiO2) are nearly the same, within a margin of error, with Eg measured for bare TiO2 (3.22 eV). These results prove that the adsorbed dye does not influence the band gap energy of TiO2. Since it is often hard to split the Kubelka−Munk spectrum into spectra of individual components, a simplified procedure
energy band gap ±0.03 [eV] materials
1
2
3
TiO2 MO + TiO2
3.22 2.98 3.04 3.08 2.13 3.08 3.13 2.72
3.21 3.23 3.22 3.21 3.18 3.18 3.17
3.21 3.22 3.19 3.27 3.26 3.25 3.24
MO|TiO2
where both components can interact, the resulting spectra may not be a simple sum of the components spectra. Therefore, the obtained values of band gap energy are incorrect. According to the Beer−Lambert law, the spectrum of any mixture, including a semiconductor modified by an organic dye, is the linear combination of the spectra of both components: α(hν) = a ·αs(hν) + b·αm(hν)
(4)
Figure 3. Tauc plots of the TiO2 components (extracted from the spectra of the MO|TiO2 system) and bare TiO2 (A). The Tauc plots of the differential spectra of the sample MO + TiO2 and bare TiO2 (B). The determinations of Eg for measurements 1 (4A) and 3 (4B) are shown as insets. 6815
DOI: 10.1021/acs.jpclett.8b02892 J. Phys. Chem. Lett. 2018, 9, 6814−6817
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Figure 4. Transformed reflectance spectrum plot of sample MO + TiO2 (A) and MO|TiO2 system (B). The determination of the Eg is shown.
conclusion that in the case of semiconductors modified with an organic dye, the directly applied Tauc method is the least accurate way of determining the band gap energy. We are aware that the selected organic dye serves as a pH indicator, and its spectral changes can be noticed since the surfaces of BaSO4 and TiO2 are slightly basic and acidic, respectively. However, spectral changes caused by the pH variations are insignificant and their impact on the final band gap estimation is negligible. The results obtained by applying the Tauc method give a lower estimate of Eg and often lead to incorrect conclusions concerning the reduction of Eg or photosensitization of the semiconductor. Calculating the band gap energy using the presented methods gives more accurate results in such cases. A more optimal approach to determining the band gap energy is based on the Lambert−Beer law, which allows us to deconvolute the spectrum of both components into the spectra of individual components. The direct application of Tauc method is only appropriate for spectra of bare semiconductors. If deconvolution of the spectrum into the spectra of components is not feasible, a more accurate estimate can be obtained through the use of the presented baseline method. The analysis of other dye−semiconductor systems leads to similar results, as shown for selected cases in the Supporting Information. To further demonstrate the correctness of the proposed approach, reflectance spectra of doped rutile (with Fe3+ and VO3− ions) and surface modified anatase (with catechol) were analyzed, as well as the mixture of two semiconductors (CdS| TiO2). All results are presented in the Supporting Information. It is important to understand the nature of surface modification and doping (small dopant loading ratio). The surface complex does not influence the band gap of the bulk material. The absorption band that appears at lower energies (longer wavelengths) than the absorption band of the semiconductor comes from CT complexes formed at the surface of TiO2. The Tauc plot may be used to obtain the complex excitation energy. In the case of small dopant concentration the additional electron states appear within the band gap of the semiconductor. As a result, the broad absorption band appears in the material spectrum. The results show that even if the interactions between components are stronger, the use of the baseline approach gives very satisfying results. The Tauc method was applied to the diffuse reflectance spectra of a ground mixture of titanium dioxide (TiO2, anatase, AK-1, Tronox) with methyl orange (C14H14N3NaO3S, MO, POCh) in a 1:1 mass ratio (MO + TiO2), as well as TiO2 and MO alone. The spectra were recorded using a UV−vis−NIR
can be considered. As in the method described by Tauc, the linear fit of the fundamental peak is applied. Additionally, a linear fit used as an abscissa is applied for the slope below the fundamental absorption. An intersection of the two fitting lines gives the band gap energy estimation, as shown in Figure 4 (Table 1, column no. 3). The approach presented in Figure 4 can be justified by the following analysis. When γ = 1/2 (direct band gap) and the system is composed of two components, the Tauc equation (1), according to (4), takes the following form (5) ((αs(hν) + αm(hν)) ·hν)2 = B(hν − Eg )
(5)
Expansion of the square of sum results in eq 6: (αs(hν)hν)2 + 2αs(hν)αm(hν)(hν)2 + (αm(hν)hν)2 = B(hν − Eg )
(6)
Analogously, when γ = 2 (indirect band gap) and the system is composed of two components, the Tauc equation (1), according to (4), takes the form (7) ((αs(hν) + αm(hν)) ·hν)1/2 = B(hν − Eg )
(7)
The Taylor series expansion of the square root of the sum results in eq 8:
1/2 3/2 ij i 1 yz i y 1 jj zz − 1 ·α (hν)2 ·jjj 1 zzz jjαs(hν)1/2 + · αm(hν)·jjjj m z j z jj j αs(hν) z j αs(hν) z 2 8 k { k { k 5/2 yz 1 z ji 1 zyz zz + . . . zzzz· (hν)1/2 = B(hν − Eg ) + · αm(hν)3 · jjj j αs(hν) z z 16 k { { (8)
When hν → Eg, then αs(hν) > 0 and αm(hν) > 0, and it is impossible to eradicate the αm(hν) influence on the band gap energy estimate from eqs 6 and 8. In order to do so, the αm(hν) must be equated to 0. The graphical equivalent of such operation is the use of αm(hν) as the baseline in the sub-band gap region of the Tauc plot (Figure 4). When αm(hν) ≅ 0, eq 6 takes the form (αs(hν)hν)2 = B(hν − Eg), while eq 8 takes the form (αs(hν)hν)1/2 = B(hν − Eg). Such analysis enables the band gap energy to be obtained directly from the plot. Therefore, the use of this baseline approach presented in Figure 4 leads to much more accurate values of Eg than the method presented in Figure 2. Comparing the obtained results to the independently determined band gap energy of pure TiO2 leads to the 6816
DOI: 10.1021/acs.jpclett.8b02892 J. Phys. Chem. Lett. 2018, 9, 6814−6817
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(10) Murphy, A. B. Band-gap determination from diffuse reflectance measurements of semiconductor films, and application to photoelectrochemical water-splitting. Sol. Energy Mater. Sol. Cells 2007, 91, 1326−1337.
spectrophotometer (UV-3600 Shimadzu) equipped with a 15 cm integrating sphere in the spectral range 250−800 nm. Each time the sample holder was rotated to a different position (by ∼45°). Barium sulfate (BaSO4, Riedel-de Haen) was used to dilute the samples (1:100) and was used as a reference. The collected R∞(λ) spectra were transformed according to eqs 2 and 3.
Patrycja Makuła Michał Pacia Wojciech Macyk*
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Faculty of Chemistry, Jagiellonian University in Kraków, ul. Gronostajowa 2, 30-387 Kraków, Poland
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b02892.
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Systems with different organic dyes showing the same dependence; comparison of the results obtained by Tauc plots with results obtained using Cody plots (PDF)
AUTHOR INFORMATION
Corresponding Author
*W. Macyk. E-mail:
[email protected]. ORCID
Wojciech Macyk: 0000-0002-1317-6115 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work was supported by the National Science Centre (Poland) within the project number 2015/19/B/ST5/00950 (OPUS 10) and the Foundation for Polish Science (project number TEAM/2016-3/27).
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REFERENCES
(1) Tauc, J.; Grigorovici, R.; Vancu, A. Optical Properties And Electronic Structure of Amorphous Germanium. Phys. Status Solidi B 1966, 15, 627−637. (2) Davis, E.; Mott, N. Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors. Philos. Mag. 1970, 22, 0903−0922. (3) Mott, N. F.; Davis, E. A. Electronic Processes in Non-Crystalline Materials; OUP Oxford, 2012. (4) Pankove, J. I. Optical Processes in Semiconductors; Courier Corporation, 1971. (5) Kubelka, P.; Munk, F. A Contribution to the Optics of Pigments. Z. Technol. Phys. 1931, 12, 593−599. (6) López, R.; Gómez, R. Band-gap Energy Estimation From Diffuse Reflectance Measurements on Sol−Gel and Commercial TiO2: a Comparative Study. J. Sol-Gel Sci. Technol. 2012, 61, 1−7. (7) Liu, P.; Longo, P.; Zaslavsky, A.; Pacifici, D. Optical Bandgap of Single-and Multi-Layered Amorphous Germanium Ultra-Thin Films. J. Appl. Phys. 2016, 119, 014304. (8) Nowak, M.; Kauch, B.; Szperlich, P. Determination of Energy Band Gap of Nanocrystalline SbSi Using Diffuse Reflectance Spectroscopy. Rev. Sci. Instrum. 2009, 80, 046107. (9) Raciti, R.; Bahariqushchi, R.; Summonte, C.; Aydinli, A.; Terrasi, A.; Mirabella, S. Optical Bandgap of Semiconductor Nanostructures: Methods for Experimental Data Analysis. J. Appl. Phys. 2017, 121, 234304. 6817
DOI: 10.1021/acs.jpclett.8b02892 J. Phys. Chem. Lett. 2018, 9, 6814−6817
