J Sol-Gel Sci Technol (2012) 61:1–7 DOI 10.1007/s10971-011-2582-9 ORIGINAL PAPER Band-gap energy estimation from diffuse reflectance measurements on sol–gel and commercial TiO2: a comparative study Rosendo Lo´pez • Ricardo Go´mez Received: 30 May 2011 / Accepted: September 2011 / Published online: 15 September 2011 Ó Springer Science+Business Media, LLC 2011 Abstract A comparison of the bandgap energy estimated from UV–vis reflectance spectra of TiO2 powders prepared by sol–gel route versus commercial TiO2 powders, nanopowder, bulkpowder and P25 is reported The experimental results obtained from the optical absorption spectra were reported for all the TiO2 samples Graphic representations were used to calculate Eg: absorbance versus k; F(R) versus E; (F(R) hm)n versus E, with n = for an indirect allowed transition and n = for a direct allowed transition From the results, it could be seen that Eg strongly varied according to the equation used for the graphic representation Differences in Eg up to 0.5 eV for the same semiconductor depending on the transition chosen were observed Accurate Eg estimation in the four semiconductors studied was obtained by using the general equation a (hm) & B (hm - Eg)n (where a * F(R)) and indirect allowed transition Keywords Titanium dioxide semiconductor Á Bandgap calculation Á Titanium dioxide electronic transitions Á Kubelka–Munk method Introduction The accelerated development of industrial processes around the world has produced important environmental problems In order to solve them, a large variety of alternatives has R Lo´pez Á R Go´mez (&) ´ rea de Cata´lisis, Departamento de Grupo ECOCATAL, A Quı´mica, Universidad Auto´noma Metropolitana-Iztapalapa, Av San Rafael Atlixco 186, 09340 Mexico, DF, Mexico e-mail: gomr@xanum.uam.mx R Lo´pez e-mail: ross@xanum.uam.mx been proposed Among them, the photodegradation of pollutants using semiconductors has proved to be one of the most promising methods for the degradation of organic molecules (pesticides, dyes, aldehydes, aromatic compounds, etc.) as well for the elimination of cationic metals [Hg(I), Cr(VI)] or anionic species (CN-, As4-) that are highly hazardous for the human health Without any doubt, titanium dioxide prepared by sol–gel method is the semiconductor that offers the most promising applications for environmental solutions; however, due to the bandgap (3.4–3.1 eV), UV irradiation is needed to carry out the photoprocess Metal or carbon, sulfur and nitrogen doped titania materials have been recently reported as materials in which the TiO2bandgap energy is shifted to the red region of the electromagnetic spectrum, making possible the use of tiania-based semiconductors as photocatalysts using solar irradiation as energy source In any case, doped or undoped titanium dioxide is actually the photocatalyst to which the larger number of studies has been devoted For this reason, well characterized titanium dioxide used as a starting material is absolutely demanded For example, the titania crystalline phase (brookite, anatase and rutile), crystallite size, Ti(IV) or O2- deficiency, roughness, electron density maps, XRD-Rietveld refinement for the characterization of the crystalline properties as well as the energy band value have been reported as examples of intensive titanium dioxide characterization [1–3] However, on the other hand, the evaluation of the Eg band gap, usually made by UV–vis electron absorption spectroscopy, does not seem to be totally established According to the UV spectra analysis (absorption or reflectance) as well as the type of transition band considered, directly or indirectly, the Eg value can strongly differ from one author to the other The electronic properties of a semiconductor can often be ascertained from the analysis of its energy band diagram A number of 123 J Sol-Gel Sci Technol (2012) 61:1–7 theoretical studies for a large number of semiconductors describing the electronic structure of the energy bands have been reported [4–6] The separation between the energy of the lowest conduction band and that of the highest valence band is called the band-gap, energy gap or forbidden energy gap (Eg), which is one of the most important results in semiconductor physics (Fig 1) [7] In a simplified way, Eg is evaluated from the plot obtained from the highest valence band edge and lowest conduction band edge [8] The semiconductor properties of a solid are strongly affected by the Eg parameter The illustration of the distribution of the energy states in a semiconductor on both sides of Eg suggests the existence of a well-defined edge The electrons in a solid occupy allowed energy bands separated by forbidden energy gaps Two types of band-toband transitions are suggested: Direct transitions (allowed), when the participation of a phonon is not required to conserve the momentum Direct transitions (forbidden) take into account the small but finite momentum of photons and are less likely to occur Indirect transitions, when at least one phonon participates in the absorption or emission of one phonon to conserve the momentum It is obvious that indirect and direct transitions can occur in all semiconductor materials [9] Some of the alternatives for the determination of Eg in semiconductors and amorphous solid materials are the optical methods Among the optical methods, UV–vis diffuse reflectance spectroscopy is one of the most employed This characterization technique describes the electronic behavior present in the structure of the solid Through the absorption spectra, UV–vis spectroscopy gives information about the electronic transitions of the different orbitals of a solid In principle, it is possible to describe any transition by specifying the type of orbitals that are involved in the semiconductor The optical methods used for measuring forbidden energy band gaps not depend on temperature variations or uncertainties due to surface states (electrical conductivity, Hall constant and photoconductivity techniques) Accordingly, the frequent use of diffuse reflectance spectroscopy for the determination of the electronic transitions in solid materials is highly justified The optical excitation of the electrons from the valence band to the conduction band is evidenced by an increase in the absorbance at a given wavelength (band gap energy) The study of the tail of the absorption curve of semiconductors shows that it has a simple exponential drop This drop has been suggested as the most appropriated method to determine the position of the absorption edge [10, 11] The linear section in the diffuse reflectance spectra is taken for measuring the bandgap energy In 1958, Shapiro is one of the first scientists measuring Eg by extrapolating the linear portion of the absorption curve with the wavelength axis [12] Through the years, several methods have been developed and applied to evaluate Eg from the optical absorption spectra and diffuse reflectance spectra The given value of Eg for a given semiconductor could vary depending on the extrapolation method and optical electronic transition (direct allowed, direct forbidden or indirect allowed, indirect forbidden) As it was mentioned before, important disagreements exist about the type of transitions associated with the experimental calculation of Eg In order to analyze the differences among the large variety of equations used for the calculation of the Eg, in the present work, experimental Eg values were determined from the UV–vis diffuse reflectance spectra of four TiO2 semiconductors Experimental 2.1 Preparation of photocatalyst Fig Simplified band transition representation: (a) allowed and (b) forbidden direct gap absorption of a photon with Eg energy can occur without assistance of a phonon; (c) for the indirect gap, the assistance of a phonon is required 123 The optical bandgap was determined by measuring the reflection spectra of: TiO2 anatase (Aldrich, nanopowder, 99.7%), TiO2 anatase (Aldrich, bulkpowder, 99.8%), TiO2 Degussa P25 (80–75% anatase, 20–25% rutile) samples J Sol-Gel Sci Technol (2012) 61:1–7 without pretreatment and for the home made sol–gel TiO2 The sol–gel TiO2 was prepared by mixing 18 mL of deionized distilled water and 44 mL of 1-butanol (Aldrich 99.4%) with 0.2 mL of nitric acid (Aldrich 70% in water) to obtain pH 3; the mixture was heated at 70 °C under reflux and constant stirring Finally, 44 mL of titanium (IV) butoxide (Stream Chemicals 98%) was added dropwise for h The resultant gels were dried at 70 °C for 24 h and were annealed in air at 500 °C for h with a heating rate of °C/min 2.2 Characterization A UV–Vis spectrophotometer (Varian Cary 100) with an integrating sphere attachment DRA-CA-30I for diffuse reflectance measurements was used to establish the optical bandgap The equipment was calibrated with a Spectralon standard (Labsphere SRS-99-010, 99% reflectance) The optical absorption was measured in the 200–800 nm range For comparison purposes, all the obtained spectra were arbitrarily normalized Results and discussion The literature review showing the different formulations associated to diverse transitions is reported in Table [7, 9, 13–21] In general, various authors use the equations reported in Table for the electronic transitions, but unfortunately they not justify the type of transitions considered as direct, indirect, allowed o forbidden The compiled equations of Table are valid for semiconductor materials that have direct (Ge) or indirect (GaAs) transitions It is important to mention that the indirect transitions can occur simultaneously with direct transitions, but they cannot be detected in the absorption spectrum because of their high energy and low probability The highest transition conducts the behavior of the semiconductor; however, it is very difficult to establish the corresponding transition experimentally On the other hand, the determination of Eg by applying the Kubelka–Munk (K–M or F(R)) method offers great advantages The K–M method is based on the following equation Table Summary of the equations associated with different transitions for the evaluation of the bandgap energy (Eg) Author N S Lewis Transitions References Direct 1/2, allowed 3/2, forbbiden Indirect 2, allowed 3, forbbiden a = (E) & (E - Egd)2 a = (E) & (E - Egi)1/2 a(hm) = 104(hm - Eg)1/2 a(hm) = AN(hm - Eg - ng)2 [14] a & (hm - Eg) , c = 1/2, 3/2 a & (hm - Eg ± Ep)c, c = 2,3 [7] a & (hm - Eg)1/2 a & (hm - Eg)2 [15] e2(x) & Zij(x) & (hx - Eg)2 [9] (ahx)2 or (ahxn)2 [16–18] [13] M L Rosenbluth J I Pankove S M Sze c Kwok K Ng R J Candal S A Bilmes M A Blesa M Schiavello D W Lynch e2(x) & Zij(x) & (hx - Eg)1/2,3/2 1/2 (ahx) or (ahxn) 3/2 P Apell A R Forouhi J L Gray Paul M Amirtharaj aðhvÞ % Aðhv À EG Þ1=2 B aðhvÞ % ðhv À EG Þ3=2 hv aAD = CAD(hx - Eg)1/2 À Á2 A hv À EG þ Eph eEph =kT À À Á2 A hv À EG þ Eph ae ðhvÞ ¼ À eÀEph =kT aðhvÞ ¼ aa ðhvÞ þ ae ðhvÞ aA1 & C(ABS) A1 (hx - Eg) [20] [21] 3/2 D G Seiler aFD = CFD(hx - Eg) A Miller a(x) = Co(hx - nc)1/2 a(x) & (hx ± hxpb - nc)2 3/2 a(x) & (hx ± hxpb - nc)3 a(x) = Co(hx - nc) [19] aa ðhvÞ ¼ 123 J Sol-Gel Sci Technol (2012) 61:1–7 FðRÞ ¼ ð1 À R Þ2 2R ð1Þ where R is the reflectance; F(R) is proportional to the extinction coefficient (a) This equation is usually applied to highly light scattering materials and absorbing particles in a matrix The basic K–M model assumes the diffuse illumination of the particulate coating For further information refer to [22] and [23] A modified Kubelka–Munk function can be obtained by multiplying the F(R) function by hm, using the corresponding coefficient (n) associated with an electronic transition as follows: ðFðRÞ Ã hmÞn ð2Þ By plotting this equation as a function of the energy in eV, the bandgap of semiconductor particles can be obtained Furthermore, some authors have excluded the hm factor of Eq (2); this only exerts a minor influence on the obtained Eg value [24] In the literature, several modifications of the K–M theory can be found, each one with their corresponding applications [25–28] and limitations [29, 30] A widespread opinion is that the original Kubelka–Munk theory should be used where its accuracy is sufficient, as in photocatalysis For the Eg calculation, the following equations were summarized from the bibliography; the considered type of transition is indicated À Án aðhmÞ % B hm À Eg ð3Þ n = for an indirect allowed transition (plotted as a(hm)1/2 versus E); n = for an indirect forbidden transition (plotted as a(hm)1/3 versus E); n = 1/2 for a direct allowed transition (plotted as a(hm)2 versus E); n = 3/2 for a direct forbidden transition (plotted as a(hm)2/3 versus E) Eg is the bandgap (eV), h is the Planck’s constant (J.s), B is the absorption constant, v is the light frequency (s-1) and (a) is the extinction coefficient, which is proportional to F(R) The n value for the specific transition can be experimentally determined from the best linear fit in the absorption spectra using the different equations For the graphical analysis of the Eg, the recorded UV– Vis spectrum in the reflectance mode are transformed to an F(R) magnitude and plotted versus hm (Eq 4) The Eg value was obtained by extrapolating the slope to a = For practical purposes, the bandgap energy for the different samples was calculated using Eq 4: Eg ¼ 1239:84 Â m Àb ð4Þ where Eg is in eV, and m and b are obtained by the linear fit (y = mx ? b) of the flat section of the UV–Vis spectrum 123 Some published articles pointing out the differences among the equations using graphic representations have been reported In example, Khan [31], Yang [32], He [33], Graf [34] and [12, 35, 36] estimated the Eg value for TiO2 by directly plotting the absorbance versus k or by plotting %R versus k Tang [37], Fan [38], Sudhagar [39], Cheng [40] and [41, 42] used the absorption coefficient (a) in their graphic representation by plotting a2 versus k or by plotting a1/2 versus k [43–48] In a different way, several authors applied the K-M function for the calculation of Eg by plotting F(R) versus hm [23, 49] The modified K–M function was used by Lin [50], Yeredla [49], Aguado [51] and plotted as (F(R) hm)1/2 versus hm or (F(R) hm)2 versus hm, such a representation is known as the Tauc method [52, 53] It is important to note that for the representations mentioned above, the authors not mention the type of the associated transitions; and this lack of information was also found in a large number of publications [54–60] However, controversial assumptions are found when the associated transitions are considered Some authors use the exponential only by definition in their plots for the indirect allowed bandgap transition (or for the direct allowed bandgap transition) Contrarily, other authors [61– 64] have reported the exponential for direct allowed bandgap and for indirect bandgap transitions In all the cases, the optical edge or gap was inferred by linear extrapolation of the absorbance from the high slope region obtained from the spectra As an experimental example, the Eg band was calculated for commercial TiO2 semiconductor particles (nanopowder, bulkpowder and P25) and for the home prepared sol– gelTiO2 by direct extrapolation of the absorption or reflectance spectra Figure shows the plots: (a) Abs versus k and (b) F(R) versus E (with F(R) & a, for practical purposes) As it can be seen in Fig 2a, without considering any type of transition (indirect or direct), a good fit was obtained (the spectra show a good tail) and the extrapolation yields Eg values of 3.21 eV for nanopowder, 3.19 eV for bulkpowder, 3.15 eV for P25 and 3.13 eV for sol–gel TiO2 In Fig 2b, without considering any transitions, a good fit was also obtained and the extrapolation gives values of 3.42 eV for nanopowder, 3.33 eV for bulkpowder, 3.51 eV for P25 and 3.53 eV for sol–gel TiO2 These results show that, depending on the plots for the same semiconductor sol–gel or commercial TiO2, the absorbance or F(R) present very important differences in the obtained Eg values To analyze the effect of the associated transitions on the TiO2 semiconductors mentioned above, the absorption data were fitted to the equations for both indirect and direct allowed bandgap transitions, Eq J Sol-Gel Sci Technol (2012) 61:1–7 Figure shows the plots of: (a) (F(R)E)1/2 versus E and (b) (F(R)E)2 versus E Considering indirect transitions, Fig 3a a perfect fit was obtained for all the samples giving the values of 3.25 eV for nanopowder, 3.21 eV for bulkpowder, 3.26 eV for P25 and 3.30 eV for the sol–gel TiO2 As for the direct transitions, Fig 3b, the values obtained for Eg were 3.56 eV for nanopowder, 3.44 eV for bulkpowder, 3.68 eV for P25 and 3.72 eV for the sol–gel TiO2; these results are summarized in the Table A high variation in the Eg value as a function of the chosen transition was obtained The results in Table show that a great attention must be paid to the equations used to calculate the TiO2bandgap Differences up to 0.5 eV can be obtained for P25 if the (a) (b) c a b d a b d F(R) (a.u.) Abs (a.u.) Fig Graphical representation of absorbance and F(R) spectra without considering electronic transitions: a absorbance versus k and b F(R) versus E Eg value is calculated directly from the absorption spectra or from the (F(R)E)2 function Some authors have reported that TiO2 has a direct forbidden gap, which is also degenerated with an indirect allowed transition On the other hand, other authors have reported direct allowed transitions [65] For comparison purposes, the principal problem for the experimental calculation of Eg from optical spectroscopy resides in the adequate selection of the graphic representation and of course in the type of transitions selected for TiO2 From the analysis of Table 2, where TiO2 prepared by four different methods, it can be seen that the smallest difference in Eg was obtained when it was calculated from the direct extrapolation of the absorbance spectra or by a- anatase bulk b- anatase nano c- P25 d- sol-gel 300 a- anatase bulk b- anatase nano c- P25 d- sol-gel 325 350 375 3.25 400 3.50 3.75 (a) 4.25 4.50 4.25 4.50 (b) d c a (F(R) hv) a- anatase bulk b- anatase nano c- P25 d- sol-gel (F(R)hv) (a.u.) b 1/2 (a.u.) a a- anatase bulk b- anatase nano c- P25 d- sol-gel 3.25 3.50 3.75 4.00 4.25 4.50 3.25 3.50 Method b 3.75 d c 4.00 Energy (eV) Energy (eV) Table Experimental Eg values obtained from different graphic methods for the TiO2 semiconductors 4.00 Energy (eV) Wavelength (nm) Fig Graphical representation of modified Kubelka–Munk: a (F(R)hm)1/2 versus E and b (F(R)hm)2 versus E c Bandgap energy (eV) TiO2 anatase nano TiO2 anatase bulk TiO2 Degussa P25 TiO2 sol–gel 3.13 Abs 3.21 3.19 3.15 F(R) 3.42 3.33 3.51 3.53 (F(R) E)1/2 (F(R) E)2 3.25 3.56 3.21 3.44 3.26 3.68 3.30 3.72 123 plotting (F(R)E)1/2 versus E Moreover, in both cases, the Eg values for the P25 TiO2 sample were 3.15 and 3.26 eV, respectively These values are closer to the well known 3.2 eV Eg that has been extensively reported for the commercial P25 semiconductor Since the purpose of the present article is to suggest some solutions to the high number of papers with several inconsistencies in the method used for calculating the Eg of TiO2, as it has been reviewed in the present paper, we propose the use of the equation a(hm) & B (hm - Eg)n with n = for an indirect allowed transition Conclusions In the present study, it is shown the significant differences in the absorption spectra among nanopowder, bulkpowder, P25 and sol–gel TiO2 specimens It is demonstrated that the use of graphic representations to calculate the Eg bandgap is an adequate method From the experimental results, it is shown that important variations in Eg are obtained as functions of the used equation and the considered type of transition The application of the equation a(hm) & B (hm - Eg)n with n = for indirect allowed transition is suggested because of the highly accurate results obtained with the TiO2 sol–gel and the P25 TiO2 commercial semiconductor Acknowledgments We thank to CONACYT 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Kubelka–Munk: a (F(R)hm)1/2 versus E and b (F(R)hm)2 versus E c Band gap energy (eV) TiO2 anatase nano TiO2 anatase bulk TiO2 Degussa P25 TiO2 sol gel 3.13 Abs 3.21 3.19 3.15 F(R) 3.42 3.33 3.51 3.53 (F(R)