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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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The Journal of Physical Chemistry Letters
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.
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DOI: 10.1021/acs.jpclett.8b02892
J. Phys. Chem. Lett. 2018, 9, 6814−6817
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The Journal of Physical Chemistry Letters
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
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DOI: 10.1021/acs.jpclett.8b02892
J. Phys. Chem. Lett. 2018, 9, 6814−6817
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The Journal of Physical Chemistry Letters
(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*
■
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.
■
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: macyk@chemia.uj.edu.pl.
ORCID
Wojciech Macyk: 0000-0002-1317-6115
Notes
The authors declare no competing financial interest.
■
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).
■
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.
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