Investigation of temperature-dependent optical properties of TiO2 using diffuse reflectance spectroscopy
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Temperature-dependent diffuse reflectance spectroscopy (DRS) measurements have been carried out on the polycrystalline sample TiO2. Important values from optical parameters such as band gap (Eg), Urbach energy (EU), and Urbach focus (E0) have been estimated in the range of 300–450 K. In order to understand the experimental value of band gap (Eg) of TiO2, i.e., obtained from DRS, a first-principle calculation has been performed. The dependency of EU and the slope of exponential tails (β1, β2) of the density of states has also been studied which determines the distribution of exponential tails near the valence and conduction bands in semiconducting oxides. The behavior of optical band gap and EU has also been investigated with the influence of temperature using Cody model. From the temperature dependence of band gap measurements, the value of thermodynamical parameter such as Debye temperature (θD) has also been estimated. Thus it appears that the temperature-dependent optical absorption spectroscopy is very powerful and economical tool to probe the electronic structure near band edge and also to estimate the important thermodynamical parameter.
KeywordsDiffuse reflectance spectroscopy Urbach energy DFT calculations Temperature-dependent band gap Debye temperature
Optical properties of titanium dioxide (TiO2) have been the central goal of various intensive investigations over the past few years [1, 2, 3]. The major objective is to understand the behavior of optical absorption spectra with the application of temperature [4, 5]. Diffuse reflectance spectrometer (DRS) is an effective tool to understand the absorption spectra as a function of doping or temperature. The absorption spectra obtained from DRS contain three possible transitions: (1) main absorption spectra which give the information of optical gap [6, 7], (2) near absorption edge also called Urbach tail showing amount of disorder present in samples , and (3) lower absorption spectra which confirm the presence of defect inside the sample [8, 9]. To explore the optical absorption spectra which may be affected from various parameters like temperature, structural transition, doping, etc., an influential work has been done to shape our understanding as to how band gap and disorder varies on semiconducting materials [4, 10]. To understand how the thermal and structural components of the disorder exclusively contribute to the comprehensiveness of the optical absorption tail, Cody et al.  accomplished an experimental inquiry of their specific roles.
Optical spectroscopy is a tool which can tell about not only the optical band gap of semiconducting materials but also the disorder in the form of Urbach energy as well as various defects  present in semiconducting materials. Keeping this in view, here we have performed temperature-dependent DRS and report its dependency on optical band gap , Urbach energy , and Urbach focus on TiO2 [1, 15, 16]. It is observed that Urbach energy shows opposite behavior from band gap, i.e., with the increase in temperature optical band gap decreases while due to change in optical spectra near absorption tail edge leads to increase disorder present in sample . It is clear from the experimental evidence that Urbach–Martienssen [17, 18] (U–M) tails in the optical absorption spectra showing the variation of disorder produced with the application of temperature as well as variations of band gap with Urbach energy have also been investigated.
2 Experimental and theoretical details
2.1 Structural characterizations
Commercial anatase TiO2 powder of Alfa Aesar with purity 99.999% has been used for characterization. In order to examine the structural phase purity, X-ray diffraction (XRD) experiment has been carried out on Bruker D8 diffractometer equipped with Cu target having LynxEye detector [6, 19, 20, 21]. The high-temperature X-ray diffraction measurements were performed to confirm the structural phase transition in the prepared samples. Jobin–Yvon Horiba micro-Raman spectrometer was used for Raman measurements. The micro-Raman spectrometer consists of an argon ion laser as light source.
2.2 Temperature-dependent diffuse reflectance spectroscopy (DRS) measurement
The optical band gap of prepared sample has been measured by using DRS measurements [6, 7, 8]. These measurements have been taken in the 200–800 nm wavelength range using Cary-60 UV–Vis–NIR spectrophotometer having Harrick Video-Barrelino diffuse reflectance probe in the temperature range of 300–450 K .
2.3 Theoretical methods
The first-principles calculations are executed using FP-LAPW  approach and implemented in WIEN2k code [8, 24, 25]. The Kohn–Sham equations [26, 27] were solved self-consistently using FP-LAPW method. The generalized gradient approximation (GGA + U) has been used for DFT calculation. In the present studies, we have used structural parameters from experimental X-ray diffraction analysis (experimental data). Keeping this in view, we have not used lattice relaxation for calculation. We have taken generalized gradient approximation (GGA + U) as an exchange–correlation potential with U = 5 eV. During calculations, we have used RMTKmax = 7, where Kmax is the plane wave cutoff and RMT is the minimum of all atomic sphere radii (Muffin-tin radii). We have sensibly selected the muffin-tin radii (MT) 1.93 and 1.74 a.u. for Ti and O, respectively. When the total energy of given structure is stable within 10−3 mRy, it is believed that the self-consistent calculations are converged. The k-mesh size of 5 × 5 × 3 has been used in calculation.
3 Results and discussion
3.1 Structural characterization and phase purity
3.2 Diffuse reflectance spectroscopy (DRS)
3.2.1 First-principle investigation (DFT calculations)
3.2.2 Temperature-dependent band gap
According to Shojaee et al. , Debye temperature of TiO2 is around 557 K, while using Varshni’s fitting obtained from optical spectroscopy, Debye temperature has been found to be very close to reported value , which is around 562 K. Hence it is clear that temperature-dependent DRS provide not only the variation in optical properties but a tool to estimate the thermodynamic properties like Debye temperature.
3.2.3 Determination of band tail width (Urbach energy)
In summary, the variation of band gap ‘Eg’ and Urbach energy ‘EU’ as a function of temperature has been extensively studied. From GGA + U calculations from PDOS, it is clear that the change in behavior of valence band maxima and conduction band minima is due to the overlapping of O-2p (VBM) with Ti-3d (CBM) orbitals, which can vary as disorder increases in sample. Dependency of Urbach energy and the slope of exponential tails (β1, β2) in density of states have also been studied. In the present investigation, diffuse reflectance spectroscopy used as tools to see the behavior of optical band gap with the influence of temperature and which helps to estimate the thermodynamic parameter like Debye temperature.
The authors sincerely thank DST-FIST (SR/FST/PSI-225/2016) and SIC IIT Indore for providing some of the basic characterization facilities. Mr. Vikash Mishra, M. Kamal Warshi, and Mr. Anil Kumar sincerely thank Ministry of Human Resource Development (MHRD), Government of India, for providing financial support through teaching assistantship at IIT Indore. Ms. Aanchal Sati thanks CSIR New Delhi for providing junior research fellowship under Serial Number 1061651837.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 24.Blaha P, Schwarz K, Madsen G et al (2001) WIEN2K, an augmented plane wave + local orbitals program for calculating crystal properties. Karlheinz Schwarz, Technische Universität Wien, WienGoogle Scholar
- 28.Džimbeg-Malčić V, Barbarić-Mikočević Ž, Itrić K (2012) Kubelka–Munk theory in describing optical properties of paper (II). Tech Gaz 19:191–196Google Scholar
- 49.Banwell CN (1966) Fundamentals of molecular spectroscopy. McGraw-Hill, New YorkGoogle Scholar
- 50.Sathyanarayana DN (2015) Vibrational spectroscopy: theory and applications. New Age International, New DelhiGoogle Scholar