Thermo Optical Properties and Related Electronic Polarizabilities of MoO3 Thin Films Using Ellipsometry

Corresponding Author: Zahid Hussain Imperial College of Science, Technology and Medicine Department of Electrical and Electronics Engineering Exhibition Road, London SW7 2BT UK Email: (hzzhussain@aol.com) Abstract: Thermo optical properties are reported for thermally evaporated MoO3 thin films using ellipsometry. The values of TOCs: dn/dT and dk/dT relating to MoO3 thin films are found to be negative and positive, respectively over the temperature range 295-460 K and also are found to have the same trend over the range 120-300 K, and have values of the order of 10 K and 10 K, respectively in the visible part of spectral range. The values of electronic polarizability were determined to be in the range from 8.2 to 8.21×10 cm in the temperature range 120-460 K and over the same part of spectral range. Vacuum-heating and annealing in an oxygen plasma environment certainly assists in reducing a large amount of porosity in the films, but these series of actions yield irreversible changes in the morphology of the films. Once the films during oxidative-annealing turned into black in colour and new reduced chemical states were produced, then after that, original states of the films were very hard to restore. Ellipsometric data of MoO3 thin films at or above the room temperature in the range 295-460 K seems to be controlled by first-order kinetics and could be interpreted in terms of polaronic excitations and hoppings. During the in-situ cooling runs, the changes in the ellipsometric data are interpreted in terms of bipolaronic excitations, but the possibility of simultaneous presence of polaronic and bipolaronic states cannot be ignored over the investigated temperature range.

Molybdenum trioxide is a transparent, partly ionic 4d transition metal oxide. The study of the crystal structure of the molybdenum oxide was done by several workers and it was found to be a shear structure consisting of large slabs, joined along the crystallographic shear planes (Bertrand et al., 1985;Punitha et al., 2014). MoO 3 can be easily prepared either in single crystal or in thin layer form and can display both electronic and ionic conductivity (Schollhorn et al., 1976;Li et al., 2016). When prepared in thin film form at room temperature, it has been declared to be sub-stoichiometric MoO 3 −y, where y is a small fraction (Wang et al., 2012;Madhavi et al., 2013). Thermally evaporated oxygen deficient molybdenum trioxide thin film has been revealed to be n-type semiconductor and has band gap in the range 2.9−3.15 eV (Svensson et al., 1988;Hussain, 2001;2002a). Moreover, in these thin films, Mo-Mo distances are too large to form the metallic bonds probably due to lack of overlap of 4d-wave functions (Colaitis, 1991;. After publishing ellipsometric data on M x WO 3 (M = H + , Li + , Na + ) and A x MoO 3 (A = H + , Li + ) bronzes (Hussain, 2018a;2018b) and before publishing temperature dependent ellipsometric data on tungsten and molybdenum bronzes, our present focus is entirely on to explore the optical constants of MoO 3 thin films using ellipsometry.
Investigations on the preparation and optical constants of sub-stoichiometric MoO 3 thin films are quite essential for their effective use in microbatteries, electrochromic and microelectronic devices. It should be noted that we have already published temperature dependent ellipsometric data on WO 3 thin films (Hussain, 1999).
There is a plethora of structural analysis in the literature that MoO 3 thin films still remain microcrystalline when heated below 623 K whereas films heated above 623 K turn into crystalline phase (McEvoy and Stevenson, 2003;Szekeres et al., 2002). It has also been concluded that amorphous or microcrystalline phase shows superior intercalation capability to crystalline phase Szekeres et al., 2002). We have also observed the better electrochromic performance for the "as deposited room temperature prepared films" and also for the heat treated films in the visible spectral region and over the temperature range 295-460 K.
In this paper, we report temperature dependent ellipsometric measurements on MoO 3 thin films prepared on unheated substrate by thermal evaporation. High precision single wavelength manual ellipsometry was used at fixed angle to measure in situ temperature dependent optical constants of MoO 3 thin layers. We have also measured mass densities of MoO 3 thin films in the temperature range 100-460 K. Thermo optic coefficients and electronic polarizabilities are also calculated in the visible spectral region and over the same temperature range.
The reported data has also been interpreted using polaronic and bipolaronic excitations and transitions regarding structural transformations during heating and cooling treatments.

Ellipsometry
Ellipsometry is an optical technique that measures changes in polarization (phase, ∆ and amplitude, Ψ) of monochromatic light reflecting from matter and these standard ellipsometric parameters Ψ and ∆ are related to the complex ratio of reflection coefficient for light polarized parallel p and perpendicular s to the plane of incidence. The mathematical expression (Azzam and Bashara, 1977;Tiwald, 2016) for this ratio is: and: The value of tan Ψ gives the differential change in amplitude and ∆ measures differential phase change. δ p and δ s are the phase factors of the complex Fresnel pseudo-reflection coefficients r p and r s , respectively.
High precision single wavelength manual ellipsometry at fixed angle was choosen for in situ heating and cooling experiments in order to generate a series of data on the optical constants of MoO 3 thin films in the visible range of solar spectrum. The related microstructural changes in the films were also monitored using temperature dependent mass density data.
Thickness of each film was measured by an independent technique, Talysurf and its value was compared directly with the auto-ellipsometer and with the ellipsometric numerical model while choosing the real part of the thickness with minimum imaginary number. Once the ellipsometric measurements of ∆ and Ψ are determined and the thickness is properly evaluated, the other unknown parameters, real part of the refractive index (n) and index of absorption (k), can in principle be calculated using suitable computer program.

Preparation of MoO 3 Thin Films
The source material (Koch light Ltd) was prepared by taking molybdenum powder and heaing in a platinum crucible in air at a temperature∼673 K for 20 h and then for 12 h at 973 K. This caused heavy sintering and grain growth and ultimately the obtained material (of purity 99.9%) was white in colour. Examination of the mass under the optical microscope revealed crystallites of typically 80 µm in diameter. The sintered material was broken into small lumps and put into strips, prior to evaporation. The vacuum chamber base pressure was about 1×10 −6 mm Hg; and there was a liquid nitrogen cold trap in the chamber, whose function was to reduce the water vapour pressure. The vacuum chamber was equiped with a stainless steel shutter, which was used to block the substrates (7059 glass slide and I.T.O glass plate) from the Mo boat during outgassing. With the shutter in closed position, MoO 3 powder was outgassed at 823 K for 30 min and then heated to 1023 K for 8 min for more dehydration. The current (the temperature) was then increased in order to bring the powder to its melting point. When the temperature was further raised to 1123 K, liquid nitrogen was used to decrease the base pressure to ∼ 5×10 −7 mm Hg. At this stage, the shutter (blocking the substrates) was opened and the films of thicknesses between 0.25 µm and 0.45 µm were attained with a deposition rate of about 12-14 Å/sec. Film deposition rate was constantly monitored with a quartz crystal oscillator at a boat-to-substrate distance of 20 cm. Talysurf measurements (average of four measurements) for the film thicknesses were accurate to a maximum precision of ±30Å.
Freshly evaporated MoO 3 thin films were slightly blue, perhaps due to oxygen deficiency, or because of water or hydroxyl groups present in MoO 3 . Difference in the substrate temperature and variation in evaporation rate will give rise to films of different concentration of oxygen vacancies. The reported evaporated thin films are a highly disordered microcrystalline in structure with grain size of about 60Å, as estimated by our TEM and X-rays studies (Hussain, 2007;Evans, 1987). The micro-characteristics of the reported films have also been confirmed by other workers (Shiojiri et al., 1979;Julien et al., 1995).

Calibration and Operation of Manual Ellipsometer
All the optical components of manual ellipsometer were aligned according to some standard procedure.
Full details of the alignment and calibrations are described elsewhere (Hussain, 1999;Azzam and Bashara, 1977).
A schematic of the whole apparatus is shown in Fig. 1 Red light (He-Ne laser) was passed through the polarizing section of the instrument (PSG): Consisting of a linear polarizer (P) and a quarter wave plate, Q (or a Compensator, C). This section is called the polarization state generator. After transmitting through the polarizing section of the instrument, the beam struck the sample cell at an angle ∼ 60 ο and changed into elliptically polarized light. This state of polarization was monitored by the rotational azimuth positions of the polarizer and quarter wave plate. Vacuum cryostat was built up with the ability to heat and cool the samples over a broad range of temperature, i.e., 100<T<400 K. The sample cell temperature was monitored through alumel-cromel thermocouple and regulated by a controller. After reflecting by a sample, the modified state of polarization was then controlled by the analyzing section of the instrument (PSD). This section is called the polarization state detector. It consisted of a linear analyzer (A) followed by a narrow pass filter. And then it is followed by a photomultiplier tube connected to Keithly for monitoring the output signal. At extinction, the polarizer azimuth, P, gave a measure of ∆; and the analyzer azimuth, A, delivered a value of Ψ. After alignment, the maximum uncertainty in ∆ and Ψ in an open air were found about ±0.02° and ±0.01°, respectively and with an in situ manual ellipsometer fitted with fused quartz inlet and exit optical windows, the maximum calibration errors in ∆ and Ψ were about ±0.05° and ±0.02°, respectively. Nevertheless, four-zone ellipsometric measurements were always made in order to minimize systematic errors.

Experimental Results and Error Analysis
The relations of (Ψ and ∆) to (P and A) in four zones at extinction settings are given by equations (Azzam and Bashara, 1977;Tiwald, 2016): where, i = 1, 2, 3, 4. And a p or a s (depending upon zone) denotes the analyser azimuth angle and p is the polarizer azimuth angle. The quantities to be determined from the experimental data (∆, ψ) using ellipsometric equations are the thickness of the film (t f ), the real part of the refractive index (n) and the extinction coefficient (k). Ellipsometric Eq.
(1) was solved by converting McCrackin package (McCrackin, 1969) into Fortran 77 version and also some modifications were made according to the experimental situation. We determined thickness of each film (t f ) from an independent technique, talysurf and after inserting the values of thickness (t f ) into the fortran program, (n, k) values of different samples of MoO 3 thin films under different temperature conditions were computed directly from the experimental data (∆ and Ψ).
A comparison between manual and auto ellipsometric data is shown in Table 1, which indicates that the manual ellipsometric components were aligned to very high precision. The experimental data (∆ and Ψ) and the related results under different temperature conditions are printed in Tables 2-4 and the respective plots (along with error bars) Vs temperature are displayed in Figs. 2-4. Vacuum-annealed and oxidative-annealing data are also printed in Tables 5  and 6 and their respective plots Vs time are shown in Figs. 5 and 6. A plot of (n, k) of MoO 3 thin film Vs substrate temperature is also shown in Fig. 7.
For a clean surface (7059 glass), a change of ±0.02° in the measurement of the angle of incidence due to optical window strain gives a net change of ±0.02° in Ψ value, which gives an error in n of about δn = ±0.00071.     Table 3: Vacuum-ellipsometric temperature dependent data on MoO 3 thin film  Table 4: Vacuum-low-temperature ellipsometric measurements on MoO 3 thin film using liquid nitrogen as a coolant and directing the temperature with a 407 controller      Table 6: Vacuum-annealed and oxygen plasma treated ellipsometric data on MoO 3 thin film upheld at a temperature, T = 453 K and with a pressure of the order of 10 −2 torr  Similarly, a change of ±0.04 ο in ∆ due to same degree of strain brings a net change in the index of absorption of about δk = ±0.0005. Additionally, an uncertainity of ±30Å in the thickness measurements when added to the above errors, gives a total error in n of about ∆n = ±0.0031 and a total error in k of about ∆k = ±0.002 for a film covered 7059 glass.
Ellipsometric temperature dependent data for a MoO 3 thin film over the temperature range 100<T<460 K gives an extra uncertainity in n of about ∆n′ = ±0.0019 and in k of about ∆k′ = ±0.003. Uncertainties due to oxygen plasma or because of different annealing conditions have not been taken into account in the error analysis.

Structure and Temperature Dependent Phase Transitions
Molybdenum oxide has one stable orthorhombic symmetry (space group B6nm) (Tubbs, 1974), i.e., α−ΜοΟ 3 which is white; and the other two metastable polymorphs, β−MoO 3 and β′−MoO 3 which have framework structures similar to ReO 3 (Itoh et al., 2001;Parise et al., 1987). Due to stronger distortion of the metal-oxygen octahedra in the molybdenum than in the tungsten, the structure of α−ΜοΟ 3 is not like ReO 3 (Itoh et al., 2001;Baker and Dickens, 1989). In the αorthorhombic phase it exhibits two-dimensional layered structure, as shown in Fig. 8(a), with a = 3.96Å, b = 13.86Å and c = 3.69Å (Dickens et al., 1979;Scanlon et al., 2010;Diaz et al., 2010). It consists of zigzag chains of MoO 6 octahedra linked through vertices and has fragile Van der Waals forces in between the layeres. Also in this structure, all oxygen ions are not equivalent and therefore Mo-O distance varies from 1.67 to 2.34Å (Baker and Dickens, 1989;Scanlon et al., 2010;Kuzmin and Purans, 1993), as shown in Fig. 8(b). Freshly prepared β−MoO 3 is to have a yellow colouration similar to WO 3 (Baker and Dickens, 1989;Carcia et al., 1987) and certain aspects of the stereochemistry observed for β′−MoO 3 are also common in β−MoO 3 (Parise et al., 1987;Baker and Dickens, 1989). β−ΜοΟ 3 can be converted into white αphase (α−ΜοΟ 3 . Η 2 Ο or α−ΜοΟ 3 ) by topotactic transformation when heated above 623 Κ (Parise et al., 1987;Baker and Dickens, 1989), where white α−MoO 3 .H 2 O has a structure closely related to that of α−MoO 3 , (Baker and Dickens, 1989;Gunter, 1972), consisting of two fold chains of edge-sharing MoO 6 octahedra with co-ordinated water molecules attached to molybdenum atoms. β′−MoO 3 as sketched in Fig. 9(a) has MoO 6 octahedra linked by sharing corners and is found to be isostructural with the monoclinic form of WO 3 . Mo-O bond lengths (Itoh et al., 2001;Parise et al., 1987) in this structure are shown in Fig. 9(b). β′−MoO 3 may be considered as an intermediary structural state between perovskite and the modified layered form of MoO 3 .
The molybdenum trioxide films formed at higher substrate temperature normally emerge as polycrystalline with α−β mixed phase. On thermal treatment in air at about 653 K for 4 h, the films are transformed to the  (Wang et al., 2012;Scanlon et al., 2010). The transformation from α+β mixed phase to α−phase was also observed in the films deposited at 523 K (Wang et al., 2012;Sabhapathi et al., 1995). Crystalline WO 3 and V2O 5 were found to have stable crystallographic structure, even on heating in UHV up to 850 K (Kihlborgn and Magneli, 1955) and 823 K (Bursill, 1969), respectively; but MoO 3 loses its stoichiometry and starts to decompose on heating above 773 K under vacuum (Rao et al., 2013;Diaz et al., 2010;Ohfuji, 1984). Diffusion of oxygen through the MoO 3 lattice becomes rapid at higher temperature and this temperature allows the formation of adsorption and reaction sites for the molecular state of oxygen. In the case of MoO 3 thin films, prepared (on cold substrates) either by evaporation or by sputtering techniques, the information relating to their structures is scanty and in the literature such films are declared as amorphous (Tubbs, 1974;Rao et al., 2013;Shiojiri et al., 1979;Carcia et al., 1987). A series of lower oxides, known as MoO 2.95 , MoO 2.89 , MoO 2.88 , MoO 2.85 , MoO 2.75 lie in between MoO 3 and MoO 2 (Hansen and Andersson, 1988;Kumada et al., 1986;Kihlborg, 1959). On heating around 800K, MoO 3 thin film (Epifani et al., 2004;So et al., 1988) or single crystal (Hansen et al., 1988;Wold et al., 1964) is transformed into crystallized MoO 2 by a reduction process:  [001] c The crystallized black MoO 2 cannot remain stable at room temperature (Ohfuji, 1984;Naguib and Kelly, 1972) and can be rapidly oxidized back to MoO 3 at higher temperature (∼1273 K) (Ohfuji, 1984).
In MoO 3 thin film and in its hydrogen molybdenum bronze, Mo-Mo distances are too large to form the metallic bonds, probably due to lack of overlap of 4dwave functions (Anwar and Hogarth, 1988;Rao et al., 2013). Therefore, the electronic and physical properties are interpreted by polaronic excitations and hoppings between Mo 5+ -Mo 6+ species. Figures 2 and 3 show that the temperature dependent n-values of MoO 3 are monotonically and linearly decreasing. Such behaviour is characteristic for the material in which temperature of the optical indices is associated with thermal expansion which is related to the density of the material.

Refractive Index, Film Density and Electronic Polarizability
The density of bulk material or of the film can be calculated from refractive index data using the following well known expression (Born and Wolf, 2013;Jacobson, 1975): where, ρ f is the average film density and ρ b the bulk density; n f denotes the refractive index of the film and n b the refractive index of bulk. Inserting the values of ρ f and ρ b (Hussain, 2001;2007) and n f (from Table 2) into Equation 7, the value of bulk refractive index, n b of MoO 3 is calculated as 2.7 at 0.633 µm which agrees with the other researchers (Tubbs, 1974;Deb, 1968). Using the bulk values of n b as 2.7 and ρ b as 4.71 gcm −3 , we can transform Equation (7) into: 2 2 1 6.96 .
The temperature dependent film density data of MoO 3 thin films was derived from Equation (8) using ellipsometric data (Tables 2-4) on MoO 3 over the temperature range 120<T<460 K and are displayed in Figs. 11-13. The experimental curves shown in Fig.  11 indicate that the film density and refractive index of the films decrease with the increase in temperature due to porous nature of the films, but the overall change in mass density (or in the refractive index) in the temperature range 295≤T<460 K is not more than 5% than the room temperature data. Experimental Figs. 2 and 3 also show the same trend over the same temperature range. It is also a fact in the litrature that the optical band gap energy depends on the temperature and it becomes smaller at higher temperature for MoO 3 thin films (Hussain, 2001). It should be noted that the dispersion of the refractive index has already been analysed (Hussain, 2002b) in terms of the E o (optical band gap) and E d (dispersion energy) using the single oscillator dispersion model of Wemple and Domenico (1971). Figure 13 shows that the film density goes on increasing as the temperature decreases from 297 to 120 K. The increase in the refractive index over the same temperature range can be noticed in Fig. 4. This kind of effect could be due to self-trapped charge carriers, known as small polaronic and bipolaronic species which will be explained fully in section D.
Polarizability should be defined before I discuss the relationship between refractive index, film density and polarizability.
The polarization (α tot ) is defined as the dipole moment per unit volume, averaged over the volume of a cell and it is the ability for a molecule to be polarized. The total polarizability can be expressed as: Which is the sum of electronic (αe), ionic (α݅) and dipolar (α݀) polarizabilities which molecule's internal structure. In the region of visible light, the ionic polarizability (α݅) of any material can be neglected. Because MoO 3 thin film is a non-dipolar (ionic) material, so only the electronic polarizability (α) is connected with it over the visible spectral range.
The refractive index (n f ) and film density (ρ f ) are related to electronic polarizability (α e ) through the famous Lorentz-Lorenz relation (Singh et al., 2006;Hecht, 2012): Here, N A is the Avogadro's number and M is the molecular weight of the material.
Inserting the values of N A = 6.023×10 23 ‫݈݉‬ −1 ܽ݊݀ ‫ܯ‬ = 144 ݃ ‫݈݉‬ −1 into Equation (10), the expression for electronic polarizability can be reshaped as: The temperature-dependent-electronic polarizabilities of MoO 3 thin films were calculated from Eq. (11) by the help of refractive index (n f ) data (Tables 2 and 4) and from the film density (ρ f ) data using Eq. (8). The average electronic polarizability of MoO 3 thin films as calculated from Eq. (11) at room temperature is found to be 8.20×10 −24 cm 3 . The measured electronic polarizabilities are represented in Figs. 12 and 14. It is very obvious from Figs. 12 and 14 that the values of electronic polarizability (or depolarization coefficients) of MoO 3 thin films were almost constant over the whole heating and cooling process. This kind of behaviour is characteristic for the materials for which the temperature dependence of the optical indices is associated with thermal expansion (Kang et al., 2003). It should be noted that a higher degree of crytallinity in MoO 3 thin films could give rise to a higher electronic polarizability.

Thermo-Optic Coefficients and Interpretations
Values of n obtained at λ=0.633 µm at room temperature were found to have a small range from 2.12 to 2.13 for the reported evaporated MoO 3 thin films; and this range is very close to the refractive index (n), as found in Fig. 15 using spectrophotometric technique. It is also in agreement with other reseachers (Tubbs, 1974;Hussain, 2001;Carcia et al., 1987;Abdellaoui et al., 1988). The k-values determined at room temperature are found to be in the range from 0.004 to 0.006 which are due to slight blue colouration in the reported films. This range is also comparable with the values shown in Fig. 15. It also agrees with the others in the literature (Tubbs, 1974;Hussain, 2001;Abdellaoui et al., 1988). The p-d band gap of MoO 3 thin films has been found within a range 3.05-3.07 eV (Hussain, 2001;2007), which also agrees with other workers (Miyate and Akiyoshi, 1985;Rabalais et al., 1974).
For a specific wavelength, the index with the increased (or decreased) temperature could be expressed as: Or: where, n 2 is the refractive index at temperature T 2 (higher or lower than T 1 ), n 1 is the refractive index at T 1 and dn/dT is the Thermo Optic Coefficient (TOC) normally used in opto-electronic devices.
In the first step, TOC s (dn/dT and dk/dT) of MoO 3 thin films over the range 295-460 K are calculated from Tables 2 and 3. We have developed the mathematical formulations for temperature-dependent refractive index data and the associated thermo optic coefficients, TOCs. The following are the mathematical equations which fit to the reported temperature dependent n and k data: In Eq. (14), n 0 and T 0 are initial values (room temperature values) and n and T are any choosen (or final) values of refractive index and temperature. B n is taken as an average value of dn/dT associated with reported MoO 3 thin films with some ± standard deviation. Similarly, in Eq. (15), k 0 and T 0 are initial values (room temperature values) and k and T are any choosen (or final) values of extinction coefficient and temperature. The value of D k is taken as an average of dk/dT associated with the temperature dependent kdata of reported MoO 3 thin films with somestandard deviation.
Thermo-optical coefficients (dn/dT) relating to MoO 3 thin film as determined from Table 3 are found to be negative in the visible part of spectral range and have values in the range from -6.24 to -0.291×10 −4 K −1 over the temperature range 295-460 K. Similarly, dk/dT values for MoO 3 determined from Table 3 are all positive and range from 0.1 to 3.1×10 −5 K −1 over the same temperature range. The values of dn/dT and dk/dT (TOCs) as determined from Table 3 (or measured from slopes of curves in Fig. 3) can be fitted to Eqs. (14) and (15)  Equations (16) and (17) fit well to the reported ellipsometric data within a relative accuracy of ±10.
TOCs calculated from Tables 3 are very close to the values reported in the literature (Hussain, 2001;Martinez et al., 2013;Torres et al., 2005). The small changes in TOCs are due to small changes in the electronic polarizability in the range 295-460 ‫ܭ‬ (Fig. 12). It is clearly visible from Fig. 12 that after heating in the above temperature range, the new values of optical constants of MoO 3 are not close to their initial values. So it is an irreversible process showing an unclosed thermal hysteresis for the heating cycles of the films. Figures 2 and 3 indicate that on simple heating up to 453 K, MoO 3 thin films start becoming more transparent instead of losing more oxygen. Figure 2 shows an increase in the index of absorption (or conductivity) with increasing temperature. It is interpreted by the fact that in an oxygen deficient MoO 3 thin films, a number of oxygen vacancies act as donors and are capable of capturing one or two electrons per donor, from where electrons are ionized thermally as well as optically and eventually cause an increase in the optical and electrical conductivity. Table 5 gives the TOCs: dn/dT changes from -5.59×10 −4 /K at 413 K to -5.66×10 −4 /K when annealed at 413 K for 14 h; and dk/dT changes from 2.84×10 −5 /K at 413 K to 1.644×10 −5 /K when annealed at 413 K for 14 h. Similarly, TOCs from Table 6 reflects that dn/dT changes from -3.51×10 −4 to -8.45×10 −5 /K when annealed at 453 K for 11 h and changes to -7.4×10 −4 /K when annealed with oxygen plasma for further 25 h; and dk/dT changes from initial 1.019×10 −4 to final 4.582×10 −4 /Κ under the same conditions. These small changes in TOCs indicate that the reported MoO 3 films still remain microcrystalline even after being annealed at 453 K for so long time.
During annealing mode, a lot of outgassing is involved mostly due to evolution of water which is present in the form of H 2 MoO 4 on the surface, but also in the form of great loss of oxygen from MoO 3 thin films. Annealing certainly helps in reducing the porosity with a minor rearrangement in the Mo-O bond lengths, but produces irreversible changes in the morphology of the films. Vacuum-annealing and oxidative-annealing give open hysteresis loops as shown in Figs. 5 and 6 and these irreversible results do not appear to bleach any sample in accordance with the following relations : And: The cause of this irreversibility is a partial reduction and also because of presence of hydroxy group in the films. In the case of annealing process, optical or electrical conduction can occur by the hopping mechanism between different oxidation states (emoving from M 5+ or M 4+ →M 6+ ) Torres et al., 2005). The oxidation of MoO x converts Mo 5+ (or Mo 4+ ) to Mo 6+ and also reduces the oxygen vacancy concentration, thereby increases the optical transmittance and electrical resistivity of the films. The optical modulation of the reported films is increased from 4 to 9% with increase of annealing temperature from 373 to 453 K. The optical modulation mainly depends on the quantity of H + insertion into the films during annealing. The films annealed at 453 K show good optical modulation and that may be due to more insertion of H + ions into the films because of growth of columnar structure of the films.
After exposure to oxygen plasma, the colour of the sample becomes black due to significant amount of Mo 4+ species in the sample with more annealing at higher temperatures, further reduction and additional defect structure can be produced in the film with ultimately a new stable crystallographic phase, probably a rhombic phase (Pardo and Torres, 2012). A single phase orthorhombic α-MoO 3 films could only be obtained by annealing the films at temperature above 673 K (Madhavi et al., 2013;Pardo and Torres, 2012).
Thermo optical properties of MoO 3 thin films during cooling cycles over the temperature range 120<T<300 K are represented in Table 4. Thermo-optical coefficients (dn/dT) relating to MoO 3 thin film as determined from Table 4 are found to be negative in the visible part of spectral range and have values in the range from -3.643 to -3.29×10 −4 K −1 over the temperature range 120-300 K. Similarly, dk/dT values for MoO 3 determined from Table 4 are all positive and range from 7.792 to 7.77×10 −5 K −1 over the same temperature range.
TOCs calculated from Table 4 (or measured from the slopes of curves in Fig. 4) can be fitted to Eqs. (14) and (15)  Equations (20) and (21) fit well to the experimental ellipsometric data within a relative accuracy of ±10.
It is interesting to note that the thermal treatment over the temperature range 297-129 K is virtually reversible. The values of n and k, which form closed hysteresis loops, can be perceived in Fig. 4. It is important to note that these small changes in TOCs are due to small changes in the values of electronic polarizability during the cooling cycles (Fig. 14).
The shifts in the optical constants are obviously related to the changing of the conductance of the sample during cooling processing. When the temperature goes down to 129 K the conductivity reaches its lowest value and when the temperature increases, so does the conductivity but in a slightly different way. When the sample returns to room temperature, it appears again slightly blue. The mechanism of conduction in amorphous or microcrystalline solids is believed to be due to electronic hoppings through localized levels. The localized levels are donor-like or trap-like, depending on their ability to donate or accept electrons and the position of the Fermi level depends critically on the respective distributions of donor-like or trap-like levels.
The traps are likely to spread over a broader range of energies than donors or acceptors. The degree of overlap of the donor-like (or trap-like) levels vary widely, as observed by the fact that the k-values of MoO 3 thin films vary vastly during cooling treatment. For example, as is observed in Fig. 4, the trend in the k-plot manifests metal-insulator transition features over the temperature range 200-130 K, but there are no indication of Peirels transitions (Rao et al., 2013;Pergament et al., 2014) in the investigated temperature range.

Polaronic and Bipolaronic Excitations in MoO 3 Thin Films
MoO 3 is one of the transition metal oxides which are known to have large dipole moments due to large difference between the static dielectric constant and the high frequency dielectric constant value. With such a large difference, the charge carriers are almost selftrapped small polarons or bipolarons and evidence that photo (or thermo) excited electrons and holes do so in transition metal oxides has been reported by several researchers (Gehlig and Salje, 1983;Eagles, 1984;Lakhno, 2013). Fresh MoO 3 thin film experiences some thermal decomposition during evaporation resulting in lower valence Mo 5+ and Mo 4+ states (Dasgupta et al., 2015;Peelaers et al., 2017;Mrowiecka et al., 2008). ESR (Deb, 1968;Anwar et al., 1989), XPS (Peelaers et al., 2017;Maruyama and Kanagawa, 1995;Santhosh et al., 2017) and NMR (Santhosh et al., 2017;Ritter et al., 1985) measurements show that the localization of surplus electrons is on Mo ions and not on the oxygen vacancies. We also believe that in the sub-stiochiometric oxide thin film (WO 3 , MoO 3 , etc) the charge carrier bound to the W or Mo ion is also strongly coupled to the lattice optical phonons, causing a lattice distortion around the host metallic ion. Since the optical phonon frequencies in metal oxides are usually high 0.05-0.16 eV (Svensson et al., 1988;Pardo and Torres, 2012;Gehlig and Salje, 1983) and the polaronic binding energy is also sizable E p = 0.2-0.4 (Gehlig and Salje, 1983;Eagles, 1984;Devreese and Alexandrov, 2009), thus the permitted value for the unfilled electronic band could be of the order of 0.5-1.0 eV (Mott and Davis, 1979;Arfaoui et al., 2015), which is large enough for the small polaron formation.
During any higher temperature or annealed state of MoO 3 thin film, generally, polaron jump from different lower valence states (Mo 4+ , Mo 5+ ) to the neighbouring higher valence Mo 6+ states on the basis of a variablerange hopping mechanism (Mott and Davis, 1979;Tahini et al., 2016;Gesheva et al., 2005). The shape of the polaron band goes on changing during heating and annealing cycles and the suitability about the type of polaron model in a particular annealing mode may arise because of the simultaneous presence of two types of polaron. Either small polarons hop as almost independent species or can coexist with the largeradius polarons to form delocalized states (Mott and Davis, 1979;Tahini et al., 2016) during annealing at higher temperatures. However, a rigorous theoretical treatment is needed in order to interpret the experimental data and to clarify about the applicability of proper polaron theory.
During cooling, colouration (or conductance) change is caused either by small polarons (Lakhno, 2013;Tahini et al., 2016) or by the excitation of bipolaronic entities (Mo 5+ -Mo 5+ ) Arfaoui et al., 2015). Assemblage and disassemblage of bipolarons (Mo 5+ -Mo 5+ ) is shown in Fig. 16. The bipolaronic entities (Mo 4+ -Mo 4+ ) might also exist during the cooling process (Gesheva et al., 2005). In the case of bipolaronic state, a short-range coulomb repulsion (intersite) should be below 1 eV to ensure bipolaron formation and it is quite possible because the high-frequency or short-range dielectric constant in metal oxides is usually large. A bipolaron will be energetically stable, if the static dielectric constant ε ο and polaron binding energy E b are sufficiently large and obey the condition such that bipolaron binding energy E bi (R)<2 E b (R) (Mott and Davis, 1979;Arfaoui et al., 2015;Alexandrov and Devreese, 2009). Since polarons and bipolarons in the case of transition metal oxides are formed well above the superconductivity transition temperature T c , so the reported low temperature data also need to be carefully analyzed either mostly within the picture of polaron or bipolaron or both.

Summary and Conclusion
Freshly evaporated MoO 3 thin films prepared on unheated substrates are always microcrystalline in structure. Moreover, in our case, the prepared films were slightly blue either due to deficiency in oxygen or due to water, or because of hydroxyl groups.
The reported temperature dependent ellipsometric data on MoO 3 thin films was computed to calculate optical constants n and k over the temperature range 120<T<460 K. We also measured mass densities, thermo optic coefficients (TOCs) and electronic polarizabilities of MoO 3 thin films over the same temperature range. Thermo-optical coefficients (dn/dT) relating to MoO 3 thin film are found to be negative in the visible part of spectral range and have values in the range from -6.24 to -0.291×10 −4 K −1 over the temperature range 295-460 K. Similarly, dk/dT values determined for MoO 3 are all positive and range from 0.1 to 3.1×10 −5 K −1 over the same temperature range. These tiny changes in TOCs are due to small changes in the values of electronic polarizability (α e ), which were calculated in the range from 8.203 to 8.205×10 −24 cm 3 over the temperature range 295-460 K.
Vacuum-heating and oxidative-annealing certainly removes a lot of water and definitely helps to reduce the porosity, but assists little towards bleaching process in the reported temperature range 295-460 K. Consequently our experimental annealing runs produce minor rearrangement in the Mo-O bond lengths, but create a lot ofirreversiblechanges in the morphology of the films.
For the cooling cycles, the values of dn/d for MoO 3 thin films are also found to be negative in the visible part of spectral range and have values in the range from -3.643 to -3.29×10 −4 K −1 over the temperature range 120-300 K. Similarly, dk/dT values for MoO 3 are found to be all positive and range from 7.792 to 7.77×10 -5 K −1 over the same temperature range. These meagre changes in TOCs are due to little changes in the values of electronic polarizability (α e ), which were found to be in the range from 8.203 to 8.20×10 −24 cm 3 over the temperature range 120-300 K.
In the case of cooling runs, different lower values of k were obtained during different cooling cycles, but most of the k-values returned to original when MoO 3 thin films were back to room temperature. So, for the cooling cycles, the hysteresis loops are closed for the investigated ellipsometric data. This means that the thermal treatment in the temperature range 120 to 300 K is definitely reversible. The reported ellipsometric data on MoO 3 thin films is also interpreted in terms of excitations of polarons and bipolarons. Briefly, Room temperature and higher temperature excited electronic states correspond to hopping of polarons from their donor states to the immediate neighbouring higher energetic impurity states within the polaron band. Similarly the changes in the conductivity and other film characteristics during cooling are caused either by polaronic or bipolaronic or mixed excitations.
We hope that this study will stimulate more theoretical work with a view to polaron and bipolaron theory.