Author's Accepted Manuscript Nano-quantum size effect in sol–gel derived mesoporous titania layers deposited on soda- lime glass substrate Ewa Gondek, Pawel Karasiński, Sabina Drew- niak PII: S1386-9477(14)00145-3 DOI: http://dx.doi.org/10.1016/j.physe.2014.04.018 Reference: PHYSE11586 To appear in: Physica E Received date: 1 April 2014 Revised date: 19 April 2014 Accepted date: 21 April 2014 Cite this article as: Ewa Gondek, Pawel Karasiński, Sabina Drewniak, Nano- quantum size effect in sol–gel derived mesoporous titania layers deposited on soda-lime glass substrate, Physica E, http://dx.doi.org/10.1016/j.physe.2014.04.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. www.elsevier.com/locate/physe
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Author's Accepted Manuscript
Nano-quantum size effect in sol–gel derivedmesoporous titania layers deposited on soda-lime glass substrate
Received date: 1 April 2014Revised date: 19 April 2014Accepted date: 21 April 2014
Cite this article as: Ewa Gondek, Paweł Karasiński, Sabina Drewniak, Nano-quantum size effect in sol–gel derived mesoporous titania layers deposited onsoda-lime glass substrate, Physica E, http://dx.doi.org/10.1016/j.physe.2014.04.018
This is a PDF file of an unedited manuscript that has been accepted forpublication. As a service to our customers we are providing this early version ofthe manuscript. The manuscript will undergo copyediting, typesetting, andreview of the resulting galley proof before it is published in its final citable form.Please note that during the production process errors may be discovered whichcould affect the content, and all legal disclaimers that apply to the journalpertain.
Abstract. The TiO2 nanolayers were fabricated on soda-lime glass substrates with the application of sol-gel method and dip-coating technique. In the fabricated TiO2 layers, the quantum size effect can be observed. For the sake of comparison, we investigated also the TiO2 nanolayerslayers fabricated on soda-lime glass substrates with a buffer silica layer. The fabricated layers were investigated with the application of optical measurement techniques and atomic force microscopy. The widths of energy gap and Urbach energy were determined. The diffusion of sodium ions Na+ from the glass substrate to the TiO2 layer brings about the non-monotonic dependence of the energy band gap on the thickness of TiO2 layer. In the TiO2 layers fabricated on soda-lime glass substrates pre-coated with a SiO2 layer, the influence of silicon ions on the direct energy band gap was found.
1. Introduction Titanium dioxide TiO2 is a wide energy band gap n-type semiconductor with wide application due to its optical and electrical properties. Titanium dioxide films are very versatile from the view point of its potential applications such as photocatalyst [1-3], self-cleaning glasses [4], antireflection [5] or high reflection coatings [6], electrochromic films [7], solar cell [8-10], transparent conductors [11], protective layers [12], and gas sensitive layers [13-15]. Titanium dioxide is a component used in planar optical waveguide technology [16,17]. Many different technological procedures for the fabrication of thin films of titania have been reported, such as: e-beam evaporation [14], magnetron sputtering [1,18], ultrasonic spray pyrolysis [19], chemical vapor deposition [20], metal organic chemical vapor deposition [21], pulsed laser deposition [22], and sol-gel method [3-7,10,13,15,23]. The sol-gel method has advantages, such as low temperature processing, easy coating of large area, and being suitable for preparation of porous films and homogeneous multi-component oxide films. In contrast to the other, the sol-gel method is very efficient and does not require expensive technological equipment. The most important advantage of sol-gel over other coating methods is the ability to tailor the microstructure of deposited films [23], so using the sol-gel method the titania films of controlled structure can be produced. The properties of sol-gel derived titania films depend on applied technological processes as well as applied substrates. Different procedures of fabrication technology of titania layer with the sol-gel method as well as the properties of the obtained layers have been widely reported in literature [3-7,10,13,15,23,24]. The influence of substrate type on photocatalytic properties of titania dioxide was discussed in literature in the past [25-27]. However, to the best of our knowledge, the problem involving the influence of substrate type on the width of energy gap of the titania layer has not been discussed so far. While investigating thin titania films fabricated on soda-lime glass substrates, we found that there was a non-monotonic dependence of the indirect energy band gap on layer thickness.
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And that finding stimulated us to undertake the research presented here in order to clarify the origin of the effect. To the best of our knowledge such non-monotonous dependence of indirect energy band gap on layer thickness was not explored earlier. In this paper we present results of our studies of the influence of soda-lime glass substrate on the quantum size effect in sol–gel derived mesoporous titania layers which demonstrate as blue shift of optical energy band gap. Fabricated by us via sol-gel rout titania layers on soda-lime glass (SLG) substrate exhibit both direct and indirect optical energy band gap. For the indirect transitions we obtain non monotonic dependence of the energy band gap versus layer thickness while for the direct transition we obtain monotonic one. We present both results for titania layers on SLG substrates pre-coated with the silica films of different thickness. The objective of the work was to define the influence of the thickness of the buffer silica layer on the properties of titania layers. The presented here data show that the buffer silica layers is an effective barrier for Na+ ions. However, this layer is simultaneously a cluster of Si ions, which difunds to the TiO2 layer. The concentration of Si4+ in the TiO2 has an influence on the Urbach energy magnitude. The resulting titania layers were characterized by monochromatic ellipsometry, UV-VIS spectrophotometry and atomic force microscopy (AFM). The work consists of two main sections. Section 2 of the work contains the description of technological procedures, the applied measurement methods and measurement apparatus, and the results of the carried out research and discussion are presented in Section 3.
2. Experimental procedures
2.1 Substrates The titania layers have been fabricated on SLG substrates (microscope slides, Menzel-
Glaser) and on soda-lime glass substrates precoated with a SiO2 layer (SLGC). Ultra clean SLG substrates, cleaned as per the procedure described elsewhere [17], were used for titania and silica thin film depositions. The SLG substrates used in the studies contain 14.3 wt % of Na2O as its component. At high temperature the sodium ions Na+ in SLG have high mobility and diffuse to the titania layer coated onto substrate surface [25-27]. The purpose of the silica layers coated on the SLG substrates was to reduce the diffusion of Na+ ions to the titania layer. The thickness of the silica layers was from 87nm to ∼1200 nm. The silica layers of the thickness from 87nm to 159nm were fabricated with the use of dip-coating technique with different substrate withdrawal speeds from the sol, and thicker silica layers were fabricated by multiple coating of thinner layers.
2.2 Sols preparation The processes of sol-gel technology are described in detail in a comprehensive book; ”Sol-Gel Science” by Brinker and Scherer [23]. Sol of the silica has been prepared using tetraethyl-orthosilicat (Si(OC2H5)4; TEOS) obtained from Aldrich Chem Co., deionized water, nonequeous ethyl alcohol (EtOH, obtained from POCH, Poland) as homogenizing agent and hydrochloric acid HCl 35% as a catalyst. Molar ratios of these ingredients were controlled at: TEOS:EtOH:H2O:HCl=1:12:8:0.44. Obtained solution was ultrasonically stirred in a closed glass vessel at temperature of 50°C for 3h.
Prekursor solution for titania TiO2 was prepared using tetrabutylorthotitanate (Ti(OC4H9)4; Ti(OBu)4) obtained from Aldrich Chem Co., water H2O, nonequeous EtOH, diethanolamine (NH(CH2CH2OH)2; DEA) and polyethylene glycol (HOCH2(CH2OCH2)nCH2OH, molecular weight 400; PEG400). The DEA bring about restrain the rapid hydrolysis of Ti(OBu)4. At the beginning 3.5g of DEA was dissolved in 20ml of EtOH, then to these solution were added next 20ml of EtOH and 10,7ml of Ti(OBu)4.
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Obtained solution was ultrasonically stirred in a closed glass vessel at temperature of 50°C. After 30 min of stirring to the solution was added drop by drop of 17 ml of EtOH (96%) and then 3 g of PEG400 was incorporated into the solution. The solution was still stirred ultrasonically for 30 min.
2.3 Films fabrication Two series of structures with titania layers fabricated with the dip-coating technique were
produced on two different types of substrate. The first series of structures contained titania layers of different thickness fabricated directly on SLG substrate. In this case, the particular titania layers were coated with different substrate withdrawal speeds from the sol. The second series of structures contained titania layers of the same thickness fabricated on soda-lime glass substrates precoated with silica films of different thickness. In this case, all titania layers were coated with the same substrate withdrawal speed from the sol.
The substrate withdrawal speed v from the sol is the basic parameter, which permit to control the layer thickness. For a general case, the dependence of final layer thickness d on the substrate withdrawal speed v can be expressed in the following form [28]:
0)( dvAd += χξ (1)
The proportionality index A depends on sol viscosity, its density and on the surface tension on the surface sol-environment [23,29,30], whereas ξ=(1cm-1min)-χ is a unit scaling factor of the dimension of speed inverse. The exponent χ is referred to as slope index, and its value for Newtonian liquid is within the range from 0.50 to 0.66 [23,28-30]. Detailed expressions on the dependence of film thickness on substrate withdrawal speed can be found in Ref. [30]. For a given technological process, the proportionality index A and power χ can be determined empirically. Fabricated structures have been annealed at the temperature of 500ºC for 1 hour. The temperature of annealing is sufficient to remove the residual organic matter from titania films, DEA and PEG. DEA is completely eliminated at 500°C [31] and PEG is eliminated below 500°C [32].
TiO2 exist in three main phases; anatase, brookite and rutile. As a bulk material the most stable is a routile. However, when TiO2 is produced with solution-phase methods, then principally anatse is obtained [33]. With a very small size of nanoparticles, their surface energy accounts for a considerable part of the total energy, and the surface energy of anatase is lower then those of routile and brookite [34]. We assume that in the layers presented here, which were annealed at the temperature of 500°C, only anatase [35] and amorphous phase are present. Rutile shows up in titania dioxide layers annealed above 600°C [17,35,36].
2.4 Experimental instrumentation The fabricated titania layers have been tested with application of atomic force microscope
(AFM), Ntegra Prima (NT-MDT), monochromatic ellipsometer Sentech SE400 (λ=632.8nm, Sentech, model 2003, Germany) and spectrophotometer UV-VIS AvaSpec-ULS2048LTEC (Avantes) with light source AvaLight-DH-S-BAL (Avantes). The AFM experiments on TiO2 thin layers were performed with semi-contact mode AFM. In AFM measurements the HA_NC (NT-MDT) silicon cantilever with nominal curvature radius of a tip 10 nm and resonance frequency of 250 kHz was used. The AFM image analysis was carried out using commercial NOVA 1.0.26.1644 (NT-MTD) software procedures to determine Root-Mean-Square (RMS) parameter. Ellipsometric measurements were carried out for wavelength λ=632.8 nm and spectroscopic measurements were carried out in the spectra range of 200-1100nm.
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3. Results and discussion
3.1 Titania and silica layers Fig.1 presents the influence of withdrawal speed on thickness d and refractive index n of
titania layers fabricated on SLG substrate. The experimental dependence of the refractive index on the substrate withdrawal speed was approximated with the linear dependence n=0.00154⋅v+2.04475 (v in cm/min). It can be observed that the refractive index is slightly increasing with the rise of substrate withdrawal speed v from the sol. By changing the substrate withdrawal speed v from the sol from 3.6cm/min to 16.7cm/min, we obtained titania layers of the final thickness d respectively from 44nm to 88nm. The experimental dependence of the thickness d on substrate withdrawal speed for v> 6cm/min was approximated with the dependence described with Eq. (1). The following parameters of the curve d(v) were determined: A=(15.911±0.075)nm⋅min⋅cm-1, B=(-0.06±0.34)nm and α=0.598±0.02. Within the speed v >6cm/min, the dependence d(v) is a convex function, and such dependences are typical for sols, which exhibit the properties of Newtonian liquids. Another character has the dependence d(v) for v<6 cm/min. In our earlier research studies we were obtaining the d(v) dependences having the character of a concave function. Such dependences were being observed by us within the range of lower substrate withdrawal speeds v from the sol when the sols were strongly dissolved in EtOH. The character of concave function is reflected by the dependence d(v) presented in Fig.2, determined for silica layers fabricated within the scope of the present research studies. By changing the substrate withdrawal speed v from the silica sol within the range 1.8cm/min to 6.3 cm/min, we obtained silica layers of the final thickness respectively from 85nm to 160nm.
The experimental dependence of the refractive index of silica layers on the substrate withdrawal speed was approximated with the linear function n=-0.00219⋅v+1.47403 (v in cm/min). It can be seen that the refractive index is slightly decreasing with the rise of substrate withdrawal speed v from the sol. Such dependences are typical for a polymeric sol where the polymers are weakly charged and the condensation rate is high [23]. The refractive indexes of all silica layers are higher than the refractive index of silica known from literature (1.45702). High refractive index of silica layers bespeaks of high compactness of the material, and its higher value than that known from literature may be effected by birefringence caused by high stresses which are typical for sol-gel processes.
Fig.1 Influence of substrate withdrawal speed from sol on thickness and refractive index of mesoporous titania TiO2 layers on SLG substrates.
Fig.2 Influence of substrate withdrawal speed from sol on thickness and refractive index of silica SiO2 layers on SLG substrates.
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Basing on the measured values n of the refractive index of the fabricated titania layers, their volume percentage porosity P was determined. For this purpose, the Lorentz-Lorenz equation was applied:
21
)%100
1(21
2
2
2
2
+
−−=
+
−
d
d
nnP
nn
(2)
where nd is the refractive index of anatase ≈2.52. Assuming that the pores of titania layers are filled up solely with air, their porosity calculated on the basis of (2) is PA≈19%. Using the simplified effective medium approximation n=nairP+nd(1-P) with nair=1 the porosity PA=30%.
3.2 Optical energy band gap The optical band gaps Eg of TiO2 layers have been determined with using the optical transmittance method. The band gap energy Eg was evaluated from UV-VIS transmittance spectra. If to assume parabolic energy distribution of density of states for valance and conducting band, the Eg of the titania films was determined by analysing the relationship between absorption coefficient α and photon energy hν using Tauc’s relation [37]:
( ) rgEhBh −=⋅ ννα , (3)
where: B is a constant which does not depend on hν, and r is the power coefficient which value determines the type of optical transition. The power coefficient r takes the value 2 for an indirect allowed transition and the value 1/2 for a direct allowed transition. The linear dependence of (α⋅hν)1/r on photon energy and its extrapolation to (α⋅hν)1/r=0, give the values of ind
gE (r=2) or of dirgE
(r=1/2), respectively. In the dip-coating technique, identical layers are deposited simultaneously on both sides of the substrate and hence the obtained structure (TiO2/glass/TiO2) is symmetrical. Assuming that the absorption of glass substrate is Ags, the absorption of each of titania layers is A=(1-exp(-αd)), where d is the layer thickness, and assuming that the reflectance for the structure TiO2/glass/TiO2 is R, then the transmittance can be written in the approximated form as:
( )( )( )2111 AART gs −−−= . (4)
Transmittance T, reflectance R and absorbance Ags are determined from measurements. From Eq. (3) the formula on absorption coefficient of titania is obtained:
Fig.3 Transmittance characteristics. SLG – soda lime glass substrate, SLGC – soda-lime glass substrate pre-coated with silica films of thickness 266 nm. 1-TiO2(88nm)/SLG/TiO2(88nm), 2-TiO2(56nm)/SLG/TiO2(56nm), 3-TiO2(37nm)/SLG/TiO2(37nm), 4-TiO2(34nm)/SiO2(160nm)/SLG/SiO2(160nm)/TiO2(34nm), 5-TiO2(34nm)/SiO2(87nm)/SLG/SiO2(87nm)/TiO2(34nm).
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( )( )gsART
d −−−=
11ln
21α . (5)
In Fig.3 are presented the transmittance characteristics of SLG substrate and SLGC substrate as well as transmittance characteristics of selected structures with titania layers. The visible maxima on the characteristics „1” and „2” are effected by light interference in the layers. It can be observed that within the energy range of photons >3.5eV, in which, for the titania layers, the transmittance was considerably lowered due to absorption, also the transmittance of SLG substrate is getting lower, which means the rise of absorbance Ags. Within the energy range of photons >3.5eV, the beams of light reflected inside the structure are attenuated and have inconsiderable influence on transmittance. It can be seen from the above that the approximated Eq.4 within the range of higher energies of photons, corresponding to strong light absorption in the structure, is more precise than that within the range of lower energies of photons. Fig.4 presents the plots involving the dependence of (αhν)1/2 on the energy of photon for three selected titania layers of different thickness coated directly on SLG substrates. A indirect energy gap can bespeak of the presence of anatase in the TiO2 layer. On the basis of such plots the energy band gaps were determined, considering an indirect allowed transition of TiO2 for layers with different thickness. The determined dependence of optical energy band gap Eg versus TiO2 layer thickness d is presented in Fig.5. The determined energy gaps are higher with respect to the energy gap of the bulk anatase specimens Ebulk=3.20 eV. The blue shift of the energy band gap is a consequence of quantum size effect [38-40]. We can see that the obtained dependence of energy band gap Eg versus TiO2 layer thickness is non-monotonic. Accordingly with our best knowledge, such dependences have not been presented in literature so far.
The quantity ΔE of blue shift of the energy band gap is connected with diameter D of nanocrystallites. For parabolic energy band near the band-gap, the average value of D may be estimated from the formula [39,43-45]:
*
0
2
2*
22
248.0893.02RyE
De
DmE −−=Δ
πεεπ (6)
where = 1.0545×10-34Js is the reduced Planck’s constant, )/(*
hehe mmmmm += is
Fig.4 Tauc plots of (αhν)1/2 vs. photon energy for indirect transitions.
Fig.5 Indirect energy band gap for TiO2 on SLG substrate vs. layer thickness.
Fig.6 (a) Energy band gap shift vs. crystalline diameter, (b) Crystalline size diameter vs. TiO2 layer thickness.
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the reduced effective mass of the electron-hole pair, me is the effective mass of the electron, mh is the effective mass of the hole, ε0 is the permittivity of free space, ε is the dielectric constant of anatase TiO2, ( ) ( )2
022** 4)2( επεemERy ⋅= is the effective Rydberg energy. ΔE is
a blue shift of the band-gap energy results of two competing mechanisms: a widening due to the Burstein-Moss effect, and a narrowing due electron-electron and electron-ion scattering [38]. Fig.6a shows calculated dependence of the blue shift band gap energy on the crystalline diameter D calculated on the base Eq.(6). In the calculations we have been taken into account the parameters as follow; effective masses of the electron me=m0=9.11×10-31kg and the hole mh=0.65m0 [46], dielectric constant of anatase ε=31. It is visible, that the blue shift band gap energy strongly decreases with the crystalline diameter. For the crystalline diameter ∼18nm the effect of energy band gap shift is practically not occurring any more. Fig.6b presents the dependence between the crystalline diameter of anatase and the layer thickness of the TiO2 deposited on SLG substrates, determined from the dependence presented in Fig.6a. For the presented thickness range of TiO2 layers, the diameters of anatase nanocrystals are within the range from ∼3.0nm to ∼3.8nm. It can be seen that the dependence of nanocrystal’s diameter on the TiO2 layer is non-monotonic. For thinner TiO2 layers (d<60nm) the diameters of nanocrystals are decreasing with the thickness d, and for thicker layers the diameters of nanocrystals are rising when the thickness of the TiO2 layer is growing. This non-monotonic dependence of the diameter D of anatase nanocrystals on the thickness d of the TiO2 layer (Fig.6b), and, in consequence, the non-monotonic dependence of the optical energy gap Eg for indirect transition on the thickness d (Fig.5) are caused by two effects. The first, commonly known effect states that with the rise of layer thickness the diameters of nanocrystals are rising. This effect can be viewed as dominant within the thickness range d>60nm (Fig.6b), in which we can observe that with the rise of thickness d of the TiO2 layer the nanocrystals’ diameters D are rising. For thinner layers (d<60nm), the diameters of the fabricated crystals are determined by the concentration of sodium ions Na+ present in the substrate. The presence of sodium ions Na+ brings about the rise of formation temperature of anatase and creates favorable conditions for the growth of their nanocrystals [26[. Here, the concentration of sodium ions Na+ in the TiO2 layer is presumably decreasing with the rising thickness of layer d and therefore, initially (d<60nm), when the thickness d is growing, the diameters of nanocrystals are decreasing (Fig.6b). The diffusion effect of sodium ions Na+ from the soda-lime glass substrates to TiO2 layers, which brought about the drop of their photocatalytic activity, was reported by Tada and Tanaka in Ref [47].
Fig.7 presents the plots of the dependence (αhν)2 on the energy of photon for the same three titania layers for which the results were earlier presented in Fig.4. The determined dependence
Fig.7 Tauc plots of (αhν)2 vs. photon energy for direct transitions.
Fig.8 Direct energy band gap for TiO2 on SLG substrate vs. layer thickness.
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of direct band gaps on the thickness of layer TiO2 are presented in Fig. 8. We can observe a distinct decrease of optical energy band gap for the direct transition on layer thickness. The optical band gap Eg in the presented range of thickness d is decreasing from ∼4.07eV to ∼3.89eV. The diffusion of sodium ions Na+ from the SLG substrate to the TiO2 layer can be reduced by the application of a silica buffer layer. In order to determine the efficiency of silica layers in preventing the migration of sodium ions Na+ to TiO2 layers, we investigated the influence of the layer SiO2 on the optical energy band gap of titania. On the substrates of soda-lime glass coated by silica layers of different thickness dSiO2, TiO2 layers of the thickness d=36nm were fabricated. The parameters of silica layers of the thickness up to 159nm are presented in Fig.2. In TiO2 layers fabricated on SLGC substrates, only direct energy gap was found, which may suggest that these layers are amorphous. The TiO2 layers of a similar thickness, fabricated on SLG substrate had a indirect energy gap, which resulted from the presence of anatase nanocrystals in them, and the growth of these nanocrystals was prompted by sodium ions Na+ diffusing from the substrate to the TiO2 layer. The lack of the slope energy gap bespeaks of the lack of nanocrystals in the TiO2 layer fabricated on the SLGC substrate. It results from effective blocking made by the silica layer of the diffusion of sodium ions from the SLG substrate to the TiO2 layer. The obtained results show that even the thinnest silica layers (dSiO2=85 nm) demonstrate very good masking properties. These results are in agreement with the results presented in Ref.[26]. Fig.9 presents the dependence of direct energy band gap for the TiO2 layer on the thickness of silica layer. For thinner silica layers (dSiO2<130nm), the energy band gap has the value of ∼3.79 eV. Then, for the thickness range of silica layer of 130nm<dSiO2<200nm, we can observe the drop of the value Eg. For thicker silica layers (dSiO2>200nm), we can observe that the energy band gap Eg of TiO2 is maintained on the level ∼3.74 eV. The obtained dependence of the energy band gap on the thickness dSiO2 of the silica layer can be effected by the diffusion of silicon ions from the silica layer to the TiO2 layer. Nam at al. reported that silicon ions Si4+ were observed in TiO2 layers fabricated on SLGC substrates [26]. When the buffer silica layer is thin (dSiO2<140nm) , its efficiency as the source of silicon ions Si4+ is limited, and the concentration of silicon ions Si4+ in the TiO2 layer is low. Thicker silica layers are more efficient sources of ions Si4+ and hence for the silica layers of the thickness dSiO2>200nm, we can observe a constant value of energy band gap in the TiO2 layer. However, in order to confirm the theses, the research will have to be carried out on the influence of the thickness of buffer SiO2 layer on the concentration of silicon ions Si4+ in the TiO2 layers.
3.2 Urbach’s energy It can be concluded from the presented results that the TiO2 layers have a different structure. Additional information on that subject can be obtained by the analysis of the optical absorption band tail. The slope of the Urbach tail (Urbach energy) characterizes the structural disorder in the material which produces localization of the electronic states within an energy band. It is well-known that absorption coefficient α(λ) near the band edge shows an exponential dependence on photon energy [48]:
Fig.9 Direct energy band gap for TiO2 on SLGC substrate vs. silica layer thickness. TiO2 thickness d=34nm.
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( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛ ν⋅α=να
uEhexph 0 (7)
where α0 is a constant, EU is the Urbach energy. Thus, a plot of ln[�(�ν)] versus photon energy should be linear and Urbach energy can be obtained from the slope. The value of Urbach energy EU is interpreted as the width of the tail of localized states. In the layers of fine crystalline structure of material, high Urbach energy can bespeak of high differentiation of diameters and shapes of crystals [49].
The dependences of ln[�(�ν)] on photon energy are given in Fig.10. �(�ν) is obtained from the transmittance spectra. It can be seen that the characteristics have different slope within the straight-line range. Fig.11 presents the Urbach energy for the TiO2 layers of different thickness d. We can distinctly see two levels of energy EU, dependent on the thickness d. With the thickness d∼60 nm, we can observe a jump of Urbach energy. For this thickness there occur extrema presented in Fig.5 and Fig.6b. Higher Urbach energy for the layers of the thickness d<60nm means that the material of these layers has more differentiated structure than the material in thicker layers. Higher differentiation of material structure in thinner layers and higher density of localization states are effected by the diffusion of sodium ions Na+ from SLG substrate to TiO2 layer. Fig.12 presents the influence of silica layer thickness dSiO2 on Urbach energy for TiO2 layers, for which the dependence Eg(dSiO2) was presented earlier in Fig.9. Similar as for the dependence Eg(dSiO2), we can see here two ranges [50] Initially, when the thickness of SiO2 layers is below 200nm, Urbach energy is quickly rising with the rise of dSiO2. For the SiO2 layers thicker than 200nm, we can see a linear increment of Urbach energy from the thickness dSiO2. Such a character of the dependence of Urbach energy on the thickness of silica layer is confirming the thesis put forward earlier which states that it is the silicon ions Si4+ responsible for the rise of density of the localization states in the TiO2 layer which are diffusing to the TiO2 layer.
Fig.10 Dependences of ln[�(�ν)] on photon energy corresponding to different TiO2 layer thickness. 1 – d=38nm, 2 – d=60nm, 3 – d=44nm.
Fig.11 Dependence of Urbach energy on TiO2 layer thickness, SLG substrates.
Fig.12 Dependence of Urbach energy of TiO2 versus silica layer thickness, SLGC substrates.
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3.3 Surface morphology Figure 13 shows typical semi-contact AFM images of surface of the studied titania layer (d=38.2nm) fabricated on SLG substrate. Such titania layer exhibit typical grain-type surface morphology. The root mean square surface roughness is 1.334 μm over a 0.5×0.5 μm2 area. In Fig. 13a we can observe large aggregates made of smaller grains whose diameters are ∼24nm. It is a considerably higher value than that determined from optical measurements (Fig.6b). However, if we allow for the curvature radius of the applied tip (10nm), we obtain real diameters of the grains equal to ∼4nm, which complies with the presented earlier results obtained with the optical method. Fig.13b presents a profile of the surface of TiO2 layer where for two nanocrystals their heights were marked (3.8nm and 3.6nm), and their values comply with the diameters determined with the optical method (Fig.6). Figure 14a shows typical semi-contact AFM images of the surface of the studied titania layer (d=34nm) fabricated on SLGC substrate. The root mean square surface roughness is 0.421 μm over a 0.5×0.5 μm2 area. We can see that the surface of this TiO2 layer is considerably smoother than that of the
TiO2 layer on SLG substrate. Fig.14b presents a phase AFM image. A slight degree of phase changes, being from -1.34° to +1.21° bespeaks of high homogeneity of mechanical properties of the TiO2 layer. It proves that the homogeneity of material structure of the TiO2 layer is high. The obtained result confirms the amorphous character of the TiO2 layer on the SLGC substrate. Figs 15 and 16 show the semi-contact AFM images of the surface of titania layer fabricated on SLGC substrate with different silica layer thickness, dSiO2=266nm (Fig.15) and dSiO2=1180nm (Fig.16). In both cases the root mean square surface roughness has similar values which are respectively 0.523nm, when dSiO2=266nm (Fig.15) and 0.520nm when dSiO2=1180nm (Fig.16). Phase images also in these cases confirm high homogeneity of mechanical properties of layer material.
(a)
(b)
Fig.13(a) Atomic force microscope images AFM of TiO2 layer on soda-lime glass substrate, (b) image 3D. The scale correspond to 0.5×0.5 μm2. Thickness of TiO2 layer is d=38.2nm.
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(a)
(b)
Fig.15 Atomic force microscope images AFM of TiO2 layer on pre-coated soda-lime glass substrate. (a) 2D image, (b) phase shift image. The scale correspond to 0.5×0.5 μm2.Thickness of TiO2 layer d=34 nm, thickness of SiO2 layer dSiO2=266nm. RMS=0.523 nm.
(a)
(b)
Fig.14 Atomic force microscope images AFM of TiO2 layer on precoated soda-lime glass substrate. (a) 2D image, (b) phase shift image. The scale correspond to 0.5×0.5 μm2.Thickness of TiO2 layer d=34 nm, thickness of SiO2 layer dSiO2=97nm. RMS=0.421 nm.
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4. Summary The paper presents the results of investigation studies involving the influence of soda-lime glass substrate on the properties of TiO2 layers fabricated via sol-gel route with the use of dip-coating method. In the studies on the TiO2 layer, optical methods and atomic force microscopy AFM were applied. In the TiO2 layers fabricated on soda-lime glass substrate there occurs quantum size effect, which was used to determine the diameters of anatase nanocrystals. In the TiO2 layers on SLG substrates, there occur both indirect transitions and direct transitions. The results of the investigation studies demonstrated non-monotonic dependences of the diameters of anatase nanocrystals and energy band gap for indirect transitions on the thickness of TiO2 layer. The character of these dependences is effected by the diffusion of sodium ions Na+ to the TiO2 layer and their influence on the crystallization of TiO2. For direct transitions, the energy band gap is decreasing with the rising thickness of the TiO2 layer. The TiO2 layers fabricated on SLGC substrates are of amorphous character and have only direct energy gap. For these layers, we found any influence of the thickness of the buffer SiO2 layer on the direct energy gap, which can be effected by the diffusion of silicon ions to the TiO2 layer. The AFM studies confirmed the presence of anatase nanocrystals in TiO2 layers fabricated on SLG substrates and the amorphous character of TiO2 layers fabricated on SLGC substrates. The determined Urbach energies for the investigated layers confirm the differentiation of the material of TiO2 layers, depending on their thickness, which is effected respectively by the diffusion of sodium ions Na+ and silicon ions Si4+.
Acknowledgments This work was supported by the National Science Centre on the basis of decision DEC-2011/03/B/ST7/03538.
(a)
(b)
Fig.16 Atomic force microscope images AFM of TiO2 layer on precoated soda-lime glass substrate. (a) 2D image, (b) phase shift image. The scale correspond to 0.5×0.5 μm2.Thickness of TiO2 layer d=34 nm, thickness of SiO2 layer dSiO2=1180nm. RMS=0.520 nm.
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Highlights • We studied the sol-gel derived titania layers on soda-lime glass substrate. • In titania layers, the quantum size effect is observed. • Soda-lime glass substrate influence on energy band gap of the titania layers. • The widths of energy gap and Urbach energy depend on titania layer thickness. • The kind of substrate and layer thickness influence on titania layer morphology.
