Evaluation of Bulk and Surfaces Absorption Edge Energy of Sol-Gel-Dip-Coating SnO 2 Thin Films

Advanced Materials Group & Defects in Semiconductors and Insulators Group, State University of São Paulo – UNESP, CP 473, CEP 17033-360, Bauru, São Paulo, Brazil Department of Physics – FC, State University of São Paulo – UNESP, CP 473, CEP 17033-360, Bauru, São Paulo, Brazil Modeling and Molecular Simulation Group – DM / FC, State University of São Paulo – UNESP, CP 473, CEP 17033-360, Bauru, São Paulo, Brazil Laboratory of Nanomaterials, Federal University of Minas Gerais – UFMG, CEP 31270-901, Belo Horizonte, MG, Brazil


Introduction
Electronic ceramics have received a great deal of attention in the past 10 years, in the seeking for technological innovation 1,2 .These ceramics usually are composed of metallic oxides, and play very important role as catalytic, solar cells, capacitors, gas sensors, varistors, among others 3 .Electrical and optical properties of this class of materials are strongly dependent on the final microstructure, which can be controlled by composition and chemical nature of doping, grain size and temperature of thermal annealing.Among the electronic ceramics, tin dioxide (SnO 2 ) deserves special attention due to its potentialities in optoelectronics devices.This compound has tetragonal structure of rutile type and may be characterized as an n-type semiconductor with wide bandgap, in the range 3.6-4.0eV.It presents high transparency in the visible range and high reflectivity in the infrared 4 .Its processing normally gives birth to defects such as oxygen vacancies and interstitial tin atoms, which act as donors in the SnO 2 matrix, increasing the electron density in the conduction band, explaining the n-type conduction.Then, even in the undoped form, tin dioxide presents fair n-type electrical conductivity 5 .The preferential direction of SnO 2 growth is an important parameter related to its structure and then to its electrical conductivity.These characteristics are influenced by the method of thin film deposition, molar concentration of the starting solutions, time and temperature of thermal annealing 6 .
The SnO 2 band structure diagram has been a motive of controversy among published literature, involving either experimental as well as theoretical papers.Some papers point to a direct bandgap transition 7,8 whereas others indicate indirect bandgap 9,10 .The complexity of tin dioxide electronic structure makes difficult the precise determination of the bandgap transition nature 11 .Optical absorption measurements allow estimation of the bandgap transition around the fundamental absorption edge, besides they give indications about its nature 12 .
The electrical conductivity of layers prepared by the sol-geldip-coating process is lower compared to films deposited by other techniques.This performance is generally attributed to a combination of effects associated to nanosized grains of sol-gel materials.As shown in this paper, crystallites generated by our sol-gel dip-coating route have nanoscopic dimensions.Therefore a considerable amount of crystallites is present in the material, which makes electron scattering at grain boundaries the most relevant mechanism to the film conductivity 13,14 .The physics of electronic conduction in these films is peculiar and rather unknown.Therefore, it deserves a careful investigation.
Under a theoretical point-of-view, computational simulation based on periodic first principles calculations has demonstrated great relevance in the evaluation of electronic structure of crystalline solids.The simulation leads to prediction of structure and electronic properties of solids, either qualitative as well as in a quantitative way 15,16 .Besides, it may yield properties hard or even impossible to measure experimentally.Electronic structure of bulk and SnO 2 surfaces affect directly optical, structural and electric properties of the material 6,17 .Among the several surfaces of SnO 2 , the (110) surface deserves special attention, because it is thermodynamically and electrostaticaly the most stable, even though the faces (101) and (011) are also relevant.The surface (110) presents the least surface energy when compared to other material surfaces 18 .Its structure consists of planes containing the oxygen and tin atoms separated by planes containing only oxygen atoms.This sequence may summarized as follows: O -Sn 2 O 2 -O -O -Sn 2 O 2 -O, etc, with ionic charges 2 -, 4 + and 2 - [19] .This surface is the most investigated, either experimentally as theoretically, mainly concerning the identification of atomic species present in the surface 20,21 .Band structure calculation, performed through the Tight Binding method 22 or Density functional theory 17 points to the bandgap transition of (110) surface as having indirect nature.
Another important face of SnO 2 is the (101) surface, because it is the dominant in materials with nanoscopic dimensions 20 , presenting potential application in nanostructured wires 23 .
In this work, we present results concerning the electrical transport in nanocrystalline undoped SnO 2 thin films.Photocurrent spectra are obtained by using a deuterium source to irradiate the sample in the ultraviolet range, at low temperature.In order to have the photoconductivity response of these films, spectra must be normalized, concerning the film optical absorption and the photon flux reaching the sample.The net result is the photoconductivity quantum yield, which shows marked temperature dependence 14 .The aim in this paper is to use the photocurrent spectra to determine the absorption coefficient as function of temperature and then, evaluate the bandgap transition energy.This paper also aims to bring on a correlation between theoretical and experimental approaches.The main goal is to evaluate experimentally structural and optical properties of SnO 2 thin films and compare with theoretical results obtained by the Density functional theory, applied to periodic models.This theoretical treatment is used to investigate the electronic properties of bulk and (110) and (101) surfaces, concerning the band energy diagram.These results are discussed and compared with X-ray diffraction, optical absorption and photoconductivity measurements in the ultraviolet-visible range.

Experimental Approach
Colloidal suspensions of undoped SnO 2 have been prepared through the sol-gel route, from solutions with distinct molar concentrations, which are called here method I and method II.Firstly, it has been prepared an aqueous solution of SnCl 4 .5H 2 O (0.5 M).Under stirring with a magnetic bar, NH 4 OH was then added until the pH reaches 11, leading to hydrolysis and condensation reactions.The remaining precipitated was submitted to dialysis against distilled water for proximately 10 days, in order to eliminate Cl -and NH 4 + ions.This procedure leads to a stable and transparent suspensions (sol) of SnO 2 with a volume increase of about 10 times (due to the dialysis process).This is called method I and its final concentration is 0.05M.The suspension obtained by the method I was then heated to 100 °C, until the dispersant agent (water) had 70% of this initial volume eliminated by evaporation.This procedure leads to a more viscous solution with final concentration of 0.2 M.This suspension is called method II.Thin films are deposited by the dip-coating technique on quartz substrates, starting from suspension obtained by method I and II.Quartz substrates are very important tool, since this material has absorption edge wavelength rather below the SnO 2 absorption edge (about 350 nm), which do not mask the ultraviolet spectra of films deposited on this sort of substrates.Substrates are vertically dipped into the suspension with dipping rate of 10 cm/min.Films were fired at 400 °C by 10 minutes, between each layer.The total number of layers was 30 by the film obtained by method I and 10 for the film deposited by method II.Both samples have a final annealing at 550 °C, at room pressure conditions, for 1 hour.Resulting thickness in both cases is about 300 nm, as obtained by scanning electron microscopy (SEM) of cross section.
X-ray diffraction data of films were obtained with a RIGAKU diffractometer, model D/MAX-2100/PC, coupled with a Cu K α (1.5405 Å) radiation source and a Ni filter for elimination of K β radiation.Scanning rate was 1 degree/minute in the range 20 to 80°.Optical absorbance was carried out in a Cary spectrophotometer, in the range 190 to 900 nm (ultraviolet to near infrared).Photocurrent spectra are obtained by using a deuterium source (30 W) to irradiate the sample in the ultraviolet range, through a computer controlled Oriel ultraviolet monochromator and holographic diffraction grating.The photocurrent was continuously recorded with a 6517A Keithley electrometer.The low temperature is obtained by using a closed cycle helium cryostat of APD-Criogenics and a Lake Shore temperature controller, with a 0.05 degree of precision.

Theoretical Method and Model System
SnO 2 crystallizes in tetragonal rutile structure and belongs to the space group P4 2 /mnm.The structure of the conventional rutile unit cell of SnO 2 is characterized by two lattice parameters, a and c, (Figure 1a) and an internal parameter u associated with the O atomic position.There are two formula units per primitive unit cell; with the threefold-coordinated oxygen atoms forming distorted octahedral configurations around the Sn atoms.Experimental and theoretical analysis indicates that the (110) surface is the most stable of the rutile structure with the lowest surface energy 18,21,37,39 .The surface stability order is (110) < (010) < (101) < (001) 39 .
The XCRYSDEN program 40 has been used for design of band structure of bulk and surfaces.The band structures were obtained for 80 K → points along the appropriate high-symmetry paths of the adequate Brillouin zone.

Structural properties
Figure 2 shows X-ray diffraction data for films of SnO 2 prepared respectively by methods I and II.It is easily verified that films present rutile type structure 41 .It is indicated in Figure 2 the cassiterite phase main directions as well as the crystallite size (t) calculated according to the Scherrer equation 42 .It also can be verified in Figure 2 that the thin film prepared through method II (more viscous solution) presented strong intensity in the direction (101) related to directions (110) and (211).The thin film prepared by the method I (less viscous solution) presented strong intensity in the ( 101) and (110) directions, however the peak is slightly more intense for (101) direction than the peak for direction (110).The smaller number of layers leads to less interface defects and then a cleaner diffractogram is expected, as verified in figure 1 for the method II thin film (10 layers), where the cassiterite phase structure is much better defined.
In order to evaluate the preferential growth direction, the texture coefficient (CT) of samples is calculated by relating the relative intensity of the diffraction peaks with a randomic oriented sample (reference sample).JCPDF data 41 was used for peak identification.CT is the preferential growth of crystalline plans parallel to film surface, and has been calculated by Equation 1 [43] : where I(hkl) are the intensities of X-ray diffraction peaks of investigated samples, I o (hkl) are the intensities of X-ray diffraction A periodic first-principle calculation, based on density functional theory (DFT) 24 with the Becke's three-parameter hybrid nonlocal exchange function 25 , combined with the Lee-Yang-Parr gradient-corrected correlation function 26 , B3LYP, were performed by using the CRYSTAL06 computer code 27 .This functional have yielded results comparable to more sophisticated correlated calculations or perturbation models 28 and have been employed successfully in studies on the electronic and structural properties of the bulk and surfaces of several systems [29][30][31] .
The atomic centers have been described by DB-31G 32 for O atom and DB-21G *33 , for Sn atom, where DB refers to Durand-Barthelat non-relativistic large effective core potential 34 .The experimental values of the lattice constant are: a = 4.737 Å, c = 3.186 Å [35] , and u = 0.306 [35] .From these parameters, we have carried out the optimization procedure, yielding: a = 4.702 Å, c = 3.194 Å and u = 0.306.Our results are only ~0.01%lower than the experimental data for the a parameter, ~0.01%larger for the c parameter and 0% for the internal parameter u.These results are in good agreement with other theoretical and experimental data 17,18,35 .
From this optimized parameters, two surfaces structures (110) and (101) have been modeled, by taking into account the mirror symmetry with respect to the central layers, slab models.These slabs are finite in the c-direction but periodic in a-and b-directions.Both slabs are depicted in Figure 1.
In order to select the size of the slab models, we have calculated the surface energy by using 9 to 21 layers.These energies have converged to its infinite thickness.Thus, 21 layers may be sufficient to describe the surface geometry for both surfaces.
The (110) termination results in an outermost plane of oxygen atoms that appears in rows along the [001] direction (Figure 1b).These O atoms are called "bridging" (O b ) atoms.In the second atomic layer, there are fivefold-coordinated (Sn 5c ), and sixfold-coordinated (Sn 6c ) Sn atoms and O atoms in the same plane (O p ).A third and fourth plane of oxygen atoms are located below that.The SnO 2 surface (101) consists of fivefold-coordinated Sn (Sn 5c ) atoms and of alternating rows of twofold-coordinated O (O 2c ) atoms and threefold coordinated O (O 3c ) atoms, situated slightly below the plane of the Sn atoms 36 .
The effect of relaxation has been analyzed on the (110) and (101) surfaces by fully relaxation of all atoms, i.e., the O and Sn atoms are free to move along x-, y-and z-directions.The results are presented in Table 1.
The positive displacements in z-direction, ∆z, denote relaxations toward the vacuum region and the negative displacement indicate relaxations inward the bulk.For SnO 2 (110) surface the displacements of the O b , 0.01 Å, O p , 0.11 Å and Sn 6f 0.2 Å in the z-direction are toward the vacuum region and the Sn 5f inward the bulk.The relaxation of the (101) surface show that the O b and Sn 5f are displaced toward the vacuum by 0.03 and 0.02 Å, respectively.Our results are in a similar range that previous reported data of Beltran and other theoretical results 37,38 .The displacement of the Sn atoms are larger than the oxygen atoms, leading a rumpling of the layers.peaks of a polycrystalline material with randomic orientation (reference) and N is the number of analyzed peaks in the diffractogram.CT close to 1 (one) indicates a non-texturized material, and CT close to N indicates a higher texturization.Table 2 brings the calculated values of CT, according to Equation 1, for the (hkl) crystallographic plans and relative intensities, associated with the experimental data of X-rays diffraction of films prepared by methods I and II, presented in Figure 2, as well as the reference (JCPDS -41-1445) 41 .
As can be seen in Table 2, calculation of CT indicates that the SnO 2 thin film presents the (101) direction as preferential for the growth.Besides the film prepared by the method II (more viscous suspension) presents a higher CT in this direction, compared to film prepared using method I (less viscous suspension).

Optical absorption
Optical absorption coefficient (α) may be evaluated from absorbance data, when the material thickness is known.Scanning electron microscopy of cross section (not shown) yields the thickness as about 300 nm.From the evaluation of α, the material bandgap may be estimated by using the Equation 2 [44] : where α is the absorption coefficient, A * is a constant, y is an integer, that defines the sort of transition, for y =1 (direct transition) and y = 4 (indirect transition).The energy magnitude is determined by extrapolation for the linear range of the experimental curve (αhυ) 2 to x axis.Figure 3 represents the optical absorption spectra of SnO 2 thin film, deposited on quartz substrates, produced by the method II.The inset of Figure 3 shows the bandgap evaluation of this material, assuming that the band transition is direct.It is important to mention again that the use of quartz substrates is fundamental for investigating optical properties of SnO 2 , because the quartz absorption does not coincides with the tin dioxide absorption edge, avoiding masking the bandgap evaluation 44 .From Figure 3 it is verified that the material bandgap is about 4.1 eV, in good agreement with published data 45,46 .

Relationship between photoconductivity and optical absorption
When radiation is shined on a semiconductor sample with electrical conductivity s, the fraction of the incident radiation after propagation through a distance x, is given by Equation 3 [47] : where α, the absorption coefficient, is given by Equation 4 [47] : where k is the imaginary part of the refraction index, called extinction coefficient.
From Maxwel equations, after a straightforward algebra, it may be concluded that (Equation 5): Combination of Equations 4 and 5 yield a relation between absorption coefficient (α) and electrical conductivity (s) (Equation 6):   Equation 6 may be used to evaluate the semiconductor bandgap from photo-induced electrical conductivity spectra data, where the conductivity is monitored by the wavelength of irradiating light.Figure 4 shows photoconductivity spectra data, measured for some distinct temperatures.It is easily verified that as the temperature decreases, the overall magnitude of photo-induced current also decreases.This is expected because the resistivity is supposed to increase as the film cools down, a typical semiconductor behavior.Moreover, the optical signal reaching the sample is rather low and does not promote a high free carrier excitation, which means that the resistivity follows the same shape of the dark conductivity.To obtain a normalized photoconductivity spectrum, it is important to calculate photoconductivity quantum yield 14 , where the measured photocurrent is normalized by the photon flux in order to eliminate the dependence of the excitation upon the incident light intensity  and sample absorption coefficient.This procedure can be seen elsewhere 14 but it is not the scope of this paper.Transforming the electrical photoconductivity data in absorption coefficient, according to Equation 6, the bandgap transition can be evaluated.Figure 5 shows the determination of band gap energy by considering direct band transition.The value obtained for room temperature, 4.2 eV, is about the same value obtained for evaluation directly from optical absorption data.For 200 K, Eg decrease to 4 eV and for 100 K, Eg is 3.5 eV.Decrease of band gap energy with cooling down is an expected result, because it is a typical behavior of well known semiconductor such as Si and Ge 48 .However the temperature variation rate obtained here is rather high.Absorption coefficient as function of temperature measurements are under progress and will rule as a comparison parameter for our estimation.A more complete approach where the normalization is taken into account may be important to determine the precision of band gap evaluation through photoconductivity data.On the other hand, by considering indirect transition, as shown in Figure 6, only the evaluation of room temperature band gap is possible.When the temperature is decreased, the evaluation of the band gap energy becomes impossible through this procedure, because the extrapolation for the abscissa crossing ((αhυ) 1/2 = 0) leads to negative values.We may conclude that, although the band gap variation with temperature is rather high, the application of the band gap evaluation from temperature dependent photoconductivity data works much better when direct band gap transition is assumed.The points of the Brillouin zone, chosen in our procedure, are the same used by Robertson 8 .The top of valence band (VB) is located at Γ point.The gap is direct, 3.55 eV, in accordance to the experimental optically measured gap 45,46 and other theoretical works 18,37,49 .For the (110) surface the top of the upper valence band (VB) is located between X' and Γ points bottom of the lowest conduction band (CB) is located at Γ point.The gap becomes indirect and is reduced to 2.52 eV, compared with the bulk value.On the other hand, for the (101) surface, the energy gap is direct at Γ points, 2.69 eV, in good agreement with published data 23,37 .The overall characteristics of the structural properties and electronic structure are coincident with previous investigations 37,38 .

Bulk and surface band structure diagram
The data presented in this paper lead to some correlated interpretation as follows: 1) According to evaluation through Scherrer equation, films present nanoscopic dimensions crystallites and, as already mentioned, nanometric dimension particles in general, present the surface (101) as dominant 20,23 .2) Analysis of X-ray diffraction data also lead to a material with preferential growth in the (101) direction, which is consistent with the crystallites dimensions.3) Results obtained from theoretical calculation of bulk and (101) surface yields direct band gap as the shortest transition.4) Determination of band gap from electro-optical data (photoconductivity spectra) leads to fair values when the band gap nature is assumed as direct.

Conclusion
Sol-gel dip-coating SnO 2 thin films, deposited on quartz substrates, present (101) preferential growth direction and nanometric dimension crystallites.Theoretical evaluation of (101) surface along with bulk calculation leads to direct bandgap transition at Г point.Evaluation of direct bandgap transition from optical absorption data yields 4.1eV.
Evaluation of direct transition bandgap from temperature dependent photoconductivity data yields 4.2 eV at room temperature, which decreases as the temperature is decreased.On the other hand, assuming indirect transition the calculation does not lead to physically acceptable result when the temperature is decreased Band structure analysis of bulk and (101) surface in conjunction with experimental data of X-ray diffraction, optical absorption and photoconductivity, suggest that the experimental determination of bandgap in SnO 2 sol-gel-dip-coating thin films is related to combined effects of nanocrystallite dimensions and optical absorption of (101) surface and bulk, since both present direct bandgap.

Figure 2 .
Figure 2. X-ray diffractogram for undoped SnO 2 thin film.a) Obtained by method II -10 layers and b) obtained by method I -30 layers.The three mean directions are indicated along with the evaluated crystallite size.

Figure 4 .
Figure 4. Excitation of photoconductivity spectra for SnO 2 thin film, obtained at distinct temperatures.

Figure 5 .
Figure 5. Direct bandgap evaluation using photoconductivity data for SnO 2 thin film, obtained at distinct temperatures.

Figure
Figure7aand b represents the band structures of the bulk SnO 2 , and appropriate high-symmetry paths of the adequate Brillouin zone.The points of the Brillouin zone, chosen in our procedure, are the same used byRobertson 8  .The top of valence band (VB) is located at Γ point.The gap is direct, 3.55 eV, in accordance to the experimental optically measured gap45,46 and other theoretical works18,37,49 .

Figure 6 .
Figure 6.Indirect bandgap evaluation using photoconductivity data for SnO 2 thin film, at room temperature.Inset: Attempt to evaluate indirect bandgap at 100 K.

Figure 7c ,
Figure7c, 7d and 7e represents the band structure for surface (110), the high-symmetry paths of the adequate 2D Brillouin zone and the band structures for surface (101), respectively.For the (110) surface the top of the upper valence band (VB) is located between X' and Γ points bottom of the lowest conduction band (CB) is located at Γ point.The gap becomes indirect and is reduced to 2.52 eV, compared with the bulk value.On the other hand, for the (101) surface, the energy gap is direct at Γ points, 2.69 eV, in good agreement with published data23,37 .The overall characteristics of the structural properties and electronic structure are coincident with previous investigations37,38 .The data presented in this paper lead to some correlated interpretation as follows:1) According to evaluation through Scherrer equation, films present nanoscopic dimensions crystallites and, as already mentioned, nanometric dimension particles in general, present the surface (101) as dominant20,23 .2) Analysis of X-ray diffraction data also lead to a material with preferential growth in the (101) direction, which is consistent with the crystallites dimensions.3) Results obtained from theoretical calculation of bulk and (101) surface yields direct band gap as the shortest transition.4) Determination of band gap from electro-optical data (photoconductivity spectra) leads to fair values when the band gap nature is assumed as direct.