Indium oxide doped with tin (In2O3 90%: SnO2 10%) is briefly called ITO that is from the most famous transparent conductive oxides. Grown layers’ completeness depends on the quality of interfaces which in turn depend on numbers of properties such as crystal structure and defects existence in thin film. In order to optimize above characteristics such as high transparency and low electrical resistance parameters such as thickness, doping type and level, and other conditions should be optimized deposited  -  . ITO has been specified optical property of conductive oxides such as In2O3 that heavily depends on caused imperfect density by external doping or their growth conditions. Originally, the addition of fluorine and tin atoms has been reported for external doping  . ITO films have played an important role in deciding their characteristics and achieving highly crystalline and morphologically uniform thin films on flexible or suitable substrates for two applications   . Also ITO thin films find different applications in optoelectronic system, for example, organic light-emitting diodes (OLEDs)    , transparent electrodes, transparent heating elements, coating electrodes in optoelectronics instruments (flat panel displays (FPDs)), photovoltaic cells, charge-coupled tools, electro-luminescence instruments    , photo-diodes    , windows with energy efficient, electro chromic instruments, liquid crystal displays (LCDs)  , image sensors   , solar cells  -  , gas sensors, photo crystal and photo electro crystal and heat reflector mirrors    . ITO thin films can be produced by different deposition techniques such as direct current (DC) and radio frequency (RF) magnetron sputtering although a variety of production methods have been used for making ITO films  -  , for example electron beam evaporation    , chemical vapor deposition   , spray pyrolysis   and reactive thermal evaporation  . One of the techniques, important for studying physical and structural feature of thin films is X-ray reflectivity (XRR). Also XRR is a highly efficient technique to research the structure of thin films from atomic scales to micrometer to obtain interface structures of thin film, density, thickness, and interfacial roughness. In the other word, the roughness of an interface is considered as a very important parameter in many industrial applications and quality of interfaces estimated by that   . The ITO has proven to be an advanced semiconducting material opening a new window in many electronic and optical industries due to its large optical band gap and the plasma frequency lying in the near IR spectral region  . Spray pyrolysis technique offers a simple and inexpensive experimental arrangement, ease of adding various doping materials, high growth rate and mass production capability for uniform large- area coatings which are desirable for industrial applications    . Although the dominant commercial market for laser glass is in large laser systems for inertial confinement fusion research with application to fusion energy and weapons physics science  , these materials have also found their way into a number of industrial and laboratory environments. For example, one leading application is in the field of laser shock peening  . Structural characteristics of thin films are technologically very important. Characteristics of these films are necessary to design the films with required physical properties. Grazing incidence X-ray reflectivity (GIXR) technique is becoming popular for structural characteristics of thin inorganic and organic films. This is a non-destructive tool for structural characteristics of thin films and multi-layer structures. In GIXR technique, the X-ray beam is incident on the sample at a grazing angle and the interfered reflected beam is collected by an X-ray counter. The interference occurs due to the presence of interfaces in the sample. The interference periods depend on the thickness of the layers and the amplitude of the interference oscillations depends on the contrast of the electron density between the layers and the interfacial roughness. Thus, the GIXR data contain structural information about the film such as thickness, density and roughness of the film and its individual layers  -  . This study focuses on structural properties of ITO thin films deposited by electron beam evaporation technique.
2. Materials and Methods
In this study, due to high melting point of Indium Tin Oxide (ITO; SnO2, In2O3, Merck), the electron beam evaporation method instead of thermal evaporation technique was used. Indium Tin Oxide (weight ratio; 90% In2O3 and 10% SnO2) was used as the evaporation source. Before the exposure of substrates in the vacuum chamber, they were immersed in an acid bath and hydrogen peroxide for 20 minutes, and then cleaned in pure acetone for 5 minutes. Finally, they were washed with distilled water and then dried. In order to ensure about the absence of lipid, the substrates were ultrasonically defeated in bath of alcohol Ethy- lic. After installing the substrates in the vacuum chamber of deposition, the initial pressure was adjusted to 1 × 10−6 mbar. Then by flowing of inert gas the substrate surface was bombarded. The cleaning process of substrate was performed to improve the substrate adhesion and prevent contamination of layers. Control of the partial pressure of the oxygen (purity 99.99%) was regulated in stable amount 6.2 × 10−5 mbar. The film deposition was carried out in deposition rate 0.10 nm・s−1 to produce thin films with thicknesses of about 50, 100 and 170 nm. Film thicknesses were measured with a quartz crystal microbalance. The substrate temperature, during the film deposition, was kept constant at 400˚C for 1 h.
Structures of ITO thin films were studied using X-ray diffraction (XRD; Philips Powder Diffractometer type PW 1373 goniometer) and X-ray reflectivity (XRR; XPERT-PRO reflectometer). The X-ray wavelength was 1.5405 Å and the diffraction patterns were recorded over the 2θ range 20˚ - 70˚ with a scanning speed of 0.04˚ min−1 for all thin films. The XRR diffraction patterns were recorded over the 2θ range 0˚ - 4˚ with a scanning speed of 0.002˚ min−1 for thin films with nominal thicknesses of 50 and 100 nm and a scanning speed of 0.001˚ min−1 for thin film with thickness of 170 nm.
3. Results and Discussions
3.1. XRD Characterization
The structural studies of the ITO thin films were carried out using X-ray diffraction. Figure 1 shows the X-ray diffraction pattern of ITO thin film, clearly demonstrating a crystalline structure.
The most useful information to be extracted by the XRD method is a grain size calculation, using the peak width at half height. Peak width at half height depends on the number of coherent reflector plates the crystalline structure. Using the Scherrer equation, the crystalline domain size (which can be equal to or smaller than the grain size) can be calculated from measurement of the width of the observed X-ray diffraction peaks:
Figure 1. X-ray diffraction pattern of ITO thin film with deposition rate 0.10 nm・s−1 and In2O3 spectra peaks.
In which the D represents crystalline domain size (nm), λ is the wavelength of the X-ray probe beam (0.15405 nm), B is the peak width at half height (phase peak) in terms of radians, K is the shape factor (approximately 0.94) and θ is the diffraction angle. Tables 1-3 present the values of K and λ are constant and determinate for each of 5 standard major peaks. Also B and θ values were obtained by the use of XPowderProVer.2010.01.30 software. The results of analysis material by X-ray diffraction are shown in Figure 1, which can be indexed as the primitive cubic system by comparison with data from ITO (JCPDS No. 06-0416)  . The diffraction peaks at 2θ = 21.88˚, 30.84˚, 35.81˚, 51.32˚, 60.96˚, correspond to (211), (222), (400), (440) and (622) planes respectively. The average size of nanoparticles 20 to 34 nm was obtained. X ray diffraction pattern of thin films 50, 100 and 170 nm is shown in Figure 2. The results show decreasing X-ray diffraction peak widths with increasing thickness, corresponding to more regular crystalline structure of the material and reduced structural.
3.2. XRR Analyses
3.2.1. X-Ray Interaction with Matter
The material index of refraction in the X-ray region can be written as:
where, here λ is the X-ray wavelength (λ = 1.54 Å), is the classical electron radius or Thompson scattering length (2.82 × 10−5 Å), is effective electron density and, where µ is the X-ray absorption length. Since the X-ray wavelength is comparable with atomic dimensions and the roughness of thin film surface, X-ray specular reflection can be described by Fresnel laws of classical optics. XRR critical angle
Equation (2) is resulting the evaluation of Snell’s law for small angles  . The critical angle for a layer is a function of its electron density, if one is known, the other can be determined using XRR. Figure 3 shows, the
Table 1. Characteristics of ITO thin film at thickness 50 nm.
Table 2. Characteristics of ITO thin film at thickness 100 nm.
Table 3. Characteristics of ITO thin film at thickness 170 nm.
Figure 2. X-ray diffraction pattern of ITO thin films with deposition rate 0.10 nm∙s−1 for thicknesses of 50, 100 and 170 nm.
experimental data of ITO thin films with nominal thicknesses of 50, 100 and 170 nm. The critical angles directly were obtained from XRR logarithmic curve. Then, the mean electron density (MED) of thin films was obtained from Equation (2) (Table 4).
Figure 3. XRR data of ITO thin films in different thicknesses.
Table 4. Calculated structural parameters of ITO thin films for thicknesses 50, 100 and 170 nm.
By the way, up proceedings were not carried out for thin film 250 nm due to the detection absence of Kiessig fringes. The following equation describes refraction coefficient n. Materials scattering property is with electron density ρ and scattering amplitude for each electron.
where and radiation wavelength depends on wave vector k. Elec-
tron density is in order in condensed material. In other word, with
r0 = 2.82 × 10−5 Å and k approximately 4 Å−1, is in order and less than 1 that it describe the refraction phenomenon is visible in range X ray weakly. Snell’s law with small angles and is according to equation. The critical angle is for external general reflection with control and with expansion to cosines:
By using up parameter magnitudes, is in order 1 m radian. Vertical axis shows reflected X-ray intensity from the surface and interfacial layers measured by the detector, according to the angle 2θ (Figure 3 and Figure 4). The first noted notice that attracts attention is Kiessig fringes absence of thin film of 250 nanometers. Thus, XRR technique is more suitable for thin film of less than 100 nm and preferably will have very good results for ultra-thin films (less than 20 nm)  .
Figure 4. Simulated curve of ITO thin films in different thicknesses.
Figure 5. Thin film structure information with X-ray reflectivity technique.
Figure 6. Schematic of X-ray reflectivity detector from thin film surface.
in Figure 4 is critical angle adjustment of films that it illustrates the same quality of films in the crystal structure and conditions of film deposition. In the other word, the films are relatively uniform electron density (Equations (4) and (5)). In early look at the curves; difference in the Kiessig fringes is obvious for each sample. According to Equations (4), (5) and with known critical angle, they are calculated electron density, refraction coefficient and film thickness according to Kiessig fringes of X-ray reflectivity curves. Also reflectivity curve slope is the same roughness of thin film surface. Reflectivity curve slope increases with the increasing of thin film roughness   .
3.2.2. Roughness and Thickness
Generally, there are three ways to data analyses of X-ray reflectivity for thin films:
1) The model of dynamic scattering by using of recursive formula.
2) The model of Distorted Wave Born Approximate (DWBA).
3) The model of reverse furrier transform by Born Approximate (BA).
In present work, the GENX software by DWBA was used to data analyses and real thickness of films, also Simulation and fitting X-ray reflectivity data and data analysis were carried out using MATLAB software by curve fitting tool (smooth) that simulated curves are shown in Figure 6. The Kiessig fringes result from constructive and destructive interference of X rays reflected from the two interfaces as a consequence of the angular-dependent phase shift. Their period is determined by the thickness of the layer. The film thickness is the same distance two consecutive peaks incurve and it has reverse relation with its magnitude. In the other word, thinner film has more fringes than thicker film (Figure 6).
To measure the thickness, according to Snell’s law for two consecutive peaks of the reflectivity curves:
where, d is the thickness of film. Due to the small angle approximation for Snell’s law, we have used:
Therefore, the thickness of each film is obtained (Table 4). Interference fringes are created by the phase difference between X-rays reflected from different surfaces. Roughness determines how quickly the reflected signal decays. A rougher surface produces more diffuse scatter, causing the reflected beam intensity to decay more with Theta (Figure 6). The roughness of each thin film was calculated as shown in Table 4  .
3.2.3. Optical Theory
The optical absorption coefficient, α is obtained using the optical absorbance A from, d is the film thickness and A was obtained from the equation, and I are the primary and secondary intensity of beams, respectively. The film energy gap, is calculated using the formula from Davis and Mott that for direct transition n = 2 and for an indirect transition n = 0.5, hν is the input photon energy and B is given by, is the extrapolated dc conductivity at T = 0 K, c is the light speed, Eₑ is the extent of the band tailing and nb is the refractive index of the material       . Also for the amorphous materials in the high absorption region, α can be described using the Davis and Mott formula, if the multiple reflections are neglected, the transmittance, T of the film is given by:
R is the reflectance that can be determined from measurements of both A and T using above equation, which can be rewritten in the following form:
The reflectance R of the material of refractive index, n and extinction coefficient, k is given by:
The absorption coefficient α is related to k by:
where λ is the wavelength. Using above equations the values of R, n, and k are calculated, respectively.
But, if the absorption edge in numerous amorphous materials in the low absorption region, follows the Urbach rule given by   :
where hν is the photon energy and is the terminative width of localized situations in the band causing from absence of long-range order (wonky depending on temperature)  . For optimizing the optical and physical properties of nanomaterials, the most important parameter to control is the interfacial system free energy of the system (solution)  . Whit Gibb’s adsorption equation that is the chemical potential of the adsorbed species and y is
the superficial adsorption density. where G is Gibb’s free energy and
is the amount of substance of the component or specie i. Using Gibb’s adsorption equation, the variation of water oxide surface (interfacial) tension with ionic strength (I) maximum surface charge density, and pH has been developed from Gibbs adsorption equation.
It is given as
, y, I is given in respectively, , and means interfa-
cial tension at equilibrium  . The size of the nanoparticles is directly related to the conditions for nucleation that include pH, ionic strength and concentration of precursors. Solid phases (particles, crystals thin films) evolve from solutions through nucleation and growth processes. The total change in free energy
of the system is given as, is the
chemical component while is the surface component is the free energy per unit volume. With assume that the new phase is there-fore and
spherical has a volume of. is the surface component of the free energy due to surface tension where θ is the
wetting angle differentiates the expression for change in free energy of the system from that of homogeneous nucleation   .
Using of X-ray reflectivity technique for various thin films study and investigation, the films should be very thin (approximately 20 nm and less).
In this work, ITO thin films were deposited by electron beam evaporation on white glass substrates with thicknesses of about 50, 100 and 170 nm. Using XRD and XRR, as the thickness were increased; the changes in structural properties of the ITO thin films were investigated. The results showed that ITO thin films maintained the crystalline structure and they had crystalline structure with a do- main that increased in size with increasing thickness. The distance between the Kiessig fringes is inversely proportional to the thickness of film. Hence, thicker films have smaller fringes compared with thinner films. The films with relatively uniform electron density, with increased reflectivity curve slope, increase thin film roughness. Roughness determines how quickly the reflected signal decays. Performed proceedings for each three thin films were not carried out for thin film 250 nm due to the detection absence of Kiessig fringes. Thus, XRR technique is more suitable for thin film of less than 100 nm and preferably will have very good results for ultra-thin films (less than 20 nm).
We would like to acknowledge KEFA Company (Iran, Tehran) that has supported us by providing X-ray reflectivity of thin films.
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