Structural, optical and dispersion energy parameters of nickel oxide nanocrystalline thin films prepared by electron beam deposition technique

Structural, optical and dispersion energy parameters of nickel oxide nanocrystalline thin films prepared by electron beam deposition technique

Journal of Alloys and Compounds 646 (2015) 937e945 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: http:...

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Journal of Alloys and Compounds 646 (2015) 937e945

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Structural, optical and dispersion energy parameters of nickel oxide nanocrystalline thin films prepared by electron beam deposition technique M.M. El-Nahass a, M. Emam-Ismail b, *, M. El-Hagary c a b c

Thin Film Laboratory, Physics Department, Faculty of Education, Ain Shams University, Roxy, 11757 Cairo, Egypt Physics Department, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt Physics Department, Faculty of Science, Helwan University, Helwan, 11792, Cairo, Egypt

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 April 2015 Received in revised form 10 May 2015 Accepted 11 May 2015 Available online xxx

In the present paper, we report on the structure and optical properties of non-annealed nickel oxides (NiO) nanocrystalline semiconductor thin films synthesized by electron beam deposition technique. The structure parameters of the as-deposited NiO nanocrystalline thin films are extracted from the X-ray powder diffraction (XRD) spectra and shows that the as-deposited films crystallize in the form of cubic NaCl structure with average lattice constant equal to 4.1797 Å and average lattice volume 73.018 (Å)3. In addition, the crystallite size (D) is found to increase from 15 nm to 24 nm with increasing film thickness from 151 nm to 343 nm. In a wide wavelength range, the optical parameters (absorption coefficient, refractive index and refractive index dispersion) of the nanocrystalline NiO thin films have been calculated from transmission and reflection spectra. The variation of the factors (ahn)2 and (ahn)0.5 as a function of photon energy identifying the optical transitions as direct transition with energy Edir g z z 2.924 eV and phonon energy of order 212 meV, 3.849 eV and indirect transition with energy Eindir g respectively. In the same wavelength range, the variation of the refractive index show normal dispersion behavior with single oscillator model Eo and Ed parameters obtained as 3.082 eV and 10.47 eV, respectively. The coordination number of the NiO nanocrystalline thin film is identified as 3.36. In addition, the lattice oscillator strength El, lattice dielectric constant εl, ratio of free carrier density to free carrier effective mass (N/m*) and plasma frequency (up) are extracted as 0.31 eV, 5.408, 1.043  1047 g1 cm3, 5.492  10þ14 s1, respectively. Also, the molar and volume refractions Rm, Vm and molar polarizability am, are also calculated and found to be 3.082 cm3/mol, 11.20 cm3/mol, 2.49ðA+ Þ3 , respectively. Finally, the Urbach energy Eu is also calculated and found to be 0.38 eV. © 2015 Elsevier B.V. All rights reserved.

Keywords: Nickel oxide thin films E-beam evaporation Nanomaterial Optical constants Single oscillator parameters Optical band gap

1. Introduction NiO thin films have many interesting properties, for instance, good crystallinity, very good chemical stability, wide spectral range of transparency with low resistivity, controllable transmittance for incident visible light, semiconducting material with wide band gap (3.6e4.0 eV) and thermoelectric behavior [1e3]. Therefore, all these abovementioned properties put NiO thin film as a very promising material with potential applications in antiferromagnetic layers of spin valve films [4]. NiO exhibits a cubic NaCl

* Corresponding author. E-mail addresses: [email protected], (M. Emam-Ismail). http://dx.doi.org/10.1016/j.jallcom.2015.05.217 0925-8388/© 2015 Elsevier B.V. All rights reserved.

[email protected]

structure and is made up of Ni2þ (transition metal ions) and O2 (legined ion) in which the nickel ion has an electronic configuration of 3d8 while the oxygen ion has an electronic configuration of 2p4. The extra oxygen atoms cannot be placed inside the NaCl structure; instead vacancies related to Ni2þ are created, thus giving a p-type conduction character and could be used as a p-type transparent conducting films [5]. In addition, NiO thin film is electrochromic (EC) material in which the transmission properties of the light passing through the film can be controlled by applying an external electric filed [6]. As a result, NiO thin films are extensively used in display devise Technology [7], optical smart windows and solar energy architectural windows [8]. NiO has interesting electronic band structure and therefore it has been extensively studied both experimentally and theoretically

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by a number of pioneering experimental, computational and theoretical techniques [2,9e13]. To grow good quality NiO thin films many experimental methods are used such as: thermal evaporation [14], e-beam deposition [15], spray pyrolysis [16], chemical deposition [17], solegel [18], reactive pulsed laser ablation technique [19], sputtering [7] and recently different power radio frequency magnetron sputtering [20]. The optical characterization used to optically investigate the deposited NiO thin films are mainly spectrophotometrey and spectroscopic ellipsometry techniques [21,22]. Obtaining accurate information about the optical properties of NiO thin film prepared by different deposition techniques is of clear interest from both fundamental point of view and technological purpose. There are many reported results about the optical properties of NiO thin film prepared by different deposition techniques. In most of these reported results the deposited NiO thin films are obtained after post-deposition annealing treatment [23e26]. In the present manuscript, different thicknesses high quality NiO thin film is obtained by using e-beam deposition technique without any pre or post annealing treatment. Compared with the previously reported results, our optical properties results reported here can be used as a starting point from which we can gain deep understanding about the variation of the optical properties of NiO thin films prepared under different experimental condition. In this article, we report new optical information about the structural and optical properties of NiO thin film. The article will be outline as follows:  In part 2, the experimental condition used to obtain good quality NiO nanocrystalline thin films is described.  In part 3, the structural properties of NiO in the form of powder and nanocrystalline thin films are investigated.  In the first section of part 4, the dispersion of optical absorption is investigated in wide wavelength range and also the direct and indirect transitions are identified.

 In the rest of part 4, the dispersion of refractive index is investigated in wide wavelength range and also the dispersion of the refractive index is understood with the help of using single oscillator model. Additionally, all the optical parameters extracted from the experimental data of the refractive index dispersion are obtained.

2. Experimental details The starting material used to fabricate NiO thin films was polycrystalline NiO powder produced by Aldrich chemical company of purity 99.999%. The color of the starting NiO powder was green. Such color indicates that the ratio of the Ni:O is 1:1, i.e the starting NiO powder used to prepare the films is stoichiometrically correct [27]. Different weight of NiO powder was then pressed in the form of circular pellets from which thin films will be deposited. After that, the NiO pellets were loaded into graphite boats positioned in the path of an accelerated electron beam (e-beam). On a corning glass substrate of No. 1022, the NiO film of different film thickness was deposited by an e-beam deposition technique using coating unit of type Edward 306Auto. The substrates used in the deposition process were carefully cleaned using ultrasonic hot bath, distilled water and pure alcohol. During deposition, the vacuum system was pumped to a pressure as law as 5  107 mbar. The homogeneity and uniformity of the deposited films were fully controlled by rotating substrate holder at low speed (5 rpm) with the source to the substrate distance was set at 20 cm. During deposition process, the substrate temperature was kept at 300 k. In addition, the conditions of evaporation were fully monitored by controlling the rate of evaporation which was set at 2 nm/s. Consequently, the time of film deposition was nearly about 3mints. During evaporation process, the film thickness and rate of evaporation were fully monitored using thickness monitor (model: FTM6 quartz crystal) attached to the vacuum system. Independently, the thicknesses of the deposited films were checked using F20 profile meter set up, which give thickness value for the deposited films of order 150, 220, 340 and 350 nm with accuracy of about ±5 nm. The experimental detailed used here can be found in our previously reported results [28,29]. The crystal quality, structure and phase purity of the deposited films were examined by means of conventional XRD (of type Shimadzu Diffractometer XRD 6000, Japan) with Cu-Ka1 radiation (l ¼ 1.54056 Å). The X-ray measurements were collected in stepscan modes, in a 2q mode between 10 and 80 (step-size of 0.02 and step time of 0.6 s). Pure Silicon~ Si 99.9999% was used as an internal standard. The optical measurements (transmittance and reflectance) were performed in a wide wavelength range (300e2000 nm) using JASCO V670 double beam spectrophotometer. For the deposited films, the transmittance spectrum was recorded at normal incidence while the reflectance spectrum was recorded at 6 off the normal to the sample surface. 3. Structural properties of NiO nanocrystalline thin films

Fig. 1. XRD diffractograms of the NiO powder panel (a) and thin films of different thicknesses panels (bee).

Fig. 1(a) shows the XRD of NiO powder and Fig. 1(bee) shows the XRD of the as-deposited films of different thicknesses. The XRD of the powder shows the existences of many reflection planes (111), (200), (220), (311) and (222) with 100% peak intensity observed from the planes (200). These peaks are clearly indicating that the NiO phase exist in the form of face centered cubic (FCC) of polycrystalline structure (ICSD Card No. 01-075-0269) [30]. As shown in the inset of Fig. 1(a), NiO has a rocksalt or sodium-chloride structure with two interpenetrating FCC lattices of metal (Ni2þ) and

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Table 1 (a). The following table showing the structural parameters of NiO powder. (b). The following table showing the structural parameters of NiO thin film of different thicknesses. (a) Sample NiO powder

d-spacing Å

Lattice constant (a) Å

Cell volume (V) Å3

Powder (111) (200) (220) (311) (222) aaverage

2.41113 2.08839 1.47651 1.25917 1.20557

4.177018 4.181771 4.177283 4.177025 4.178512 4.1783

72.87843 73.12750 72.89231 72.87880 72.95335 72.946

Lattice constant (a) Å

Thin film (200) plane t ¼ 151 nm 4.1795 t ¼ 217 nm 4.1849 t ¼ 337 nm 4.1772 t ¼ 343 nm 4.1772 Average 4.1797

Cell volume (V) Å3

Crystallite size (D) nm

Strain (ε) (lines-2nm)

Dislocation density(d) lines/nm2103

Number of crystallites per unit area (N) 102 nm2

73.00 73.29 72.89 72.89 73.018

15.17 19.67 23.89 23.98

9.564 12.42 15.10 15.11

4.34 2.58 1.75 1.74

4.325 2.851 2.472 2.490

ligand (O2) atoms which are displaced by (1/2)a along <100> direction where a is the cubic cell dimension [31]. The d-spacing, lattice constant and cell volume of the NiO powder of the cubic crystal structure calculated from the observed diffraction peaks are listed in Table 1 with an average lattice constant 4.1783 Å and lattice volume 72.946 Å3. For the as-deposited films and at a small thickness (t ¼ 151 nm), the XRD depicted in Fig. 1(b) shows a dominate amorphous behavior with very little peaks observed at 2q ¼ 37.16 and 43.28 . As the film thickness increases to approach 217 and above (337 nm and 343 nm) Fig. 1(cee), the XRD patterns of the as-deposited films show a characteristic peaks located at 2q ¼ 37.16 and 43.27 which corresponding to (111) and (200) reflection planes, respectively. The observation of the well resolved diffraction peak observed at 2q ¼ 43.27 is a direct clear evidence that the as deposited films have a preferred orientation along (111) and (200). The XRD presented in Fig. 1(cee) shows also that the intensity reflected from (200) plane is stronger than the intensity reflected from (111) plane which indicate improved epitaxial growth along (200) plane [21,16]. In addition, the degree of crystallization of the deposited films is greatly improved with increasing thicknesses. For the asdeposited thin films, the analysis of the well resolved diffraction peak originates from (200) reflection planes give an average lattice constant 4.1797 Å and d-spacing 2.08984 Å which agree very well with cubic NiO (JCPDS Card No. 47-1049). For the as-deposited NiO thin films of different thicknesses, the various structure parameters are listed in Table 1(b). These structure parameters including lattice constant, cell volume, crystallites size, strain, dislocation density and number of crystallites. Such parameters are defined in the following lines. The lattice constant a of the cubic unit cell of the as-deposited films is determined from to the following relation:

1=2  a ¼ d h2 þ k2 þ l2

(1)

where d is the interplanner spacing of the atomic planes whose Miller indices are (hkl). The cell volume is calculated as V ¼ (a)3 Å3. The average crystalline size (D) of the as deposited NiO films is calculated from the full width at half maximum (FWHM) of the (200) diffraction peak using Scherrer formula [32]:

kl D¼ b2q cos q

(2)

where k is Scherrer's constant (k ¼ 0.9), l is the wavelength of the x-ray radiation used (1.54056 Å), b2q is the full width at half maximum of the diffraction peak (FWHM) in radians and q is the Bragg diffraction angle. The strain introduced as a result of the difference between lattice constant of the as-deposited films and the substrate can be evaluated from the following relation:

ε¼

D 4 tan q

(3)

The dislocation density has also been calculated using the following relation [33]:



1

(4)

D2

The number of crystallites per unit area (N) of the as-deposited NiO films is calculated from the following relation [21]:



t

(5)

D3

where t is the film thickness. The data listed in Table 1(b) shows that the lattice constant and cell volume are independent of the film thickness and have a constant average values 4.1797 Å and 73.018 Å3, respectively. In addition, Table 1(b) clearly shows that with increasing film thickness, an increases in crystallite size (D) is associated with a visibly decrease in dislocation density (d) and number of crystallites per unit area (N) is observed. These results

1.0

T&R Intensities

(b) Sample

0.5

T R

0.0

500 1000 1500 Wavelength (nm)

t=151nm t=217nm t=337nm t=343nm

2000

Fig. 2. Optical transmission (T) and reflection (R) spectra of NiO nanocrystalline thin films deposited on thick transparent (tsubstrate ¼ 1.5 mm) corning glass substrate.

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indicate that the quality of the larger thickness film is very good. The structure properties obviously show that good quality polycrystalline NiO thin films is obtained using e-beam deposition technique without any annealing or substrate temperature [16], which is an advantage when comparing with other published works that report the same kind of structure but only after thermal treatment [24e27]. 4. Optical properties of NiO nanocrystalline thin films The experimental transmission (T) and reflection (R) spectra of the as-deposited nanocrystalline NiO films measured in a wide spectral range (280e2000 nm) are depicted in Fig. 2. The T or R spectra show that for small thickness (t ¼ 151 nm) no interference fringes is observed which is attributed to the low value of the optical thickness of the as-deposited film. As the thicknesses of the asdeposited films increases from 217 up to 343 nm a clear distinct interference fringes are observed at longer wavelength. The appearance of these interference fringes is a direct indication that the quality of the as-deposited films is greatly improved and also to the increase of the optical thickness of the as-deposited films. Such improvement is fully supported by the XRD pattern shown in Fig. 1(cee) and the data presented in Table 1b. In addition, the transmission spectra presented in Fig. 2 shows that for all thicknesses the transmission spectra approach zero (band gap energy) almost nearly at the same wavelength. Also, as clearly observed in Fig. 2, at larger film thicknesses, the T spectra display two regions. The first one is the transparency region (weak and medium absorption 1000e2000 nm), where the frequency of the probe wave propagating through the film is far away from the frequency corresponding to optical band gap of the investigated NiO as-deposited nanocrystalline thin films. The second one is the strong absorption region (280e700 nm), where the frequency of the probe wave approaches the frequency corresponding to optical band gap of the investigated NiO as-deposited nanocrystalline thin film. In the transparency region (low absorption region), the probe wave bounce back and forth between different interfaces (air-film, film-substrate and substrateeair interfaces) producing different reflected and transmitted waves. Such waves interfere coherently to produce the interference fringes observed in either T or R spectra. Such fringes are called fringes of equal chromatic order (FECO) of thin film [32,34]. In addition, the appearances of smooth interference fringes in T spectrum (Fig. 2) with high transmittance intensity indicate that the deposited films have low surface roughness and good thickness homogeneity. In the strong absorption region, the intensity of the propagating wave decrease drastically until it drop to zero at a frequency corresponding to the transition from valance to conduction band (optical band gap). Due to strong absorption process within the conduction band, the intensity of the interference fringes decreases drastically until it disappears completely at the optical band gap.

Fig. 3. Absorption coefficient a as a function of incident photon energy calculated for nanocrystalline NiO thin film.

i0:5 # h " ð1  RÞ2 þ ð1  RÞ4 þ 4R2 T2 1 a ¼ ln d 2T

(6)

where T, R and d are the transmittance, reflectance and thickness, respectively. As shown in Fig. 3, the absorption coefficient a is almost zero in the energy 2e2.5 eV (transparency region) and start to increases slightly in the energy range 2.5e3 eV (low absorption region). At higher energy 3e4.3 eV the absorption increases substantially to approach 3.8  105 cm1 (strong absorption region) where the frequency of the wave propagating through the NiO film approach the fundamental optical gap of the investigated film. For all investigated films, the optical energy gap EOpt can be calculated g by fitting the optical absorption a to Tauc's relation [37]:

 p ðahnÞ ¼ ao hn  Eg

(7)

where ao ¼ ðe2 =nch2 m*e Þð2mr Þ3=2 is a constant that depends on carriers effective mass (m*), mr is the reduced mass and n is the refractive index of the investigated films, Eg is the energy gap of the investigated film which is the minimum energy gap between top of the valance band and the bottom of the conduction band. The factor (hn) represents the energy measured in eV of the probe wave (photon) propagating within the investigated NiO film and p is the exponent which specify the type of band transitions involved in the absorption process; p ¼ 1/2, 3/2 for the allowed and forbidden direct interband transition, respectively, and p ¼ 2, 3 for the allowed and forbidden indirect interband transition, respectively. Equation (7) shows that the fundamental energy gap Eg dependence on the energy variation of the absorption coefficient. In order to find the

4.1. Absorption coefficient calculation for NiO nanocrystalline thin films Absorption process occurs within the NiO as-deposited thin film, is directly related to the reduction of the intensity of the transmitted electromagnetic wave as it approach the optical band gap of the investigated film. Therefore, understanding the absorption process in the film material can give important information about the type of transitions occur inside the gap of the film material [35]. The absorption coefficient a within the investigated NiO films is calculated from the measurement of the transmittance and reflectance spectra within the strong absorption region using the following relation [36]:

Fig. 4. The variation of the (ahn)1/2 as a function of hn for a NiO nanocrystalline thin film.

M.M. El-Nahass et al. / Journal of Alloys and Compounds 646 (2015) 937e945

fundamental band gap Eg and consequently types of interband transition, the factor (ahn) to the power 1/2 or 2 versus hn (Tauc relation) is plotted. Such graph is expected to show linear behavior at the higher energy region, which is the region close to absorption edge of the investigated film. Extending the linear dependence of the factor (ahn)0.5 to intersect with the energy axis (hn) at the value of (ahn)0.5 ¼ 0 will give the value of the energy of the fundamental optical band gap of the investigated film. Fig. 4 shows the dependence of the (ahn)0.5 as a function of the incident photon energy (hn). The dependence of the factor (ahn)0.5 as a function of the photon energy is a clear evidence for indirect allowed transition which can be described by the following relation [22,38]:

2  ðahnÞ ¼ B hn  Eind g ±Ep

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therefore be employed to investigate the optical transitions within the NiO films material. Following the hybridized model proposed by many authors [41e44] the valance band of the NiO consists of states 3d of Niþ2 which is located at about 2 eV below the Fermi energy. These states overlapped with the extend energy 2p states of O2 band with energy cover the range z4 eV up to 8 eV from the Fermi level. The 3d states of Niþ2 and 2P states of O2 are almost completely hybridized leading to a splitting between the 3d of Niþ2 with different spins directions. The direct optical band gap of order z4 eV and the indirect energy gap of order z2.92 eV obtained from the experimental results reported here may arise from the separation between minority spin states t2g and eg bands with hybridized values G4: 2.9 eV, G5: 3.6 eV and G2:4.3 eV [48,45,46].

(8)

where B is constant, Eind is the indirect energy gap and Ep is the g energy of the absorbed (þ) or emitted () phonons. As clearly shown in Fig. 4, two dissimilar straight line portions with two different slopes are clearly observed. The first line is in the lower photon energy region which corresponds to phonon absorption and has an intercept with energy axis at (Eind g  Ep ). The second line is at higher photon energy which corresponds to phonon emission and has an intercept with energy axis at (Eind g þ Ep ). From the intercepts of these two lines with the energy axis, we can deduce the value of the indirect energy gap Eind and phonon energy Ep. The g value of Eind g is found to be 2.924 eV and Ep is found to be 212 meV. These values of Eind g and Ep agree very well with the values reported earlier for NiO film prepared by atomic layer deposition [22] and DC reactive magnetron supporting [39]. The variation of the factor (ahn)2 as a function of the photon energy hn is depicted in Fig. 5. The figure show that a direct interband transition exists in the investigated sample of NiO thin film. The direct fundamental energy gap Edg is identified by extending the linear portion of the plot of (ahn)2 against hn to the point where a ¼ 0. For the as deposited NiO film, the value of Edg is found to be 3.849 eV. This value of Edg is found to agree very well with the value reported by many authors [9,17]. It is worth noting that our calculation shows that the absorption coefficient and energy gap of the asdeposited films are independent on the films thickness. This result may be attributed to the case where the energy gap of NiO thin film depends on oxygen ion vacancies rather than film thickness [40]. In this section, an attempt to understand the origin of the direct energy gap (Edg ¼3.849 eV) will be made. As mentioned in the structural properties section, NiO has a rocksalt FCC structure and it is made up of Ni2þ (transition metal ions) and O2 (legined ion). The nickel ion has the electronic configuration of 3 d8 while the oxygen ion has the electronic configuration of 2p4. The absorption process occurred in NiO thin films link between occupied states of the valance band with the empty states of the conduction band and may

Fig. 5. The variation of the (ahn)2 as a function of hn for a NiO nanocrystalline thin film.

4.2. Refractive index calculation and dispersion energy parameters of NiO nanocrystalline thin films Refractive index of material is considered as a one of the important property of a material because it is directly related to the electronic polarizability of ions and the electric field confined within the material [47]. Therefore, our objective in this section is to extract the refractive index of the as-deposited NiO nanocrystalline films from the measured quantities R and T in a precise way. In addition, the variation of the refractive index as a function of wavelength (dispersion of refractive index) is also considered as one of the most important optical parameters which characterize thin film material through which electromagnetic wave propagating. Beside the dispersion, electromagnetic wave propagating through thin films subjected to so called absorption in which the intensity of such wave decreases as its frequency approaches the frequency of the fundamental optical gap. As the absorption takes place within the film, the refractive index becomes complex quantity denoted as n* and is composed of real term called refractive index n and imaginary term k called extension coefficient or absorption index. The absorption coefficient is a parameter measure the total optical losses caused by both absorption and scattering occur within the film material. The real (n) and imaginary (k) terms of the complex refractive index are given by the following relations [48]:



al 4p

1þR þ n¼ 1R

(9a)

4R ð1  RÞ2

!0:5 k

2

(9b)

where a is the absorption coefficient and l is the wavelength of the light wave propagating inside the investigated NiO nanocrystalline

Fig. 6. A plot showing the variation of the refractive index versus photon wavelength for NiO nanocrystalline thin films.

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thin film. Substituting with the data of T and R spectra presented in Fig. 2 into Eqs. (6) and (9a) the extension coefficient k can be calculated at different wavelengths. Substituting the dispersion values of the absorption coefficient k(l) into Eq. (9b), then the spectral variation of the real refractive index n can be calculated. In Fig. 6, the spectral variation of the real refractive index is depicted. At short wavelength, Fig. 6 shows that the real refractive index n approaches its maximum value and as the wavelength increases the real refractive index n decreases monotonically indicating the normal dispersion behavior. Our refractive index calculation indicates that the spectral behavior of the refractive index is independent on the film thickness. In order to have a close look understanding of the optical properties (refractive index dispersion) of the NiO film for potential optical applications, the dispersion energy parameters can be extracted by applying the concept of single oscillator model proposed by Wemple and DiDomencio (WDD) in the form [48,49]:

n2  1 ¼

Ed Eo E2o

 E2

1 E   1  o n2  1  E2 ¼ Eo Ed Ed

n2  1 ¼

(11)

as shown in Fig. 7, the oscillator parameters Eo and Ed are directly identified from the slope, (EoEd)1, and the intercept, Eo/Ed on the vertical axis. For all NiO films with different thicknesses, the values of the WDD oscillator parameters calculated from Fig. 7 are Eo ¼ 3.082 eV and Ed ¼ 10.476 eV. Additionally, one of WDD model successes is the ability of the model to relate dispersion energy parameter Ed to other physical and chemical properties of the material under investigation (NiO). The empirical formula which correlate between Ed and other physical and chemical properties of the investigated films take the form [49,50].

Fig. 7. A plot showing the variation of the refractive index factor (n2  1)1 versus photon energy square (hn) for NiO nanocrystalline thin films.

(12)

where b is a two-valued constant with either ionic value (bi ¼ 0.26 ± 0.03 eV) or covalent value (bc ¼ 0.37 ± 0.04 eV), Nc is the effective coordination number (CN) of the cation nearest neighbor to anion, Za is the formal chemical valency of the anion, Ne is the total number of valance electrons per anion. For NiO film under investigation bi take the value 0.26 ± 0.03 eV because NiO is ionic in nature, Za ¼ 2, Ne ¼ 6. The calculated coordination number Nc for NiO film is 3.36 [53,54]. Such value agrees very well with the reported value for NiO film prepared by radio frequency magnetron sputtering at 100 W [21]. Another important and interesting relation who connects the two optical energy parameters Eo and Ed to so called lattice oscillator strength El is proposed [50]. The parameter El is proposed to give more information about the bond strength in ionic compound. For a lattice contribution to a single oscillator model a formula is proposed of the following form [51]:

(10)

where E is the incident photon energy, Eo and Ed are the dispersion energy parameters. Where Eo is defined as the average oscillator energy (average energy gap) and Ed is defined as the dispersion energy of the oscillator or its electronic oscillator strength which is responsible for the interband optical transitions. In WDD model defined by Eq. (10), the refractive index data are modeled below the fundamental band edge, where the normal dispersion of the material under investigation (NiO) is considered. The experimental verification of Eq. (10) is obtained by plotting the refractive index factor (n2  1)1 against E2 {(hn)2} and fitting the experimental data to straight line equation of the form:



Ed ¼ bNc Za Ne

E2 Ed Eo  l2 2 E E

Eo2

(13)

where El is the lattice oscillator strength in eV2. For the case in which the average electronic energy gap Eo is lager than the energy of the lattice oscillator strength El, the following approximation is valid Eo2 > > E2 , Eq. (13) will take the following form:

n2  1 ¼

Ed El2  : Eo E2

(14)

The value of El is obtained by plotting a graph showing the relation between the factor (n2  1) and E2. In Fig. 8, a graph showing the relation between (n2  1) and E2 is depicted. As Fig. 8 shows the linear behavior predicated by Eq. (14) is observed in the range 2.32e6.76 (eV)2. This linear part of the graph is fitted to Eq. (14). The slope of the straight line gives El ¼ 0.31 eV and intersection a ratio between (Ed/Eo) ¼ 3.67 which is very close to the value obtained from WDD single oscillator model (Ed/Eo) ¼ 3.41. For NiO nanocrystalline films, another two important parameters which are the ratio of free carrier density to free carrier effective mass (N/m*) and lattice dielectric constant εL can be obtained from the relation relating refractive index n and wavelength l in the normal dispersion region. This relation is of the form [51]:

ε1 ¼ n2 ¼ εL 

e2 N l2 4pεo m* c2

(15)

Fig. 8. A plot showing the variation of the refractive index factor (n2  1) versus inverse of photon energy square (hn)2 for NiO nanocrystalline thin films.

M.M. El-Nahass et al. / Journal of Alloys and Compounds 646 (2015) 937e945

 Rm ¼

n2o  1 n2o þ 2

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  2  M no  1 ¼ Vm d n2o þ 2

(18)

where M and d are molecular weight and density, respectively. Eq. (18) gives the average molar refraction of substances. The molar fraction Rm is directly related to the molar polarizability am by the following relation:

Rm ¼

Fig. 9. A graph showing the variation of ε1 or refractive index as a function of wavelength square for NiO nanocrystalline thin films.

4p N am 3 A

(19)

where NA is Avogadro's number. With am in ð AÞ3 Eq. (19) will take the following form [53]:

Rm ¼ 2:52am where εL is the lattice dielectric constant, e is electron charge, c is the velocity of light, εo is the free space dielectric constant (8.854  1012 F/m) and (N/m*) is the ratio of free carrier density to free carrier effective mass. The behavior of the variation of the term n2as a function of l2 is depicted in Fig. 9. As the figure shows at wavelength 1 mm2 and above the behavior is almost linear which satisfying Eq. (15). The lattice dielectric constant εL is extracted from the intersection of the linear part with y-axis (l2 ¼ 0) while the ratio (N/m*) is obtained from the slope of the linear part. For NiO nanocrystalline film, the obtained value of εL is 5.408 and the ration of (N/m*) is 1.043  1047 g1 cm3. So far the spectral variation of the refractive index is been modeled using single oscillator model. In this model, the electron is assumed to be tightly attracted to the atomic nuclii by a restoring force and under the effect of the electric filed of the incident photon the electron starts to oscillate with natural frequency uo. There is condition in which the restoring force holding the electron to the nuclii is vanished. In this case, the electrons become free and moving as if it is in a metal like medium. In this case, the electron charge density oscillates with so called plasma frequency. At the plasma frequency the material behaved as if it has metallic behavior in which free carrier absorption exist. Therefore, at the plasma frequency the real part of the complex refractive index is vanishes. The plasma frequency up is given by the following relation [52]:

up ¼

  !0:5 e2 N m* εo

(16)

As Eq. (16) shows the plasma frequency up is directly proportional with the square root of the free carriers concentration. For NiO nanocrystalline films the value of up is equal to 5.492  1014 s1. Finally, the static refractive index of the NiO nanocrystalline thin films no (n at E or hn / 0) is calculated using the following relation:

n2o ¼ 1 þ

Ed Eo

(20)

it is worth mention that the factor am represents the total polarizability which is the sum of electronic, free-ion electronic and molecular polarizabilities of the material under investigation. An empirical formula which relate molar refraction Rm, molar volume Vm and the energy gap Eg for simple oxides is proposed by Duffy [54]. The formula has the following form:

Eg ¼ 20ð1  Rm =Vm Þ2

(21)

also, the molar refraction Rm can be obtained from Eq. (21) in respect to energy gap Eg as:

qffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi Rm ¼ Vm 1  Eg 20

(22)

The value of no can be obtained by plotting the factor  n 1 against photon energy (hn). This plot is depicted in Fig. 10. n2 þ2



2

By fitting the linear portion of the plot in the range 0.8e3.6 eV, we can obtain a linear relation whose intercept with y-axis occur at the   n2 1 value no2 þ2 . With the help of the molecular weight and density o

data tabulated in Table 3 of the NiO material, we can easily calculate the value of Rm and Vm. Using the obtained data of Rm and Vm and using Eq. (21), we can calculate the energy gap of the NiO nanocrystalline thin film as 4.38 eV which is very close to the data obtained in the absorption section. In addition, the average polarizability am is also calculated for the NiO nanocrystalline thin film. The value of am is found to be 2.49 ðA+ Þ3 which is agree very well with the reported value [54].

(17)

the value of the static dielectric constant εs ¼ n2o ¼ 4:41. Also the variation of the refractive index data can be used to obtain the polarizability. Polarizability is a quantity which is introduced to measure the amount of response of the bound electron to the external electric field. For NiO nanocrystalline thin film, the Lorentz-Lorenz equation which relates molar refraction Rm to refractive index no and molar volume Vm is of the form [48]:

 Fig. 10. A graph showing the variation of the factor for NiO nanocrystalline thin films.

n2 1 n2 þ2

 as a function of energy (hn)

944

M.M. El-Nahass et al. / Journal of Alloys and Compounds 646 (2015) 937e945

Table 2 The following table showing the variation fundamental optical parameters for NiO nanocrystalline thin film. Egd eV

Egind eV

EPho meV

Ed eV

Eo eV

Nc

El eV

εl

no

(N/m*)  1047 g1 cm3

up  10þ14 s1

Eu eV

3.849

2.924

212

10.47

3.082

3.36

0.31

5.408

2.1

1.043

5.492

0.38

Table 3 The following table showing the fundamental electronic polarizability information of NiO nanocrystalline thin film. M (g/mol)

d (g/cm3)

Vm (cm3/mol)

Rm (cm3/mol)

Egd eV

am ðA+ Þ3

74.69

6.67

11.20

3.082

4.38

2.49

4.3. Urbach function for NiO nanocrystalline thin film The absorption of photons of energy less than the band gap energy hn < Eg in either amorphous or polycrystalline solids involves the localized tail states. This tail is called Urbach's tail which occurs due to static disorder or so called structure disorder. In the tail edge region the absorption coefficient is expressed by so called Urbach formula which take the form [55]:

  hn aðnÞ ¼ ao exp Eu

5. Conclusion The structure and optical properties of non-annealed NiO nonocrystalline thin films are investigated using spectrophotometric technique. The XRD spectra of the deposited films show that the obtained films crystallize in the form of NaCl cubic structure with enhanced degree crystallinity increases with increasing film thickness. From the analysis of the XRD spectra all the structure parameters of the deposited films are accurately identified. The direct, the indirect optical band gaps and the phonon energy are accurately identified. Additionally, all the optical parameters like coordination number, lattice oscillator strength El, lattice dielectric constant εl, ratio of free carrier density to free carrier effective mass (N/m*) and plasma frequency up are all estimated. Furthermore, the molar refraction and volume Rm, Vm, molar polarizability am, are also calculated. Lastly, the Urbach energy Eu is also calculated.

(23) References

where ao is constant and Eu is the Urbach energy which characterizes the slope of the exponential edge range and its inverse gives the width of the localized states associated with the disorder states embedded within the band gap of the investigated thin film. It is believed that the exponential dependence of the absorption coefficient on photon energy may arise from the random fluctuations of the internal fields associated with structural disorder occurred in the investigated thin film. Moreover, the exponential behavior of the absorption coefficient arises from the electronic transitions between localized states and their density falls off exponentially with photon energy. Taking the logarithmic of both side of Eq. (23) we have the following formula:

lnðaðnÞÞ ¼ lnðao Þ þ

hn Eu

(24)

Plots of ln(a(n)) against the photon energy hn for the as deposited NiO thin films is depicted in Fig. 11. The Eu value calculated from the slopes of plotted line is listed in Table 2. The value of Eu (z0.38 eV) is very small relative to the energy gap Eg (z3.849 eV) indicates that the region of localized sates is very narrow compared to the width of the energy gap.

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

Fig. 11. A graph showing the variation of the Urbach energy factor ln(a) as a function of photon energy for NiO nanocrystalline thin films.

[33] [34]

R.J. Powell, W.E. Spicer, Phys. Rev. B 2 (1970) 2182. G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 53 (1984) 2339. R.H. Kodama, S.A. Makhlouf, A.E. Berkowitz, Phys. Rev. Lett. 79 (1997) 1393. S. Mao, A. Mack, E. Singleton, J. Chen, S.S. Xue, H. Wang, Z. Gao, J. Li, E. Murdock, J. Appl. Phys. 87 (2000) 5720. H. Sato, T. Minami, S. Takata, T. Yamada, Thin Solid Films 236 (1993) 27. G.A. Niklasson, C.G. Granqvist, J. Mater. Chem. 17 (2007) 127. K. Yoshimura, T. Miki, S. Tanemura, Jpn. J. Appl. Phys. 34 (1995) 2440. C.G. Granqvist, Sol. Energy Mater. Sol. Cells 91 (2007) 1529. R. Newman, R.M. Chrenko, Phys. Rev. 114 (1959) 1507. R.J. Powell, W.E. Spicer, Phys. Rev. B 2 (1970) 2182. J.M. MacKay, V.E. Henrich, Phys. Rev. Lett. 53 (1984) 2343. D. Adler, J. Feinlieb, Phys. Rev. B 2 (1970) 3112. B.H. Brandow, Adv. Phys. 26 (1977) 651. B. Sasi, K.G. Gopchandran, P.K. Manoj, P. Koshy, P.P. Rao, V.K. Vaidyan, Vacuum 68 (2002) 149. S. Pereira, A. Gonçalves, N. Correia, J. Pinto, L. Pereira, R. Martins, E. Fortunato, Sol. Energy Mater. Sol. Cells 120 (2014) 109. H. Kamal, E.K. Elmaghraby, S.A. Ali, K. Abdel-Hady, J. Cryst. Growth 262 (2004) 424. A.J. Varkey, A.F. Fort, Thin Solid Films 235 (1993) 47. P.K. Sharma, M.C.A. Fantini, A. Gorenstein, Solid State Ionics 457 (1998) 113. B. Sasi, K.G. Gopchandran, Sol. Energy Mater. Sol. Cells 91 (2007) 1505. K.S. Usha, R. Sivakumar, C. Sanjeeviraja, J. Appl. Phys. 114 (2013) 123501. H.L. Lu, G. Scarel, M. Alia, M. Fanciulli, Shi-Jin Ding, D.W. Zhang, Appl. Phys. Lett. 92 (2008) 222907. I. Valyukh, S. Green, H. Arwin, G.A. Niklasson, E. Wackelg, C.G. Granqvist, Sol. Energy Mater. Sol. Cells 94 (2010) 724. X.H. Xia, J.P. Tu, J. Zhang, X.L. Wang, W.K. Zhang, H. Huang, Sol. Energy Mater. Sol. Cells 92 (2008) 628. K.K. Purushothaman, S. Joseph Antony, G. Muralidharan, Sol. Energy 85 (2011) 978. D.S. Dalavi, M.J. Suryavanshi, D.S. Patil, S.S. Mali, A.V. Moholkar, S.S. Kalagi, S.A. Vanalkar, S.R. Kang, J.H. Kim, P.S. Patil, Appl. Surf. Sci. 257 (2011) 2647. H. Huang, J. Tian, W.K. Zhang, Y.P. Gan, X.Y. Tao, X.H. Xia, J.P. Tu, Electrochim. Acta 56 (2011) 4281. R. Simon, M. Schroder, Encyclopedia of Inorganic Chemistry, second ed., Wiley, 2005. M. Emam-Ismail, E.R. Shaaban, M. El-Hagary, I. Shaltout, Philos. Mag. 90 (2010) 3499. M. Emam-Ismail, M. El-Hagary, E.R. Shaaban, S. Althoyaib, J. Alloys Compd. 529 (2012) 113. A.C. Sonavane, A.I. Inamdar, P.S. Shinde, H.P. Deshmukh, R.S. Patil, P.S. Patil, J. Alloys Compd. 489 (2010) 667. L.F. Mattheiss, Phys. Rev. B 5 (1972) 290. B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, Reading, Massachusetts, 1956. S. Venkatachalam, D. Mangalaraj, Sa K. Narayandass, Phys. B 393 (2007) 47. S. Tolansky, Multiple Beam Interferometry of Surface and Films, Dover Publication, New York, 1970.

M.M. El-Nahass et al. / Journal of Alloys and Compounds 646 (2015) 937e945 [35] O. Stenzel, The Physics of Thin Film Optical Spectra an Introduction, Springer Verlag, Berlin Heidelberg, Germany, 2005. [36] M.A. Butler, J. Appl. Phys. 48 (1977) 1914. [37] J. Tauc, Amorphous and Liquid Semiconductor, 1974. New York. [38] J. George, C.K. Valsala Kumari, K.S. Joseph, J. Appl. Phys. 54 (1980) 5347. [39] T.C. Peng, X.H. Xiao, X.Y. Han, X.D. Zhou, W. Wu, F. Ren, C.Z. Jiang, Appl. Surf. Sci. 257 (2011) 5908. [40] A.N. Gunnar, C.G. Granqvist, J. Mater. Chem. 17 (2007) 127. [41] J. Feinleib, D. Adler, Phys. Rev. Lett. 21 (1968) 1010. [42] D. Adler, J. Feinleib, Phys. Rev. B 2 (1970) 2182. [43] B. Koiller, L.M. Falicove, J. Phys. C. Solid State Phys. 7 (1974) 299. [44] T.M. Schuler, D.L. Ederer, S. Itza-Ortiz, G.T. Woods, T.A. Callcott, J.C. Woicik, Phys. Rev. B 71 (2005) 115113.

945

[45] B.H. Brandow, Adv. Phys. 26 (1977) 651. [46] S. Hüfner, Adv. Phys. 43 (1994) 183. [47] M. Born, E. Wolf, Principles of Optics, seventh ed., Cambridge University Press, United Kingdom, 2003. [48] S.H. Wemple, DiDomenico, Phys. Rev. B 3 (1971) 1338. [49] S.H. Wemple, Phys. Rev. B 7 (1973) 3767. [50] S.H. Wemple, Appl. Opt. 18 (1979) 31. [51] M.M. El-Nahass, A.F. El-Deeb, H.S. Metwally, A.M. Hassanien, Eur. Phys. J. Appl. Phys. 52 (2010) 10403. [52] R.J. Bell, M.A. Ordal, R.W. Alexander Jr., Appl. Opt. 24 (1985) 3680. [53] V. Dimitrov, S. Sakka, J. Appl. Phys. 79 (1996) 1736. [54] J.A. Duffy, J. Solid State Chem. 62 (1986) 145. [55] F. Urbach, Phys. Rev. 92 (1953) 1324.