On the Mechanism of Electrical Conduction in Cobalt-Doped Zinc

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Apr 18, 2012 - in Cobalt-Doped Zinc Oxide Nanocrystalline Thin Films. Abdullah YILDIZ and Felicia .... The temperature dependence of electrical conductivity.
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Journal of the Physical Society of Japan 81 (2012) 054602 DOI: 10.1143/JPSJ.81.054602

On the Mechanism of Electrical Conduction in Cobalt-Doped Zinc Oxide Nanocrystalline Thin Films Abdullah YILDIZ and Felicia IACOMI1  Department of Energy Systems Engineering, Faculty of Engineering and Natural Sciences, Yldrm Beyazt University, Ankara, Turkey 1 Faculty of Physics, ‘‘Alexandru Ioan Cuza’’ University, 11 Carol I Blvd., 700506-Iasi, Romania (Received December 9, 2011; accepted February 8, 2012; published online April 18, 2012)

ZnO and Co-doped ZnO thin films (3 and 11 at. %) were grown on glass substrates by spin coating method and structurally investigated by X-ray diffraction, X-ray photoelectron spectroscopy and UV–vis absorption spectroscopy. It was established that Co enters into ZnO wurtzite lattice by substitution. The electrical conductivity of undoped and Co-doped ZnO nanocrystalline thin films was measured in the temperature range of 300–425 K. The electrical conduction mechanism of the films is explained on the basis of the multiphonon assisted hopping model with a weak electron–phonon coupling. We found that the conductivity first increases with incorporation in ZnO structure of an amount of 3 at. % Co but then it decreases when the amount of Co is increased to 11 at. %. This situation is well explained by the fluctuation in the hopping rate. KEYWORDS: spin-coating, Co doped ZnO, structure, electrical conductivity, multiphonon hopping

1.

Introduction

The interest in determining electrical conduction properties of doped ZnO films is motivated by the need to develop and understand the material response to impurities introduced by doping. Recently, the growth of ZnO films doped with various elements such as Ni, Al, Mn, and Co has been studied in order to control their electrical properties.1–4) Addition of such impurities into ZnO lattice generally induces dramatic changes in the electrical conductivity.1–5) Since intrinsic ferromagnetic ordering occurs in Co-doped ZnO films, they are preferred for spin electronic devices.6,7) The presence of the localized states in ZnO can be of significant concern for certain device applications. Survey of literature shows that there are few reports on the electrical properties related to the localized states in ZnO.8,9) The conduction mechanism in ZnO thin film, when it has a high resistivity due to a higher number of defect centers, may not consist in electron conduction in the conduction band but in hopping process of charged carriers among localized defects. In such a case, the electrical properties of ZnO films are generally explained on the basis of a single phonon-assisted variable-range hopping (VRH) conduction at low temperatures.8,9) On the other hand, the single phonon-assisted VRH process should replace the multiphonon hopping (MPH) process with rising the temperature.9–12) This has been attributed to a weak localization of the carriers, which should decrease the probability of single phonon hopping, enhancing the contribution of weak coupling MPH to the conductivity. In a previous paper, we performed a study on the mechanism of electrical conduction in Co-doped ZnO thin films deposited by spin-coating method.13) We found that the conductivity showed a change when the Co concentration varied from 15 to 25%. The observed increase of conductivity with increasing Co concentration was interpreted through the grain boundary conduction model. In this paper we report a comprehensive study on the mechanism of electrical conduction in ZnO thin films doped with 3 and 

E-mail: f [email protected]

11% cobalt. The electrical conduction mechanism is studied in the temperature range 300–425 K and we demonstrate that, for these concentrations, the conduction mechanism is governed by the MPH conduction with a weak electron– phonon coupling. 2.

Experimental

Undoped and Co-doped ZnO thin films were deposited by spin coating. The zinc acetate and cobalt acetate solutions in N,N-dimethylformamide (2 g metal acetate in 10 ml DMF) were mixed in order to have Co=ðCo þ ZnÞ ratios of 0.00, 0.03, and 0.11. Cleaned microscope glass slides were used as substrates for thin film depositions. The deposition process involved depositing a small volume of a certain solution onto the center of a glass substrate and then spinning with a speed of 1500 rpm during 30 s. After spinning, thin films were annealed at 373 K for 1 min. The procedure was repeated 10 times. Finally, the as-obtained spin-coated were annealed at 673 K for 90 min in order to evaporate the residual solvent from the films and to obtain oxide nanocrystalline thin films. Thin film thicknesses were measured by using a DEKTAK profilometer and were found to be around 150 nm. Structural phase identification of the films was carried out by standard and grazing angle X-ray diffraction (XRD)  Shimadzu techniques with Cu K radiation ( ¼ 1:5418 A, LabX XRD-6000). Compositional analysis of the thin film surface was conducted using X-ray photoelectron spectroscopy (XPS; PHI VERSA PROBE 5000, Al K source, 1486.6 eV). Charge neutralization was used for all samples. Charge referencing was used for all spectra by applying charge correction to the saturated hydrocarbon C 1s peak at the binding energy of 284.6 eV. The UV–vis absorption spectra were registered at room temperature by using a Specord M42 spectrophotometer in the wavelength range 200–900 nm. The temperature dependence of electrical conductivity was investigated in a temperature range T ¼ 300{425 K by using a two point arrangement and a Keithley 6517A Electometer.

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J. Phys. Soc. Jpn. 81 (2012) 054602

A. YILDIZ and F. IACOMI

Table I. Thin film structural characterization from XRD, XPS, and UV– vis investigations. Co content (at. %)

(a)

(b) Fig. 1. Thin film XRD patterns: (a) standard XRD patterns; (b) grazing XRD pattern of 11% Co–ZnO thin film.

3.

Results and Discussion

The standard and grazing XRD patterns of undoped and Co-doped ZnO films are shown in Figs. 1(a) and 1(b). The XRD patterns reveal that the films are polycrystalline in nature. The main XRD peaks are belonging to the (100), (002), and (101) crystalline planes of wu¨rtzite structure. The relative intensity of the peaks changes with Co doping concentration. An increase in Co content determines an increase in the intensity of (002) XRD peak respectively a decrease in I100 =I002 X-ray intensity ratios (Table I). Both standard and grazing XRD results indicate that the Co ions systematically substitute for the Zn ions in the films without changing the wurtzite structure and a c-axis preferred texture growth of the ZnO films for 11 at. % Co. No other crystalline phases were evidenced. Unit cell parameter values as determined by using XLATCell Parameter Refinement software show small increases in a or c parameter as a function of Co content (Table I).14,15) The grain sizes (D) of thin films were calculated from the full-width at half-maximum (FWHM) of more intense XRD peaks using Scherrer formula:16) D¼

0:9 ; B cos 

ð1Þ

where B is the FWHM of XRD diffraction peak,  is Bragg angle, and  is the X-ray wavelength, respectively. The calculated values of the D are given in Table I.

a  (A)

c  (A)

I100 =I002

I101 =I002

D100  (A)

D002  (A)

D101  (A)

80.0

123.0 3.21

Eg (eV)

0

3.248 5.207

4.62

4.59

98.3

3

3.263 5.197

0.75

1.07

129.0 115.5 123.0 3.24

11

3.252 5.213

0.40

0.48

134.6 148.6 130.0 3.19

The XPS spectra analysis confirmed that the concentration of Co on the surface of the Co-doped ZnO thin films is very close to 3 and 11 at. %. XPS investigations evidenced that Zn is in 2+ valence state as the binding energy position of Zn 2p spectra is close to the standard data of zinc oxide [Fig. 2(a)].17,18) Co 2p XPS spectra showed that the intensity of the peaks is increasing indicating that the Co doping content is increasing. Figure 2(b) shows the Co 2p XPS spectrum of 11 at. % Co-doped ZnO thin films. The binding energy of Co 2p3=2 is located at 780.01 eV while the Co 2p1=2 peak is at 795.88 eV. These values are comparable with those observed by X. Su et al.19) The presence of shakeup satellites on the higher binding energy of Co 2p peaks confirm the presence of Co2þ homogeneously surrounded by oxygen tetrahedra.20) The O 1s XPS spectra of the studied thin films showed an asymmetric peak very close to 530 eV. O 1s XPS spectra can be considered as a result of superposition of two XPS peaks which for ZnO thin film are located at 529.2 and 531.02 eV respectively. The first O 1s peak was attributed to O2 ions surrounded by Zn atoms in the wurtzite structure and the second O 1s peak to the presence of loosely bound oxygen species or hydroxyl groups on the surface of the films.1,21) In the cobalt doped thin films, O 1s peak attributed to O2 ions surrounded by Zn atoms in the wu¨rtzite structure is shifted to higher energy values. The maximum value of 529.5 eV was observed for ZnO thin film doped with 11 at. % Co [Fig. 2(c)]. Figure 3 shows the room temperature absorbance spectra of thin films. Cobalt dopping determines an increase in thin film absorbance and shifts in absorption edges, suggesting changes in thin film band structure.22–25) The absorption spectrum consist of low energy band at about 3.5 eV and a band at about 4.5 eV. The optical energy gap, Eg , was determined from the absorption spectra by plotting ðhÞ2 versus h and taking the intercept of the extrapolation to zero absorption with photon energy axis. A small increase or a decrease in Eg values was evidenced for x ¼ 0:03 and 0.11 Co contents, respectively. Increases or decreases in optical band gap energy values were evidenced with the increase of Co contents by different authors. In a previous paper we evidenced a decrease in optical band gap energy values for cobalt concentrations higher than 15 at. %.13) This dependence was attributed to the sp–d exchange between the ZnO band electrons and localized d-electrons associated with the doped Co2þ cations.22–28) The broadening of the absorption spectra near the absorption onset indicates that there are impurity levels developed within the band gap. Absorbance spectra evidence the presence of three absorption bands, located at 657 nm (1.89 eV), 610 nm

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J. Phys. Soc. Jpn. 81 (2012) 054602

(a)

A. YILDIZ and F. IACOMI

Fig. 3. UV–vis absorption spectra as a function of photon energies.

0

0,40

3% 0% 11 %

0,35

Ea (eV)

-2

ln σ (Ω-1 cm-1)

-4

0,30 0,25 0,20 0,15 0,10

-6

300 320 340 360 380 400 420

T (K)

-8 -10 -12 -14 2,4

2,6

2,8

3,0

3,2

1000/T (K-1)

(b)

Fig. 4. Temperature dependence of the conductivity plotted as ln  vs 1000=T for the films. The inset of the Fig. 4 represents double logarithmic plot of the temperature dependence of the differential activation energy Ea ðT Þ of the films.

Table II.

VRH parameters for the undoped and Co-doped thin films.

Co  RT content (1 cm1 ) (at. %)

0 (1 cm1 )

T0 (K)

  (A)

0

2:11  106 1:28  1010  2:12 3:79  108  115 1:89  108

3

1:67  104 5:28  1018  2:91 1:77  109  466 2:12  1017

11

4:76  107 4:13  1011  3:06 6:75  108  562 4:39  1010

(c) Fig. 2. XPS spectra of thin films: (a) Zn 2p XPS spectra; (b) Co 2p XPS spectrum of 11% Co-doped ZnO thin film; (c) O 1s XPS spectrum of 11% Co-doped ZnO thin film.

(2.03 eV), and 567 nm (2.20 eV), assigned to d–d absorption levels of high-spin Co2þ (3d7 ) ions in a tetragonal crystal field. These absorptions were ascribed to charge transfer between donor and acceptor ionization levels located within the band gap of the ZnO host and are dependent on Co2þ content.26,27) Figure 4 shows the electrical conductivity () as a function of the reciprocal temperature for the films deposited at various Co doping levels. The room temperature conductivity values ( RT ) are collected for the investigated films in Table II. The  exhibits a strong dependence on Co content. The  first increased with incorporation of a small

amount of Co (3 at. %). However, when amount of Co is further increased (11 at. %), the  begins to decrease. A similar behavior was observed by Acosta et al.5) It was reported that the  of the ZnO thin films evolves from low values for the undoped thin films to high values as the cobalt is incorporated into ZnO. They observed that the  increases two orders of magnitude for a ½Co=½Co þ Zn ¼ 3 at. % ratio, while the  decreases approximately two orders of magnitude for a ½Co=½Co þ Zn ¼ 11 at. % ratio. This is consistent with our observation (Table II). In order to clearly understand the conductivity behavior in the investigated films, the numerical evaluation of the activation energy was performed from the relation29)

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Ea ¼ kB

 ln½ðT Þ : ð1=T Þ

ð2Þ

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0 ¼

3e2 ph ½NðEF Þ1=2 ; ð8Þ1=2

0 -2

Figure 5 displays the lnðT 1=2 Þ as a function of the T 1=4 . The characteristic temperature T0 and the pre-exponential factor  0 are obtained from linear fits of these plots (Table II). There is an indication of the inappropriate form of these equations which results from extraction of the  by resolving eqs. (4) and (5) for the best fits to each of the data sets. Since the estimated  values provide unphysical small values, the single phonon-assisted VRH should be rule out for the studied films. The multiphonon hopping (MPH) conduction model with electron–phonon coupling is an alternative model for interpreting conduction in metal–oxide systems.11,12) In the MPH model, there are two possible cases depending on the strength of the electron–phonon coupling. If there is a sufficiently strong electron–phonon interaction in these structures, small polarons are formed and the electrical conduction occurs by the hopping of small polarons between the ions of low and high valence states of the transition metal ions.30–32) On the other hand, if the strength of the electron– phonon interaction is sufficiently weak, no small polaron can be formed.11,12) We first consider the weak coupling case. The hopping rate due to a multiphonon tunneling of localized carriers with weak coupling can be expressed as11,12)

-3 -4 -5 -6 2,48 2,50 2,52 2,54 2,56 2,58 2,60 2,62

-4

log T (K)

-6 -8 -10 -12 0,220

0,225

0,230

0,235

0,240

T -1/4 (K-1/4)

Fig. 5. Temperature dependence of the electrical conductivity plotted as lnðT 1=2 Þ vs T 1=4 for the films. Solid lines are the best-fit lines with eq. (3). The inset of Fig. 5 represents temperature dependence of the electrical conductivity plotted as log  vs log T for the films. Solid lines in the inset of the Fig. 5 are the best-fit lines with eq. (7).

  kB T p  ¼ C expð pÞ ; h0

ð6Þ

and the electrical conductivity, respectively, by the relation

ð4Þ

where e is the electron charge, vph is the phonon frequency associated with hopping process (1013 Hz),  is the localized state wave function, which represents the exponential decay of electronic wave function at large distances. It is expected that  is of the order 1 nm in the VRH regime.10) The characteristic temperature coefficient T0 is dependent on the density of states NðEF Þ at the Fermi level in the form10) 18 T0 ¼ : ð5Þ 3 kB  NðEF Þ

-2

3% 0% 11 %

2

log σ (Ω -1 cm -1)

By plotting Ea with respect to temperature (the inset of the Fig. 4) it is found that Ea has not a constant value but a fluctuating one with temperature. This suggests that the electrical conduction in the films is not dominated by a simple thermal activation process (Arrhenius law). Therefore, an alternative approach is necessary to explain the experimental conductivity data of the studied films. Seeking for a better fit, we take into account the single phonon-assisted VRH conduction mechanism.10) When the motion of charge carriers is considered localized in disordered potentials, the conduction mechanism changes from thermally activated conduction to the VRH conduction. In the VRH conduction mechanism, phonons are necessary to conserve energy during a hop from site to site. In a disordered system, contribution to the electrical conduction is possible only by hopping from one filled state to an empty state. In this regime, the conduction occurs via VRH of the charge carriers in the localized states near the Fermi level, and is characterized by Mott’s relation,10)   T0 1=4 1=2  ¼ 0 T exp  : ð3Þ T The pre-exponential factor,  0 , is defined by the relation

A. YILDIZ and F. IACOMI

ln [σT 1/2] (Ω-1 cm -1K1/2 )

J. Phys. Soc. Jpn. 81 (2012) 054602



nc e2 R2  : 6kB T

ð7Þ

In these relations C  0 , nc ¼ NðEF ÞkB T ¼ R3 and ¼ lnð=EM Þ  1. The parameter EM or is a measure of the carrier–phonon coupling strength. 0 is the frequency of the acoustical phonon which is most effectively coupled to localized electrons. The 0 value is approximately given by ða0 =aB  ÞD 12) and estimated as 3:77  1012 s1 . Here a0 is the average lattice separation (a0 ¼ 0:325 nm), aB  is Bohr radius (aB  ¼ 1:5 nm),33) and D is Debye frequency (D ¼ D kB =h ¼ 1:74  1013 s1 ).34) Note that we can not consider here the grain boundary conduction even if the films have a polycrystalline structure,1,35) since the values of crystalline size are almost the same and the change in electrical conductivity is dramatically. Namely, an increase in electrical conductivity is not related to an increase in crystalline size of our polycrystalline films. In polycrystalline materials, the hopping conduction process exists in the grain boundaries at temperatures at which the carriers do not have sufficient energy to cross the potential barrier and to transfer themselves into the crystallite by the process of thermo ionic emission.35) In eq. (7), R is the hopping distance which may be taken to be the mean crystalline size of our polycrystalline films. A measure of the number of phonons participating in transport between hopping sites is also given by p ¼ =h0 , with the ratio expressed as the average site energy difference  to the average energy h0 of the phonon modes coupled to the electrons. We have from eqs. (6) and (7)  ¼ AT p ; where

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ð8Þ 

NðEF Þe2 R2 C expð pÞ A¼

6

kB h0

p ð9Þ

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J. Phys. Soc. Jpn. 81 (2012) 054602 Table III. MPH parameters for the studied thin films.

A. YILDIZ and F. IACOMI

(11 at. %). This situation is well explained by the fluctuation in the hopping rate.

Co content (at. %)

R  (A)

p



EM =h0

 (s1 )

0

100

8:76  0:29

2.15

0.375

2:04  106

Acknowledgements We are thankful to Dr. V. Nica and Dr. M. Dobromir for carrying out XRD and XPS measurements.

3

120

9:99  0:28

1.49

0.828

1:94  108

11

140

11:5  0:37

1.86

0.659

6:47  105

The MPH process involves absorption and emission of p phonons but it can be a non-integral number.11,12) The inset of the Fig. 5 shows log  versus log T plots for the films. The values of p are estimated from these plots (Table III). The single phonon assisted VRH mechanism requires the condition h0 > . Since the p > 1, the condition of single phonon assisted VRH h0 >  is not fulfilled for the films namely the single-phonon assisted VRH cannot take place in the investigated temperature range for the films. We also obtain from the fit the values of , EM =h0 , and  (Table III). The estimated values of are reasonable for the weak electron–phonon coupling regime.11,12) We should also rule out strong carrier–phonon interaction with these values of for the films. In case of strong carrier–phonon interactions p must be larger than 4.30–32) The condition of the MPH with the weak electron–phonon coupling EM =h0 < 111) is fulfilled for the films. Therefore, we conclude that the MPH conduction with the weak electron–phonon coupling is the most probable conduction mechanism in the films. Finally, we should note here that observed conductivity behavior depending on Co doping level is consistent with the fluctuation in the hopping rate (). We should note that the value of  is essentially determined by h0 as can be seen from eq. (6). However, in our calculations, h0 is estimated as the same for all films. Hence, the value of p which is dependent of Co composition becomes effective on determining the value of . Therefore, it can be considered that the hopping rate is dependent on the Co concentration. The increase in the  reflects the values of electrical conductivity (Table III). We conclude that the increase in electrical conductivity by Co doping is due to an increase in the . The highest conductivity value is found for 3 at. % Co having the highest  value. 4.

Conclusion

Undoped and Co-doped nanocrystalline thin films, with Co concentrations of 3 and 11 at. %, were deposited on glass substrates XRD, XPS and UV–vis absorption studies evidenced that Co entered into ZnO lattice as Co2þ . Substitution of Zn by Co determined small increases in a or c unit cell parameter and also in grain sizes having (002) orientation and band gap values. The electrical conductivity behavior of the undoped and Co-doped ZnO nanocrystalline thin films, prepared by spin-coating method, were investigated as a function temperature. Measurements of electrical conductivity of the undoped and Co-doped ZnO nanocrystalline thin films, in the temperature range of 300–425 K, lead to the conclusion that the MPH conduction with the weak electron–phonon coupling is dominant. We observed that the conductivity first increases with incorporation of amount of Co (3 at. %) but then it decreases when amount of Co is further increased

1) A. Yildiz, B. Kayhan, B. Yurduguzel, A. P. Rambu, F. Iacomi, and S. Simon: J. Mater. Sci.: Mater. Electron. 22 (2011) 1473. 2) P. Prepelita, C. Baban, and F. Iacomi: J. Optoelectron. Adv. Mater. 9 (2007) 2166. 3) J. Han, P. Q. Mantas, and A. M. R. Senos: J. Eur. Ceram. Soc. 21 (2001) 1883. 4) Z. Zhou, K. Kato, T. Komaki, M. Yoshino, H. Yukawa, M. Morinaga, and K. Morita: J. Eur. Ceram. Soc. 24 (2004) 139. 5) D. R. Acosta, L. Castaneda, A. Lopez-Suarez, and A. GuillenSantiago: Physica B 404 (2009) 1427. 6) C. Liu, F. Yun, and H. Morkoc: J. Mater. Sci.: Mater. Electron. 16 (2005) 555. 7) J. Hu, H. Qin, T. Xue, E. Cao, and D. Li: Appl. Phys. Lett. 93 (2008) 022510. 8) S. P. Heluani, G. Braunstein, M. Villafuerte, G. Simonelli, and S. Duhalde: Thin Solid Films 515 (2006) 2379. 9) M. W. Khan, R. Kumar, M. A. M. Khan, B. Angadi, Y. S. Jung, W. K. Choi, and J. P. Srivastava: Semicond. Sci. Technol. 24 (2009) 095011. 10) N. F. Mott and E. A. Davis: Electronic Processes in Non-Crystalline Materials (Oxford University Press, London, U.K., 1971). 11) N. Robertson and L. Friedman: Philos. Mag. 33 (1976) 753. 12) D. Emin: Adv. Phys. 24 (1975) 305. 13) A. Yildiz, B. Yurduguzel, B. Kayhan, G. Calin, M. Dobromir, and F. Iacomi: J. Mater. Sci.: Mater. Electron. 23 (2012) 425. 14) Y. Z. Yoo, T. Fukumura, Z. Jin, K. Hasegawa, M. Kawasaki, P. Ahmet, T. Chikyow, and H. Koinuma: J. Appl. Phys. 90 (2001) 4246. 15) T. A. Schaedler, A. S. Gandhi, M. Saito, M. Ruhle, R. Gambino, and C. G. Levi: J. Mater. Res. 21 (2006) 791. 16) Polycrystalline Semiconductors: Physical Properties and Applications, ed. G. Harbeke (Springer, Berlin, 1985). 17) B. Pandey, S. Ghosh, P. Srivastava, D. Kabiraj, T. Shripati, and N. P. Lalla: Physica E 41 (2009) 1164. 18) S. Ghosh, P. Srivastava, P. M. Saurav, P. Bharadwaj, D. K. Avasthi, D. Kabiraj, and S. M. Shivaprasad: Appl. Phys. A 90 (2008) 765. 19) X. Su, L. Wang, J. Chen, X. Wan, X. P. Zhang, and R. P. Wang: J. Phys. D 44 (2011) 265002. 20) Y. Z. Peng, T. Liew, V. D. Song, C. W. An, C. W. Teo, and T. C. Chong: J. Supercond. Novel Magn. 18 (2005) 97. 21) L. Wei, Z. Li, and W. F. Zhang: Appl. Surf. Sci. 255 (2009) 4992. 22) S. F. Zhao, C. H. Yao, Q. Lu, F. Q. Song, J. G. Wan, and G. H. Wang: Trans. Nonferrous Met. Soc. China 19 (2009) 1450. 23) M. Fonin, G. Mayer, E. Biegger, N. Janen, M. Beyer, T. Thomay, R. Bratschitsch, Y. S. Dedkov, and U. Rudiger: J. Phys.: Conf. Ser. 100 (2008) 042034. 24) Y. X. Wang, X. Ding, Y. Cheng, Y. J. Zhang, L. L. Yang, H. L. Liu, H. G. Fan, Y. Liu, and J. H. Yang: Cryst. Res. Technol. 44 (2009) 517. 25) B. Pal and P. K. Giri: J. Appl. Phys. 108 (2010) 084322. 26) P. Singh, G. Deepak, N. R. Goyal, A. K. Pandey, and D. Kaur: J. Phys.: Condens. Matter 20 (2008) 315005. 27) J. M. Kim, H. Kim, D. Kim, S. G. Yoon, and W. K. Choo: Solid State Commun. 131 (2004) 677. 28) M. K. Patra, K. Manzoor, M. Manoth, S. R. Vadera, and N. Kumar: J. Phys. Chem. Solids 70 (2009) 659. 29) A. Helmbold, P. Hamer, J. U. Thiele, K. Rohwer, and D. Meissner: Philos. Mag. B 72 (1995) 335. 30) N. F. Mott: J. Non-Cryst. Solids 1 (1968) 1. 31) A. Yildiz, F. Iacomi, and D. Mardare: J. Appl. Phys. 108 (2010) 083701. 32) A. Yildiz, S. B. Lisesivdin, M. Kasap, and D. Mardare: Physica B 404 (2009) 1423. 33) Y. Natsume and H. Sakata: Thin Solid Films 372 (2000) 30. 34) D. L. Rode: Semicond. Semimet. 10 (1975) 1. 35) A. Yildiz, N. Serin, M. Kasap, T. Serin, and D. Mardare: J. Alloys. Compd. 493 (2010) 227.

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