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Effects of Al doping concentration on optical parameters of ZnO:Al thin films by sol–gel technique
ARTICLE IN PRESS
Physica B 381 (2006) 209–213 www.elsevier.com/locate/physb
Effects of Al doping concentration on optical parameters of ZnO:Al thin films by sol–gel technique S.W. Xuea,b, X.T. Zua,c,, W.G. Zhengd, H.X. Denga, X. Xianga a
Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China b International Center for Material Physics, Chinese Academy of Sciences, Shengyang 110015, People’s Republic of China c Department of Physics, Zhanjiang Normal College, Zhanjiang 524048, People’s Republic of China d Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, People’s Republic of China Received 18 November 2005; received in revised form 4 January 2006; accepted 6 January 2006
Abstract ZnO:Al thin films doped with different aluminum concentration were deposited on (0 0 0 1) sapphire substrates by sol–gel technique. Kramers–Kronig relationship was used to determine the optical parameters of ZnO:Al thin films in wavelengths with a range of 300–600 nm. Calculated results show that all optical parameters keep constant in the visible region. The refractive index, the extinction coefficient and the real and imaginary components of dielectric are 1.6, 0.08, 2.5, and 0.27, respectively. Optical constants change distinctly near the optical absorption edge. In the ultraviolet region, doping concentration strongly affects the optical parameters of ZnO:Al thin films. Optical parameters tend to decrease with increasing doping concentration. r 2006 Elsevier B.V. All rights reserved. PACS: 74.25.Gz; 42.70.a; 78.20.e Keywords: ZnO thin films; Refractive index; Al doping; Sol–gel; Optical transmission
1. Introduction ZnO:Al thin films have high conductivity and optical transmittance in visible region. It is suitable for fabrication of transparent electrode of solar cells. Recently, many techniques were applied to deposit high quality ZnO thin films like RF magnetron sputtering [1,2], chemical vapor deposition [3], pulsed laser deposition [4] and sol–gel process [5,6]. Among them, the sol–gel technique offers the possibility of preparing a small- as well as large-area coating of ZnO thin films at low cost for technological applications. Nevertheless, the resultant properties of the films by this method do not exactly correspond to those prepared by other methods. Knowledge of the optical parameters such as the real part of refractive index n and Corresponding author. Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, P.R. China. E-mail addresses: [email protected], [email protected] (X.T. Zu).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.342
extinction coefficient k as well as the complex dielectric constant e of ZnO:Al thin semiconductor films is essential for comparison of samples which are produced using different methods and in different laboratories. Some groups have developed different methods to calculate the spectral dependence of the real part of refractive index and extinction coefficient [7–10]. There are no reports on the effects of Al doping concentration on the optical parameters of ZnO:Al thin films. In this work, another method to calculate the optical parameters of transparent thin films was proposed, and the influence of Al doping concentration on the optical parameters was investigated. 2. Experiment ZnO:Al thin films were prepared by the sol–gel method. Zinc acetate dihydrate (Zn(CH3COO)2 2H2O) was used as a starting material. Two-methoxyethanol and MEA (monoethanolamine) were used as a solvent and stabilizer,
ARTICLE IN PRESS 210
S.W. Xue et al. / Physica B 381 (2006) 209–213
At short wavelengths ðl0 ol01 Þ, the optical absorption coefficient aðlÞ of a direct band gap semiconductor near the band edge, for photon energy greater than the band gap energy of the semiconductor, is given by [12]: 1=2 hc 0 aðl Þ ¼ A 0 E g , (2) l where A is a constant, h is Planck’s constant, c is the speed of light, E g is the band gap. In the wavelength range of l0 ol01 , we suppose that there is only one absorption band and aðlÞ satisfies Eq. (2). By combining Eqs. (2) and (1), we have the contribution j 1 of aðlÞ at short wavelengths to the refractive index. In the computation of j 1 , the following cases must be considered: Fig. 1. Optical transmission of ZnO:Al thin films as a function of the wavelength.
respectively. The dopant source aluminum is (Al(NO3)3 9H2O). Zinc acetate dihydrate and dopant were first dissolved in a mixture of 2-methoxyethanol and MEA solution at room temperature. The molar ratio of MEA to zinc acetate (Zn(CH3COO)2) was 1.0 and the concentration of zinc acetate was 0.35 M. The solution was stirred at 60 1C for 2 h to yield a clear and homogeneous solution, which served as the coating solution after cooling to room temperature. The coating was made 24 h after the solution was prepared. The solution was dropped onto sapphire substrates, which were rotated at 4000 rpm for 30 s. After depositing by spin coating, the films were dried at 300 1C for 10 min over a hot plate to evaporate the solvent and remove organic residuals. The procedures from coating to drying were repeated 12 times until the thickness of the sintered films reaches 800 nm. The films were then inserted into a furnace and annealed in air at 600 1C for 1 h. In order to investigate the influence of doping concentration on the optical parameters of ZnO:Al thin films, we prepared three batches of samples. The doping concentration ranges from 0.01 to 1 mol%. Optical transmittance measurements were carried out using a UV–vis spectrophotometer (SHIMADZU UV2550) in the wavelength range of 300–800 nm (Fig. 1). The resistivity of the films was measured by the four-point probe method. 3. Theory According to the Kramers–Kronig relationship, the absorption coefficient aðlÞ and the refractive index nðlÞ of thin films can be related by Z 1 1 aðl0 Þ dl0 nðlÞ 1 ¼ 2 : (1) 0 2p 0 1 l 2 =l2 Given aðlÞ, we will get nðlÞ from Eq. (1). Nevertheless, we could only obtain aðlÞ in the wavelength l01 –l02 nm from optical transmission experiments. For aðlÞ at short and long wavelengths, we need to properly speculate on them.
(i) If
hc l0
E g 40, Al ½ðhc E g lÞ=l1=2 4p2 ffi 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðhc E g lÞ=l þ hc=l1 E g lnpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðhc E g lÞ=l hc=l01 þ E g
j1 ¼
Al ½ðE g l þ hcÞ=l1=2 2p2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # l hc arctg Eg E g l þ hc= l01 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p . þ 2 2p 2 l
hc l0
E g ¼ 0, 1=2 Al j 1 ¼ 2 ðE g l þ hcÞ=l 2p "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # l hc arctg Eg E g l þ hc= l01 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p . þ 2 2p 2 l
(ii) If
ð3Þ
ð4Þ
E g o0, 1=2 Al j 1 ¼ 2 ðE g l hcÞ=l 2p "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # l hc arctg Eg E g l hc= l01 "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # Al E g l hc l hc Eg arctg 2 2p E g þ hc l01 l rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p ð5Þ . þ 2 2p 2 l
(iii) If
hc l0
At long wavelengths (l0 4l02 ), the optical absorption is small as seen in Fig. 1. We suppose there is no other absorption band in this region. Hence, aðlÞ is nearly constant. Let aðl0 Þ ¼ aðl02 Þ and put it into Eq. (1); we get
ARTICLE IN PRESS S.W. Xue et al. / Physica B 381 (2006) 209–213
211
the contribution of aðlÞ at long wavelengths to refractive index. aðl02 Þl l þ l02 (6) ln j2 ¼ l l0 . 4p2 2 Data of aðl0 Þ in the wavelength range l01 –l02 can be determined by experiments. We have used a simple method generally followed by others to calculate aðlÞ from the transmittance spectra only [11]. The optical absorption coefficient, aðlÞ, is defined as T ¼ exp½aðl0 Þd,
(7)
where T is transmittance and d is the thickness of thin films. Putting transmittance in Fig. 1 and the thickness of thin films into Eq. (7), we get aðlÞ in the wavelength range l01 –l02 . Putting aðl0 Þ obtained from Fig. 1 into Eq. (1) results in the contribution of aðlÞ in the wavelength range l01 –l02 to refractive index.
Fig. 2. Absorption coefficients of ZnO:Al thin films as a function of the wavelength.
l0
j3 ¼
2 1 X aðl0 Þ Dl0 . 0 2 2p l0 1 l 2 =l2
(8)
1
0
Dl in Eq. (8) is the computation step. In Eq. (8), l0 ¼ l is a singular point. The value at the singular point can be determined by 1 aðl0 ÞDl0 aðlÞl ¼ . 02 2 2 4p2 l !l 2p 1 l =l lim 0
(9)
Consequently, the refractive index, the extinction coefficient, the real and the imaginary components of the complex dielectric constant of thin films are nðlÞ ¼ 1 þ
3 X
ji ,
(10)
i¼1
Fig. 3. Refractive index of ZnO:Al thin films as a function of the wavelength.
aðlÞl , kðlÞ ¼ 4p
(11)
e1 ¼ n2 ðlÞ k2 ðlÞ,
(12)
e2 ¼ 2nðlÞkðlÞ,
(13)
respectively. 4. Results and discussion According to the theory above, we applied Visual Basic to compute the optical parameters of ZnO:Al thin films. Fig. 2 shows the absorption coefficients of ZnO:Al thin films as a function of the wavelength. We find that the absorption coefficients in the ultraviolet region are larger than those in the visible region and decrease with the increase of the Al doping concentration. Nevertheless, those in the ultraviolet region change little with the increase of the Al doping concentration. It implies that increasing Al doping concentration could decrease the optical absorption in the ultraviolet region.
The calculated refractive indices of all ZnO:Al thin films are shown in Fig. 3 and exhibit a function of the wavelength. From Fig. 3 we find that the refractive index decreases with the increase of the Al doping concentration. The decrease of refractive index with the increase of the Al doping concentration can be mainly attributed to an increase of the carrier concentration in the ZnO:Al films as confirmed by resistivity measurements in Fig. 4. Fig. 4 shows that the resistivity decreases with the increasing dopant concentration, indicating that the carrier concentration increases with the increase of the dopant concentration. Kim and Qiao et al. [13,14] found that the refractive index is inversely related to the carrier concentration. It is well known [15,16] that Al impurity doped into ZnO films can act as an effective donor as a result of substitutional introduction of Al3+ into the Zn2+ site or incorporation of Al ions in interstitial positions, generating free carriers. With the increasing dopant concentration, the carrier concentration in the ZnO:Al films is increased. Therefore, the refractive index is decreased. However, after
ARTICLE IN PRESS S.W. Xue et al. / Physica B 381 (2006) 209–213
212
Resistivity / Ωcm
80
60
40
20
0.0
0.2 0.4 0.6 0.8 Dopant concentration/mol %
1.0
Fig. 4. The resistivity of ZnO:Al thin films as a function of dopant concentration.
Fig. 6. Imaginary component of complex dielectric constant as a function of the wavelength.
Fig. 5. Extinction coefficient of ZnO:Al thin films as a function of the wavelength. Fig. 7. Real component of complex dielectric constant as a function of the wavelength.
a certain level (0.9 mol%) of doping, the dopant atoms in the crystal grain and grain boundaries tend to saturate [17]. In this case, a high dopant concentration will lead to ionized impurity scattering from the substitutional donors and scattering from the interstitials [18], resulting in indistinct variation of the carrier concentration. In our study, for all samples, the refractive index in the visible region changes little, and tends to be a constant 1.6. Our calculated results in the visible region are very similar with those calculated by Bandyopadhyay [19] with other methods. It is noted that the refractive index increases sharply near the optical absorption edge. The refractive index dispersion data below the band gap can be fitted to the Sellmeyer approximation [20], n2 ¼ A þ
S l2 l2 l20
ðwith l in nmÞ,
(14)
where n is the refractive index, A represents a dispersionless background and S the oscillator strength of the absorption band with resonance wavelength l0 . Nevertheless, the refractive index dispersion data near and above the band gap cannot be fitted to Sellmeyer approximation and increase with wavelength, i.e. anomalous dispersion. In the region of anomalous dispersion, it is very difficult to measure the refractive index of thin films with optical method due to strong optical absorption. It is convenient to investigate the refractive index approximately in the anomalous dispersion region using our method. Figs. 5–7 show the dependence of the extinction coefficients and the real and imaginary components of complex dielectric constant on the wavelength. From these
ARTICLE IN PRESS S.W. Xue et al. / Physica B 381 (2006) 209–213
we find that these optical parameters in the visible region are smaller than those in the ultraviolet region and change little with the concentration and wavelength. The extinction coefficient, the real component and the imaginary component of complex dielectric are 1.6, 0.08, 2.5, 0.27, respectively. Moreover, the extinction coefficient, the real component and the imaginary component of dielectric also decrease with the increase of the Al doping concentration. The decrease of these parameters with the increase of the Al doping concentration may also be attributed to an increase of the carrier concentration in the ZnO:Al films. Near the optical absorption edge, the extinction coefficient, the real component and the imaginary component of complex dielectric all reach extremes. 5. Conclusion ZnO:Al thin films were fabricated by sol–gel technique, and their optical parameters in wavelengths with a range of 300–600 nm were investigated using the method introduced above. Calculation shows that all optical parameters in the visible region change little with Al doping in the range 0.01–1 mol%. Nevertheless, in the ultraviolet region the optical parameters change distinctly and decrease with Al doping. Acknowledgments This study was financially supported by the Program for New Century Excellent Talents in University and by the Ph.D. Funding Support Program of Education Ministry of
213
China (20050614013) and by the NSAF Joint Foundation of China (10376006). References [1] T.L. Yang, D.H. Zhang, J. Ma, H.L. Ma, Y. Chen, Thin Solid Films 326 (1998) 60. [2] Y. Zhou, P.J. Kelly, A. Postill, O. Abu-Zeid, A.A. Alnajjar, Thin Solid Films 447 (2004) 33. [3] T.M. Barnes, J. Leaf, C. Fry, C.A. Wolden, J. Crystal Growth 274 (2005) 412. [4] J. Mass, P. Bhattacharya, R.S. Katiyar, Mater. Sci. Eng. B 103 (2003) 9. [5] V. Musat, B. Teixeira, E. Fortunato, Monteiro, P. Vilarinho, Surf. Coat. Technol. 180 (2004) 659. [6] G. Westin, M. Wijk, A. Pohl, J. Sol–Gel Sci. Technol. 31 (2004) 283. [7] T. Gungor, B. Saka, Thin Solid Films 467 (2004) 319. [8] D.A. Minkov, J. Phys. D, Appl. Phys. 22 (1989) 1157. [9] M. Sreemany, S. Sen, Mater. Chem. Phys. 83 (2004) 169. [10] J.A. Dobrowolski, F.C. Ho, A. Waldrof, Appl. Opt. 22 (1983) 3191. [11] K.H. Kim, K.C. Park, D.Y. Ma, J. Appl. Phys. 81 (1997) 7764. [12] E. Ziegler, A. Heinrich, H. Oppermann, G. Stover, Phys. Stat. Sol. A 66 (1981) 635. [13] H. Kim, A. Pique, J.S. Horwitz, et al., Thin Solid Films 377–378 (2000) 798. [14] Z.H. Qiao, C. Agashe, D. Mergel, Thin Solid Films 496 (2006) 520. [15] H. Sato, T. Minami, Y. Tamura, et al., Thin Solid Films 246 (1994) 86. [16] J. Hu, R.G. Gordon, J. Appl. Phys. 71 (1992) 880. [17] M. Jin, J. Feng, M. Honglei, et al., Thin Solid Films 279 (1996) 213–215. [18] W. Tang, D.C. Cameron, Thin Solid Films 238 (1994) 83. [19] S. Bandyopadhyay, G.K. Paul, S.K. Sen, Sol. Energy Mater. Sol. C 71 (2002) 103. [20] K. Clays, N.J. Armstrong, T.L. Penner, J. Opt. Soc. Am. B 10 (1993) 886.
Physica B 381 (2006) 209–213 www.elsevier.com/locate/physb
Effects of Al doping concentration on optical parameters of ZnO:Al thin films by sol–gel technique S.W. Xuea,b, X.T. Zua,c,, W.G. Zhengd, H.X. Denga, X. Xianga a
Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China b International Center for Material Physics, Chinese Academy of Sciences, Shengyang 110015, People’s Republic of China c Department of Physics, Zhanjiang Normal College, Zhanjiang 524048, People’s Republic of China d Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, People’s Republic of China Received 18 November 2005; received in revised form 4 January 2006; accepted 6 January 2006
Abstract ZnO:Al thin films doped with different aluminum concentration were deposited on (0 0 0 1) sapphire substrates by sol–gel technique. Kramers–Kronig relationship was used to determine the optical parameters of ZnO:Al thin films in wavelengths with a range of 300–600 nm. Calculated results show that all optical parameters keep constant in the visible region. The refractive index, the extinction coefficient and the real and imaginary components of dielectric are 1.6, 0.08, 2.5, and 0.27, respectively. Optical constants change distinctly near the optical absorption edge. In the ultraviolet region, doping concentration strongly affects the optical parameters of ZnO:Al thin films. Optical parameters tend to decrease with increasing doping concentration. r 2006 Elsevier B.V. All rights reserved. PACS: 74.25.Gz; 42.70.a; 78.20.e Keywords: ZnO thin films; Refractive index; Al doping; Sol–gel; Optical transmission
1. Introduction ZnO:Al thin films have high conductivity and optical transmittance in visible region. It is suitable for fabrication of transparent electrode of solar cells. Recently, many techniques were applied to deposit high quality ZnO thin films like RF magnetron sputtering [1,2], chemical vapor deposition [3], pulsed laser deposition [4] and sol–gel process [5,6]. Among them, the sol–gel technique offers the possibility of preparing a small- as well as large-area coating of ZnO thin films at low cost for technological applications. Nevertheless, the resultant properties of the films by this method do not exactly correspond to those prepared by other methods. Knowledge of the optical parameters such as the real part of refractive index n and Corresponding author. Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, P.R. China. E-mail addresses: [email protected], [email protected] (X.T. Zu).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.342
extinction coefficient k as well as the complex dielectric constant e of ZnO:Al thin semiconductor films is essential for comparison of samples which are produced using different methods and in different laboratories. Some groups have developed different methods to calculate the spectral dependence of the real part of refractive index and extinction coefficient [7–10]. There are no reports on the effects of Al doping concentration on the optical parameters of ZnO:Al thin films. In this work, another method to calculate the optical parameters of transparent thin films was proposed, and the influence of Al doping concentration on the optical parameters was investigated. 2. Experiment ZnO:Al thin films were prepared by the sol–gel method. Zinc acetate dihydrate (Zn(CH3COO)2 2H2O) was used as a starting material. Two-methoxyethanol and MEA (monoethanolamine) were used as a solvent and stabilizer,
ARTICLE IN PRESS 210
S.W. Xue et al. / Physica B 381 (2006) 209–213
At short wavelengths ðl0 ol01 Þ, the optical absorption coefficient aðlÞ of a direct band gap semiconductor near the band edge, for photon energy greater than the band gap energy of the semiconductor, is given by [12]: 1=2 hc 0 aðl Þ ¼ A 0 E g , (2) l where A is a constant, h is Planck’s constant, c is the speed of light, E g is the band gap. In the wavelength range of l0 ol01 , we suppose that there is only one absorption band and aðlÞ satisfies Eq. (2). By combining Eqs. (2) and (1), we have the contribution j 1 of aðlÞ at short wavelengths to the refractive index. In the computation of j 1 , the following cases must be considered: Fig. 1. Optical transmission of ZnO:Al thin films as a function of the wavelength.
respectively. The dopant source aluminum is (Al(NO3)3 9H2O). Zinc acetate dihydrate and dopant were first dissolved in a mixture of 2-methoxyethanol and MEA solution at room temperature. The molar ratio of MEA to zinc acetate (Zn(CH3COO)2) was 1.0 and the concentration of zinc acetate was 0.35 M. The solution was stirred at 60 1C for 2 h to yield a clear and homogeneous solution, which served as the coating solution after cooling to room temperature. The coating was made 24 h after the solution was prepared. The solution was dropped onto sapphire substrates, which were rotated at 4000 rpm for 30 s. After depositing by spin coating, the films were dried at 300 1C for 10 min over a hot plate to evaporate the solvent and remove organic residuals. The procedures from coating to drying were repeated 12 times until the thickness of the sintered films reaches 800 nm. The films were then inserted into a furnace and annealed in air at 600 1C for 1 h. In order to investigate the influence of doping concentration on the optical parameters of ZnO:Al thin films, we prepared three batches of samples. The doping concentration ranges from 0.01 to 1 mol%. Optical transmittance measurements were carried out using a UV–vis spectrophotometer (SHIMADZU UV2550) in the wavelength range of 300–800 nm (Fig. 1). The resistivity of the films was measured by the four-point probe method. 3. Theory According to the Kramers–Kronig relationship, the absorption coefficient aðlÞ and the refractive index nðlÞ of thin films can be related by Z 1 1 aðl0 Þ dl0 nðlÞ 1 ¼ 2 : (1) 0 2p 0 1 l 2 =l2 Given aðlÞ, we will get nðlÞ from Eq. (1). Nevertheless, we could only obtain aðlÞ in the wavelength l01 –l02 nm from optical transmission experiments. For aðlÞ at short and long wavelengths, we need to properly speculate on them.
(i) If
hc l0
E g 40, Al ½ðhc E g lÞ=l1=2 4p2 ffi 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðhc E g lÞ=l þ hc=l1 E g lnpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðhc E g lÞ=l hc=l01 þ E g
j1 ¼
Al ½ðE g l þ hcÞ=l1=2 2p2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # l hc arctg Eg E g l þ hc= l01 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p . þ 2 2p 2 l
hc l0
E g ¼ 0, 1=2 Al j 1 ¼ 2 ðE g l þ hcÞ=l 2p "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # l hc arctg Eg E g l þ hc= l01 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p . þ 2 2p 2 l
(ii) If
ð3Þ
ð4Þ
E g o0, 1=2 Al j 1 ¼ 2 ðE g l hcÞ=l 2p "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # l hc arctg Eg E g l hc= l01 "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # Al E g l hc l hc Eg arctg 2 2p E g þ hc l01 l rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Al E g l þ hc p ð5Þ . þ 2 2p 2 l
(iii) If
hc l0
At long wavelengths (l0 4l02 ), the optical absorption is small as seen in Fig. 1. We suppose there is no other absorption band in this region. Hence, aðlÞ is nearly constant. Let aðl0 Þ ¼ aðl02 Þ and put it into Eq. (1); we get
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211
the contribution of aðlÞ at long wavelengths to refractive index. aðl02 Þl l þ l02 (6) ln j2 ¼ l l0 . 4p2 2 Data of aðl0 Þ in the wavelength range l01 –l02 can be determined by experiments. We have used a simple method generally followed by others to calculate aðlÞ from the transmittance spectra only [11]. The optical absorption coefficient, aðlÞ, is defined as T ¼ exp½aðl0 Þd,
(7)
where T is transmittance and d is the thickness of thin films. Putting transmittance in Fig. 1 and the thickness of thin films into Eq. (7), we get aðlÞ in the wavelength range l01 –l02 . Putting aðl0 Þ obtained from Fig. 1 into Eq. (1) results in the contribution of aðlÞ in the wavelength range l01 –l02 to refractive index.
Fig. 2. Absorption coefficients of ZnO:Al thin films as a function of the wavelength.
l0
j3 ¼
2 1 X aðl0 Þ Dl0 . 0 2 2p l0 1 l 2 =l2
(8)
1
0
Dl in Eq. (8) is the computation step. In Eq. (8), l0 ¼ l is a singular point. The value at the singular point can be determined by 1 aðl0 ÞDl0 aðlÞl ¼ . 02 2 2 4p2 l !l 2p 1 l =l lim 0
(9)
Consequently, the refractive index, the extinction coefficient, the real and the imaginary components of the complex dielectric constant of thin films are nðlÞ ¼ 1 þ
3 X
ji ,
(10)
i¼1
Fig. 3. Refractive index of ZnO:Al thin films as a function of the wavelength.
aðlÞl , kðlÞ ¼ 4p
(11)
e1 ¼ n2 ðlÞ k2 ðlÞ,
(12)
e2 ¼ 2nðlÞkðlÞ,
(13)
respectively. 4. Results and discussion According to the theory above, we applied Visual Basic to compute the optical parameters of ZnO:Al thin films. Fig. 2 shows the absorption coefficients of ZnO:Al thin films as a function of the wavelength. We find that the absorption coefficients in the ultraviolet region are larger than those in the visible region and decrease with the increase of the Al doping concentration. Nevertheless, those in the ultraviolet region change little with the increase of the Al doping concentration. It implies that increasing Al doping concentration could decrease the optical absorption in the ultraviolet region.
The calculated refractive indices of all ZnO:Al thin films are shown in Fig. 3 and exhibit a function of the wavelength. From Fig. 3 we find that the refractive index decreases with the increase of the Al doping concentration. The decrease of refractive index with the increase of the Al doping concentration can be mainly attributed to an increase of the carrier concentration in the ZnO:Al films as confirmed by resistivity measurements in Fig. 4. Fig. 4 shows that the resistivity decreases with the increasing dopant concentration, indicating that the carrier concentration increases with the increase of the dopant concentration. Kim and Qiao et al. [13,14] found that the refractive index is inversely related to the carrier concentration. It is well known [15,16] that Al impurity doped into ZnO films can act as an effective donor as a result of substitutional introduction of Al3+ into the Zn2+ site or incorporation of Al ions in interstitial positions, generating free carriers. With the increasing dopant concentration, the carrier concentration in the ZnO:Al films is increased. Therefore, the refractive index is decreased. However, after
ARTICLE IN PRESS S.W. Xue et al. / Physica B 381 (2006) 209–213
212
Resistivity / Ωcm
80
60
40
20
0.0
0.2 0.4 0.6 0.8 Dopant concentration/mol %
1.0
Fig. 4. The resistivity of ZnO:Al thin films as a function of dopant concentration.
Fig. 6. Imaginary component of complex dielectric constant as a function of the wavelength.
Fig. 5. Extinction coefficient of ZnO:Al thin films as a function of the wavelength. Fig. 7. Real component of complex dielectric constant as a function of the wavelength.
a certain level (0.9 mol%) of doping, the dopant atoms in the crystal grain and grain boundaries tend to saturate [17]. In this case, a high dopant concentration will lead to ionized impurity scattering from the substitutional donors and scattering from the interstitials [18], resulting in indistinct variation of the carrier concentration. In our study, for all samples, the refractive index in the visible region changes little, and tends to be a constant 1.6. Our calculated results in the visible region are very similar with those calculated by Bandyopadhyay [19] with other methods. It is noted that the refractive index increases sharply near the optical absorption edge. The refractive index dispersion data below the band gap can be fitted to the Sellmeyer approximation [20], n2 ¼ A þ
S l2 l2 l20
ðwith l in nmÞ,
(14)
where n is the refractive index, A represents a dispersionless background and S the oscillator strength of the absorption band with resonance wavelength l0 . Nevertheless, the refractive index dispersion data near and above the band gap cannot be fitted to Sellmeyer approximation and increase with wavelength, i.e. anomalous dispersion. In the region of anomalous dispersion, it is very difficult to measure the refractive index of thin films with optical method due to strong optical absorption. It is convenient to investigate the refractive index approximately in the anomalous dispersion region using our method. Figs. 5–7 show the dependence of the extinction coefficients and the real and imaginary components of complex dielectric constant on the wavelength. From these
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we find that these optical parameters in the visible region are smaller than those in the ultraviolet region and change little with the concentration and wavelength. The extinction coefficient, the real component and the imaginary component of complex dielectric are 1.6, 0.08, 2.5, 0.27, respectively. Moreover, the extinction coefficient, the real component and the imaginary component of dielectric also decrease with the increase of the Al doping concentration. The decrease of these parameters with the increase of the Al doping concentration may also be attributed to an increase of the carrier concentration in the ZnO:Al films. Near the optical absorption edge, the extinction coefficient, the real component and the imaginary component of complex dielectric all reach extremes. 5. Conclusion ZnO:Al thin films were fabricated by sol–gel technique, and their optical parameters in wavelengths with a range of 300–600 nm were investigated using the method introduced above. Calculation shows that all optical parameters in the visible region change little with Al doping in the range 0.01–1 mol%. Nevertheless, in the ultraviolet region the optical parameters change distinctly and decrease with Al doping. Acknowledgments This study was financially supported by the Program for New Century Excellent Talents in University and by the Ph.D. Funding Support Program of Education Ministry of
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