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Optical properties of amorphous PbZrxTi1−xO3 (x=0.52) thin films prepared by RF magnetron sputtering
Thin Solid Films 437 (2003) 223–229
Optical properties of amorphous PbZrxTi1yxO3 (xs0.52) thin films prepared by RF magnetron sputtering Zhigao Hu*, Zhiming Huang, Zhenquan Lai, Genshui Wang, Junhao Chu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yu Tian Road, Shanghai 200083, PR China Received 26 March 2002; received in revised form 21 November 2002; accepted 13 December 2002
Abstract The optical properties of amorphous PbZr0.52 Ti0.48 O3 thin films on vitreous silica and sapphire substrates by the RF magnetron sputtering method have been investigated by transmittance measurements. For a single-layer thin film on the transparent substrate, the inverse synthesis or fitting method with the six fitting parameters was given and used to calculate the optical constants such as the refractive index n, the extinction coefficient k, and the absorption coefficient a. The film thickness d, which was one of the fitting parameters, is simultaneously obtained. According to Tauc’s law, the optical transition in amorphous PbZr0.52Ti0.48O3 thin films is direct in nature. The direct band gaps of amorphous PbZr0.52Ti0.48 O3 thin films on vitreous silica and sapphire substrates were found to be 3.36 and 3.25 eV, respectively. The dispersions of the refractive index in films were studied by considering a single-oscillator model. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Optical properties; Amorphous; PbZr0.52Ti0.48O3; Inverse synthesis method
1. Introduction Ferroelectric thin films have attracted great attention primarily due to their applications in non-volatile random access memory device applications w1–9x. The most popular material is lead zirconate titanate PbZrxTi1yxO3 (PZT) ferroelectric thin film, which is considered to be a very promising material due to its ability to maintain adequate pyroelectric, ferroelectric and electro-optic properties. There have been numerous proposals for applications in optoelectronic devices such as optical switches and optical modulators w10,11x. The PZT thin films can be prepared by various methods such as RF magnetron sputtering w1,2x, sol–gel processing w3–5x, metallo-organic decomposition process w6,7x, ion-beam sputter deposition w8x, and chemical vapor deposition w9x on a variety of substrates. Because its composition can span a very wide range, this produces materials with different dielectric and optical characteristics. *Corresponding author. Tel.: q86-21-65420850; fax: q86-2165830734. E-mail address: [email protected] (Z. Hu).
‘Amorphous ferroelectricity’ was first suggested by Lines w12x, and some observations of ferroelectric or ferroelectric-like phase transition in LiNbO3 and PbTiO3 systems have been reported where RF sputtering was used to form amorphous films w13,14x. Xu et al. w3,4x have found that some amorphous PZT thin films exhibit a polarization–electric (P–E) field hysteresis loop, stable pyroelectric current, and piezoelectric resonance peaks in the dielectric spectrum. These excellent properties show that further studies, including optical measurements, need to be performed for the amorphous PZT thin films. Trolier-Mckinstry et al. w5,8x have studied the optical properties of the PZT thin films by spectroscopic ellipsometry. In their work, however, most samples used are crystalline, and the measured wavelength range is rather narrow: 300–700 nm, so the spectrum of refractive index n show monotonic behavior and the spectrum of extinction coefficient k have not been given. Zhu et al. w15x and Li et al. w16x have studied optical properties of the amorphous PLZT thin films (lanthanum modified PZT thin films) by spectroscopic ellipsometry. However, up to now, the optical
0040-6090/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0040-6090(03)00016-6
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Z. Hu et al. / Thin Solid Films 437 (2003) 223–229
properties of the amorphous PZT thin films prepared by the RF magnetron sputtering method have not been determined in the wide spectral range. For a single-layer thin film on the transparent substrate, the optical constants of the amorphous PZT thin films can be determined by the transmittance spectrum alone w6,17,18x. There, however, are three questions: (i) the envelope curves are manually determined, (ii) some assumptions must be met, and (iii) a significant error appears near the turning point (the optical absorption edge). Recently, a formalism of the extinction coefficient k in a wide range of energy is derived by Forouhi and Bloomer w19x. Their equation is based on a quantummechanical theory of absorption. From the extinction coefficient k, the refractive index dispersion n is also deduced in accordance with the Kramers–Kronig relation. With the formalism most amorphous materials can be described by a single oscillator, and hence only one set coefficient (A, B, C, n` and Eg) is enough to express n and k of an amorphous thin film. In the present paper, an inverse synthesis or fitting method with the formalism of Forouhi and Bloomer, which is used with transmission analysis for the simultaneous determination of n, k and the thickness d is established. With this method, the optical constants, the absorption coefficient, the singleoscillator energy and the optical band gap were obtained. 2. Experimental details In this study, the samples of amorphous PbZr0.52Ti0.48O3 thin films are prepared by RF magnetron sputtering technique. A 10-cm-diameter PbZr0.52 Ti0.48O3 target is used for deposition. Before deposition, the target is pre-sputtered for 30 min with the substrate shutter closed to achieve stable conditions. The vacuum chamber pumped by a turbo-molecular pump produces a base pressure of 7=10y6 Pa and is raised to 1.6 Pa by admitting Ar. The 30-mm-diameter vitreous silica and 20-mm-diam sapphire (0 0 0 1) substrates are mounted with silver paste onto a resistively heated substrate holder. During the sputtering, the temperature of the substrate holder is kept at 400 8C and the RF power on the target is 100 W, operating at 13.56 MHz, yielding a growth rate of approximately 3–4 nm miny1. With 100% Ar sputtering plasma guided onto the target, the thin films are sputtered inside a commercial vacuum coater. The as-grown PZT thin films with the desired thickness are amorphous. After sputtered samples are cooled inside the chamber, optical measurements and the thickness measurement are made. The compositions of the thin films were analyzed using inductively coupled argon plasma atomic emission spectrometry, and were represented by x and y in the formula of composition Pby(ZrxTi1yx)O3 . In the paper, the optical properties are measured for the PZT thin
Fig. 1. Schematic diagram of the layer structure of amorphous PZT thin film and related optical parameters used in the fitting calculation of the optical constants.
films with 0.50-x-0.52 and 1.01-y-1.05 composition. There is excessive Pb for the PZT thin films. The optical transmission characteristics of amorphous PZT thin films have been studied by using a double beam ultraviolet–visible (UV–Vis) spectrophotometer (Perkin Elmer UV–Vis spectrometer Lambda 2S) in the wavelength range of 200–1100 nm. The transmission spectra of uncoated vitreous silica and sapphire substrates are also measured for a comparison. 3. Results and discussion 3.1. Inverse synthesis or fitting method The inverse synthesis method is based on the structural modeling followed by the fitting of the simulated result to the experimental alone w20–23x. The reliability of the inverse synthesis method mainly depends on the validity of the optical model and the fitting statistics. For the configuration of an absorbing thin film on the transparent substrate as shown in Fig. 1, the transmittance can be written as follows: Ts
nsZEtZ2Ž1yR32. n0Ž1yR2R3.
, Ets
t1t2exp(yid) 1qr1r2exp(y2id)
n0ynf nfyns nsyn0 ; r 2s ; r 3s ; n0qnf nfqns nsqn0 nfsnyik; RisZriZ2, tis1qri, is1 to 3.
(1)
r 1s
(2)
where incoherent interference is assumed inside the thick substrate. Here ns is the substrate refractive index, n0 is the refractive index of the surrounding medium (in this case for air n0s1), ds2pd(nyik)yl and n, k, d are refractive index, extinction coefficient, and the thickness of the thin film, respectively; r1, r2, and r3 are the Fresnel reflection coefficients at the interfaces air–film, film–substrate, and substrate–air, respectively; t1 and t2 are the Fresnel transmission coefficients at the interfaces air–film and film–substrate, respectively, as designated in Fig. 1.
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225
Fig. 2. Transmission spectra and fitted curve of amorphous PZT thin film (a) on vitreous silica and (b) sapphire substrates.
From Eq. (1), if the layer structure of the film and the optical parameters of each layer are known, the thickness of the film can be accurately determined. Firstly, considering the thick substrate alone (0.5 mm) in the absence of a film, the interference-free transmission is given by the well-known expression, where Texp,s is the measured transmittance of the substrate in the absence of a film: Texp,ss
2ns . n q1
(3)
2 s
The transmittance in Eq. (3) can be inverted to yield the refractive index ns: nss
1 Texp,s
B
1
qC
2
D Texp,s
E1y2
y1F G
.
(4)
For the refractive index ns below the transparent regions (256 nm for the vitreous silica and 320 nm for the sapphire), however, are taken from Palik w24x. Then, according to the formalism of n and k given by Forouhi and Bloomer w19,25x, the optical constants of amorphous dielectrics can be parameterized using a five parameter model, which is n(E)sn`q
B9EqC9 , E yBEqC
and
E2yBEqC
.
(6)
where A, B, C, are the fitting parameters, n` is the high-frequency refractive index, and Eg is the band gap energy. Thus, the fitting model of the optical constants is obtained by Eqs. (1)–(6). The six fitting parameters are A, B, C, n`, Eg, and the thickness d. With a computer program, the fitting process can be routine work. The fitting process progresses with the systematic change of dispersion constants from their initial values, which are obtained from some reports on amorphous PLZT w15,16x, and can be guided by a deviation parameter s, which is defined as s 2s
1 m ŽTexp,iyTcal,i.2. m8 is1
(7)
where Texp,i and Tcal,i are the measured and calculated values at the ith data of m wavelength. A least squaresfitting procedure employing the modified Levenberg– Marquardt algorithm, the convergence of which is faster than that of the SIMPLEX algorithm, is used in the fitting. In short, the fitting is a process of minimizing s with the optimized values of the six fitting parameters. 3.2. Determination of optical constants
2
where AŽyB2q2EgBy2E2gq2C. B9s , Ž4CyB2.1y2 A ?BŽE2gqC.y4EgC@ C9s . Ž4CyB2.1y2
k(E)s
AŽEyEg.2
(5)
The transmission spectra of the uncoated vitreous silica substrate and amorphous PZT thin films on it are shown in Fig. 2a. Similarly, the transmission spectra of the uncoated sapphire substrate and amorphous PZT thin films on it are shown in Fig. 2b. The transmission spectrum of amorphous PZT thin films on sapphire shows the same feature to that of amorphous PZT thin films on vitreous silica. The transmittance of the uncoat-
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Table 1 Parameters of six-parameter model used for fitting the optical functions of amorphous PZT thin films Sample
PZTySiO2
PZTyAl2O3
n` Eg (eV) A B (eV) C (eV2) d (nm) s
2.131"0.00027 1.548"0.006 0.235"0.006 6.257"0.02 12.067"0.065 266.35"0.15 0.0039
2.190"0.0033 1.342"0.01 0.149"0.004 6.615"0.02 12.686"0.083 258.73"0.26 0.0049
The 90% confidence limits are given with (").
ed vitreous silica is greater than 93% over the entire spectrum region except for a slight decrease at short wavelengths below 256 nm, an effect that is due to light scattering by bubbles inside the vitreous silica. However, the transmittance of the uncoated sapphire is greater than 80% over the entire spectrum region except for a sharp decrease at short wavelengths below 320 nm, an effect that is the same to that of the vitreous silica. The transmission spectra of amorphous PZT thin films on vitreous silica and sapphire show quite a different feature to the spectra of the uncoated substrates. Transmittance increases gradually from 200 nm (10y5) and reaches its peak values of 89 and 80% at 656 nm, respectively. These values are slightly less than the transmittance of the uncoated substrates. On the other hand, the strong interference oscillation at higher wavelengths above 656 nm is due to the interference between amorphous PZT thin films and the substrates. In fact, the absorption tails of amorphous PZT thin films are very wide by the transmission spectra measured, and the optical band gaps cannot be determined by the sharp absorption edges. So Eqs. (5) and (6) can describe the dispersion correlation of amorphous PZT thin films in the wide energy range measured. The best fitting can be achieved after the fine adjustment of model parameters. The fitted results of the transmittance are shown by the solid lines in Fig. 2a and b, respectively. The results of the six fitting parameters are simultaneously obtained and listed in Table 1. As can be seen in Fig. 2a and b, the fitting curves agree well with the experimental data in the wide energy range. The indicator of the fitting s, which is listed in Table 1, is small enough to guarantee the accuracy of the optical constants within 2% in the measured andyor fitting range. The fitted thicknesses are in agreement with values measured by a Rank ‘Talystep’ thickness profiler. It indicates that the inverse synthesis method is valid and can be used to describe the dispersion correlation of amorphous PZT thin films on the transparent substrates. The distributions of the calculated refractive index n and extinction coefficient k with wavelength are shown in Fig. 3. The refractive index of amorphous PZT thin films on vitreous silica and sapphire substrates increase
rapidly, reach maximum values of 2.62 and 2.65 at 408 nm, respectively, and gradually fall with further increase of the wavelength. At 632.8 nm, the refractive indices are 2.45 and 2.50, respectively. These values are larger than 2.20 of amorphous PZT thin film prepared by sol– gel method w3x, but close to the value of amorphous PLZT w16x and PMZT (manganese modified PZT thin films) w2x. Meanwhile, these values are also smaller than 2.56 of the PZT thin film w6x. The extinction coefficients increase rapidly as the wavelength increases, reaching maximum values of 0.478 at 295 nm and 0.494 at 264 nm for amorphous PZT thin films prepared on vitreous silica and sapphire substrates, respectively, and falling rapidly at higher wavelengths. At 632.8 nm, the extinction coefficients are 1.6=10y2 and 1=10y2. In the interference region, the extinction coefficients of the two samples are close to 0. The refractive index and the extinction efficient characteristics of amorphous PZT thin films are different for the two substrates. The electrical and optical properties of PZT thin films can be affected by many factors, such as the substrate, preparation method, annealing temperature and crystallinity. For amorphous PZT thin films prepared on vitreous silica and sapphire substrates, the interactions between amorphous PZT thin films and the substrates are different and this may lead to the discrepancy of the microstructures for amorphous PZT thin films. In addition, the surface roughness of amorphous PZT thin films prepared on vitreous silica and sapphire substrates may be also different and this point cannot be considered in the inverse synthesis method. Therefore, the discrepancy for the optical properties of amorphous PZT thin films on vitreous silica and sapphire substrates may ascribe to the above factors. The absorption coefficient a of amorphous PZT thin films is calculated from the relation as4pkyl. Fig. 4 shows that the plot of log(a) as a function of energy
Fig. 3. Refractive index n and extinction coefficient k of amorphous PZT thin films prepared on vitreous silica and sapphire substrates as a function of wavelength.
Z. Hu et al. / Thin Solid Films 437 (2003) 223–229
227
Fig. 4. Photon energy dependence of the absorption coefficient of amorphous PZT thin films prepared on vitreous silica and sapphire substrates. The inset is the linear fitting curves for obtaining Ee values.
Fig. 5. Optical absorption coefficient vs. photon energy of amorphous PZT thin films prepared on vitreous silica and sapphire substrates near the absorption edges.
(hn) of the incident photons. The each log(a) curve for the two samples can be divided into two regions w26– 28x. The first region, for the higher values of the absorption coefficient, a(hn)0104 cmy1 corresponds to the transition between extended states in both valence and conduction bands, where the power law behavior of Tauc:
asa0expŽhnyEe..
(9)
ahnsC1ŽhnyEgdopt.1y2,
(8a)
where a0 is a constant and Ee is the Urbach energy which is interpreted as the width of the tails of localized states in the band gap, the absorption in this region is due to transitions between extended states in one band and localized states in the exponential tail of the other band w30x. From plotting log(a) as a function of energy(hn), as shown in Fig. 4, the calculated values of Ee are 0.90"0.015 and 1.04"0.016 eV, respectively.
2 ahnsC2ŽhnyEiopt g . .
(8b)
3.3. Determination of oscillator energy
for allowed direct and indirect transition, respectively, applies. In Eqs. (8a) and (8b), C1 and C2 are two constants and Edopt and Eiopt are the direct and indirect g g band gaps, respectively. The graph of (ahn)2 vs. (hn) is found to lead to straight lines over any part of the optical absorption spectrum, thus supporting the interpretation of direct rather than indirect band gap for all vacuum-deposited film w29x. Fig. 5 shows the plot of (ahn)2 as a function of energy (hn) of the incident photons. The straight line between (ahn)2 and (hn) will provide the value of the optical band gap Edopt g , which is extrapolated by the linear portion of the plot to(ahn)2s0. These values of 3.36 and 3.25 eV, obtained from Eq. (8a) for the PZT thin films, are less than the values between 3.59 and 3.88 eV w6x, 3.75 eV for amorphous PLZT thin films w15x, and 3.80 eV for amorphous PLZT thin films w16x. This shift may be due to the different substrates and the different preparation techniques. The second region is for the lower values of the absorption coefficient, which is a-104 cmy1, where the absorption at lower photon energy usually follows the Urbach rule w28x:
The dispersion data of the refractive index indicates that the interband transition region follows a single
Fig. 6. Experimental values and single electronic oscillator mode fit curve as a function of (1yl2) for the amorphous PZT thin films prepared on vitreous silica and sapphire substrates.
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228
Table 2 Sellmeier’s dispersion parameters for measured sample and samples from references Sample
l0 (nm)
S0 (1014 my2)
E0 (eV)
E0yS0 (10y14 eV m2)
PZTySiO2 (this work) PZTyAl2O3 (this work) PMZT (4 40 60) w2x PLZT (9 65 35) annealed w30x PLZT (14 0 100) annealed w31x
258.8 311.2 233 226–228 224
0.62 0.81 0.615 0.82–0.88 0.88
4.80 3.98 5.33 5.44–5.49 5.54
7.74 4.91 8.66 6.23–6.35 6.29
electronic oscillator mode w31x. Therefore, the refractive index in the region of oscillating absorption should follow the relation: n(l)2y1sS0l02y ?1yŽl0yl.
@
2
(10)
where S0 is the oscillator strength, l0 is the average oscillator position, and E0 is the oscillator energy given by E0shcyel0 (c is the light velocity, h is Plank’s constant, and e is the charge of the electron) w32x. For analyzing the above formula for the present case we have plotted the quantity (1y(n 2y1)) vs. (1yl2) for the amorphous PZT films in Fig. 6. The data fit to a straight line indicating the applicability of Sellmeier’s dispersion formula for the amorphous PZT thin films. The values of S0 and l0 are estimated from the slope (y1yS0) and the infinite wavelength intercept (1yS0l20) of the (1y(n 2y1)) vs. (1yl2) plot. The equations for the best fitting straight line are given by: 1yŽn(l)2y1.sy1.61=10y14=1yl2q0.24
(11a)
1yŽn(l)2y1.sy1.23=10y14=1yl2q0.22
(11b)
where l is in nm. For the samples the parameters S0, l0, E0, and the refractive index dispersion parameter hcy(el0S0) are listed in Table 2. The parameters for amorphous PMZT (4 40 60) thin film, and PLZT (14 0 100) thin film, and PLZT (9 65 35) from Refs. w2,33,34x, respectively, are also included in Table 2. The above analyses indicate that the S0 parameter of the amorphous films is smaller than that of the crystalline films, and the l0 parameter of the amorphous films is higher than that of the crystalline films. Therefore, the ratio (E0 yS0) depends on the characteristics of the interband transitions, enters directly into the evaluation of the electro-optical and non-linear optical constant of the amorphous thin films and is higher than that of the crystalline films except for amorphous PZT thin films on sapphire substrate. This may be due to the reduced density and higher optical band gap as compared with the crystalline films. 4. Conclusions In conclusion, the optical properties of the amorphous PbZr0.52Ti0.48O3 thin films on vitreous silica and sapphire
substrates have been investigated by transmittance measurements in the wavelength range of 200–1100 nm. The inverse synthesis or fitting method, which is based on the thin film structure with transmittance measurement, is given in the wide energy range. The refractive index n, the extinction coefficient k, the absorption coefficient a, and the film thickness d are simultaneously determined. The results indicate that the absorption tail of amorphous PZT thin films is very wide and there is no sharp absorption edge. The fitted thickness values of the two samples are 266.35 and 258.73 nm, respectively. The maximum values of the refractive index are 2.62 and 2.65, and those of the extinction coefficient are 0.478 and 0.494, respectively. These values of the refractive index and the extinction coefficient are close to that of amorphous PZT or PLZT reported. It indicates that the Forouhi and Bloomer five-parameter model can be used to fit the optical constants of amorphous PZT thin films. According to Tauc’s law, the direct band gaps Edopt of the amorphous PZT thin films are found to be g 3.36 and 3.25 eV, which are less than that of amorphous PZT or PLZT thin films reported. The dispersion of the refractive index in the transparent region is interpreted successfully in terms of a single electronic oscillator with the oscillator energy and strength are 4.80, 3.98 eV and 0.62=1014 my2, 0.81=1014 my2, respectively. Acknowledgments The authors gratefully acknowledge the support of the National Natural Science Foundation of China, No. 60076029. The authors would like to acknowledge Dr X.J. Meng, Dr T. Lin, Dr Q. Zhao for their technical assistance. References w1x L. Wang, A. Pignolet, F. Levy, ´ Mater. Res. Bull. 25 (1990) 1495. w2x J. Krempasky, ´ ´ L. Wang, M. Proctor, A. Pignolet, F. Levy, Solid State Commun. 78 (1991) 1039. w3x Y.H. Xu, C.H. Peng, J.D. Mackenize, J. Non-Cryst. Solids 170 (1994) 1. w4x Y.H. Xu, C.H. Peng, R. Xu, J.D. Mackenzie, in: M.J. HampdenSmith, W.G. Klemperer, C.J. Brinker (Eds.), Better Ceramics Through Chemistry V, Mater. Res. Soc. Symp. Proc. 271 (1992) 359.
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Optical properties of amorphous PbZrxTi1yxO3 (xs0.52) thin films prepared by RF magnetron sputtering Zhigao Hu*, Zhiming Huang, Zhenquan Lai, Genshui Wang, Junhao Chu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yu Tian Road, Shanghai 200083, PR China Received 26 March 2002; received in revised form 21 November 2002; accepted 13 December 2002
Abstract The optical properties of amorphous PbZr0.52 Ti0.48 O3 thin films on vitreous silica and sapphire substrates by the RF magnetron sputtering method have been investigated by transmittance measurements. For a single-layer thin film on the transparent substrate, the inverse synthesis or fitting method with the six fitting parameters was given and used to calculate the optical constants such as the refractive index n, the extinction coefficient k, and the absorption coefficient a. The film thickness d, which was one of the fitting parameters, is simultaneously obtained. According to Tauc’s law, the optical transition in amorphous PbZr0.52Ti0.48O3 thin films is direct in nature. The direct band gaps of amorphous PbZr0.52Ti0.48 O3 thin films on vitreous silica and sapphire substrates were found to be 3.36 and 3.25 eV, respectively. The dispersions of the refractive index in films were studied by considering a single-oscillator model. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Optical properties; Amorphous; PbZr0.52Ti0.48O3; Inverse synthesis method
1. Introduction Ferroelectric thin films have attracted great attention primarily due to their applications in non-volatile random access memory device applications w1–9x. The most popular material is lead zirconate titanate PbZrxTi1yxO3 (PZT) ferroelectric thin film, which is considered to be a very promising material due to its ability to maintain adequate pyroelectric, ferroelectric and electro-optic properties. There have been numerous proposals for applications in optoelectronic devices such as optical switches and optical modulators w10,11x. The PZT thin films can be prepared by various methods such as RF magnetron sputtering w1,2x, sol–gel processing w3–5x, metallo-organic decomposition process w6,7x, ion-beam sputter deposition w8x, and chemical vapor deposition w9x on a variety of substrates. Because its composition can span a very wide range, this produces materials with different dielectric and optical characteristics. *Corresponding author. Tel.: q86-21-65420850; fax: q86-2165830734. E-mail address: [email protected] (Z. Hu).
‘Amorphous ferroelectricity’ was first suggested by Lines w12x, and some observations of ferroelectric or ferroelectric-like phase transition in LiNbO3 and PbTiO3 systems have been reported where RF sputtering was used to form amorphous films w13,14x. Xu et al. w3,4x have found that some amorphous PZT thin films exhibit a polarization–electric (P–E) field hysteresis loop, stable pyroelectric current, and piezoelectric resonance peaks in the dielectric spectrum. These excellent properties show that further studies, including optical measurements, need to be performed for the amorphous PZT thin films. Trolier-Mckinstry et al. w5,8x have studied the optical properties of the PZT thin films by spectroscopic ellipsometry. In their work, however, most samples used are crystalline, and the measured wavelength range is rather narrow: 300–700 nm, so the spectrum of refractive index n show monotonic behavior and the spectrum of extinction coefficient k have not been given. Zhu et al. w15x and Li et al. w16x have studied optical properties of the amorphous PLZT thin films (lanthanum modified PZT thin films) by spectroscopic ellipsometry. However, up to now, the optical
0040-6090/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0040-6090(03)00016-6
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properties of the amorphous PZT thin films prepared by the RF magnetron sputtering method have not been determined in the wide spectral range. For a single-layer thin film on the transparent substrate, the optical constants of the amorphous PZT thin films can be determined by the transmittance spectrum alone w6,17,18x. There, however, are three questions: (i) the envelope curves are manually determined, (ii) some assumptions must be met, and (iii) a significant error appears near the turning point (the optical absorption edge). Recently, a formalism of the extinction coefficient k in a wide range of energy is derived by Forouhi and Bloomer w19x. Their equation is based on a quantummechanical theory of absorption. From the extinction coefficient k, the refractive index dispersion n is also deduced in accordance with the Kramers–Kronig relation. With the formalism most amorphous materials can be described by a single oscillator, and hence only one set coefficient (A, B, C, n` and Eg) is enough to express n and k of an amorphous thin film. In the present paper, an inverse synthesis or fitting method with the formalism of Forouhi and Bloomer, which is used with transmission analysis for the simultaneous determination of n, k and the thickness d is established. With this method, the optical constants, the absorption coefficient, the singleoscillator energy and the optical band gap were obtained. 2. Experimental details In this study, the samples of amorphous PbZr0.52Ti0.48O3 thin films are prepared by RF magnetron sputtering technique. A 10-cm-diameter PbZr0.52 Ti0.48O3 target is used for deposition. Before deposition, the target is pre-sputtered for 30 min with the substrate shutter closed to achieve stable conditions. The vacuum chamber pumped by a turbo-molecular pump produces a base pressure of 7=10y6 Pa and is raised to 1.6 Pa by admitting Ar. The 30-mm-diameter vitreous silica and 20-mm-diam sapphire (0 0 0 1) substrates are mounted with silver paste onto a resistively heated substrate holder. During the sputtering, the temperature of the substrate holder is kept at 400 8C and the RF power on the target is 100 W, operating at 13.56 MHz, yielding a growth rate of approximately 3–4 nm miny1. With 100% Ar sputtering plasma guided onto the target, the thin films are sputtered inside a commercial vacuum coater. The as-grown PZT thin films with the desired thickness are amorphous. After sputtered samples are cooled inside the chamber, optical measurements and the thickness measurement are made. The compositions of the thin films were analyzed using inductively coupled argon plasma atomic emission spectrometry, and were represented by x and y in the formula of composition Pby(ZrxTi1yx)O3 . In the paper, the optical properties are measured for the PZT thin
Fig. 1. Schematic diagram of the layer structure of amorphous PZT thin film and related optical parameters used in the fitting calculation of the optical constants.
films with 0.50-x-0.52 and 1.01-y-1.05 composition. There is excessive Pb for the PZT thin films. The optical transmission characteristics of amorphous PZT thin films have been studied by using a double beam ultraviolet–visible (UV–Vis) spectrophotometer (Perkin Elmer UV–Vis spectrometer Lambda 2S) in the wavelength range of 200–1100 nm. The transmission spectra of uncoated vitreous silica and sapphire substrates are also measured for a comparison. 3. Results and discussion 3.1. Inverse synthesis or fitting method The inverse synthesis method is based on the structural modeling followed by the fitting of the simulated result to the experimental alone w20–23x. The reliability of the inverse synthesis method mainly depends on the validity of the optical model and the fitting statistics. For the configuration of an absorbing thin film on the transparent substrate as shown in Fig. 1, the transmittance can be written as follows: Ts
nsZEtZ2Ž1yR32. n0Ž1yR2R3.
, Ets
t1t2exp(yid) 1qr1r2exp(y2id)
n0ynf nfyns nsyn0 ; r 2s ; r 3s ; n0qnf nfqns nsqn0 nfsnyik; RisZriZ2, tis1qri, is1 to 3.
(1)
r 1s
(2)
where incoherent interference is assumed inside the thick substrate. Here ns is the substrate refractive index, n0 is the refractive index of the surrounding medium (in this case for air n0s1), ds2pd(nyik)yl and n, k, d are refractive index, extinction coefficient, and the thickness of the thin film, respectively; r1, r2, and r3 are the Fresnel reflection coefficients at the interfaces air–film, film–substrate, and substrate–air, respectively; t1 and t2 are the Fresnel transmission coefficients at the interfaces air–film and film–substrate, respectively, as designated in Fig. 1.
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225
Fig. 2. Transmission spectra and fitted curve of amorphous PZT thin film (a) on vitreous silica and (b) sapphire substrates.
From Eq. (1), if the layer structure of the film and the optical parameters of each layer are known, the thickness of the film can be accurately determined. Firstly, considering the thick substrate alone (0.5 mm) in the absence of a film, the interference-free transmission is given by the well-known expression, where Texp,s is the measured transmittance of the substrate in the absence of a film: Texp,ss
2ns . n q1
(3)
2 s
The transmittance in Eq. (3) can be inverted to yield the refractive index ns: nss
1 Texp,s
B
1
qC
2
D Texp,s
E1y2
y1F G
.
(4)
For the refractive index ns below the transparent regions (256 nm for the vitreous silica and 320 nm for the sapphire), however, are taken from Palik w24x. Then, according to the formalism of n and k given by Forouhi and Bloomer w19,25x, the optical constants of amorphous dielectrics can be parameterized using a five parameter model, which is n(E)sn`q
B9EqC9 , E yBEqC
and
E2yBEqC
.
(6)
where A, B, C, are the fitting parameters, n` is the high-frequency refractive index, and Eg is the band gap energy. Thus, the fitting model of the optical constants is obtained by Eqs. (1)–(6). The six fitting parameters are A, B, C, n`, Eg, and the thickness d. With a computer program, the fitting process can be routine work. The fitting process progresses with the systematic change of dispersion constants from their initial values, which are obtained from some reports on amorphous PLZT w15,16x, and can be guided by a deviation parameter s, which is defined as s 2s
1 m ŽTexp,iyTcal,i.2. m8 is1
(7)
where Texp,i and Tcal,i are the measured and calculated values at the ith data of m wavelength. A least squaresfitting procedure employing the modified Levenberg– Marquardt algorithm, the convergence of which is faster than that of the SIMPLEX algorithm, is used in the fitting. In short, the fitting is a process of minimizing s with the optimized values of the six fitting parameters. 3.2. Determination of optical constants
2
where AŽyB2q2EgBy2E2gq2C. B9s , Ž4CyB2.1y2 A ?BŽE2gqC.y4EgC@ C9s . Ž4CyB2.1y2
k(E)s
AŽEyEg.2
(5)
The transmission spectra of the uncoated vitreous silica substrate and amorphous PZT thin films on it are shown in Fig. 2a. Similarly, the transmission spectra of the uncoated sapphire substrate and amorphous PZT thin films on it are shown in Fig. 2b. The transmission spectrum of amorphous PZT thin films on sapphire shows the same feature to that of amorphous PZT thin films on vitreous silica. The transmittance of the uncoat-
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Table 1 Parameters of six-parameter model used for fitting the optical functions of amorphous PZT thin films Sample
PZTySiO2
PZTyAl2O3
n` Eg (eV) A B (eV) C (eV2) d (nm) s
2.131"0.00027 1.548"0.006 0.235"0.006 6.257"0.02 12.067"0.065 266.35"0.15 0.0039
2.190"0.0033 1.342"0.01 0.149"0.004 6.615"0.02 12.686"0.083 258.73"0.26 0.0049
The 90% confidence limits are given with (").
ed vitreous silica is greater than 93% over the entire spectrum region except for a slight decrease at short wavelengths below 256 nm, an effect that is due to light scattering by bubbles inside the vitreous silica. However, the transmittance of the uncoated sapphire is greater than 80% over the entire spectrum region except for a sharp decrease at short wavelengths below 320 nm, an effect that is the same to that of the vitreous silica. The transmission spectra of amorphous PZT thin films on vitreous silica and sapphire show quite a different feature to the spectra of the uncoated substrates. Transmittance increases gradually from 200 nm (10y5) and reaches its peak values of 89 and 80% at 656 nm, respectively. These values are slightly less than the transmittance of the uncoated substrates. On the other hand, the strong interference oscillation at higher wavelengths above 656 nm is due to the interference between amorphous PZT thin films and the substrates. In fact, the absorption tails of amorphous PZT thin films are very wide by the transmission spectra measured, and the optical band gaps cannot be determined by the sharp absorption edges. So Eqs. (5) and (6) can describe the dispersion correlation of amorphous PZT thin films in the wide energy range measured. The best fitting can be achieved after the fine adjustment of model parameters. The fitted results of the transmittance are shown by the solid lines in Fig. 2a and b, respectively. The results of the six fitting parameters are simultaneously obtained and listed in Table 1. As can be seen in Fig. 2a and b, the fitting curves agree well with the experimental data in the wide energy range. The indicator of the fitting s, which is listed in Table 1, is small enough to guarantee the accuracy of the optical constants within 2% in the measured andyor fitting range. The fitted thicknesses are in agreement with values measured by a Rank ‘Talystep’ thickness profiler. It indicates that the inverse synthesis method is valid and can be used to describe the dispersion correlation of amorphous PZT thin films on the transparent substrates. The distributions of the calculated refractive index n and extinction coefficient k with wavelength are shown in Fig. 3. The refractive index of amorphous PZT thin films on vitreous silica and sapphire substrates increase
rapidly, reach maximum values of 2.62 and 2.65 at 408 nm, respectively, and gradually fall with further increase of the wavelength. At 632.8 nm, the refractive indices are 2.45 and 2.50, respectively. These values are larger than 2.20 of amorphous PZT thin film prepared by sol– gel method w3x, but close to the value of amorphous PLZT w16x and PMZT (manganese modified PZT thin films) w2x. Meanwhile, these values are also smaller than 2.56 of the PZT thin film w6x. The extinction coefficients increase rapidly as the wavelength increases, reaching maximum values of 0.478 at 295 nm and 0.494 at 264 nm for amorphous PZT thin films prepared on vitreous silica and sapphire substrates, respectively, and falling rapidly at higher wavelengths. At 632.8 nm, the extinction coefficients are 1.6=10y2 and 1=10y2. In the interference region, the extinction coefficients of the two samples are close to 0. The refractive index and the extinction efficient characteristics of amorphous PZT thin films are different for the two substrates. The electrical and optical properties of PZT thin films can be affected by many factors, such as the substrate, preparation method, annealing temperature and crystallinity. For amorphous PZT thin films prepared on vitreous silica and sapphire substrates, the interactions between amorphous PZT thin films and the substrates are different and this may lead to the discrepancy of the microstructures for amorphous PZT thin films. In addition, the surface roughness of amorphous PZT thin films prepared on vitreous silica and sapphire substrates may be also different and this point cannot be considered in the inverse synthesis method. Therefore, the discrepancy for the optical properties of amorphous PZT thin films on vitreous silica and sapphire substrates may ascribe to the above factors. The absorption coefficient a of amorphous PZT thin films is calculated from the relation as4pkyl. Fig. 4 shows that the plot of log(a) as a function of energy
Fig. 3. Refractive index n and extinction coefficient k of amorphous PZT thin films prepared on vitreous silica and sapphire substrates as a function of wavelength.
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227
Fig. 4. Photon energy dependence of the absorption coefficient of amorphous PZT thin films prepared on vitreous silica and sapphire substrates. The inset is the linear fitting curves for obtaining Ee values.
Fig. 5. Optical absorption coefficient vs. photon energy of amorphous PZT thin films prepared on vitreous silica and sapphire substrates near the absorption edges.
(hn) of the incident photons. The each log(a) curve for the two samples can be divided into two regions w26– 28x. The first region, for the higher values of the absorption coefficient, a(hn)0104 cmy1 corresponds to the transition between extended states in both valence and conduction bands, where the power law behavior of Tauc:
asa0expŽhnyEe..
(9)
ahnsC1ŽhnyEgdopt.1y2,
(8a)
where a0 is a constant and Ee is the Urbach energy which is interpreted as the width of the tails of localized states in the band gap, the absorption in this region is due to transitions between extended states in one band and localized states in the exponential tail of the other band w30x. From plotting log(a) as a function of energy(hn), as shown in Fig. 4, the calculated values of Ee are 0.90"0.015 and 1.04"0.016 eV, respectively.
2 ahnsC2ŽhnyEiopt g . .
(8b)
3.3. Determination of oscillator energy
for allowed direct and indirect transition, respectively, applies. In Eqs. (8a) and (8b), C1 and C2 are two constants and Edopt and Eiopt are the direct and indirect g g band gaps, respectively. The graph of (ahn)2 vs. (hn) is found to lead to straight lines over any part of the optical absorption spectrum, thus supporting the interpretation of direct rather than indirect band gap for all vacuum-deposited film w29x. Fig. 5 shows the plot of (ahn)2 as a function of energy (hn) of the incident photons. The straight line between (ahn)2 and (hn) will provide the value of the optical band gap Edopt g , which is extrapolated by the linear portion of the plot to(ahn)2s0. These values of 3.36 and 3.25 eV, obtained from Eq. (8a) for the PZT thin films, are less than the values between 3.59 and 3.88 eV w6x, 3.75 eV for amorphous PLZT thin films w15x, and 3.80 eV for amorphous PLZT thin films w16x. This shift may be due to the different substrates and the different preparation techniques. The second region is for the lower values of the absorption coefficient, which is a-104 cmy1, where the absorption at lower photon energy usually follows the Urbach rule w28x:
The dispersion data of the refractive index indicates that the interband transition region follows a single
Fig. 6. Experimental values and single electronic oscillator mode fit curve as a function of (1yl2) for the amorphous PZT thin films prepared on vitreous silica and sapphire substrates.
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Table 2 Sellmeier’s dispersion parameters for measured sample and samples from references Sample
l0 (nm)
S0 (1014 my2)
E0 (eV)
E0yS0 (10y14 eV m2)
PZTySiO2 (this work) PZTyAl2O3 (this work) PMZT (4 40 60) w2x PLZT (9 65 35) annealed w30x PLZT (14 0 100) annealed w31x
258.8 311.2 233 226–228 224
0.62 0.81 0.615 0.82–0.88 0.88
4.80 3.98 5.33 5.44–5.49 5.54
7.74 4.91 8.66 6.23–6.35 6.29
electronic oscillator mode w31x. Therefore, the refractive index in the region of oscillating absorption should follow the relation: n(l)2y1sS0l02y ?1yŽl0yl.
@
2
(10)
where S0 is the oscillator strength, l0 is the average oscillator position, and E0 is the oscillator energy given by E0shcyel0 (c is the light velocity, h is Plank’s constant, and e is the charge of the electron) w32x. For analyzing the above formula for the present case we have plotted the quantity (1y(n 2y1)) vs. (1yl2) for the amorphous PZT films in Fig. 6. The data fit to a straight line indicating the applicability of Sellmeier’s dispersion formula for the amorphous PZT thin films. The values of S0 and l0 are estimated from the slope (y1yS0) and the infinite wavelength intercept (1yS0l20) of the (1y(n 2y1)) vs. (1yl2) plot. The equations for the best fitting straight line are given by: 1yŽn(l)2y1.sy1.61=10y14=1yl2q0.24
(11a)
1yŽn(l)2y1.sy1.23=10y14=1yl2q0.22
(11b)
where l is in nm. For the samples the parameters S0, l0, E0, and the refractive index dispersion parameter hcy(el0S0) are listed in Table 2. The parameters for amorphous PMZT (4 40 60) thin film, and PLZT (14 0 100) thin film, and PLZT (9 65 35) from Refs. w2,33,34x, respectively, are also included in Table 2. The above analyses indicate that the S0 parameter of the amorphous films is smaller than that of the crystalline films, and the l0 parameter of the amorphous films is higher than that of the crystalline films. Therefore, the ratio (E0 yS0) depends on the characteristics of the interband transitions, enters directly into the evaluation of the electro-optical and non-linear optical constant of the amorphous thin films and is higher than that of the crystalline films except for amorphous PZT thin films on sapphire substrate. This may be due to the reduced density and higher optical band gap as compared with the crystalline films. 4. Conclusions In conclusion, the optical properties of the amorphous PbZr0.52Ti0.48O3 thin films on vitreous silica and sapphire
substrates have been investigated by transmittance measurements in the wavelength range of 200–1100 nm. The inverse synthesis or fitting method, which is based on the thin film structure with transmittance measurement, is given in the wide energy range. The refractive index n, the extinction coefficient k, the absorption coefficient a, and the film thickness d are simultaneously determined. The results indicate that the absorption tail of amorphous PZT thin films is very wide and there is no sharp absorption edge. The fitted thickness values of the two samples are 266.35 and 258.73 nm, respectively. The maximum values of the refractive index are 2.62 and 2.65, and those of the extinction coefficient are 0.478 and 0.494, respectively. These values of the refractive index and the extinction coefficient are close to that of amorphous PZT or PLZT reported. It indicates that the Forouhi and Bloomer five-parameter model can be used to fit the optical constants of amorphous PZT thin films. According to Tauc’s law, the direct band gaps Edopt of the amorphous PZT thin films are found to be g 3.36 and 3.25 eV, which are less than that of amorphous PZT or PLZT thin films reported. The dispersion of the refractive index in the transparent region is interpreted successfully in terms of a single electronic oscillator with the oscillator energy and strength are 4.80, 3.98 eV and 0.62=1014 my2, 0.81=1014 my2, respectively. Acknowledgments The authors gratefully acknowledge the support of the National Natural Science Foundation of China, No. 60076029. The authors would like to acknowledge Dr X.J. Meng, Dr T. Lin, Dr Q. Zhao for their technical assistance. References w1x L. Wang, A. Pignolet, F. Levy, ´ Mater. Res. Bull. 25 (1990) 1495. w2x J. Krempasky, ´ ´ L. Wang, M. Proctor, A. Pignolet, F. Levy, Solid State Commun. 78 (1991) 1039. w3x Y.H. Xu, C.H. Peng, J.D. Mackenize, J. Non-Cryst. Solids 170 (1994) 1. w4x Y.H. Xu, C.H. Peng, R. Xu, J.D. Mackenzie, in: M.J. HampdenSmith, W.G. Klemperer, C.J. Brinker (Eds.), Better Ceramics Through Chemistry V, Mater. Res. Soc. Symp. Proc. 271 (1992) 359.
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