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Abstract
In this study, the influence of the linear permittivity on the thermally-induced nonlinear optical properties of aluminum-doped zinc oxide thin films was investigated in the visible range, namely at 405, 532, and 650 nm. The strength of the nonlinear response in the films at these wavelengths represented by the thermal nonlinear index of refraction ($n_2^{th}$) and the absorption coefficients (β) magnitudes followed dispersive changes in the films’ permittivity function. These changes were dominantly scattering events within the films, which strongly influenced the nonlinear absorption behavior alternating between saturable absorber and reverse saturable absorber trend. In this research, the results and qualitative description of this relationship are presented.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Aluminum doped zinc oxide (AZO) thin films is a wide bandgap semiconductor that has many potential applications such as thin film transistors [1,2], solar cells [3,4], light emitting diodes [5], and gas and biological sensors [6,7]. In the majority of these applications, light is restricted to the linear interaction with the fabricated films being mainly transparent contacts. In high power applications, damage and uncontrolled nonlinear phase shifts might cause failure on these devices. Nevertheless, when moderately pulsed energies and cw operations are used, doped Zn-oxide can be utilized as a nonlinear optical limiting or switching medium [8–12]. In particular, AZO exhibit strong optical nonlinearity in what is called epsilon-near-zero (ENZ) regimes, which is around the important 1.3 µm communication and THz applications ranges [13–17]. Yet, this high nonlinear response is locked at this wavelength and cannot be tuned with the same strength, which imposes limitations on future applications. However, when strong operational nonlinearity is required, one can always revert to the thermally-induced responses which can be generated at any spectral range and it is much stronger than those originating from electronic excitations. The only drawback here is the comparatively slow response they hold, although there are some reports discussing ultrafast thermal nonlinearities in nanostructured materials [18]. Hence, in applications where high nonlinearities are on demand but not requiring ultrafast response such as in optical limiting or spectral sensing, thermally-induced optical nonlinearity could be an adequate mechanism. The thermal nonlinearity of AZO thin films has been reported in the visible range by several groups [19–25]. However, in most of these studies, the response was generated by monochromatic laser beam and tuning was not discussed. In this study, the thermally-induced nonlinear response of fabricated AZO thin films is reported at different wavelengths for the same samples, spanning the visible range, namely at 405, 532, and 650 nm. The nonlinearity was investigated with a z-scan apparatus pumped by a cw laser diodes operating at these wavelengths. The open and closed aperture scans are generated and the extracted nonlinear coefficients are explored as function of these wavelengths. The strength of the nonlinear response in general, can become wavelength dependent due to changes in the permittivity function [26,27]. For example, in optical limiting, the transient power is locked to a maximum level which became subject to the spectral shifts due to local thermal changes in the permittivity. A correlation of the spectral variation of the nonlinear coefficients obtained in this study is made to this permittivity function. The interplay between the linear permittivity and the changes in the thermally induced nonlinear coefficients is discussed. A model based on scattering events of the free electrons in AZO films at the operating wavelengths is proposed for this relationship.
2. Experimental procedure
AZO thin films were deposited on 25 × 25 × 1.1 mm corning 7059 glass substrates by radio frequency magnetron sputtering system. The glass substrates were ultrasonically cleaned with acetone and distilled water and then dried prior to loading into the deposition chamber. A circular-shaped sputtering AZO target with dimensions of 100 mm diameter × 3.2 mm thickness from Plasmaterials, Inc. was used for the deposition. The target contained 98 (ZnO) and 2 (Al2O3) wt% (these are called green targets). The distance between the target and the substrate holder in the deposition chamber was 70 mm. The glass substrates were inserted into the sputtering chamber and the vacuum was brought down to 5×10−8 Torr. The AZO thin films grew at 5 mTorr in the Ar (99.999% purity) ambient. The Ar flow rate was set to 20 sccm and the 13.5 MHz sputtering power source was maintained at 150 W. The deposition continued for 30 minutes, during which the substrate temperature was set to 40°C. The crystallinity and crystallographic orientation of the films were obtained from the X-ray diffraction (XRD) patterns generated using Cu Kα radiation ( = 1.5406Å). The surface morphology of the films was investigated with scanning electron microscopy (SEM) using FEI versa 3D system. The resistivity of deposited films was determined to be 5×10−4 Ω.cm using four-point probe method. Woolman variable angle spectroscopic ellipsometry (VASE) system equipped with an adjustable compensator was used to obtain the thickness and the optical functions of the fabricated films. The ellipsometic analysis was done using completeEASE software with three-phase structure (i.e., air/ effective AZO film/Cauchy substrate) to model the layered films. The model was used to fit the measured ellipsometric Ψ and Δ parameters at different angles of incidence. For the nonlinear optical measurements, a single beam z-scan setup equipped with three cw diode-laser systems operating at wavelengths of 405, 532, and 650 nm was employed. The laser power from each of these diodes in the far field was measured to be 100 mW. The samples were fixed on a pc-controlled translation stage and moved in the propagation direction (z-axis) of a narrowly focused Gaussian beam using 50 cm focusing lens. The beam waists (${\omega _0}$) at the focal plane for the 405, 532, and 650 nm beams were calculated to be 25.4, 34.4, and 50.9 µm, respectively. The corresponding intensities based on these results were 9.87, 5.37 and, 2.46 kW/cm2, respectively. The transmitted signal passing the thin film as a function of its position relative to the lens focus was detected in the far field in the normalization process. The z-scan measurements were repeated on various spots across the samples and consistent results were obtained indicating that the used laser powers did not reach the laser damage threshold in the samples.
3. Results
3.1 Surface and structure properties
The surface morphology and structure properties of the AZO thin films are shown in Fig. 1. The granule surface shown in the SEM image is normal for depositing AZO films at low temperature. The particle size analysis is shown in the inset of the figure at the upper right corner indicating an average size of 25-35 nm. The inset at the lower left corner shows the XRD pattern of AZO thin films. The thin films had diffraction peaks which clearly indicates the polycrystalline characteristics in the films. The films exhibit hexagonal wurtzite structure of ZnO confirmed by the presence of a preferred orientation peak (002) planes at 34.43°. The grain size t in the films could be calculated using Scherrer formula as follows:
where λ is the wavelength of the x-ray used, $\theta $ is the Bragg diffraction angle and B is the FWHM of the XRD peak. The calculated grain size was 34 nm using this formula which is within the values estimated from the SEM image analysis. The diffraction pattern also showed small peak (004) at 72.5° which confirms a c-axis preferred orientation. These results revealed that the Al+3 ions were successfully incorporated into Zn+2 host lattice. No characteristic peaks of metallic Zn or Al were observed.
Fig. 1. SEM image of the fabricated AZO films. The inset at the upper right corner represents the particle analysis made on the SEM image. The inset at the lower left corner represents the XRD pattern of the fabricated films. The peak at 34.43° indicate the hexagonal wurtzite structure in the films.
3.2 Spectral ellipsometry analysis
The spectra of Ψ and Δ parameters obtained from the spectral ellipsometery at different angles of incidence for the samples are shown in Fig. 2.
Fig. 2. The fitting of spectral ellipsometric Ψ and Δ parameters at different angles of incidence. The three phase model generated these parameters represented by the solid lines in the figure. The thickness of the films obtained from the fitting procedure was 420 nm.
It is found that the calculated Ψ and Δ (represented by the solid lines) proposed by the three phase model are consistent with the experimental data (represented by the small circules). The determination of the complex refractive index n ($n = {n_r} + i{n_i}$) as a function of the wavelength λ was done by fitting the ellipsometric data with the model given as [28]:
Fig. 3. (a) The index of refraction and (b) the extinction coefficient generated from the ellipsometric fitting process as functions of wavelength.
Using these values, the transmittance spectrum was calculated for the AZO films following a procedure implementing Hadley equations [28] and outlined in Refs. [29,30]. The results of these calculations are presented in Fig. 4(a). The optical band gap Eg of the AZO films was determined from the absorption spectra using the formula [31]:
where, α is the absorption coefficient ($\alpha = 4\pi {n_i}/\lambda $), B is a constant that depends on the electron-hole mobility, h is the Planck constant, $\nu $ is the frequency of the incident photon. From the transmitted spectrum, calculation of the quantity ${(\alpha h\nu )^2}$ versus the photon energy was plotted in Fig. 4(b). The sharp absorption edge for the AZO films can be determined by the linear fit. The Eg value of 3.5 eV was determined by the extrapolation method. This band gap magnitude is in good agreement with literature value for AZO. The dielectric function $\varepsilon = {\varepsilon _1} + i\; {\varepsilon _2}$, where ${\varepsilon _1}$, ${\varepsilon _2}$ are the real and imaginary parts of this function was obtained as: Figure 5 shows the variation of these functions with the incident wavelength in the fabricated films. The permittivity function ${\varepsilon _1}$ decrease monotonically with the wavelengths acting as a transparent material. The imaginary part ${\varepsilon _2}$, on the other hand, exhibit a weak oscillatory behavior with a small amplitude alternating between positive and negatives values. The positive values indicate absorption losses at the incident wavelength whereas the negative values resemble saturable absorption related to resonance in the oscillating electrons with the impinging electric field.Fig. 4. (a) The calculated transmittance spectra of the films obtained using Hadley equations and a procedure outlined in Refs. [29,30]. (b) Tauc plots used to calculate the energy band gap of the films.
3.3. Thermally-induced nonlinear optical properties
The thermally-induced optical nonlinearity was conducting using a single beam z-scan technique pumped by the laser diodes operating at 405, 532 and 650 nm. The closed and open aperture z-scan traces of the AZO-films pumped at these wavelengths are presented in Fig. 6.
Fig. 5. The permittivity function ε: (a) the real part (ε1) (b) the imaginary part (ε2). The colored arrows indicate the different values of the imaginary part at the laser irradiation wavelength.
Fig. 6. (a) The closed-aperture scan traces at the different pumping wavelengths with 100 mW of beam power. (b) the corresponding open-aperture scan results.
As shown in Fig. 6(a), the closed-aperture z-scan of the fabricated films showed a negative nonlinear trend indicated by a peak, followed by a valley. The difference between the peak and valley ($\Delta {T_{p - v}}$) was maximum at 405 nm and minimum at 650 nm. At 532 nm the peak and valley ($\Delta {T_{p - v}}$) showed relatively intermediate behavior. For the open-aperture scan shown in Fig. 6(b), the nonlinearity strength was somewhat different where the maximum response in this measurement was at 650 nm indicated by the reverse saturable absorber (RSA) trend. At 405 nm the samples showed RSA behavior but with smaller dip in the transmittance spectrum. On the other hand, the samples’ response at 532 nm was that of saturable absorber (SA). In normal z-scan measurements, the normalized peak and valley ($\Delta {T_{p - v}}$), the axial phase shift $\Delta \varphi $, thermally-induced third-order nonlinear refractive index $n_2^{th}$, thermo-optic coefficient ($\partial n/\partial T$), and the nonlinear absorption coefficient $\beta $ are associated as follows:
where λ is the wavelength of the laser, I0 is the intensity of the beam at the focus, r is the aperture radius, ${\omega _a}$ is the beam radius on the aperture, α is the linear absorption coefficient, and L is the sample thickness, $\Delta {T_{op}}$ is the nonlinear transmittance in the z-scan trace of the open-aperture measurement. The calculated values of the third-order nonlinear coefficients ($n_2^{th}$ and $\beta $) using Eqs. (7)–(12) versus the irradiating wavelengths are plotted in Fig. 7. The obtained values at the different wavelengths are consistent with those reported in the cw regime [23,24].Fig. 7. The calculated nonlinear coefficients (${n_2}$ and $\beta $) calculated at the different pumping wavelengths.
4. Discussion
4.1. Correlating the linear permittivity function to the nonlinear optical response
The local permittivity of a transparent medium represented by the complex dielectric function is described by the Drude formula:
4.2. Interpretation of the nonlinear optical results
From the observed dependence of the difference between the peak and valley transmittance ($\Delta {T_{p - v}}$) on the pumping wavelength seen in Fig. 6, it is suggested that the highest observed light energy was in the samples irradiated at 405 nm. The open-aperture trace at this wavelength showed a dip in the transmittance spectrum indicating RSA behavior of the samples under the cw regime. It is instinctively natural to assume that the mechanism involved for this behavior is a two photon absorption (TPA) process. However, since the stimulus for this process was a cw beam, the thermo-optic effects play a major role in the thermal lensing process. This process can result in bleaching of carriers in the ground state only if the absorption cross section of ground state is much larger than the absorption cross section of excited state [25]. According to the results obtained from the open aperture scans at 405 nm it seems that this is not the case, where RSA behavior is being observed. This trend can be explained by incorporating the effects of the imaginary part of the permittivity function (ε2) into the big picture. The ε2 value at this wavelength indicated by the purple arrow in Fig. 5(b) is small but yet having a positive value. The linear absorption process in the material represented by ε2 are in general related to the existence of scattering events. These events could be engendered from different source like defect site, surface scattering, lattice scattering, to name a few. Nevertheless, it is not within the scope of the current research to investigate the scattering mechanisms in AZO films where the focus will be in correlating the effects of these events in the optical nonlinear response in AZO films. The positive existence of these scattering events strongly broadens the absorption cross section of the excited states. The broadening in turn allows for the TPA to ensue and become the dominant mechanism in the nonlinear absorption process. This broadening also affects the nonlinear index of refraction through the increase in the linear absorption coefficient (α) which subsequently increase the ($\Delta {T_{p - v}}$) magnitude. When the samples are irradiated with the 532 nm cw laser, the results of the open-aperture scan exhibited a saturable absorber behavior. Following the same analysis logic, it is noticed that the ε2 value indicated by the green arrow in Fig. 5(b) is much smaller than the one at 405 nm. This mean that the scattering events are reduced at this wavelength, mainly due to lower energies delivered by the photons to the participating electrons. Therefore, the bleaching of the ground state is expected and the chances for the TPA occurrences are inhabited promoting the SA behavior as observed in the open aperture z-scan measurement at this wavelength. In the 650 nm irradiating regime, caution should be made in following the same approach in interpreting the z-scan results. This is so because the ε2 value at this wavelength indicated by the red arrow in Fig. 5(b) is negative. This means that saturable absorption is already taking place within the linear regime in the films as a result ground state bleaching to immediate excited or intermediate states. When strong laser intensity is applied to promote the nonlinear regime, the TPA and free carrier generation are easily obtained as excited carries jump into higher empty states. It is noticed that the closed-aperture scan at this wavelength produces very small response indicating much lower electron scattering at this wavelength.
Based on the above scenario relating the material’s linear permittivity to the observed thermal nonlinearities in the films, it is concluded that this permittivity plays an important role in the nonlinear optical properties of AZO films. Therefore, it is importance to determine the linear permittivity functions for the transparent conducting oxides in order to stand on a total description of its nonlinear behavior in the continuous wave operations.
5. Conclusion
The results and qualitative descriptions of the linear permittivity influence on thermally-induced nonlinear optical properties of aluminum-doped zinc oxide thin films was presented. The imaginary part of the permittivity represents scattering events that strongly affect the nonlinear optical behavior of the films. Depending on the thermo-optic effects, the ground state in the films will be bleached enhancing the saturable absorber behavior. However, if the absorption permittivity is positive, the reverse saturable absorber behavior will manifest itself with the strong two photon absorption assisted by the intermediate states at the grain boundaries. This study shows the importance of determining the linear permittivity functions for the transparent conducting oxides in order to stand on the total description of its nonlinear behavior in the continuous wave operations.
Funding
German-Jordanian University (SBSH 2016/32).
Acknowledgments
I would like to thank Dr. H. Naseem from the electrical engineering department at the University of Arkansas, Dr. Husam El-Nasser form Al al-Bayt University and Ms. Raza R. Al-Esseili from the German Jordan University for providing assistance in preparation and characterization of the samples.
Disclosures
The author declares no conflicts of interest.
References
1. X. Zhou, D. Han, J. Dong, H. Li, Z. Yi, X. Zhang, and Y. Wang, “The effects of post annealing process on the electrical performance and stability of Al-Zn-O thin-film transistors,” IEEE Electron Device Lett. 41(4), 569–572 (2020). [CrossRef]
2. X. Chen, J. Wan, H. Wu, and C. Liu, “ZnO bilayer thin film transistors using H2O and O3 as oxidants by atomic layer deposition,” Acta Mater. 185, 204–210 (2020). [CrossRef]
3. W. Hu, N. D. Quang, S. Majumder, E. Park, D. Kim, H.-S. Choi, and H. S. Chang, “Efficient photo charge transfer of Al-doped ZnO inverse opal shells in SnS2 photoanodes prepared by atomic layer deposition,” J. Alloys Compd. 819, 153349 (2020). [CrossRef]
4. T. Subramanyam, “Studies on DC magnetron sputtered AZO thin films for HIT solar cell application,” (2020).
5. X. Jiang, G. Liu, L. Tang, A. Wang, Y. Tian, A. Wang, and Z. Du, “Quantum dot light-emitting diodes with an Al-doped ZnO anode,” Nanotechnology 31(25), 255203 (2020). [CrossRef]
6. K. Gherab, Y. Al-Douri, U. Hashim, M. Ameri, A. Bouhemadou, K. M. Batoo, S. F. Adil, M. Khan, and E. H. Raslan, “Fabrication and characterizations of Al nanoparticles doped ZnO nanostructures-based integrated electrochemical biosensor,” J. Mater. Res. Technol. 9(1), 857–867 (2020). [CrossRef]
7. V. Samoei and A. H. Jayatissa, “Aluminum doped zinc oxide (AZO)-based pressure sensor,” Sens. Actuators, A 303, 111816 (2020). [CrossRef]
8. L. Castañeda, O. Morales-Saavedra, D. Acosta, A. Maldonado, and M. de la L. Olvera, “Structural, morphological, optical, and nonlinear optical properties of fluorine-doped zinc oxide thin films deposited on glass substrates by the chemical spray technique,” Phys. Status Solidi A 203(8), 1971–1981 (2006). [CrossRef]
9. O. Morales-Saavedra, L. Castaneda, J. Banuelos, and R. Ortega-Martinez, “Morphological, optical, and nonlinear optical properties of fluorine-indium-doped zinc oxide thin films,” Laser Phys. 18(3), 283–291 (2008). [CrossRef]
10. S. Abed, K. Bouchouit, M. Aida, S. Taboukhat, Z. Sofiani, B. Kulyk, and V. Figa, “Nonlinear optical properties of zinc oxide doped bismuth thin films using Z-scan technique,” Opt. Mater. 56, 40–44 (2016). [CrossRef]
11. M. A. Lamrani, M. Addou, Z. Sofiani, B. Sahraoui, J. Ebothé, A. El Hichou, N. Fellahi, J. Bernede, and R. Dounia, “Cathodoluminescent and nonlinear optical properties of undoped and erbium doped nanostructured ZnO films deposited by spray pyrolysis,” Opt. Commun. 277(1), 196–201 (2007). [CrossRef]
12. K. Nagaraja, S. Pramodini, A. S. Kumar, H. Nagaraja, P. Poornesh, and D. Kekuda, “Third-order nonlinear optical properties of Mn doped ZnO thin films under cw laser illumination,” Opt. Mater. 35(3), 431–439 (2013). [CrossRef]
13. X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-near-zero photonics: a new platform for integrated devices,” Adv. Opt. Mater. 6(10), 1701292 (2018). [CrossRef]
14. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017). [CrossRef]
15. L. Caspani, R. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, and V. M. Shalaev, “Enhanced nonlinear refractive index in ε-near-zero materials,” Phys. Rev. Lett. 116(23), 233901 (2016). [CrossRef]
16. N. Kinsey, C. DeVault, J. Kim, M. Ferrera, V. Shalaev, and A. Boltasseva, “Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths,” Optica 2(7), 616–622 (2015). [CrossRef]
17. M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. Shalaev, and A. Boltasseva, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8(1), 1–7 (2017). [CrossRef]
18. J. B. Khurgin, G. Sun, W. T. Chen, W.-Y. Tsai, and D. P. Tsai, “Ultrafast thermal nonlinearity,” Sci. Rep. 5(1), 17899 (2016). [CrossRef]
19. A. Ghasedi, E. Koushki, and J. Baedi, “Optical nonlinearity, saturation in absorption andoptical bistabilityof AZO films synthesized in presence of sodium hydroxide,” Phys. B 587, 412148 (2020). [CrossRef]
20. Z. M. Htwe, Y.-D. Zhang, C.-B. Yao, H. Li, and P. Yuan, “Ultrafast carrier dynamics and third order nonlinear optical properties of aluminum doped zinc oxide (AZO) thin films,” Opt. Mater. 66, 580–588 (2017). [CrossRef]
21. A. Jilani, M. S. Abdel-wahab, A. A. Al-ghamdi, A. sadik Dahlan, and I. Yahia, “Nonlinear optical parameters of nanocrystalline AZO thin film measured at different substrate temperatures,” Phys. B 481, 97–103 (2016). [CrossRef]
22. D. J. Edison, W. Nirmala, K. D. A. Kumar, S. Valanarasu, V. Ganesh, M. Shkir, and S. AlFaify, “Structural, optical and nonlinear optical studies of AZO thin film prepared by SILAR method for electro-optic applications,” Phys. B 523, 31–38 (2017). [CrossRef]
23. G. P. Bharti and A. Khare, “Structural and linear and nonlinear optical properties of Zn 1-x Al x O (0≤ x≤ 0.10) thin films fabricated via pulsed laser deposition technique,” Opt. Mater. Express 6(6), 2063–2080 (2016). [CrossRef]
24. A. Antony, S. Pramodini, P. Poornesh, I. Kityk, A. Fedorchuk, and G. Sanjeev, “Influence of electron beam irradiation on nonlinear optical properties of Al doped ZnO thin films for optoelectronic device applications in the cw laser regime,” Opt. Mater. 62, 64–71 (2016). [CrossRef]
25. K. Sandeep, S. Bhat, and S. Dharmaprakash, “Nonlinear absorption properties of ZnO and Al doped ZnO thin films under continuous and pulsed modes of operations,” Opt. Laser Technol. 102, 147–152 (2018). [CrossRef]
26. L. Irimpan, V. Nampoori, and P. Radhakrishnan, “Spectral and nonlinear optical characteristics of nanocomposites of ZnO–CdS,” J. Appl. Phys. 103(9), 094914 (2008). [CrossRef]
27. L. Irimpan, V. Nampoori, and P. Radhakrishnan, “Spectral and nonlinear optical characteristics of ZnO nanocomposites,” Sci. Adv. Mater. 2(2), 117–137 (2010). [CrossRef]
28. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User's Guide (Wiley, 1999).
29. D. E. Gray, “American Institute of Physics handbook,” (1972).
30. J. Gong, R. Dai, Z. Wang, and Z. Zhang, “Thickness dispersion of surface plasmon of Ag nano-thin films: Determination by ellipsometry iterated with transmittance method,” Sci. Rep. 5(1), 1–5 (2015). [CrossRef]
31. J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi B 15(2), 627–637 (1966). [CrossRef]
32. R. W. Boyd, Nonlinear Optics (Academic Press, 2019).
33. H. Abu-Safe, R. Al-Esseili, M. Sarollahi, M. Refaei, H. Naseem, M. Zamani-Alavijeh, T. AlAbdulaal, and M. Ware, “Thermally-induced nonlinear optical properties of silver nano-films near surface plasmon resonance,” Opt. Mater. 105, 109858 (2020). [CrossRef]
34. N. Kinsey and J. Khurgin, “Nonlinear epsilon-near-zero materials explained: opinion,” Opt. Mater. Express 9(7), 2793–2796 (2019). [CrossRef]
35. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “Z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86(11), 6200–6205 (1999). [CrossRef]
