Open Access
Add to BibSonomy
Abstract
HfO2 films are widely used for optical coatings due to the high refractive index and low absorption, especially in the ultraviolet (UV) band. In this work, HfO2 film samples were prepared with the optimized assistant source power and deposition temperature by dual-ion beam sputtering (DIBS), followed by annealing treatments in vacuum and atmosphere, respectively. For samples with different annealing temperatures from 200 to 450 °C, the microstructure, morphology, film stress and optical properties from 200 to 1000 nm were systematically investigated. A monoclinic phase, a refractive index inhomogeneity along the film thickness and an absorption of shoulder-shape in the 250-300 nm band were found in the as-deposited samples. For samples annealed in vacuum, 400 °C annealing leaded to more oxygen defects, which in turn caused aggravated UV absorption. For samples annealed in atmosphere, the shoulder-shaped absorption weakened obviously above 300 °C annealing, which was suspected due to the reduction of oxygen defects during the crystallization process with sufficient oxygen. Scattering loss was investigated and found negligible for as-deposited and annealed samples. Additionally, film stress varied from compressive state to tensile state with increasing annealing temperature, and the zero-stress temperature is between 300-350 °C, which is due to the obvious crystallization behavior. Production methods and physical mechanisms for low absorption and scattering loss DIBS deposited HfO2 films were proposed and discussed in detail.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Hafnium oxide (HfO2) has achieved significant attentions in the fields of optics, optoelectronics and semiconductors, due to its excellent physical performance, such as high dielectric constant, high refractive index, wide bandgap, wide transparent region and high laser damage threshold. The wide bandgap (5.6-6.2 eV) leads to a large optically transparent range from ultraviolet (UV) to infrared (IR) (0.22-12 µm) [1,2]. The relatively high refractive index (∼2.0) and high transparency make it one of the most promising optical materials [3,4]. Besides, HfO2 has been applied in optical film for high-energy laser due to its high melting point (2758 °C) and thermal stability [5–7]. Moreover, the high dielectric constant (∼25) allows it to be a potential alternative to SiO2 as the gate dielectric material in complementary metal oxide semiconductor (CMOS) technology [8,9].
There are four different crystalline phases for HfO2, including monoclinic, tetragonal, cubic and orthorhombic. Monoclinic HfO2 with the space group P21/c, which has the lowest free energy of formation and the largest volume, is the most thermodynamically stable phase at ambient conditions of temperature and pressure [10]. The monoclinic phase of HfO2 transforms to the tetragonal phase (P42/n) at about 1800K and further to the cubic phase (Fm3m) above 2700 K. It transforms to the orthorhombic-I structure (Pbca) at the pressure ∼4.3 GPa and to the orthorhombic-II structure (Pnma) at the pressure 14.5 GPa [11].
To get lower scattering, absorption and film stress, and higher packing density and refractive index, various physical and chemical deposition methods have been used to fabricate HfO2 thin films, including electron beam evaporation [12,13], atomic layer deposition [4,8,14], pulsed laser deposition [15], magnetron sputtering [16,17], ion beam sputtering [18–21], etc. It has been proved that process parameters have direct and significant influence on the chemical stoichiometry, structure characteristics and optical properties of HfO2 films. Besides, elements doping and thermal annealing were also applied to modulate the properties of HfO2 thin films [3,14,22–24].
Dual-ion beam sputtering (DIBS) is an efficient method for fabricating highly dense thin films with highly consistent quality from batch to batch, which is due to the configuration of dual ion source with high energy. Recently, attentions have been focused on the effect of DIBS process parameters and post-annealing effect on the properties of HfO2 thin films [18–21,25,26]. However, optical properties of DIBS deposited HfO2 films around its bandgap (230-300 nm) still remain unstable and difficult to regulate effectively, which is especially important for HfO2-based UV optical films.
In this work, we optimized the assist ion source power and deposition temperature of DIBS process parameters to obtain HfO2 film with low UV absorption and scattering. The film samples were further annealed at different temperatures in both vacuum and atmosphere environment. The influences of annealing temperature on the structure, film stress and optical properties from 200 nm to 1000 nm of DIBS deposited HfO2 films were systematically studied.
2. Experimental details
2.1 Preparation and heat treatment methods
The HfO2 films were deposited on both Si (001) and fused silica substrates with deposition rate about 0.16 nm/s by a DIBS system (Spector, Veeco, USA). The DIBS system contains two ion sources: the main radio-frequency source with 16 cm diameter grid (RF16) and the assist radio-frequency source with 12 cm diameter grid (RF12). High purity (99.95%) metal Hf target was used for film deposition. Before deposition, vacuum chamber pressure was pumped below 1 × 10−5 Torr (1.33 × 10−3 Pa) and Hf target was pre-sputtered for 10 min to remove contaminants and the natural oxide from the target surface and eliminate sputtering inconsistency over time [26]. The voltage and current of the RF16 ion source were 1250 V and 600 mA, respectively. The oxygen gas flow was 15 sccm. The deposition time for these samples was 15 min. Detailed deposition parameters for different samples were listed in Table 1.
Table 1. Different assistant source and deposition temperature parameters
Furthermore, optimized deposition parameters with assistant source voltage 100 V, current 20 mA and deposition temperature 140 °C were adopted to prepare samples for annealing treatment. The deposition time for these samples was 20 min to make the transmission spectra show more interference fluctuations as well as more evident absorption performance. In the heat treatment process, atmosphere annealing furnace (CMF1100, Kejing, China) and vacuum annealing furnace (VTHK550, Technol, China) were used for annealing. Six samples A2-A7 were annealed in atmosphere for 12 h at different temperatures of from 200 °C to 450 °C per 50 °C, respectively. Besides, three samples A8-A10 were annealed in vacuum for 12 h at the temperatures of 200 °C, 300 °C and 400 °C, respectively. The heating rate was 4 °C/min and natural cooling to room temperature was used. Table 2 gives the detailed annealed parameters.
Table 2. Different annealing conditions for HfO2 samples
2.2 Characterization methods
Grazing incidence X-ray diffraction (GIXRD, D8 Discover, Bruker, Germany) was used to obtain the compositional structure and crystalline state of the films with the diffraction angle range of 20-60° and Cu Kα radiation (λ = 0.154178 nm). Secondary electron signal of scanning electron microscope (SEM, SU8220, Hitachi, Japan) was used to characterize film thickness and cross-section morphology. Atomic force microscope (AFM, Prima, NT-MDT, Russia) images were examined to analyze surface RMS roughness and morphology with an area of 5 µm × 5 µm. Stress characteristics were determined by an interferometer (Zegage, Zygo, USA). To obtain the optical properties of HfO2 films, transmission and reflection spectra in the wavelength range of 200-1000 nm were measured by a spectrophotometer (Cary5000, Agilent, USA). The integral transmission and reflection spectra in the wavelength range of 240-1000 nm were measured by an integrating sphere accessory. Spectroscopic ellipsometry (SE) measurements were performed on the Si-based samples by a variable angle spectroscopic ellipsometer (V-VASE, J.A. Woollam, USA) in the wavelength range 240-1000 nm with three different incidence angles of 60°, 65° and 70° and a fixed angle ellipsometer (M2000XF, J.A. Woollam, USA) in the wavelength range 200-240 nm with the incidence angle of 65°.
3. Results and discussion
3.1 Optimization of sputtering process
Assistant source power and deposition temperature have evident influence on the performance of thin films by ion beam sputtering [20,25]. In this section, both parameters were optimized for high refractive index and low absorption. Figure 1(a) shows the transmittance spectra of HfO2 films S1-S4 with assistant source voltage 0-300 V. As a whole, with increasing voltage, the interference peaks increase and while the amplitude of fluctuation decrease, which indicate that both the light loss and the refractive index decrease. It also shows that samples S1 and S2 have similar refractive index. However, the peak transmittance of S1 is lower in UV region, which indicates a higher optical loss. Figure 1(b) shows the transmittance spectra of HfO2 films S5, S6 and S2 with deposition temperature 50 °C, 90 °C and 140 °C. By comparing the spectra, the sample S2 has the highest refractive index and lowest optical loss, which means high substrate temperature is preferred. However, higher temperatures are not recommended due to equipment temperature limitations. As a result, assistant source (100 V voltage, 20 mA current) and deposition temperature (140 °C) were adopted to fabricate HfO2 samples in subsequent experiments.
Fig. 1. Transmission spectra of samples S1-S6 with (a) different assistant source power and (b) different substrate temperature.
3.2 Effects of annealing environment
To improve the UV optical properties, HfO2 samples were annealed subsequently at different temperatures, and effects of annealing environment of vacuum and atmosphere were compared. Figure 2 shows the transmission spectra for HfO2 samples A1-A10 at different annealing temperature in vacuum and atmosphere. After annealing in vacuum, the peak transmittance of HfO2 samples in the UV region increase slightly with 200 °C and 300 °C annealing, but drop obviously from 73.7% to 45.1% at the wavelength 230 nm with 400 °C annealing, which could be attributed to that the HfO2 film may be deoxidized during crystallization in 400 °C vacuum annealing environment [22]. As a comparison, the UV transmittance of the HfO2 samples annealed in atmosphere with sufficient oxygen were improved obviously, especially with temperature above 400 °C. It seems that there was oxygen insufficiency in the as-deposited samples and annealing in atmosphere could help reducing the oxygen defects. The peak transmittance at 230 nm for atmosphere annealed samples of 200 °C, 300 °C and 400 °C are 74.4%, 79.1%, 83.2%, respectively. Besides, the transmittance peak of the HfO2 samples exceed the baseline of substrate a little at about 760 nm, which signifies a little inhomogeneity of the HfO2 samples [27]. Annealing is an effective way to improve the optical properties of HfO2 films, while both the temperature and oxygen atmosphere both play a key role.
Fig. 2. The transmission spectra for HfO2 samples annealed at different temperatures in (a) vacuum and (b) atmosphere.
3.3 Characterization of atmosphere annealed samples
3.3.1 Structure analysis
GIXRD pattern peaks of HfO2 films A1-A7 on silicon substrates are presented in Fig. 3(a). By comparing with standard card PDF#43-1017, it can be found that all HfO2 samples are monoclinic [17]. Diffraction peak (-111) is the strongest for all samples. As the (-111) planes are the closet-packed set, having the lowest energy in a monoclinic baddelyite-type crystal [27], leading to this direction being the thermodynamically preferred orientation. Other diffraction peaks corresponding to (111), (002), (200), (211), (220), (202) and (013) planes were also detected with comparatively lower intensity. With annealing temperature increasing, the diffraction peak (-111) becomes stronger and sharper. The relative intensity of (-111) peak for the as-deposited sample is relatively small, which indicates that the as-deposited sample is mainly amorphous. An obvious change of the relative intensity of (-111) peak could be found on the 200 °C and 400 °Cannealed samples, demonstrating that the crystallinity improves significantly at these temperatures. With the increasing annealing temperature, the diffraction peak position (-111) moves to a big angle and the deviation from the standard value becomes smaller, which indicates a film stress change from compressive stress to tensile stress. The crystallite size D was calculated according to Debye–Scherrer formula [28], as Eq. (1):
where λ, θ and β are the X-ray wavelength, Bragg diffraction angle and line width at half maximum of the most dominant peak, respectively. As seen in Fig. 3(b), the grain size increases from 8.5 to 10.0 nm with the increasing annealing temperature. Small crystallite size is beneficial for UV multilayer coating to minimize light scattering [3].Fig. 3. (a) GIXRD pattern peaks of HfO2 films A1-A7 on silicon substrates and (b) calculated grain size of A1-A7.
The relative intensity of (-111) peak was obviously improved after 200 °C annealing, which could be explained by that the amorphous phase transferred to crystal phase at this temperature [29]. The grain size increases with increasing annealing temperature, especially above 300 °C, since higher temperature provides higher kinetic energy for the atoms to overcome the grain boundary energy, resulting in a migration of the grain boundary and the formation of bigger grains. For samples annealed above 400 °C, obviously enhancement of crystallinity was observed, which may be ascribed by the improvement of grain migration capacity at temperature above 400 °C. When grain migration is enhanced, more grains can be accommodated within the film layer, and more oxygen atoms will be able to enter the interior of the film, eliminating oxygen defects of films and thus reducing optical absorption. As can be seen in Fig. 2(b), the peak transmittance at 230 nm for atmosphere annealed samples reaches highest above 400 °C. However, grain migration might lead to deterioration of the surface roughness of the films, which would be verified in the following surface morphology characterization.
3.3.2 Morphology analysis
In order to further analyze the process of crystalline state change due to annealing, SEM measurements on the samples were performed. Figure 4(a-g) show the cross-section SEM morphology of HfO2 samples A1-A7. The film thickness slight increases with the annealing temperature, especially above 300 °C, as shown in Fig. 4(h). A clear expansion of the crystalline boundary from the surface of the film to the substrate can be seen on the SEM images of the samples of 350-450 °C, which is in good agreement with the tendency of the grain size results of GIXRD patterns. Since grain boundary diffusion is accompanied by intense atomic migration and repair of oxygen defects by ambient oxygen, this leads to an increase in the overall film mass and thickness, and may also lead to bigger surface roughness.
Fig. 4. (a–g) The cross-section SEM morphology of HfO2 films A1-A7 on silicon substrates and (h) film thickness of A1-A7 from SEM.
The surface morphology by AFM is presented in Fig. 5. AFM images indicate that RMS roughness is about 2.10 nm below 250 °C and increases gradually to 2.56 nm with temperature raising to 400 °C. The increase in roughness could be due to the agglomeration of smaller grains to form bigger grains [24], or the variation of defect density and film stress [30]. As analyzed by GIXRD patterns and SEM images, the trend of surface roughness with annealing temperature is consistent with the change of crystallization state.
Fig. 5. (a-g) Surface morphology of HfO2 films A1-A7 on silicon substrates and (h) RMS value of A1-A7 from AFM.
3.3.3 Optical properties analysis
Generally, optical constants can be obtained by SE [31,32]. In order to accurately measure the optical constants of HfO2, variable-angle spectroscopic ellipsometry was employed. Ellipsometric parameters ψ and Δ of Si-based samples were acquired for model fitting in the range of 207-1000 nm at three angles of incidence 60°, 65° and 75°.
SE data were analyzed using a five-phase model of Si substrate / SiO2 thin layer / HfO2 film / surface roughness layer / air ambient, as presented in Fig. 6(a). Unknown parameters, including HfO2 film thickness (dSE), roughness layer thickness (dR) and dielectric functions (ε) of HfO2 films were defined as fitting variables. The roughness layer was characterized using a Bruggeman effective medium approximation (EMA) model containing 50% HfO2 and 50% voids [33].
Fig. 6. (a)Adopted five-phase model as the film structure for SE analysis, (b) adopted simple EMA graded layer model for SE analysis.
Tauc-Lorentz (T-L) dispersion model, which has been widely employed for dielectric film materials, was used to describe the dispersion relation of HfO2 films [16,34–36]. The imaginary part (ε2) and real part (ε1) of dielectric function in Tauc-Lorentz model are described as following Eq. (2) and Eq. (3) [37]:
The measured SE results were fitted by minimizing the root mean squared error (RMSE) value from the measured and calculated values of ψ and Δ, and RMSE is defined as Eq. (4) [37]:
Considering the film inhomogeneity as seen in SEM micrographs, a simple EMA graded layer model was used to describe the inhomogeneity of optical constants along the thickness direction. As shown in Fig. 6(b), 5 sublayers model was adopted and optimized for the HfO2 film. Single T-L oscillator was firstly used during the fitting procedure. However, there was big deviation between the fitted and measured values in the range of 250-290 nm. The inconsistency was greatly reduced after using two oscillators, and finally two oscillators T-L model was chosen in the SE fitting. Figure 7 shows the experimental and fitted SE data for (a) as-deposited and (b) 400 °C annealed HfO2 samples.
Fig. 7. Experimental and fitted SE data for (a) as-deposited and (b) 400 °C atmosphere annealed HfO2 samples.
The refractive index n and extinction coefficient k of the HfO2 films A1-A7 from 207 nm to 1000 nm fitted by SE results were given in Fig. 8. The refractive index n increases slightly with annealing temperature increasing to 250 °C, and decreases slightly with temperature raising above 300 °C. Combined with the XRD and SEM data, the increase of the refractive index for annealed films below 250 °C is probably due to the crystallization of the amorphous matrix in the film [15]. The decrease the refractive index for annealed films above 300 °C is due to the obvious growth of grains and decrease of film density. By contrast, the extinction coefficient k shows two distinct features. Feature I: there is an absorption of shoulder-shape from 240 to 300 nm for as-deposited and annealed samples till 250 °C, which is considered caused by oxygen defects [38,39]. Below 250 °C, there is not enough kinetic energy for atoms to overcome the grain boundary energy and oxygen defects in HfO2 films exist obviously. Feature II: extinction coefficient k below 240 nm keeps almost unchanged till 250 °C annealing and decreases with annealed temperature increasing from 300 °C, which could be explained by improvement of crystallinity and was intrinsic to monoclinic HfO2 [40].
Fig. 8. Refractive index n (a) and extinction coefficient k (b) of the HfO2 samples A1-A7 from 207 to 1000 nm fitted by SE results, refractive index n (c) and extinction coefficient k (d) of A1-A7 at 250 nm.
Figure 9(a) gives the comparison results of transmittance (T) and reflectance (R) between integral ball photometer (IB) and normal spectrophotometer for as-deposited and 400 °C annealed HfO2 samples, to determine the cause of optical loss. It can be seen that the transmittance and reflectance spectra for both measurement methods are similar, indicating that scattering loss is negligible. Considering no scattering loss for the HfO2 samples, the absorption (A) is deduced by Eq. (5):
Fig. 9. Measured transmittance and reflectance spectra by IB photometer and normal spectrophotometer for as-deposited and 400 °C annealed samples (a), calculated absorption results for HfO2 samples A1-A7 (b)
The calculated absorption results for the HfO2 films A1-A7 from 200 nm to 1000 nm are given in Fig. 9(b). There is an obvious absorption of shoulder-shape for the as-deposited sample in 250-300 nm wavelength range. This absorption weakens after annealing, especially above 300 °C. Besides, the absorption below 240 nm decreases with the increasing annealed temperature. The tendency is in well consistent with the extinction coefficient k feathers from SE measurement.
Due to SE fitting is not sensitive for low absorption but sensitive for adequate refractive index, the refractive index n and extinction coefficient k were also evaluated by fitting transmission, as shown in Fig. 10. The refractive index n fitted by transmission decreases slightly with annealing temperature increasing and the extinction coefficient k has distinct absorption from 250 to 300 nm, which are consistent with the trend by SE fitting. Figure 10(c) shows that the extinction coefficient k fitted by transmission is in the same order of magnitude compared SE fitting results.
Fig. 10. Refractive index n (a) and extinction coefficient k (b) of the HfO2 samples A1-A7 from 207 to 1000 nm fitted by transmission results, extinction coefficient k (c) of A1-A7 at 250 nm, and (d) comparison of film thickness from SEM and transmission and SE fitting for A1-A7 samples.
Comparison of film thickness from SEM and transmission and SE fitting is given in Fig. 10(d). As can be seen, film thickness from transmission and SE fitting increase slightly with the annealing temperature, especially above 300°C. The tendencies are in agreement with the result from SEM observation. However, there are some differences for the thickness values. There are mainly three reasons. Firstly, there exists inhomogeneity for the refractive index, which will influence the precise evaluation of physical thickness. Secondly, SE and SEM measurements were based on Si substrate while transmittance measurements were based on fused silica. We adopted a five-phase model of Si substrate / SiO2 thin layer / HfO2 film / surface roughness layer / air ambient. The existence of SiO2 thin layer and surface roughness layer will increase the observed physical thickness of SEM results. Thirdly, different substrates would also make some difference after annealing.
3.3.4 Film stress analysis
According to the surface deformation results of samples, the film stress properties of the HfO2 samples were calculated by Stoney formula [41]. Figure 11 shows the relationship between film stress and annealing temperature. The film stress of as-deposited sample is compressive. With further increasing the temperature, film stress varies from compressive state to tensile state. Film stress changes obviously between 250°C and 400 °C, which could be ascribed to the migration of grain boundary and the crystallization and structure results discussed above. There exists a zero-stress point between 300 °C and 350 °C. Similar variation tendency was revealed in other works [18,42]. The zero-stress state of annealed HfO2 film would be very useful in the production of low deformation thin film component.
4. Conclusion
Aiming to fabricate low UV absorption and scattering loss HfO2 films by DIBS, the assistant source power (100 V, 20 mA) and substrate temperature (140 °C) were optimized. The as-deposited HfO2 samples were annealed at different temperatures in vacuum and atmosphere environment, respectively, where atmosphere environment was found to be more efficient. The as-deposited HfO2 film was mixed of less monoclinic and more amorphous phase, with calculated grain size of 8.5 nm and 2.08 nm surface RMS. The SE and spectra measurements both revealed that as-deposited sample had an absorption shoulder at 250-300 nm, which is ascribed to the oxygen vacancy defect. With the annealing temperature increasing to 250 °C, the crystallization was improved obviously. With the annealing temperature increasing above 300 °C, due to migration of the grain boundary, more obvious growth of grain size and change of film stress were observed. The shoulder-shaped absorption at 250-300 nm weakens obviously above 300 °C, which was suspected to be related with the reduction of oxygen defects. Scattering loss is negligible for as-deposited and annealed samples. The film stress varied from compressive state to tensile state and changes obviously between 250°C and 400 °C, which could be ascribed to the migration of grain boundary and the obvious crystallization behaviour. A zero-stress point is found between 300-350 °C annealing. This work should be useful for making HfO2-based low optical absorption and low stress thin films, especially in the UV band. Further work will focus on the elimination of oxygen defects in the deposition process, based on the annealing mechanism for eliminating oxygen defects.
Funding
National Key Research and Development Program of China (2021YFB2012601); National Natural Science Foundation of China (62275256, U2230108); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2019241).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
References
1. O. Razskazovskaya, M. T. Hassan, T. T. Luu, et al., “Efficient broadband highly dispersive HfO2/SiO2 multilayer mirror for pulse compression in near ultraviolet,” Opt. Express 24(12), 13628–13633 (2016). [CrossRef]
2. Y. J. Wang, Z. L. Lin, X. L. Cheng, et al., “Study of HfO2 thin films prepared by electron beam evaporation,” Appl. Surf. Sci. 228(1-4), 93–99 (2004). [CrossRef]
3. G. Abromavicius, S. Kicas, and R. Buzelis, “High temperature annealing effects on spectral, microstructural and laser damage resistance properties of sputtered HfO2 and HfO2-SiO2 mixture-based UV mirrors,” Opt. Mater. 95, 109245 (2019). [CrossRef]
4. L. Aarik, T. Arroval, H. Mandar, et al., “Influence of oxygen precursors on atomic layer deposition of HfO2 and hafnium-titanium oxide films: Comparison of O3- and H2O-based processes,” Appl. Surf. Sci. 530, 147229 (2020). [CrossRef]
5. H. F. Jiao, T. Ding, and Q. Zhang, “Comparative study of Laser induce damage of HfO2/SiO2 and TiO2/SiO2 mirrors at 1064 nm,” Opt. Express 19(5), 4059–4066 (2011). [CrossRef]
6. K. R. P. Kafka, B. N. Hoffman, A. A. Kozlov, et al., “Dynamics of electronic excitations involved in laser-induced damage in HfO2 and SiO2 films,” Opt. Lett. 46(7), 1684–1687 (2021). [CrossRef]
7. H. Wang, H. J. Qi, B. Wang, et al., “Defect analysis of UV high-reflective coatings used in the high power laser system,” Opt. Express 23(4), 5213–5220 (2015). [CrossRef]
8. R. Kumar, V. Chauhan, N. Koratkar, et al., “Influence of high energy ion irradiation on structural, morphological and optical properties of high-k dielectric hafnium oxide (HfO2) thin films grown by atomic layer deposition,” J. Alloys Compd. 831, 154698 (2020). [CrossRef]
9. V. Dave, P. Dubey, H. O. Gupta, et al., “Effect of sputtering gas on structural, optical and hydrophobic properties of DC-sputtered hafnium oxide thin films,” Mater. Today Commun. 232, 425–431 (2013). [CrossRef]
10. J. B. Wu, “Impact of oxygen vacancies on monoclinic hafnium oxide and band alignment with semiconductors,” Mater. Today Commun. 25, 101482 (2020). [CrossRef]
11. P. Ondracka, D. Holec, D. Necas, et al., “Accurate prediction of band gaps and optical properties of HfO2,” J. Phys. D: Appl. Phys. 49(39), 395301 (2016). [CrossRef]
12. M. Ramzan, M. F. Wsiq, A. M. Rana, et al., “Characterization of e-beam evaporated hafnium oxide thin films on post thermal annealing,” Appl. Surf. Sci. 283, 617–622 (2013). [CrossRef]
13. J. N. Dong, J. Fan, S. D. Mao, et al., “Effect of annealing on the damage threshold and optical properties of HfO2/Ta2O5/SiO2 high-reflection film,” Chin. Opt. Lett. 17(11), 113101 (2019). [CrossRef]
14. M. Lapteva, V. Beladiya, S. Riese, et al., “Influence of temperature and plasma parameters on the properties of PEALD HfO2,” Opt. Mater. Express 11(7), 1918–1942 (2021). [CrossRef]
15. Z. F. Ying, W. T. Tang, Z. G. Hu, et al., “Annealing behaviors of structural, interfacial and optical properties of HfO2 thin films prepared by plasma assisted ractive pulsed laser deposition,” J. Mater. Res. 25(4), 680–686 (2010). [CrossRef]
16. S. M. Haque, K. D. Rao, J. S. Misal, et al., “Study of hafnium oxide thin films deposited by RF magnetron sputtering under glancing angle deposition at varying target to substrate distance,” Appl. Surf. Sci. 353, 459–468 (2015). [CrossRef]
17. T. T. Tan, Z. T. Liu, H. C. Lu, et al., “Chemical structure and electrical properties of sputtered HfO2 films on Si substrates annealed by rapid thermal annealing,” Vacuum 83(9), 1155–1158 (2009). [CrossRef]
18. H. S. Liu, Y. G. Jiang, L. S. Wang, et al., “Effect of heat treatment on properties of HfO2 film deposited by ion-beam sputtering,” Opt. Mater. 73, 95–101 (2017). [CrossRef]
19. I. Stevanovic, Z. B. Michels, and A. Bachli, “Influence of the Secondary Ion Beam Source on the Laser Damage Mechanism and Stress Evolution of IBS Hafnia Layers,” Appl. Sci. 11(1), 189 (2020). [CrossRef]
20. S. Papernov, M. D. Brunsman, J. B. Oliver, et al., “Optical properties of oxygen vacancies in HfO2 thin films studied by absorption and luminescence spectroscopy,” Opt. Express 26(13), 17608–17623 (2018). [CrossRef]
21. D. P. Zhang, P. Fan, C. J. Wang, et al., “Properties of HfO2 thin films prepared by dual-ion-beam reactive sputtering,” Opt. Laser Technol. 41(6), 820–822 (2009). [CrossRef]
22. M. F. Al-Kuhaili, S. M. A. Durrani, I. A. Bakhtiari, et al., “Influence of hydrogen annealing on the properties of hafnium oxide thin films,” Mater. Chem. Phys. 126(3), 515–523 (2011). [CrossRef]
23. S. B. Khan, Z. J. Zhang, and S. L. Lee, “Annealing influence on optical performance of HfO2 thin films,” J. Alloys Compd. 816, 152552 (2020). [CrossRef]
24. A. Vinod, M. S. Rathore, and N. S. Rao, “Effects of annealing on quality and stoichiometry of HfO2 thin films grown by RF magnetron sputtering,” Vacuum 155, 339–344 (2018). [CrossRef]
25. H. S. Liu, Y. G. Jiang, L. H. Song, et al., “Correlation between properties of HfO2 films and preparing parameters by ion beam sputtering deposition,” Appl. Opt. 53(4), A405–411 (2014). [CrossRef]
26. S. B. Fang, C. Ma, W. M. Liu, et al., “Effect of oxygen flow on the optical properties of hafnium oxide thin films by dual-ion beam sputtering deposition,” Appl. Phys. A 128(12), 1097 (2022). [CrossRef]
27. P. Rauwel, E. Rauwel, C. Persson, et al., “One step synthesis of pure cubic and monoclinic HfO2 nanoparticles: Correlating the structure to the electronic properties of the two polymorphs,” J. Appl. Phys. 112(10), 104112 (2012). [CrossRef]
28. A. L. Patterson, “The Scherrer Formula for X-Ray Particle Size Determination,” Phys. Rev. 56(10), 978–982 (1939). [CrossRef]
29. M. Vargas, N. R. Murphy, and C. V. Ramana, “Structure and optical properties of nanocrystalline hafnium oxide thin films,” Opt. Mater. (Amsterdam, Neth.) 37, 621–628 (2014). [CrossRef]
30. A. F. Khan, M. Mehmood, A. M. Rana, et al., “Effect of annealing on electrical resistivity of rf-magnetron sputtered nanostructured SnO2 thin films,” Appl. Surf. Sci. 255(20), 8562–8565 (2009). [CrossRef]
31. E. T. Hu, Q. Y. Cai, R. J. Zhang, et al., “Effective method to study the thickness-dependent dielectric functions of nanometal thin film,” Opt. Lett. 41(21), 4907–4910 (2016). [CrossRef]
32. Z. Y. Wang, S. J. Yuan, D. H. Li, et al., “Influence of hydration water on CH3NH3PbI3 perovskite films prepared through one-step procedure,” Opt. Express 24(22), A1431–1443 (2016). [CrossRef]
33. E. Franke, C. L. Trimble, M. J. DeVries, et al., “Dielectric function of amorphous tantalum oxide from the far infrared to the deep ultraviolet spectral region measured by spectroscopic ellipsometry,” J. Appl. Phys. 88(9), 5166–5174 (2000). [CrossRef]
34. L. S. Gao, Q. Y. Cai, E. T. Hu, et al., “Optimization of optical and structural properties of Al2O3/TiO2 nano-laminates deposited by atomic layer deposition for optical coating,” Opt. Express 31(8), 13503–13516 (2023). [CrossRef]
35. J. B. He, W. Jiang, X. D. Zhu, et al., “Optical properties of thickness-controlled PtSe2 thin films studied via spectroscopic ellipsometry,” Phys. Chem. Chem. Phys. 22(45), 26383–26389 (2020). [CrossRef]
36. C. Wang, C. Ma, J. B. He, et al., “Optical properties of Sub-30 nm-thick ZnS films studied by spectroscopic ellipsometry,” Mater. Sci. Semicond. Process. 142, 106454 (2022). [CrossRef]
37. H. Fujiwara, “Tauc-Lorentz model,” in Spectroscopic Ellipsometry: Principles and Applications, John Wiley & Sons, Ltd. (2007) pp.170–172.
38. J. W. Park, D. K. Lee, D. Lim, et al., “Optical properties of thermally annealed hafnium oxide and their correlation with structural change,” J. Appl. Phys. 104(3), 033521 (2008). [CrossRef]
39. T. Ito, M. Maeda, K. Nakamura, et al., “Similarities in photoluminescence in hafnia and zirconia induced by ultraviolet photons,” J. Appl. Phys. 97(5), 054104 (2005). [CrossRef]
40. E. E. Hoppe, R. S. Sorbello, and C. R. Aita, “Near-edge optical absorption behavior of sputter deposited hafnium dioxide,” J. Appl. Phys. 101(12), 123534 (2007). [CrossRef]
41. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909). [CrossRef]
42. M. Bischoff, T. Nowitzki, O. Vob, et al., “Postdeposition treatment of IBS coatings for UV applications with optimized thin-film stress properties,” Appl. Opt. 53(4), A212–220 (2014). [CrossRef]
