Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Effect of microstructure on the optical properties of sputtered iridium thin films

Open Access Open Access

Abstract

The refractory metal iridium has many applications in high performance optical devices due to its high reflectivity into X-ray frequencies, low oxidation rate, and high melting point. Depositing Ir via magnetron sputtering produces high quality thin films, but the chamber pressure and sputter conditions can change Ir film microstructure on the nanoscale. Film microstructure is commonly examined through microscopy of film cross-sections, which is both a destructive characterization method and time consuming. In this work, we have utilized a non-destructive characterization technique, spectroscopic ellipsometry, to correlate the optical properties of the metal films with their structural morphologies, enabling large-scale inspection of optical components or the ability to customize the metal refractive index for the application at hand. The optical properties of Ir thin films deposited at chamber pressures from 10 mTorr to 25 mTorr are reported and compared to microscopy and resistivity results. The measurements were conducted with films deposited both on a bare wafer and on a titanium sublayer.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

High-quality metal films are widely used in optical components, particularly for mirrors and custom optics made from metamaterials. The importance of individual film characteristics – e.g. reflectance, oxidation resistance, and temperature performance – can vary depending on the application at hand. For example, mirrors for telescopes need high reflectivity across a large frequency band but must resist oxidation to ensure consistent performance over the lifetime of the device [1]. Plasmonic applications focus more on high conductivity and stable refractive indices, though a high melting point becomes of paramount importance when talking about high temperature metamaterial selective emitters [2]. Though gold and silver are more commonly used in optics, gold does not reflect well at higher frequencies, giving rise to its yellow color, and silver is prone to oxidation and tarnish. Both materials have melting points near 1000 °C, so high temperature applications, such as waste heat reclamation at industrial foundries where temperatures can exceed 900 °C, are restricted. The refractory metal iridium (Ir) is a good candidate for these applications due to its low oxidation rate, high reflectivity over a wide frequency range, and high melting point.

With its high reflectivity into the x-ray regime and low oxidation rate, Ir is frequently a candidate for x-ray telescope mirrors [1,3]. Storage at room temperature in air for six months resulted in no decrease in reflection [4]. Annealing below 700 K in air does not generate an oxide layer on Ir [5], with most IrO studies looking at formation at temperatures in excess of 1000 K [68] unless exposed to an electric potential [9]. Its high melting point of roughly 2700 K also makes Ir well suited as a protective coating [8] or for high temperature plasmonics [10,11]. Sputtering is a common method of deposition for Ir due to its high melting point but changing plasma conditions can change the properties of the resulting Ir film. For example, the stress in very thin Ir films can be altered by changing the chamber pressure during deposition [12], resulting in higher surface roughness as the pressure increases. However, including a sublayer under the Ir film can relieve some of the residual stress.

In this study, we extracted the refractive index and extinction coefficient for several Ir thin films deposited via magnetron sputtering at chamber pressures ranging from 10 mTorr to 25 mTorr using spectroscopic ellipsometry. The film morphology was analyzed using scanning electron microscopy and transmission electron microscopy to identify the structural condition, inform the ellipsometry model development, and to understand the microstructural reasons for changes in the optical properties. Results were compared for Ir films deposited directly on silicon substrates and on a titanium sublayer, as the Ti thermal expansion coefficient lies between that of the substrate and iridium film [13,14]. Ultimately, we show ellipsometry is an effective, non-destructive, characterization tool for monitoring structural quality of Ir thin films

2. Method

2.1. Film preparation

The metal thin films were deposited on silicon substrates. The wafers were solvent cleaned in acetone followed by isopropyl alcohol and rinsed in deionized water. After rinsing the substrates were blown dry with nitrogen gas and then underwent an O2 plasma clean to remove any remaining organic residue. The films were deposited with a DC magnetron sputtering system using argon gas. The deposition chamber pressure was varied from 10 mTorr to 25 mTorr while the deposition time and power was held constant at 10 minutes and 160 W, respectively, for each sample run. On half of the samples, a 10 nm layer of Ti was deposited at 4 mTorr and 200 W prior to the Ir deposition. To minimize source contamination, the target was pre-sputtered for 3 minutes while the substrate was covered with the shutter. All films were optically opaque and mirror-like after deposition with a thickness around 100 nm.

2.2. Film analysis

After fabrication, scanning transmission electron microscopy (STEM) of film cross-sections was used to observe grain structure. Cross-sectional samples were prepared by focused ion beam (FIB) and imaged at 200kV on a JEOL 200F ARM. Atomic force microscopy (AFM) on an Asylum Cypher S in tapping mode was used to characterize the surface roughness and grain size of the film. Scanning electron microscopy (SEM) on a FEI Helios 660 was used to obtain larger-area images and observe any cracks in the films. Resulting images were analyzed using the Gwyddion analysis software [15]. Film resistivity was measured using a four-point probe at several locations on each sample so the standard error could be calculated.

Ellipsometry was performed on a J. A. Woollam variable angle spectroscopic ellipsometer (VASE), and optical data was collected at 65° and 70° angles of incidence in the ultraviolet (UV) to near infrared (NIR) spectral range, 200 nm to 2 µm. The optical characteristics of the films were calculated from the spectroscopic ellipsometer parameters psi (ψ) and delta (Δ), which relate the reflection intensity and phase change of polarized light after it interacts with a film [16]. The real and complex components of the refractive index were extracted by modeling the film with a combination of Drude and Gaussian oscillators using the WVASE software [17]. The mean square error between the measured data and the calculated values was compared to determine the quality of the fit. The oscillators were adjusted until a good fit was obtained. AFM-measured surface roughness was incorporated into the model to ensure the oscillator model was representative of the film and not the roughness. The Ir layer was optically opaque, so though a Ti underlayer was included in the model for the relevant samples, it had no impact on the extracted optical constants.

3. Results

3.1. Surface morphology

When Ir is deposited via magnetron sputtering, the grain shape and surface morphology change with deposition chamber pressure as a result of compressive or tensile stress in the film [18]. At low pressure, the sputtered atoms experience few collisions and reach the substrate with sufficient kinetic energy to rearrange themselves, leading to films with few voids. At high pressures, surface motion is reduced as the atoms lose their kinetic energy and directionality to collisions with gas molecules [19]. As the sputtered atoms are less likely to fill in the voids, shadowing effects impact the structure growth, leading to branching structures. While previous studies looked at Ir directly on substrates like silicon [18] or glass [19], we found that change in morphology due to deposition parameters occurred even with the inclusion of a titanium layer. Figure 1 shows the cross-sectional bright-field STEM images of two Ir films grown on a Ti sublayer, one at a chamber pressure of 10 mTorr and the other at 25 mTorr. The film deposited at 10 mTorr produces a dense film with columnar grains, as seen in Fig. 1(a). Increasing the pressure to 25 mTorr results in branching structures, seen in Fig. 1(b), with many voids. These structures are consistent with Ir films under compressive and tensile stress, respectively. Selected area electron diffraction patterns from both cross-sections show no preferred orientation for the grains. To see if the Ti layer had a broader effect on the film quality, top-down SEM images were taken of Ir films deposited with and without the use of the sublayer.

 figure: Fig. 1.

Fig. 1. Bright-field STEM images of Ir deposited at 10 mTorr results in a dense film with grains that are columnar in nature (left). At higher pressures, a branching structure is observed (right), resulting in lower electrical conductivity and lower optical absorption in the NIR. Both images are from films deposited on Ti.

Download Full Size | PDF

Two Ir film sample sets were fabricated, one with the Ti layer and one without. Both sets contained Ir films that were deposited using chamber pressures of 10, 15, 20, and 25 mTorr. The surface features of each sample were imaged using SEM, as shown in Fig. 2. The top row, Fig. 2(a-d), show the films that were deposited directly on the Si substrate while the bottom row, Fig. 2(e-h), contains the films that were deposited on a Ti sublayer. Both rows show increasing chamber pressure going from left to right. The samples deposited at 10 mTorr, shown in Fig. 2(a) and Fig. 2(e), show similar grain formation. Based on AFM measurements, these films had an RMS roughness of 1.3 nm and 1.2 nm, respectively. As the pressure in the deposition chamber was increased, the surface roughness also increased to 1.87 nm and 2.52 nm at 25 mTorr for the films without and with the Ti layer, respectively. AFM characterization could not effectively pick up the large voids that are evident in the SEM images, so the roughness for the high-pressure films only holds for the areas between the cracks. Film cracking only occurred in the Ir films deposited directly on the substrate, suggesting the Ti provided enough adhesion to prevent cracking at higher film stresses.

 figure: Fig. 2.

Fig. 2. SEM images of Ir thin films deposited directly on a silicon wafer (a-d) or after a Ti layer (e-h). The Ir was deposited via sputtering at pressures of 10 mTorr (a,e), 15 mTorr (b,f), 20 mTorr (c,g) and 25 mTorr (d,h). The scale bar on the right applies to all images. The inclusion of a Ti sublayer improves the quality of iridium thin films. Without the sublayer, significant cracking occurs when the deposition pressure is above 10 mTorr.

Download Full Size | PDF

Resistivity measurements using a four-point probe are consistent with the appearance of cracks with increasing deposition pressure, as shown in Fig. 3. At low pressures, the films deposited with and without the Ti layer are nearly identical with a resistivity of about 3×10−5 Ohm·cm. At 25 mTorr, the resistivity increases to 3.3×10−4 Ohm·cm with the Ti layer and 4.9×10−4 Ohm·cm without. The largest difference occurs at 20 mTorr, with a resistivity of 9.45×10−5 Ohm·cm with the Ti layer and 6.2×10−4 Ohm·cm without. STEM imaging of 20 mTorr with a Ti layer (not shown) demonstrates a branched morphology similar to 25 mTorr but with significantly fewer voids.

 figure: Fig. 3.

Fig. 3. As the pressure is increased, leading to more voids in the Ir film, the resistivity increases as well. Inclusion of the Ti layer results in a less dramatic shift in resistivity with increasing pressure. Error bars show standard error for the measurements.

Download Full Size | PDF

The increase in voids from 20 to 25 mTorr, even with the Ti layer, results in a large increase in resistivity. The highest resistivity measured in this study, 20 mTorr without Ti, is attributed to the large number of cracks shown in Fig. 2(c). A slight decrease in resistivity from 20 to 25 mTorr without Ti is attributed to the decrease in visible cracks between Fig. 2(c) and 2(d). AFM measurements were used to guide inclusion of surface roughness into the optical models used to analyze spectroscopic ellipsometry data. As this information was intended for application-driven uses, we did not include porosity or voids in the model as they contribute to the overall optical response of the film.

3.2. Optical properties

 figure: Fig. 4.

Fig. 4. The refractive index of thin Ir films stabilizes at a lower value as the deposition pressure increases regardless of the presence of a Ti sublayer. Without the Ti layer (a), two distinct regimes appear, while the Ti (b) enables a gradual transition. See Data File 1 for underlying values.

Download Full Size | PDF

The real (n) and imaginary (k) components of the complex refractive index for the Ir films are shown in Fig. 4 and Fig. 5 as calculated from ellipsometry models. Tabulated values can be found in Data File 1. The n and k values for the films deposited at 10 mTorr are consistent with previously found values for sputtered iridium films [20]. Figure 4 compares the refractive index across different deposition pressures for samples without a Ti layer (a) and for samples with a Ti layer (b). At low deposition pressures, both sample sets displayed an increase in the refractive index as the wavelength increased from the UV range. At higher deposition pressures on the sample without the Ti layer, n is approximately stabilized after 850 nm. With the Ti, n decreases after 850 nm.

 figure: Fig. 5.

Fig. 5. The extinction coefficient exhibits the same decreasing behavior when the Ir is deposited directly on the substrate (a) as when a Ti layer is used (b). Again, deposition pressure is the dominating factor for altering the optical properties. See Data File 1 for underlying values.

Download Full Size | PDF

Without the Ti layer, two distinct regimes appear for films deposited at pressures below and above 20 mTorr, shown in Fig. 4(a). For the low pressures n increases up to 4.3 at 2 µm, while at high pressures n stays at about 3.3 from 850 nm out to 2 µm. This is consistent with the increase in voids and surface roughness at higher pressures, which both introduce air or areas of low refractive index and bring down the effective n of the film. As the pressure is reduced, the film behavior approaches that of a solid metallic film. When the Ti sublayer is incorporated, the transition between the high- and low-pressure regimes becomes more gradual, as seen in Fig. 4(b). At 10 mTorr, n again increased to about 4.2 at 2 µm. However, as the deposition pressure is increased, n at 2 µm decreases and reaches 2.4 when the film is deposited at 25 mTorr. Though the refractive index decreases with increasing pressure regardless of the presence of the Ti layer, its inclusion leads to a gradual decrease rather than a sudden shift at pressures higher than 20 mTorr. The divergence of n at wavelengths longer than 1 µm make the 1- 2 µm range ideal for differentiating between film morphologies, especially for single-wavelength or other fixed-wavelength ellipsometry systems.

While the change in pressure results in a large shift in refractive index, it produces an even larger shift in the extinction coefficient, k, as seen in Fig. 4. Both sample sets produce k values near 12 at a wavelength of 2 µm when the Ir film is deposited at 10 mTorr. This value drops below 2 when the deposition pressure is increased to 25 mTorr. As with n, the presence of the Ti layer again led to a gradual decrease in k rather than a sharp regime shift. However, it did not have as significant of an impact as the pressure.

The shift in quality of the films and an indication of their performance as mirrors is more apparent in the graph of the reflectivity for each film shown in Fig. 6 as calculated from the extracted complex refractive indices in Figs. 4 and 5. For high k films, the reflectivity, R, for normally incident light at the air-film interface is given by Eq. (1),

$$ R = \frac{{{{({n - 1} )}^2} + {k^2}}}{{{{({n + 1} )}^2} + {k^2}}}$$
where the refractive index of air is 1and n and k are the complex refractive index of the Ir film.

 figure: Fig. 6.

Fig. 6. Reflectivity was calculated from the complex refractive indices extracted from the ellipsometry models for each film. As reflection is also dependent on extinction coefficient for large values of k, the films deposited at low pressures showed the highest reflectivity. Films deposited directly on the substrate (dashed lines) showed similar reflectivity values to those on a Ti sublayer (solid lines) deposited at the same pressure.

Download Full Size | PDF

The films deposited at 10 mTorr show reflectivity approaching 0.9 at a wavelength of 2 µm while those deposited at and 20 and 25 mTorr average 0.5 at the same wavelength. Higher reflection with an increase in k is consistent with Eq. (1) and the behavior of other highly reflective metals used for mirrors such as gold. With the optical parameters and models established, some trends in their structure became apparent.

For all samples, optical models were created by combining a Drude dispersion layer with a few Gaussian oscillators. The Drude model accounts for free carriers within the film while the Gaussian oscillators cover mixed absorption modes. These modes can include interband transitions, phonons, and increased electron scattering not covered by the Drude model. We found that the dominating absorption mechanism varied based on the deposition pressure. At 10 mTorr, the Drude model dominated the permittivity, as shown in Fig. 7(a), with minor Gaussian peaks that improve the fit. When the pressure is increased to 25 mTorr, the behavior flips such that the Gaussian oscillators are the primary contributors with a minor influence from the Drude model, as seen in Fig. 7(b). This indicates that electrons can flow more freely in the 10 mTorr films, behaving like the “electron gas” described by the Drude model. This implies that the film will be a good conductor. At the higher pressures, the Drude model is no longer applicable on its own, indicating a more resistive film. This is consistent with both the microstructures shown in Fig. 1 and Fig. 2 and the resistivity measurements reported in Fig. 3.

 figure: Fig. 7.

Fig. 7. Ellipsometry modeling of an Ir film on Ti deposited at 10 mTorr (left) shows the absorption can be primarily described by a Drude model, implying the film will be a good conductor. The same film stack deposited at 25 mTorr (right) shows a higher dependence on the free carrier and interband absorption, as modeled by Gaussian oscillators, resulting in a more resistive film. A similar trend occurs with Ir films deposited without the Ti layer.

Download Full Size | PDF

4. Conclusions

We have reported the changes in refractive index and extinction coefficient that accompany film morphology changes in iridium thin films deposited via magnetron sputtering at different chamber pressures. Comparison of film quality of the Ir films as deposited on the substrate versus on a titanium sublayer show higher film uniformity and fewer surface cracks with the inclusion of the Ti layer. However, it was the chamber pressure that largely dictated the behavior of the optical constants. At low pressure, the optical properties of the dense Ti/Ir film could be reasonably approximated by the Drude model, with n and k values that increased with increasing wavelength to 4.2 and 12, respectively, at 2 µm. At high pressures, branching structures developed, leading to an increase in voids and lower n and k values of 2.4 and 2.3, respectively, at 2 µm. For both sample sets, as the microstructure became less dense, the electronic conduction decreased as shown by an increase in resistivity. This is also consistent with the ellipsometry models as the Drude model, typically used to describe good conductors that can be approximated as free electron gasses, was less able to correctly model the permittivity for the high-pressure samples. The correlation between optical properties and microstructure presented in this paper enables the use of in-situ or large-scale surveying of Ir film quality using non-destructive methods, capabilities that are useful for quality control of large astronomy mirrors or other applications. Single wavelength ellipsometry measurements at wavelengths longer than 1.5 µm would provide the best analysis for quality given the large difference in refractive index at those wavelengths. Additionally, understanding the optical behavior of otherwise similar films will also inform design and fabrication decisions for plasmonic and frequency selective surfaces, allowing some customization of constituent film properties for these devices.

Funding

Office of Naval Research (DURIP N00014-17-1-2591., N00014-15-1-2946); National Science Foundation (EEC-1444926, GRFP DGE-1000169618).

Disclosures

The authors declare no conflicts of interest.

References

1. A.-C. Probst, T. Döhring, M. Stollenwerk, M. Wen, and L. Proserpio, “Iridium coatings for space based x-ray optics,” International Conference on Space Optics — ICSO 2016, 105621E (25 September 2017).

2. N. A. Pfiester and T. E. Vandervelde, “Selective emitters for thermophotovoltaic applications,” Phys. Status Solidi A 214(1), 1600410 (2017). [CrossRef]  

3. D. D. M. Ferreira, F. E. Christensen, A. C. Jakobsen, N. J. Westergaard, and B. Shortt, “ATHENA optimized coating design,” Proc. SPIE 8443, 84435L (2012). [CrossRef]  

4. G. Hass, G. F. Jacobus, and W. R. Hunter, “Optical properties of evaporated iridium in the vacuum ultraviolet from 500 Å to 200 Å,” J. Opt. Soc. Am. 57(6), 758 (1967). [CrossRef]  

5. S. Kohli, D. Niles, C. D. Rithner, and P. K. Dorhout, “Structural and optical properties of iridium films annealed in air,” Adv. X-ray Anal. 45, 352 (2002).

6. R. T. Wimber and H. G. Kraus, “Oxidation of iridium,” Metall. Trans. A 5(7), 1565–1571 (1974). [CrossRef]  

7. Y. Huang, S. Bai, H. Zhang, and Y. Ye, “Oxidation of iridium coating on rhenium coated graphite at elevated temperature in stagnated air,” Appl. Surf. Sci. 328, 436–443 (2015). [CrossRef]  

8. L. Zhu, S. Bai, H. Zhang, Y. Ye, and W. Gao, “Long-term high-temperature oxidation of iridium coated rhenuium by electrical resistance heating method,” Int. J. Refract. Hard Met. 44, 42–48 (2014). [CrossRef]  

9. S. Siracusano, V. Baglio, S. A. Grigoriev, L. Merlo, V. N. Fateev, and A. S. Aricò, “The influence of iridium chemical oxidation state on the performance and durability of oxygen evolution catalysts in PEM electrolysis,” J. Power Sources 366, 105–114 (2017). [CrossRef]  

10. N. A. Pfiester, “Metamaterial devices for enhancement of thermophotovoltaics and mid-IR photodetectors,” Tufts University, ProQuest Dissertations Publishing, 13425920 (2019).

11. N. A. Pfiester, N. Naka, and T. E. Vandervelde, “Platinum metamaterials for thermophotovoltaic selective emitters,” European Photovoltaic Solar Energy Conference, Hamburg, Germany (2015).

12. D. M. Broadway, J. Weimer, D. Gurgew, T. Lis, B. D. Ramsey, S. L. O’Dell, M. Gubarev, A. Ames, and R. Bruni, “Achieving zero stress in iridium, chromium, and nickel thin films,” Proc. SPIE 9510, 95100E (2015). [CrossRef]  

13. G. K. White and A. T. Pawlowicz, “Thermal expansion of rhodium, iridium, and palladium at low temperatures,” J. Low Temp. Phys. 2(5-6), 631–639 (1970). [CrossRef]  

14. H. Tada, A. E. Kumpel, R. E. Lathrop, J. B. Slanina, P. Nieva, P. Zavracky, I. N. Miaoulis, and P. Y. Wong, “Thermal expansion coefficient of polycrystalline silicon and silicon dioxide thin films at high temperatures,” J. Appl. Phys. 87(9), 4189–4193 (2000). [CrossRef]  

15. D. Nečas and P. Klapetek, “Gwyddion: an open-source software for SPM data analysis,” Open Phys. 10(1), 181 (2012). [CrossRef]  

16. H. G. Tompkins and E. A. Irene, Handbook of Ellipsometry, William Andrew Publishing, 3 (2005).

17. WVASE. Version 3.908, Lincoln: J. A. Woollam Company (2016)

18. M. A. El Khakani, M. Chaker, and B. Le Drogoff, “Iridium thin films deposited by radio-frequency magnetron sputtering,” J. Vac. Sci. Technol., A 16(2), 885–888 (1998). [CrossRef]  

19. A. Büttnera, A.-C. Probst, F. Emmerich, C. Damm, B. Rellinghaus, T. Döhring, and M. Stollenwerk, “Influence of sputtering pressure on microstructure and layer properties of iridium thin films,” Thin Solid Films 662, 41–46 (2018). [CrossRef]  

20. L. Yan and J. A. Woollam, “Optical constants and roughness study of dc magnetron sputtered iridium films,” J. Appl. Phys. 92(8), 4386–4392 (2002). [CrossRef]  

Supplementary Material (1)

NameDescription
Data File 1       The data file includes extracted refractive index information for sputtered Ir thin films deposited at a range of chamber pressures.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. Bright-field STEM images of Ir deposited at 10 mTorr results in a dense film with grains that are columnar in nature (left). At higher pressures, a branching structure is observed (right), resulting in lower electrical conductivity and lower optical absorption in the NIR. Both images are from films deposited on Ti.
Fig. 2.
Fig. 2. SEM images of Ir thin films deposited directly on a silicon wafer (a-d) or after a Ti layer (e-h). The Ir was deposited via sputtering at pressures of 10 mTorr (a,e), 15 mTorr (b,f), 20 mTorr (c,g) and 25 mTorr (d,h). The scale bar on the right applies to all images. The inclusion of a Ti sublayer improves the quality of iridium thin films. Without the sublayer, significant cracking occurs when the deposition pressure is above 10 mTorr.
Fig. 3.
Fig. 3. As the pressure is increased, leading to more voids in the Ir film, the resistivity increases as well. Inclusion of the Ti layer results in a less dramatic shift in resistivity with increasing pressure. Error bars show standard error for the measurements.
Fig. 4.
Fig. 4. The refractive index of thin Ir films stabilizes at a lower value as the deposition pressure increases regardless of the presence of a Ti sublayer. Without the Ti layer (a), two distinct regimes appear, while the Ti (b) enables a gradual transition. See Data File 1 for underlying values.
Fig. 5.
Fig. 5. The extinction coefficient exhibits the same decreasing behavior when the Ir is deposited directly on the substrate (a) as when a Ti layer is used (b). Again, deposition pressure is the dominating factor for altering the optical properties. See Data File 1 for underlying values.
Fig. 6.
Fig. 6. Reflectivity was calculated from the complex refractive indices extracted from the ellipsometry models for each film. As reflection is also dependent on extinction coefficient for large values of k, the films deposited at low pressures showed the highest reflectivity. Films deposited directly on the substrate (dashed lines) showed similar reflectivity values to those on a Ti sublayer (solid lines) deposited at the same pressure.
Fig. 7.
Fig. 7. Ellipsometry modeling of an Ir film on Ti deposited at 10 mTorr (left) shows the absorption can be primarily described by a Drude model, implying the film will be a good conductor. The same film stack deposited at 25 mTorr (right) shows a higher dependence on the free carrier and interband absorption, as modeled by Gaussian oscillators, resulting in a more resistive film. A similar trend occurs with Ir films deposited without the Ti layer.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

R = ( n 1 ) 2 + k 2 ( n + 1 ) 2 + k 2
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.