1. Introduction

Aluminum is the only material that can provide broad-band IR-optical-UV and far ultraviolet (FUV) reflectance. Unfortunately, aluminum begins oxidizing immediately upon air exposure. Even under high-vacuum conditions, oxidation [1–8] and loss of vacuum ultraviolet (VUV) reflectance are observed. [9] The aluminum oxide which forms, though only 3.5-5 nm thick, effectively blocks aluminum’s high reflectance above about 9 eV (<140 nm), which is the point at which sapphire’s absorption constant rises above 0.01/nm. [10] To circumvent oxidation, wide-bandgap, dielectric (low-atomic-number metal fluoride) thin films are deposited on the aluminum film before it is exposed to air. [4,11–15] MgF₂ and LiF thin barrier layers have been used for decades to protect aluminum reflectors, particularly for VUV applications including space telescopes. Space telescopes place large demands on reflective coatings. Hubble’s far UV performance was due to its MgF₂ on Al mirror coatings. Concept plans for two potential NASA missions of the 2030’s -the Large UV-Optical-IR Surveyor (LUVOIR) and the Habitable Exoplanet Imaging Mission (HabEx)- call for substantial reflectance down to 100 nm. [16–18] Recent efforts to achieve this goal have focused on depositing the fluorides on heated substrates, [11] using barriers containing LiF, [19] employing atomic layer deposition (ALD), [17,20–22] and using capping layers including AlF₃. [12,19] This has allowed aluminum’s useful region of high reflectance to be expanded to somewhat shorter wavelengths.

In addition to optical performance, there are significant environmental requirements. Coatings must survive years of storage prior to launch. This environment may not be optimal for survival during portions of this time. This is particularly an issue for LiF which is hygroscopic and for thinner overcoats. Lifetime tests show that some processes produce layers that should survive some exposure to humid environments. [19] However, these are macroscopic tests. The question of the nature of the degradation on the atomic level has not been addressed. Fundamental knowledge of atomic-scale changes could provide technologists insights in identifying problems and allowing problems to be corrected early. This could also help formulate accelerated lifetime tests and give confidence that the final coatings will survive to launch and beyond.

In spite of the importance of barrier-layer protected mirrors, tools that can easily detect and quantify the time-dependent oxidation of aluminum under protective fluoride barrier layers have been late in coming. Here we show that variable-angle, spectroscopic ellipsometry (VASE) in combination with XPS can be such tools and present a systematic study of MgF₂-protected Al mirrors as an example of its use. VASE is known to be useful in obtaining the thicknesses and optical constants of ultrathin metal films. [23] Recently this technique was expanded to observing the thickness of ultrathin aluminum under a fluoride barrier decrease with time. [24–27] The concomitant appearance and growth of a dielectric layer on top of the aluminum under the fluoride layer was also noted. While this was inferred to be aluminum oxide, it took an XPS study on the same series of MgF₂ layers on Al to show definitively that the dielectric material, which ellipsometry measures to be increasing in aging samples, is oxide. [28,29] This study also indicates that the oxidation is uniform across the sample. That is, the data does not support the hypothesis that the oxidation is primarily from pinholes. It may be that oxygen/water penetration is via grain-boundary transport and these oxidizers, having reached the top of the alumina layer which is forming on the top surface of the aluminum, must again diffuse inward through that alumina layer to complete the reaction. Grain sizes for films such as these are typically much less than the wavelength of light used to probe them via ellipsometry. Thus, the values for thickness determined by ellipsometry average the effect of many paths. We also show that, while the Cabrera-Mott approach can fit the oxide thickness derived from XPS, that thickness is fit better by a simpler expression. Oxide thickness increases linearly with the logarithm of time. Also, as anticipated, the slopes of the equation for the time-dependent thickness decrease with increasing fluoride thickness. This approach potentially might be useful to project mirror lifetimes. The films studied here were deposited at room temperature. However, the technique described here is amenable to samples deposited at elevated temperatures or via ALD and should be adaptable to studying other barriers such as LiF and other mirror metals such as silver.

2. Experimental

2.1 Sample preparation and deposition

Silicon pieces with Si₃N₄ overlayers (ca. 300 nm) were used as substrates for Al + MgF₂ deposition. The stacks were characterized at each stage of development. This is referred to as a bottom-up method of thin-film analysis. This approach allows one to constrain the underlayers’ properties while the thicknesses and compositions of the overlayers are determined. This provides confidence in the deduced layer thickness even for multilayer stacks. Except as specifically described below, all aluminum and MgF₂ films were deposited without substrate heating in a Denton DV-502A thermal evaporator. The base pressure prior to deposition was >10⁻⁴ Pa. Details are described elsewhere. [24,25,29] The sample substrates were cleaved from Si (100) wafers. In studying aluminum films, the wafer utilized was purchased with a nominal 300 nm of CVD Si₃N₄. The CVD Si₃N₄ dielectric layer on the substrate is referred to as the interference layer (IL) and aids in the quantification of oxide growth on Al via ellipsometry. [24] The Al was deposited at a rate of 3.5 nm/sec to achieve a thickness of 150 Å. During the Al deposition the system pressure rose to a maximum of 10⁻³ Pa. The MgF₂ was then immediately deposited (time between depositions was less than 60 seconds) on the Al film at a rate of ca. 0.3nm/sec. The time for both depositions was 35 to 45 s. The time between the end of the evaporation of the aluminum film and the beginning of the evaporation of the overcoat was minimized to avoid oxide build up on the freshly evaporated Al and was usually less than 60 seconds. Past work has shown that high rates are conducive for producing the purest (highly reflective) aluminum layers. The high rates limit the incorporation of oxygen into the film. A quartz crystal monitor (QCM) was employed to close the shutter between the source and the substrate when the programed thickness was reached.

Our goal was not the replication of state-of-the-art, protected, front-surface aluminum mirrors in every detail. Rather, we aimed at producing materials and structures that facilitated study via SE and XPS but were otherwise as similar as possible to the relevant aspects of the best mirrors. Ours were test samples for addressing scientific/technological questions, such as, “What is the rate of oxidation of aluminum coatings protected by a certain thickness of barrier?” And “since it is known that heating the substrate as the fluoride is deposited enhances optical properties, can the same be said for barrier-layer properties?” We hypothesize that small amounts of oxygen incorporation are not likely to change oxidation rates significantly, though this should be investigated. Likewise, it was hypothesized that aluminum thickness would not affect aluminum oxidation rates. Thus, the behavior of our ultrathin aluminum coatings (thickness ∼150 Å) should be useful in understanding state-of-art aluminum mirrors (>700 Å).

2.2 Characterization

Ellipsometric data was acquired using a J.A. Woollam M-2000D, variable-angle, spectroscopic ellipsometer (J.A. Woollam Company, Lincoln, NE, USA) over the wavelength range of 190-1688 nm. SE data were obtained on these samples via two modes. Long-term measurements were obtained by making SE measurements over a range of angles at various times up to several months. This is the more common mode for data collection since, at least for thicker films, having data from many angles constrains the thickness and indices of the overlayers. Since changes slowed with time logarithmically, we decreased the time period commensurately. Dynamic mode was the second mode of collecting data. [30] Time-dependent SE measurements of Δ and Ψ were acquired every 2.3 s for 4 h for various MgF₂ on Al samples (abbreviated as Al + MgF₂) at 75˚. The advantage of dynamic mode is that one can observe Δ and Ψ change over time. The indices of Al obtained later from the variable-angle measurements then allow these to be interpreted as growth of the oxide moment by moment. Representative dynamic data is archived elsewhere. The demonstration of dynamic fit procedure can be found in supporting information Visualization 1.[31] The first measurements were performed as soon as the samples were prepared, then we let all the samples age and repeated the measurements.

Data were subsequently modeled using the CompleteEASE SE instrument analysis software. The model in Fig. 1 shows the layers present in the actual stacks prepared and studied. The optical constants for all layers except #2 (CVD Si₃N₄) and #4 (Al) were modeled with the optical constants in the CompleteEASE database. The substrate was Si-JAW. Layers 1 and 3 were SiO2-JAW (silicon native oxide). These Si and SiO₂ optical constants are from Herzinger. [32] The optical constants of Layer 5 (Al₂O₃) and 6 (MgF₂) the software uses are taken from Lichtenstein and Dodge respectively. [33–34] MgF₂ is birefringent. We did not know whether the MgF₂ was amorphous or polycrystalline, or the orientation of the MgF₂ grains if the film were crystalline. If the orientation were random, the indices of the composite would most closely match the ordinary ray, since there is only one extraordinary axis. Thus, a Sellmeier model of the ordinary-ray refractive indices of MgF₂ was chosen to fit the fluoride thickness. However, the relative differences in thicknesses using the extraordinary indices varied no more than a few percent and was a consistent fraction of the thickness from sample-to-sample. The substrate and layers 1-3 come as a unit. As mentioned above, for each sample these layers were premeasured and analyzed prior to deposition of the Al/MgF₂. This allows us to have good confidence in the measured thicknesses of Al, MgF₂, and aluminum oxide layers. While it is impossible to know the thickness of the oxide under the Si₃N₄, analyses showed its thicknesses did not have any influence on the determined thicknesses of the overlayers. We set it to 1.4 nm, which is a typical thickness for native oxide on Si wafers. With SE we learned that the native oxide on top of our CVD Si₃N₄ is about 2 nm. This is from measuring wafer pieces after etching in buffered HF to remove only the oxide layer. The optical constants for ‘Layer 2 CVD Si₃N₄’ were obtained by measuring a number of CVD nitride-coated substrates prior to deposition. [24] We found that the optical constants of CVD silicon nitride could be parameterized successfully as a Tauc-Lorentz oscillator plus a Gaussian oscillator located about 7.4 eV. In general, the variation in Si₃N₄ thickness from sample to sample was less than 1%. However, the Si₃N₄ thicknesses were measured on each specific sample prior to the deposition of the aluminum and the fluoride. The parameters used to fit the substrates were then held fixed during the analysis of the Δ and Ψ data to determine the Al (Layer 4) and Al₂O₃ (Layer 5) thicknesses.

 

Fig. 1. A generic representation of the optical stacks analyzed in this work. The bottom layers up through Layer 3 represent the Si/Si₃N₄ substrate. Layers 4 and 6 represent the Al and MgF₂ deposited on the substrate. Layer 5 represents the aluminum oxide.

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The effective optical properties (n and k) for the aluminum films were obtained from multisample analyses (MSA) as described in the results section. Interference enhancement, as the technique is known, has been found to increase significantly the sensitivity to the absorber layer (here, Al) optical properties and thickness. [23] The purpose of a thick dielectric layer between the aluminum layer and the Si substrate is to enhance the information content of multiple-angle measurements. [24] Spectroscopic ellipsometry and transmitted or reflected intensity was shown, for example, to produce a unique result for the Cr films on fused silica substrates. [23] It should be noted that the Al in the films suitable for these ellipsometric studies (target thickness 15 nm) is a factor of 4-5 times thinner than standard telescope mirrors

XPS was performed with a Surface Science SSX-100 instrument (maintained by Service Physics, Bend, OR, USA) with a hemispherical analyzer. The instrument employs monochromatic Al Kα X-rays. Survey scans were collected with an X-ray spot size of 800 × 800 μm² with a resolution of 4, nominal pass energy of 150 eV, 6 passes/scans, and a step size of 1 eV. High resolution scans were collected over the Al 2s region, centered at a binding energy of 120 eV, with an energy window of 40 eV and a step size of 0.0625 eV. The number of scans ranged between 15 and 35, and the spot size was 800 × 800 μm² with a resolution of 3 (nominal pass energy of 100 eV). Area ratios were calculated using the CasaXPS modeling software (Casa Software Ltd., Version 2.3.18PR1.0).

2.3 MgF₂ thickness standard preparation

MgF₂ thickness standards for XPS analysis allow the thickness of MgF₂ on Al films to be measured via XPS. To prepare the standards, MgF₂ films of seven different thicknesses on Si were deposited on unheated (that is, about 300 K) substrates. These were approximately 25 × 25 mm silicon pieces cleaved from a single-side polished 150 mm diameter crystalline silicon wafer. The samples were cleaned by a low-pressure air plasma (Herrick model PDC-32G). The native oxide thickness on each sample was then measured via ellipsometry prior to MgF₂ deposition. The native oxide thickness was about 1.5 nm. After the fluoride deposition, the thicknesses of the MgF₂ layers were measured via SE at an angle of 75°. The ellipsometric data was modeled using the optical models in the instrument software for MgF₂ [MgF₂ (Sellmeier-ordinary ray)] to obtain the fluoride thickness, while Si and SiO₂ used Si JAW and SIO2_JAW, respectively. An additional set of five MgF₂ standards of varying thicknesses were prepared on heated substrates (ca. 500 K) by the processes described above except the substrate heating. Differences in the attenuation coefficient of the two sets showed the importance of substrate heating for maximum density; as will be discussed below.

After deposition, the standards were analyzed with XPS to assess the attenuation length of the MgF₂. This included narrow scans of the Mg 2s and Al 2p features. It should be noted that the thickest MgF₂ in the films suitable for these XPS studies are a factor of 3-4 times thinner for standard protected mirrors due to analysis depth limitations of XPS. On the other hand, for ellipsometry the fluoride layer can be arbitrarily thick.

3. Results and discussion

3.1 Determination of fluoride thickness

Ellipsometric measurements depend on reflecting light of a known polarization from a surface and measuring changes in that polarization. Spectroscopic ellipsometry utilizes a suite of colors, in our case, >700 individual wavelengths. Through the creation of parametric models of layers and adjustment of the parameters in them, ellipsometric measurements can be used to determine a variety of material properties including film thicknesses, surface roughness, and optical constants of materials. In the case of multi-angle measurements this can yield as many as 10000 individual values of Δ and Ψ which can be fit with a model possessing far fewer adjustable parameters. This can remarkably constrain layer thicknesses. Parameterization also decreases the correlation between constants while maintaining smooth and continuous optical properties.

However, due to the potential presence of two dielectric layers- the MgF₂ overlayer and any aluminum oxide- above the aluminum in the Al + MgF₂ bilayer (see Fig. 1), the individual thicknesses of the MgF₂ overlayer and the oxide cannot be determined with precision using spectroscopic ellipsometry alone. This is unless the thickness of one of the layers is known, and it is known that the overlayer itself does not change with time. MgF₂ thin films are stable, as is discussed in section 3.2. While the thickness monitor provided thickness control of the magnesium fluoride deposited, an independent measurement of the thickness and stability of the deposited MgF₂ layer was desired. XPS satisfies this requirement.

In this analysis, we employed an equation from Cumpson, which is based on Hill’s equation. [35,36] It is as follows:

Here, I_o and s_o are the intensity and sensitivity factor respectively of the Mg 2s photoelectrons in the top layer of the MgF₂ standards (here, the MgF₂ film), and I_s and s_s are the intensity and sensitivity factor of the Si 2p electrons from the substrate (here, the Si/SiO₂ layer), and the take-off angle [cos θ in Eq. (1)] of our XPS system is 35°.

Finally, the attenuation coefficient, λ_o, for MgF₂ needs to be known. This was the purpose of the MgF₂-films-on-silicon standards described in section 2.2. SE could be used to determine their thickness [here, d in Eq. (1)]. This is possible because there was no aluminum or aluminum oxide to confound the identification of the magnesium fluoride layer’s thickness. Then the samples were measured via XPS and Eq. (1) was solved iteratively to determine the attenuation coefficient, λ_o, for MgF₂. Peak areas (I_o and I_s here) and binding energies (E_o and E_s for Mg 2s and Si/SiO₂ 2p photoelectrons, respectively) were calculated. This resulted in four different values of λ_o for the samples deposited on unheated substrates. These are: (1.6 nm MgF₂, λ_o: 6.1 nm), (2.1 nm MgF₂, λ_o: 5.3 nm), (3.3 nm MgF₂, λ_o: 4.6 nm), and (5.1 nm MgF₂, λ_o: 4.2 nm) and are plotted in Fig. 2.

 

Fig. 2. Measured (apparent) XPS electron attenuation length as a function of MgF₂ thickness from SE. The top curve guides the eye for values () for samples deposited on unheated substrates. The bottom curve joins values () for samples deposited at ∼500 K.

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Note that the value of the attenuation coefficient decreased as MgF₂ thickness increased. This can be understood if the thinner fluoride layers were more porous than thicker ones. Porous films logically would have larger attenuation lengths since the void in the films does not absorb electrons. However, the ellipsometer would measure a greater film thickness than if the MgF₂ film were fully dense. The index of the porous layer was not noticeably smaller than that of bulk fluoride. The fact that the index of water is close to that of MgF₂ may account for this. Ellipsometric measurements are made in ambient air. Under these conditions, small pores fill with water by capillary action even in conditions of low humidity. Water has an index not much smaller than that of magnesium fluoride, so the combination of fluoride and water is a layer that resembles bulk magnesium fluoride. (The water will leave in the vacuum of the XPS, however, and thus will not be detected by that technique.)

It is well known that the initial layers of dielectrics are frequently porous when deposited on substrates at ambient temperatures. The films become denser as the film thickness increases, but bulk densities are often not achieved without adding energy during deposition. Substrate heating is thought to produce denser films at all thicknesses by increasing the surface mobility of adatoms. While ion bombardment works well for oxides, fluoride films are damaged by this technique.

To achieve higher density films, the five fluoride films of different thicknesses deposited at about 500 K were subjected to XPS analysis. The attenuation length of these films does not vary with thickness as seen in Fig. 2 (bottom set of points marked by triangles). The average value of λ_o was 3.79 ± 0.21 nm for the heated MgF₂ films.

This value of the attenuation length, 3.79 nm, was then used in Eq. (1) to determine the thickness of the various MgF₂ layers deposited on aluminum. Here, Al 2p electrons coming from the aluminum film were used to compute the Al/Al₂O₃ ratio. E_o and E_s are the binding energies of Mg 2s and Al 2p photoelectrons respectively, and λ_o is the attenuation coefficient of the aforementioned Mg 2s photoelectrons. These thicknesses were within 5% of the value programmed into the QCM used to control the deposition thicknesses in the evaporator. Thus, overall, this approach accounted for any run-to-run variation in the deposition of the MgF₂.

3.2 Observations of the oxidation of Al under MgF₂ from SE

As described earlier, to study the oxidation of aluminum under MgF₂, Al (nominal thickness of ca. 15 nm), followed by MgF₂ (various thicknesses) were deposited onto fully characterized Si/SiO₂/Si₃N₄/SiO₂ substrates. Since the lower layers were well characterized, this approach allowed the thickness of the overlayers: Al, aluminum oxide and MgF₂ to be determined with high confidence. These Si/SiO₂/Si₃N₄/SiO₂/Al/MgF₂ stacks were then removed from the evaporation chamber. Once in air “the clock started” for the sample’s aging. As quickly as possible – usually 5-6 minutes, each sample was moved to the ellipsometer, and a four-hour run was commenced that repeatedly collected SE data from the sample at 75°. Some of the samples were then analyzed by XPS to determine the thicknesses of its MgF₂ and oxide layers. The Δ and Ψ ellipsometric data was then analyzed to obtain the time-dependent thickness of the oxide for each four-hour set of SE data.

The changes cannot be due to the changes in MgF₂. Of the commonly used fluoride overcoats for aluminum, magnesium fluoride is the most stable. Our ellipsometric study of 15 nm MgF₂ on Si films showed no changes for samples stored in laboratory air over a period of a day. Thus, calculations proceeded attributing all changes in SE data to the appearance of an aluminum oxide film on the Al. Prior work had shown that the SE data was not compatible with the interpretation that the oxide is forming below the Al. [24]

Three approaches for parameterizing the specific Al optical constants necessary to determine the aluminum and aluminum oxide thicknesses for the Al + MgF₂ stacks were explored. In all cases, a Lorentz-oscillator model with seven oscillators was used. During the fitting process, only the amplitude and breadth of the oscillators were varied. The energy of each oscillators was held constant. As discussed above, both approaches used the previous SE characterizations of the individual Si/SiO₂/Si₃N₄/SiO₂ substrates applied to each different stack modeled. In the first approach, the same Al optical constants were used for all samples. This is Model 1. These Al constants had been obtained from an MSA involving most of the samples, as detailed elsewhere. [37] This approach had a significant problem but was not unfruitful. The problem was this: the fits to SE for most samples generated apparent oxide thicknesses less than zero. The MSE is shown in the second column (labeled Model 1) of Table 1. The reason the MSE of the fifth sample (2.92 nm) cannot be fit well is not clear.

Table 1. Mean square error for fitting aluminum and aluminum oxide for Model 1, 2, and Model 3. Model 1 uses the same Al optical constants for all samples. For model 2 they are optimized individually for each sample. The initial oxide thickness is set to 0 in Model 3 and then the Al optical constants are fit.

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Negative oxide thicknesses are not physical, but neither are they very important. They are an artifact of not allowing the optical constants of the Al layers to not vary as much as required for the particular sample. Fitting the amplitude and breadth of the oscillators in the optical constants model of the aluminum in each individual stack individually resulted in more reasonable fits for the oxide thickness and yielded significantly lower MSE values. This is the 3^rd column in Table 1, labeled Model 2. They are not so important since it is differences in thicknesses that are tracked (see Fig. 3). They represent an arbitrary starting point which is shown in Table 1 Model 3 where all initial alumina thicknesses were set to 0 and then Al optical constants and Al thickness were fit. Setting the initial alumina thickness to zero had little to no effect on either MSE or the k_SE value. Compare Models 2 and 3 in Table 1. It should be noted, however, that the fitting of the oxide growth with time and the size of the prefactor in model 3 are reasonable. The changes in aluminum oxide thickness as a function of time based on model 3 in shown in Fig. 3.

 

Fig. 3. Aluminum oxide thickness as computed by Model 3 increases with time, for five Al + MgF₂ bilayers. From top to bottom MgF₂ thicknesses are 0, 2.59, 2.99, 3.81, and 4.97 nm. The closely spaced points correspond to the dynamic fit. Representative data is archived elsewhere. [31] Representative error bars at the end of the dynamic fit for each of the MgF₂ thicknesses are 0.023, 0.025, 0.034, 0.012, 0.045, respectively.

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Interestingly, in spite of the fact that Model 1 yielded apparent negative Al₂O₃ thicknesses for a significant fraction of the samples, the trends, with increasing time, in apparent Al₂O₃ and Al thicknesses for all samples that could be fit, were not unreasonable. The apparent Al₂O₃ thicknesses was observed to increase with time accompanied by a decrease in the Al thicknesses. To visualize these trends, thickness data were plotted against log of time (Fig. 3).

Using log of time allowed data taken over many orders of magnitude to be plotted on the same graph. When this was done, it was noted that the data of the Al₂O₃ thicknesses vs. time for the different samples lay on approximately straight lines. That is, they could be reasonably fit to an equation of the form:

The negative thicknesses for Al₂O₃ produced by Model 1 Al constants are unphysical. It is reasonable to hypothesize that this is due to the requirement that the same optical constants for Al be applied to all samples regardless to differences in deposition conditions. In the case of dielectric thin films this often a good assumption. However, as previously noted, optical constants for extremely thin metal films cannot be expected to be constant. [23,37–39] Since the photon energy in the SE characterization are significantly less than aluminum’s plasma edge of 15 eV, anything that affects the number, or scattering behavior, of free electrons could markedly change a Al film’s optical constants. [40] In fact, the oscillatory motion of free electrons in an ultrathin aluminum film in a photon’s electromagnetic field could be impeded both by the film’s top and bottom surfaces [41] and the presence of numerous grain boundaries [42] arising from the extremely small grain size characteristic of ultrathin films deposited at a small fraction of their melting temperature. (The general effect on microstructure of thickness and deposition temperature is treated by a number of authors. [43,44]) Nguyen et al. used spectroscopic ellipsometry to comprehensively study the effect of Al thickness on optical constants, observing that for thicknesses >6 nm, “the interband relaxation time increases with thickness, providing evidence that grain-boundary scattering is the dominant mechanism controlling the optical properties in the bulk film stage.” [42] The smaller MSE values for Model 2 (see Table 1) suggests that fitting the Al optical constants in each sample separately is justified, lending support to the hypothesis that the Al optical constants vary between the samples. Two additional indications that this approach is an improved representation of our materials are the facts that all of the samples could be fit with Model 2, and that only two of the ten samples used showed any negative Al₂O₃ thicknesses.

Plots of Al₂O₃ thickness vs. the log of time were also found to be quite linear for the second approach as well as the first and were fit with Equation 2. The slopes (that is, the k_SE values) in equation 2 arising from the application of the two Al models are plotted in Fig. 4 as a function of the MgF₂ overlayer thickness in each of ten samples. It is clear that k_SE decreases as the thickness of the MgF₂ overlayer increases, which is the expected behavior for a barrier layer.

 

Fig. 4. Values of k_SE determined from Eq. (2) from data generated from Models 1 (squares and lower curve) and 2 (circles and lower curve) employed in this study

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It is significant that the two curves nearly overlap. That is, these results suggest that while the absolute thicknesses of oxides using the first model might be incorrect, the changes with time are meaningful, and, furthermore, that the values of k_SE determined here, and the fact that they decrease with increasing MgF₂ thickness, are not artifacts of either approach. The best fit equation used for the red line is k_SE = 0.17e^-0.27x, where x is the thickness of the MgF₂ barrier film in nm.

3.3 X-ray photoelectron spectroscopy analysis

The thickness of the MgF₂ layer on Al could not be modeled unequivocally using SE due to potential correlation with the developing aluminum oxide layer, as noted previously. Therefore, to measure the thickness of the MgF₂ layer, XPS itself was used in conjunction with SE. XPS is the most widely used technique for obtaining information from the surface of a material i.e., the top ca. 5-10 nm. The signal collected is photoelectrons (core electrons) generated by the absorption of X-rays incident on a sample’s surface. The energy of these photoelectrons provides information about the elemental composition of the surface and also the chemical environment of those elements. The surface sensitivity of this technique is a result of short distances (mean-free-path) that electrons can travel in a solid without losing energy. In our studies, XPS verified the changes observed in SE were from the oxidation of the Al thin films. XPS data are modeled using curve fitting techniques that account for differences in composition. This peak fitting is important because XPS line widths and chemical shifts due to changes in oxidation states are of comparable size. [30] To study the oxidation rates of Al as a function of MgF₂ thickness, as discussed in section 2.1, seven Al + MgF₂ samples were prepared. All samples were analyzed at the Al 2s binding energy (BE) position of 118 eV. While the intensities of the Al 2p region were very similar, the Al 2s region was selected because the spin-orbit splitting seen in Al 2p regions does not need to be considered for peak fitting.

Fig. 5 shows that the Al surface below the MgF₂ oxidizes to Al₂O₃ over time. The extent of oxidation can be measured by plotting the Al₂O₃/Al ratios vs. time. Photoelectrons do not come out of the surface with the same energy but are broadened to a Lorentzian shape by the exponential decay probability for the core hole. The spectrum is further broadened to have a more Gaussian shape by phonon interactions and disorder. In fitting the Al 2s peak, two types of synthetic line shapes were considered: Gaussian-Lorentzian product (GLP) functions, and Gaussian-Lorentzian sum (GLS) functions. [45] Because they fit the data better than GLP functions, GLS functions were employed here. These partition the peak into Gaussian and into Lorentzian components. It has been observed that the Al peak from pure Al is more Lorentzian than Al in Al₂O₃. [45,46] This is attributed both to the oxide’s greater disorder and to phonon broadening. [47–49]

 

Fig. 5. XPS spectra (aluminum x-rays) as binding energies for the aluminum 2s peak. The left-hand curve corresponds to oxidized aluminum. The right-hand curve corresponds to reduced aluminum. The top curve is from a sample that was placed in the XPS shortly after it was evaporated. The bottom curve showing considerably more oxidation was analyzed after 725 minutes.

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The figure of merit for determining the quality of the XPS fits was the standard deviation of the residuals (STDEVRes). In addition, the residuals were examined to confirm that there was no significant ‘structure’ in them, i.e., the residuals should appear as random noise. In the bare Al samples, the Al₂O₃ peaks were best fit with GLS functions with 20% Lorentzian character (the value of the mixing parameter was 0.2), thus yielding percent Lorentzian character values of 50 and 20 for the Al and Al₂O₃ peaks, respectively. In the samples with a MgF₂ protective layer, percent Lorentzian character values of 50 and 0 for Al and Al₂O₃, respectively, fit the data best. The decreased Lorentzian peak character from the bare to the protected oxide layers suggests increased disorder in the XPS oxide [47] under the MgF₂ overlayer. Using these parameters, we determined the areas under the Al₂O₃ and Al peaks as well as the full width half maximum (FWHM) values of the peaks from seven samples. The samples included two bare samples (0 nm thickness MgF₂) and five samples with different thicknesses of MgF₂ as overlayers. Each of the samples was measured six or seven different times over time as shown in Fig. 6. The average and standard deviation of these measurements are recorded in Table 2. Our data showed the average FWHM for the Al signal to be 1.75 ± 0.07 eV for both bare and coated samples. On the other hand, the Al₂O₃ 2s peaks for the bare and coated samples averaged 2.45 ± 0.1 eV and 2.92 ± 0.13 eV, respectively. The oxide FWHM values fell within the range of literature γ-Al₂O₃ and Al values. [48–51] In addition, the binding energy (BE) difference between the Al₂O₃ and Al peaks was 2.57 ± 0.12 eV averaged over all the samples. It may be that the differences in the FWHM values are attributable to (i) differences between oxide formed with (under) and without a MgF₂ overlayer, and/or (ii) differential charging.

 

Fig. 6. Extent of aluminum oxidation as measured by XPS, i.e., the ratio of the area of the Al peak in aluminum oxide divided by the area of the aluminum peak from unoxidized aluminum as a function of time on a log graph.

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Table 2. Averages and standard deviations of FWHM values, peak energy (BE) differences, and ratios of FWHM values for the Al and Al₂O₃ fit components in the Al 2s narrow scans considered in this study.

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The consistency of the statistics in Table 2 also increased our confidence in the validity of our data. Using these standards, we were able to quantify aluminum oxidation changes over time. Accordingly, we can show graphically changes in the aluminum oxidation starting from immediate removal of the sample from the evaporator chamber and extending to 8 months. In Fig. 6, Al₂O₃/Al ratios are graphed as functions of the log of time. It can be observed that plotting the data points as a function of the log of time shows points fall, more or less, on a straight line. Empirically, then, oxidation followed a logarithmic model over an extended time-period of observation. That the rate of oxidation decreases with time is not surprising since as the oxide film thickness grows, it creates a protective boundary that greatly reduces atmospheric oxygen or water access to the aluminum metal surface. [24]. As shown, the rates were empirically fit using regression analysis to the general equation using the Al₂O₃ to Al ratios shown in Eq. (3):

Here, k_XPS is the slope. Table 3 gives values of the oxidation prefactors as a function of the MgF₂ thicknesses.

Table 3. Oxidation rate XPS prefactors from different MgF₂ thicknesses

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1.1 Discussion of models of aluminum oxidation under protective layers

Understanding the mechanism behind thin-film oxidation is a century-old problem. [52] While applying protective or barrier overcoats to isolate a surface from the environment is a common approach to slow degradation, the study of the kinetics of the oxidation under that barrier is much less common. The exceptions arise when the overlayer is ultrathin as is the case of graphene on Cu. [53,54] Even in these cases, however, appeals to classic oxidation theory are rare. Here is the problem. Rather than a two-layer model (an oxide on a metal substrate) a trilayer (barrier/oxide/metal) model must be invoked. The difficulty is not just that there are more interfaces. In our case, the barrier is structurally and chemically quite different from the oxide forming below it. The formation of Mott potentials and mechanisms of mass and charge transport can be expected to change, transitioning between the growing oxide and the magnesium fluoride overcoat.

Nevertheless, the fact that oxide thicknesses on a log-of-time plot fall on straight lines whose slopes depend on the MgF₂ thickness suggests that consideration of classical oxidation models may yield insight. The fact the slopes decrease with increasing fluoride thicknesses suggests that the limiting factor to oxidation is the MgF₂ layer. Perhaps it limits diffusion of an oxygen containing species through it to the MgF₂-oxide interface.

The oxidation of many metals at low temperatures, after the initial nucleation and lateral consolidation of oxide, is said to be logarithmic, either direct or inverse. The Cabrera-Mott (CM) model predicts an inverse logarithmic relationship. Replotting some of the oxide thickness data according to the CM model allows a comparison to be made. In the CM model, charged surface-oxygen species and metal ions generate a (Mott) potential that drives oxidation. If the CM model is applicable, the placement of the thickness data on the graph will produce straight lines. This is done in Fig. 7. Here the plot is done according to the form corrected by Ghez. [55] It can be seen in this figure that, while there is rough agreement with the Cabrera Mott model, the agreement is worse than for a direct logarithmic plot. In Table 4 furthermore, the goodness-of-fit (R²) values of direct logarithmic and CM are recorded for several samples. The middle column is for CM and the right column for direct logarithmic. In all but one case the R² value for direct logarithmic is significantly closer to 1.0 than the CM model is. 1.0 would be a perfect fit. Note that two of the plots are for bare Al, and in agreement with other researchers [4,56–58] we find that oxidation of bare aluminum is fit well by the log of time approach. Note that Grimblot and Eldridge [58] also stated that both the CM and direct logarithmic models worked well for the oxidation of Al films.

 

Fig. 7. Bare aluminum films and Al films under various thickness of MgF₂. Cabrera-Mott type plot. 1/thickness vs log (time/ thickness²)

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Table 4. R² Values for XPS Fits

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While failure of data to be fit well by the CM model cannot be interpreted as implying that the CM model is not applicable, [59] it is profitable to look for those models which predict direct logarithmic dependence. An early model proposed by Mott posited electron tunneling through the oxide as rate determining. For this case, a direct logarithmic expression for the growth of oxide films is identical to equations two and three. Fehlner also observed on page 204, [52] that direct logarithmic kinetics are observed for group I and II elements. Magnesium is a group II element, but there is no reason why one would expect its fluoride to block oxygen or water passage like its oxide does.

2. Summary and conclusions

Ellipsometric studies show changes in evaporated aluminum films under ultrathin films of evaporated magnesium fluoride that can be interpreted as oxidation of the aluminum forming an oxide layer between the top barrier and the Al layer. The application of SE to the measurement of the growth of buried oxide layers is novel. XPS measurements in this study unequivocally confirmed that, in the case of room-temperature deposited MgF₂ films with thicknesses between 0-6 nm, these changes are due to the slow oxidation of the underlying aluminum film. This is seen both in the increase of the signal from oxygen and in the chemical shift in the Al 2s electron emission peak toward higher binding energy as the surface of the metal oxidizes to Al⁺³. The extent of oxide growth can be modeled from the relative area of each peak once they are corrected for attenuation through the MgF₂ layer. We discussed the figure-of-merit used to choose the fraction of Lorentzian or Gaussian character for fitting the area of Al in the Al₂O₃ and Al peaks, and with this standard we showed, by plotting the Al₂O₃/Al ratios, that the amount of oxidation increases with the logarithm of time. Using XPS data obtained from MgF₂ layers of different thicknesses, we were able to calculate the Mg 2s photoelectron attenuation length (λ_o) in MgF₂ to be $3.8 \pm 0.2$ nm using the Cumpson equation.

Both XPS and SE allow the growth of the aluminum oxide to be tracked and quantified. Based on graphs of oxidation as a function of time, we produce a phenomenological formula: oxide thickness(y), y = k_SE*log(t) + y_o, which fits the measured time-dependent aluminum oxide thickness on aluminum surfaces protected by MgF₂. k_SE is a factor that depends on MgF₂ thickness and decreases with increasing MgF₂ thickness. Values for k for both techniques for various thicknesses are presented. These differ only slightly between SE and XPS data. For room-temperature deposited MgF₂ k_SE = 0.17e^-0.27x, where x is the thickness of the MgF₂ film in nm. The Cabrera-Mott approach is shown to be inferior to the phenomenological approach.

This study also contributes to the use of SE and XPS as analytical techniques generally. The fact that attenuation depths decrease with increasing thickness indicates that the porosity of ultrathin MgF₂ films deposited at ambient temperature decreases with increasing thickness. We also show that for each SE sample, because the optical constants of ultrathin metals films depend strongly on deposition conditions and their thickness, the optical constants for Al, as well as the Al and Al₂O₃ thicknesses, need to be individually fit. Similarly, as another first, we show how dynamic SE data track oxide growth over a period of several hours after the evaporated Al + MgF₂ bilayer is first exposed to the air. In dynamic SE, measurements are made every few seconds. Representative data are archived elsewhere. [31]

The SE and techniques developed and presented here will be generally applicable for ultrathin metal films protected by thin barrier layers. These techniques may allow for extrapolation of barrier-layer effectiveness for room-temperature deposited MgF₂ on Al to thicker fluoride films and point the way to producing survey methods for identifying which films might qualify for further study. In particular, the study of fluoride barriers prepared at elevated temperatures will be important. However, it should be noted that the Al in the films suitable for these ellipsometric studies are a factor of 3-4 times too thin for standard telescope mirrors.