1. Background

Thin films consisting of SiO₂ nanorods or np-SiO₂ are of great interest because they tend to have a refractive index lower than the bulk value of about 1.46, which is especially useful in distributed Bragg reflectors [1] and anti-reflection coatings [2]. In principle, there is an inverse relationship between film porosity and refractive index because the air trapped between nanorods reduces the composite refractive index of the film. Oblique-angle deposition makes it possible to grow these nanorods due to the self-shadowing effect [1]. A DBR made of the same material can be also realized by this oblique angle deposition [3]. Increasing the porosity, however, also causes the film to interact unfavorably with the external environment so that material properties such as refractive index and coefficient of thermal expansion (CTE) are unstable. For instance, water, with a refractive index of 1.33, can be trapped in the pores and boost the overall refractive index of a thin film, with the effect depending heavily on the level of humidity in the surroundings [4]. In addition to SiO₂, there are many other films whose mechanical properties are dependent on the ambient as well, for example, zirconium tungstate thin films [5] show different CTE in dry versus wet environments.

In this paper we demonstrate that it is possible to stabilize these material properties to prevent the porous films from interacting with the ambient by coating ALD Al₂O₃ on top of the unstable dielectric films. This technique will be extremely important not just for mirrors which need to be precisely controlled over temperature, but also for making thermally invariant mirrors [6].

2. Experimental results and discussion

Thin films of np-SiO₂ were deposited on 250µm (100) Si wafers by electron beam evaporation, with the substrates at room temperature and mounted at an oblique angle of 60° relative to the source material. The oblique angle is typically defined as an angle between vapor flux and the substrate normal [1], and that is the convention used here. The refractive index versus temperature of the resulting films was measured at 632.8nm by a Gaertner ellipsometer in a clean-room environment with 40% relative humidity (RH). Heating and cooling was performed with a thermoelectric heating element and temperature controller. Wafer curvature versus temperature measurements were performed with Frontier Semiconductor FSM-900TC commercial stress measurement equipment. These measurements were made both in clean-room air at 40%RH, and in a dry N₂ ambient with continuous flow rate of roughly 2000 sccm.

Figure 1 shows how measured film properties vary with changes in ambient conditions. Figure 1(a) indicates that the refractive index drastically decreases as the temperature increases. The thermo-optic coefficient (dn/dT) of the np-SiO₂ film is almost -3×10^-3/°C in the range of 10°C~70°C, over two orders of magnitude larger than the roughly 10^-5/°C expected from changes in intrinsic material properties [7]. This is most simply explained by the presence of pores that can easily desorb and adsorb the water vapor from the external environment as temperature increases and decreases, respectively. Figures 1(b) and 1(c) show the measured curvature change with respect to temperature in air and N₂, respectively. The sign of the slope depends upon the CTE value of the substrate; a slope of zero would indicate the film CTE exactly matches that of the substrate. When the CTE of a thin film is lower than the substrate it curves upward upon heating. Similarly, the substrate curves downward upon heating when film CTE is larger than substrate CTE. Therefore, the positive and negative slopes in Fig. 1(b) and 1(c) occur even though both np-SiO₂ CTE values are positive.

Quantitatively, the np-SiO₂ film CTE in each case is extracted from the slope of each dataset using a linear, multilayer analysis based on free-plate theory [6], with assumptions of substrate and film biaxial modulus. For this particular film, the CTE change between air and N₂ is roughly one order of magnitude (0.4ppm/°C to 4.3ppm/°C), which would make it difficult to model and use in a multilayer optical design where thermomechanical performance is also of interest. As with refractive index, the observed CTE instability is most likely caused by adsorption and desorption of water vapor contained in the air ambient by the nanoporous film, changing its properties. In contrast, as the temperature is cycled in an N₂ environment any moisture in the film tends to outgas until the film reaches a “steady-state”, with thermal expansion behavior dominated by intrinsic film properties [8].

 

Fig. 1. The properties of np-SiO₂ change significantly with ambient conditions. Measurements of (a) refractive index versus temperature in the presence of humidity, and wafer curvature change versus temperature (b) in air and (c) in dry N₂ indicate that the film adsorbs and desorbs water from the ambient. Extracted np-SiO₂ CTE values are indicated on each plot.

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Many dielectric materials made by electron beam evaporation even without oblique-angle deposition show similar ambient dependence [8]. After numerous attempts to keep the CTE and optical constant stable, we found that ALD Al₂O₃ works quite well. ALD Al₂O₃ films were deposited with a Cambridge NanoTech, Inc. Savannah system, using alternating pulses of H₂O and trimethylaluminum at a process temperature of 250°C and pressure 1 torr, with N₂ as the carrier gas flowing at 20 sccm. Figure 2(a) shows the np-SiO₂ optical constant change with temperature when encapsulated by ALD Al₂O₃. The refractive index for the buried np- SiO₂ layer was calculated indirectly based on the Ψ and Δ of the total reflection obtained from ellipsometry, assuming constant film thicknesses and ALD Al₂O₃ index. The dn/dT of np-SiO₂ was found to be 4.3×10^-5/°C, which is similar to the intrinsic property of fused silica (about 10^-5/°C [7]). Since the dn/dT of bulk Al₂O₃ is also ~10^-5/°C [9], the exact quantitative result for dn/dT of encapsulated np-SiO₂ may be somewhat lower than what we measured, but the overall point remains. The refractive index of np-SiO2 is stabilized by ALD Al₂O₃.

 

Fig. 2. (a). The refractive index of np-SiO₂ encapsulated ALD Al₂O₃, plotted on the same scale as Fig. 1(a), shows very little change with temperature. Similarly, the CTE values extracted from measurements of curvature versus temperature indicate a np-SiO₂ CTE of (b) 6.1ppm/°C in air, and (c) 6.2ppm/°C in N₂, assuming a constant Al₂O₃ CTE of 3.4ppm/°C.

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As shown in Fig. 2(b) and 2(c), ALD Al₂O₃ can also encapsulate the np-SiO₂ in terms of thermomechanical properties. The measured film thicknesses for the system in Fig. 2 are 1302 Å of Al₂O₃ and 2037 Å of np-SiO₂. We determined the refractive index of the Al₂O₃ to be 1.65 compared to 1.6–1.7 reported in [10]. The instability of the underlying film CTE between air and N₂ has dropped from ~3.9ppm/°C to~0.1ppm/°C when encapsulated, the latter being a much more manageable level of variation for design purposes. These results agree with recent observations that ALD Al₂O₃ is believed to be a gas diffusion and moisture permeation barrier [11, 12]. While that research was based on encapsulation of polymer materials, our measurements indicate ALD Al₂O₃ is a promising moisture permeation barrier for low-index np-SiO₂.

We developed and fabricated a DBR based on np-SiO₂, TiO₂ made by electron beam evaporation, and ALD Al₂O₃, as shown in Table 1. In order to make a DBR mirror with more than 90% reflectance, simulations suggest we must put 8 layers of alternating np-SiO₂ and TiO₂, with the top TiO₂ layer replaced by ALD Al₂O₃ as a barrier. A simulation of this coating on a silicon substrate is shown in Fig. 3, along with actual measured reflectance; both have a 15° angle of incidence relative to normal. Data were measured on a J.A. Woollam Co. VASE spectroscopic ellipsometer system. The discrepancy between the model and the data possibly comes from deviations in actual thickness and refractive index of the DBR layers. It could be partially due to ALD Al₂O₃ penetration into the top np-SiO₂ layer, since the resulting increase in np-SiO₂ refractive index would be expected to induce a similar red-shift in peak reflectance. It is noted that if standard silica was used instead of the reduced-index np-SiO₂, simulations indicate that more than 12 layers would be needed to achieve a similar peak reflectance.

Table 1. Parameters measured for the various layers in the 4-pair DBR mirror

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Fig. 3. Simulated and measured reflectance versus wavelength for the encapsulated 4-pair DBR on Si. Both include a 15° angle of incidence relative to normal, since measurement at 0° was not practical. Reasonable agreement with simulation is observed, with expected variations due to some uncertainty in the thickness and refractive index of each layer.

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The encapsulation capability of ALD Al₂O₃ is also confirmed with this DBR mirror, as seen in Fig. 4(a) and 4(b). The measured curvature versus temperature of the DBR coated wafer does not vary based on ambient conditions. We also performed a fit to the experimental data using a multilayer model to extract the CTE of the TiO₂ layers in each case. To do this we assume that the CTE of np-SiO₂ and ALD Al₂O₃ remain constant at the values in Table 2, and that all TiO₂ layers have identical CTE. This fit indicates that the CTE of the TiO₂ films is 3.6ppm/°C in air and 4.0ppm/°C in N₂, a difference of only ~0.4ppm/°C. Although it is based on several assumptions, this result gives a sense of the coating stability in a changing ambient. For comparison, we measured the curvature change of a three-layer structure consisting of a silicon wafer with thin films of np-SiO₂ and e-beam evaporated TiO₂. Assuming that np-SiO₂ properties remain constant underneath for simplicity, we found that the difference in TiO₂ CTE between air and N₂ was about 5 ppm/°C. This suggests the TiO₂ would be a poor encapsulant, and could also have a nanoporous structure.

 

Fig. 4. Curvature measurements versus temperature of the 4-pair DBR on Si, (a) in air and (b) dry N₂. The axes are scaled identically, and we observe no significant change due to ambient conditions.

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Table 2. Material properties of the DBR materials used in themomechanical modeling.

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Figure 5(a) shows a cross-sectional scanning electron microscope (SEM) image of the np-SiO₂ films showing the nanorod structure, which seem to be ~30–60 nm in diameter. It is noted that the film thickness of this particular sample was roughly 300 nm, somewhat thicker than the others. In other films we had difficulty seeing these nanorods clearly, even though all films exhibited a low refractive index when deposited in this manner. It is believed that porosity plays an important role in lowering its optical constant so that even films without this particular nanorod structure have low refractive index. Figure 5(b) indicates how the ALD Al₂O₃ deposition process at 250°C may influence the np-SiO₂ films. The np-SiO₂ remains porous, although it is difficult to see if ALD Al₂O₃ can penetrate into the pores. One thing that we do notice, however, is that the refractive index of np-SiO₂ when encapsulated by ALD Al₂O₃ (in Fig. 2(a)) is about 0.08 higher than the “dry” np-SiO₂ film without encapsulation, near T=60°C in Fig. 1(a), which suggests that ALD Al₂O₃ may partially penetrate into np-SiO₂. Furthermore, the 8-layered DBR can be seen in Fig. 5(c), showing that all of the np-SiO₂ films, except perhaps the top np-SiO₂ layer (layer 7), appear to maintain a significantly nanoporous structure.

 

Fig. 5. Cross-sectional SEM images of (a) a np-SiO₂ film, indicating the nanorod structure, (b) a np-SiO₂ film encapsulated by ALD Al₂O₃, and (c) the 8-layered DBR discussed above.

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3. Conclusion

We successfully demonstrate that the optical and thermomechanical properties of a SiO₂ nanorod array or np-SiO₂ can be stabilized by encapsulation with ALD Al₂O₃, while maintaining the very useful reduction in refractive index to ~1.33. The dn/dT of encapsulated np-SiO₂ is only 4.3×10^-5/°C in a humid environment, which is much less than the -3×10^-3/°C observed in the exposed film. Similarly, the encapsulated np-SiO₂ CTE difference between air and dry N₂ was only 0.1 ppm/°C, compared to a shift of 3.9 ppm/°C in the bare film. The successful demonstration of this encapsulation ability is also done with a 4-pair DBR design, showing very little curvature dependence on ambient gas, while maintaining about 90% reflectance. This technique could be useful to stabilize entire coatings, or in patterning specific regions of a film for optical and mechanical stability.