1. Introduction

Recently, there has been an increasing interest in utilization of metallic nano- and microstructures. These kinds of structures exhibit unique properties and can be used in a wide range of applications including devices such as chiral polarization rotators [1] and metallic mesh structures that are used as infrared filters [2]. Also resonance film stacks, where alternating layers of metal and dielectric material cause enhanced transmission [3] are well known. In the field of nonlinear optics, for example, L-shaped nanostructures offer novel means to show a secondorder nonlinear optical response [4].

In order to design such devices and calculate the optical responses, the optical properties of the metallic structure should be known. In the literature [5, 6], accurate tabulated data exist for metals that are processed under extremely carefully prepared conditions to have compact structures and smooth surfaces. However, as is shown in this paper, the optical properties of these metals differ substantially from those of more commonly processed ones.

Generally, metallic nanostructures are fabricated into metallic thin films using lithographical processes. These thin films can be deposited by electroplating, sputtering, atomic layer deposition (ALD), and evaporation. Electroplating is an electrochemical process whereas sputtering and evaporation are physical processes. ALD is based on surface reactions and this is why the film growth during the process is self-limiting.

Thin films can be analyzed as a compound composed of air and metallic clusters, which means that the optical properties can be considered as effective. Since the volume of air and other inhomogeneities differs between different fabrication processes, it is inevitable that the optical properties are also unequal. For example, ALD makes it possible to produce compact structures, whereas evaporated films have more porous and non-uniform structure.

In this paper we compare the refractive indexes and extinction coefficients of evaporated aluminium and iridium films and atomic-layer-deposited iridium films. We demonstrate that the optical properties depend on the film deposition technique. We also show that the properties depend on film thickness. In the following section, we present the fabrication and analysis methods for the metal films. The experimental results for the refractive indexes and extinction coefficients are given in Section 3 and the conclusions are drawn in Section 4.

2. Fabrication and analysis methods

The aluminum and iridium films were evaporated by an electron beam gun. The target for aluminium was 99,999 % pure and for iridium 99,9 %. The evaporation rate for aluminium was 1.8–2.2 Å/s and for iridium 0.6–1.0 Å/s. The pressure at the beginning of the deposition processes was approximately 3×10^-6 torr but in the case of iridium it rose to 5×10^-5 torr during the evaporation. The substrate temperatures was held between 300 and 345 K. The substrates were mounted in a spherical holder and rotated to obtain uniform film thickness. The vapor deposition was controlled by using a shutter mounted above the targets. The shutter was opened when the targets were uniformly heated and the evaporation reached a constant speed, and it was closed when the desired film thickness was obtained.

The substrates for the evaporated aluminium and iridium films were fused silica plates of one inch diameter and 3 mm and 0.5 mm thick, respectively. The substrates were first cleaned in an ultrasonic cleaning bath filled with isopropanol. The surface roughness of the fused silica substrates was 11±0.5 Å, which was measured with the variable angle spectroscopic ellipsometer (VASE) [7] and modelled by Bruggeman’s effective medium theory. For the atomiclayer- deposited iridium, we used 1-mm-thick borosilicate substrates with a 5-nm-thick aluminium oxide adhesion layer. Borosilicate was chosen since it can withstand the heat required in the ALD process. The borosilicate substrates were cleaned in an ultrasonic cleaner filled with ethanol and water.

Cross section and surface images were taken using a LEO 1550 field emission scanning electron microscope (SEM) [8]. Optical measurements were made with a VASE that used a rotating analyzer design and thus made possible measurements over a broad wavelength range from 300 nm to 2000 nm at 10-nm intervals. The refractive indexes and extinction coefficients of aluminium and iridium were calculated using the Wvase32 [9] ellipsometric analysis program. This fitting software finds a minimum difference between the experimental data and calculated values using the Levenberg-Marquardt algorithm [10]. In the modelling, we assumed that each sample consisted of a homogenous metal film on a substrate. In the case of aluminium, we also included a 3-nm-thick alumina surface layer in the model.

With the VASE, we measured the ellipsometric parameters ψ and Δ at two different angles, 65 and 75 degrees. In the case of non-opaque films we also measured the transmittance at normal incidence. The thicknesses of the non-opaque films were determined during the fitting procedure using initial values obtained from the thickness monitor in the evaporation chamber and also measured with a profilometer. In the case of opaque films, we did not have the same thickness sensitivity in the fitting process. Hence, the thicknesses reported for the opaque films were determined by the monitor in the evaporation chamber, the profilometer, and also by the SEM values, since the SEM resolution was better for the thicker films.

3. Results

The refractive indexes of different layer thicknesses for ALD and electron-beam-gunevaporated iridium are compared to values presented in the literature [6] in Fig. 1(a). The literature values were for large polycrystalline samples that were cut from a crystal rod of iridium. The samples were mechanically polished to obtain specular surfaces, boiled in aqua regia, and heated in a vacuum of 10^-7 torr to produce clean, strain-free surfaces for the optical measurements [11].

For both fabrication methods, the refractive indexes increase as the thickness decreases. However, for the ALD films, the change with thickness is not as large as for the evaporated ones, as one would expect since the ALD process produces tightly packed films with uniform structure. The refractive indexes have higher values than the literature values excluding the 144-nm-thick ALD film at visible wavelengths.

The extinction coefficients of the same samples are shown in Fig. 1(b). Also, in this case, the measured extinction coefficients of the ALD films are larger than the literature values for the entire wavelength range. On the contrary, the measured values for the evaporated films are smaller than those in the literature. However, they increase as the thickness decreases. The ALD films behave in the same way. Again, the thickness does not have as much effect on the extinction coefficients of the ALD films compared to the evaporated ones.

The behavior of the ALD films is caused by the nature of the ALD process. The tightly packed structure of the ALD films results in high refractive indexes and extinction coefficients. The thickness dependence, in turn, is a consequence of irregularities in the atomic structure that increase with the number of deposited layers. The more layers there are, the more defects exist, which lowers the refractive indexes and extinction coefficients. For evaporated iridium, the thickness dependence is mainly caused by poor adhesion and different thermal expansion coefficients of the fused silica substrate and iridium film. As the film thickness increases, the sizes and numbers of cracks in the film surface becomes so large that it lowers the refractive index and extinction coefficient of the film. In Fig. 2 the cracks in the surface of the 115-nmthick evaporated iridium film are shown.

The refractive indexes for several thicknesses of the electron-beam-gun-evaporated aluminium films are shown and compared to the literature values [6] in Fig. 3(a). The literature values are for ultrahigh-vacuum-evaporated aluminium (more information was not available).

 

Fig. 1. Refractive indexes (a) and extinction coefficients (b) of 44 nm, 90 nm, and 144 nm thick atomic-layer-deposited iridium films compared to 30 nm, 110 nm, and 115 nm thick evaporated iridium films and the literature values [6] as a function of wavelength.

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Fig. 2. Surface structure of the 115 nm thick evaporated iridium film. The cracks are due to a poor adhesion and different thermal expansion coefficients between the substrate and iridium.

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As a whole, the values for the thicker films are closer to the ones in the literature. Nevertheless, in some cases the results are not consistent. For example, near a wavelength of 800 nm, the values for the 37-nm-thick layer are closer to the literature values than those for the 70-nm-thick layer. Corresponding results for the extinction coefficients can be found in Fig. 3(b).

The low extinction coefficient values of evaporated aluminium can be explained by considering the grain evolution of a thin film in the evaporation process. The large kinetic energy of electron-beam-gun-evaporated atoms enables them to migrate on the substrate surface to form different sizes of crystallites. Thus, the grain structure evolves during film growth, which often results in structure in which the grain size tends to be the same as and scale with the film thickness [12]. In this way the grain size of thicker films tends to be larger than that of thinner films. As long as the electronic mean free path length in the material is a small fraction of the distance between grain boundaries, the presence of these boundaries cannot significantly influence the conductivity. However, as the width or diameter of a grain approaches the mean free path length, a considerable fraction of the conduction electrons strike and scatter at the grain boundaries, reducing the conductivity and extinction coefficient [13]. This explains the decrease of the extinction coefficient as the film becomes thinner, particularly in the infrared region where optical absorption is dominated by the conduction electrons [14].

In Fig. 4(a) a top view of a 270-nm-thick electron-beam-gun-evaporated aluminium layer is shown. Comparing the grain size to that of a 100-nm-thick aluminium layer in Fig. 4(b), a significant difference can be seen. The average grain size of the 270-nm-thick layer seems to be almost 100 nm in diameter, nearly twice as large as for the thinner layer. A similar difference in the grain sizes can be seen in Figs. 5(a) and (b) where the cross-sectional views of 270 nm and 100 nm thick electron-beam-gun-evaporated aluminium layers on fused silica substrates are shown. In the cross-sectional figures, the grooves in the substrates were formed during the cutting of the sample plates and the nanometer-size particles on the substrates are sputtered gold that was used to increase the conductivity in SEM imaging.

The refractive index and extinction coefficient of evaporated aluminium also strongly depend on the proportion of alumina inside the thin film structure. A reasonable assumption is that the volume of alumina is higher for porous material, that is for thinner films, which results in more effective-like optical properties that are difficult to predict. The amount of alumina can be reduced with lower vacuum pressure and higher evaporation rate [15]. However, if we increase the evaporation rate, the surface roughness increases if we are not able to improve the vacuum.

 

Fig. 3. Refractive indexes (a) and extinction coefficients (b) of 37 nm, 70 nm, 163 nm, 206 nm, and 290 nm thick evaporated aluminium films compared to aluminium values given in the literature [6] as a function of wavelength.

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This in turn leads to less reliable ellipsometric measurements.

 

Fig. 4. Top view of 270 nm (a) and 100 nm (b) thick electron beam gun evaporated aluminium layer.

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Fig. 5. Cross-sectional view of 270 nm (a) and 100 nm (b) thick electron beam gun evaporated aluminium layer on fused silica substrate.

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Typical relative errors for measured ψ and Δ values are between 0.02–0.5 %. For transmittance, the numerical uncertainty is defined by the Wvase32 software as approximately 0.5 %. In Fig. 6(a) the 90 % confidence limits of the refractive indexes for the 30-nm-thick iridium and 163-nm-thick aluminum films are shown. Furthermore, the 90 % confidence limits for the extinction coefficients of the same samples are shown in Fig. 6(b). These figures represent the typical uncertainties for all of our measured films. It can be seen that the confidence limits are very close to the reported values. However, in the case of aluminum, the change in the thickness of the aluminum oxide surface layer in the modelling process produces much greater uncertainties than the 90 % confidence limits. We can approximate the change in n and k by estimating that the difference that we obtain by changing the thickness of the aluminium oxide layer in the modelling by 1 nm is roughly 1.25×10^-4×λ [nm] for n and 3.5×10^-4×λ [nm] for k. Nevertheless, if we assume that the thickness of the oxide layer is constant for all of our

aluminium films, since the measurements were made on freshly prepared samples of the same age, the thickness dependence remains similar, even though the values for the refractive indexes and extinction coefficients change.

 

Fig. 6. 90 % confidence limits of refractive indexes (a) and extinction coefficients (b) for 30-nm-thick electron-beam-gun-evaporated iridium and for 163-nm-thick electron-beamgun- evaporated aluminum films.

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4. Conclusions

In this paper we have shown how the refractive indexes and the extinction coefficients of aluminium and iridium films depend on the thicknesses of the films. We have also shown how those properties depend on the deposition technique as well. It is probable that the same dependencies also apply to other metallic thin films.

These results indicate that in order to predict the optical behavior of thin metallic films, it is not necessarily advisable to use values published in the literature since they could have been measured on different thickness films prepared using different techniques from the studied materials. For example, if we calculate the transmittance of a 30-nm-thick evaporated iridium layer at a wavelength of 633 nm using the literature values and the values measured in this paper, the results differ by approximately 20 %. In the case of metallic nano- and microstructures, the optical values of the metal doubtless differ even from the values of a thin film with the same thickness.