DISCUSSION Sample reflectivity results are shown for various wavelengths as a function of the angle of incidence on the dielectric-metal interface, for the two types of film thicknesses (50 nm and 20 nm). The modeling procedure would involve getting the dielectric function from ellipsometry and getting roughness estimates from ellipsometric model and from measurements using the phase-shifting interferometer setup. Only p-polarization data is presented in detail as the s-polarization data does not reveal any absorption or reflection features. To illustrate the point, one sample s-polarization curve is shown that exhibits a fairly featureless reflectivity curves (nearly monotonic) as predicted by a simple application of Fresnel’s equations (see figure 2). In other words, no plasmon solution is expected for the s-polarization, and no corresponding feature is ever seen in the s-polarization data. As clear from the figures, the theoretical model does a reasonably good job of explaining the data. While figure 2 shows the reflectivity for the 20 nm film with its high reflectance, figure 3 show the results of p-polarization reflectivity for the 50 nm Nichrome film with the SPR feature (now absorption) present prominently in at an angle of about 41.5o. Theoretical calculations for the plasmon angle with the appropriate choice of the dielectric functions result in an angle of 41.9o [3]. While this is close to the observed value, the difference is not insignificant. It is hoped that a more detailed investigation into the nature of the roughness and the dielectric function will result in better agreement. It should also be noted that Nickel does not show any such feature for the p-polarization geometry for the corresponding 50 nm single metal films. The theroetical model in general, predicts a slightly higher reflectivity but that is mostly due to losses on the slightly inferior surface of the BK7 prism (as opposed to the fused silica prisms). On the other hand the case for chromium is more complicated. While it shows no corresponding features for the shorter wavelength (633 nm) used in the experiment, a weak absorption feature is present for the 1550 nm excitation wavelength. Attempts to meodel this feature using the dielectric fnction for bulk chromium or companion layers has, to date, not met with success. It is strongly suspected that this complication is a result of a thin oxide layer that may be present on the metal surface. Given that this is a native oxide, attempts to etch it and then do the experiment are not likely to succeed, unless the experiment is carried out in an environment that can inhibit regrowth of the oxide layer. Presently we are trying to systematically study this layer and incorporate its optical properties into the model, and hope to deal with the case of chromium in detail in aletr publication. It is worth noting that the 20 nm film shows fundamentally different behavior for the case of 633 nm excitation wavelength. The primary absorption feature is now replaced by a strong reflection peak. In order to model this data, Nichrome dielectric function values for 633 nm are obtained from the ellipsometric measurements. The starting thickness is assumed to be 50 nm but once reasonable agreement is found between experimental data and the corresponding model, thickness is allowed to vary by a small amount and surface roughness is built into the model. The real and imaginary parts of the dielectric function are 2.06 and 25.98, respectively. Typically, for the surface plasmon to be excited the real part of the dielectric function for the metal should be negative. Moreover, for metals like silver and gold that show very large SPR response with reflectivity varying over 98% in the neighborhood of the plasmon angle (compared to ~18% for Nichrome), the imaginary part of the dielectric function is very small. That is also not the case for Nichrome. The relatively large imaginary part of the dielectric function is easier to interpret than the positive real part. The large imaginary part of the dielectric function implies strong damping of the plasmon and that is evident from the relatively shallow absorption feature associated with the plasmon absorption in Nichrome. The positive real part is more difficult to explain. Another complication is the nature of roughness. The interferometer results suggest a roughness that is on the order of the thickness of the thinner of the two sets of films. This really suggests that the surface profile for both types of films may be fairly corrugated and the model should really be refined to make the interface more of a textured surface with some kind of an effective medium approximation. This would also modify our present approach as regards to the dielectric function of the two nichrome layers (50 nm and 20 nm). Presently, the companion layer analysis suggests that the same dielectric function is used for both layers. However, if an effective medium approximation is to be used then clearly, the 20 nm layer incorporates greater void fraction than the 50 nm layer. Indeed, it is surprising that the present model explains the results, as well as it does for all the wavelengths examined. 225
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