CHAPTER 2. DESIGN AND SIMULATION OF WAVEGUIDE
2.2.3. The thickness of metal layer
Surface Plasmon Polariton only exists on the interface of a metal medium and a dielectric medium. The metal medium has complex dielectric permittivity with negative real part.
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Table 2.1 Parameters used for simulating SPP mode
Symbol Value Definition
1.55 àm Wavelength in vacuum
l 10 àm Length of waveguide
h 1 àm Height of waveguide
nSi 3.4757 Refractive index of silicon
nSiO2 1.4957 Refractive index of silicon dioxide layer nAg 0.15649 11.567i Complex refractive index of Silver
nAu 0.23823 11.263i Complex refractive index of Gold
nm 60 Number of elements per wavelength
ns 9 Number of elements sweep
54.7o Sidewall angle
t (10:10:200) nm Thickness of metal layer
The dielectric function of metal is described by Drude model [20]. In this model, valence electrons are assumed to be completely detached from their ions, move freely in the lattice to form free electron gas. This is entirely correct in metals that have high electron mobility such as alkali metals, transition metals and highly doped semiconductors. In this study, we used two metals: gold and silver, which are common in plasmonic technology to simulate. The metal layer can be deposited onto triangular silicon waveguide by sputtering technique. The thickness of metal can be controlled accurately to several nanometers. To ensure that the thickness of
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metal film is the same throughout the structure, the wedge of metal is fillet with a ed radius equal to the thickness of metal layer.
Table 2.1 presents optical parameters and structural parameters us for this ed simulation. The thickness is studied in each step of 10 nm in the range from 10 to 200 nm.
Figure 2.4 Distribution of normalized electric field on the cross-section of waveguide at various thickness of silver and gold layer: (a) for Ag with the es thicknesses of 10 nm and 200nm and (b) for Au with the thicknesses of 10 nm
and 200nm.
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Figure 2.4 (a) shows the distributions of electric field that are normalized with respect to maximum value. For both metal, the maximum electric field values are almost the same. When the thickness of metal layer increases, the maximum electric field values also increase. The electric field distributes in air medium, and concentrates mainly on the area round the wedge of waveguide. This electric field reaches the maximum value at metal surface and decline rapidly when it is always from the surface. Figure 2.4 (b) describes more clearly about the sharp decline of
shown in Fig. 2.1). The field falls off expo the intersection of these curves with 1/e line giving a quantity estimation of the
confinement of electromagnetic energy. As seen in Fig. 2.4 (b), the mode size is almost constant for two metals. In the case of very thin metal layer (10nm), the field fall off to 1/e at a distance of only a few tens of nanometers. Otherwise, s in the case of thick metal film (200nm), the mode size increases to about 400 nm. Thus, the confinement of waveguide mode does not depend on the nature of metal, but depends strongly on the thickness of metal layer.
Transmission characteristics of the waveguide at various metal thicknesses are shown in Fig. 2.5. Here, we evaluate three feature parameters being effective mode index neff (the ratio of wave number of WPP mode and wave number in vacuum), propagation length (the distance at which the field intensity decreases e time) and mode area (area bounded by a curve where electric field falls off to 1/e) (Figs. 2. 5 (a)-(c)). Figure 2.5 (d) shows the shape of mode area (the red area at the wedge of waveguide). When the metal thickness increases, the effective mode index decreases and the propagation length increases. Both these quantities tend asymptotically to a value corresponding to the infinite thickness. The mode area of gold and silver are almost the same and increases strongly with the thickness. With the same structural parameters, the attenuation using gold is stronger than using silver about two times, while other characteristics are almost the same. So, we choose silver as a metal medium for the later study.
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Figure 2.5 Transmission characteristics of WPP mode at various thicknesses of metal (a-c) and the shape of mode area (d).
As seen in Fig. 2.5 (b), at the thickness t = 20 nm, the propagation length has a minimum value. That means that at 20 nm thickness, the attenuation of wave is maximized. To clarify this phenomenon, we plot the distribution of electric field while the saturation value of color range was reduced by 5 times (Fig. 2.6). We can observe that the field not only concentrates on the metal wedge, but also distributes inside the silicon waveguide. The shape of distribution inside the silicon waveguide is the same for both the case of silver and gold, which might be the shape of a high order mode in the triangular silicon waveguide. When the metal thickness changes, the wavenumber of WPP mode and high order mode also vary but with different rate. At 20 nm thick, the wavenumber of two modes is equal and the coupling of two modes is strongest. This coupling phenomena causes a rapid increase in the loss of WPP mode. Increasing the thickness of metal layer, the coupling decreases. The reason can be considered as the wavenumbers to become different, but the main
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reason that the field falls off quickly in metal. At the thickness more than 150nm, the coupling is negligible.
Figure 2.6 Distribution of electric field of WPP mode at 20nm thickness of Silver metal (top row) and Gold (bottom row) .