The size of photonic components is fundamentally limited by diffraction and it is a great challenge to design sub-wavelength devices using only dielectric materials. On the other hand, at optical frequencies, noble metals demonstrate a highly negative dielectric constant and the penetration depth of the electromagnetic field into them does not exceed a few tens of nanometers. Furthermore, plasmonic modes can be excited at metal-dielectric interfaces, which allows to break down the conventional diffraction limit. However, reducing the mode size in the metal structure, one increases the portion of the electromagnetic field in the metal, which results in high ohmic losses and consequently low quality factors and short propagation lengths. This process is governed by the imaginary part of the dielectric function, which can be represented through the Drude damping rate Γ given by the sum of three different processes: electron-phonon scattering, electron-electron scattering and electron scattering on structural defects. Gold and silver are known to have small Γ, but, being inert metals, they are hardly compatible with conventional microelectronic fabrication techniques, such as CMOS processes.
Here we present low loss polycrystalline copper films and a theoretical model, which brings together their optical, electrical and structural properties. Thin Cu layers were deposited on the silicon substrate by an electron-beam evaporator and their optical properties were obtained with a spectroscopic ellipsometer. At the same time, we used an atomic force microscope and a four-point probe system to measure structural and electrical properties, respectively. Fig. 1 shows that the imaginary part of the dielectric function of Cu is as low as 1.5 for thick films at λ=800 nm, which is in a good agreement with the theory. Moreover, the theory predicts that absorption losses can be further reduced by controlling the structural parameters of copper films.
Figure 1. (a) Imaginary part of the dielectric function of Cu measured by ellipsometry and calculated theoretically. (b-c) AFM images of 30 nm (b) and 170 nm (c) thick copper films.
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