Semi-Empirical Plasmon Coefficients of Metals for Nanoplasmonics

The paper considers a program for determining the plasmonic parameters of some metals using the least squares method based on experimental data. Analytical expressions are obtained for the real part of the dielectric function as a function of the wavelength of the incident light. It is found that in all metals at a wavelength of the incident light   0.7 m, nanoplasmons can be formed. The dependence of the dielectric constants of Au, Ag, Cu, Al, Ni, Pt, Zn, and Ti nanoparticles, which are used for solar energy today, on the wavelength is studied. Also, the wavelengths that create the nanoplasmonics effect are determined. It is found that the plasmonic wavelength for gold, silver and platinum nanoparticles is equal to 142.9 nm, 79.1 nm, and 163.9 nm, respectively. Among metal nanoparticles, Al has the shortest plasmon wavelength and Pt has the longest wavelength. Metal nanoparticles are introduced into silicon-based solar cells mainly to modify photons in the infrared spectrum to photons in the visible range, because silicon mainly absorbs photons in the visible range but cannot absorb photons in the infrared range. In order for a metal nanoparticle to convert infrared photons into visible photons, the plasmon wavelength must be larger. Therefore, Pt nanoparticle is considered to have the best plasmon coefficient for input into silicon solar cells. The real part of the dielectric constant is spread over the Taylor series and the unknown coefficients are determined by the least squares method. One of the main parameters is the wavelength-independent part of the dielectric coefficient. It is equal to 8.76, 14.154, 26.95, 4.830, 0.189, 6.72, and 3.688 for Au, Ag, Cu, Al, Ni, Pt, Zn, and Ti, respectively. Therefore, it is found that Pt has the smallest dielectric coefficient and Al has the largest. The smallest error in the calculation according to the least squares method occurs in Pt and the largest error occurs in Al.