On the size and frequency dependences of the parameters of the Drude model for ultrathin metal films

The formula proposed here for calculating the transmission coefficient of nanometer-thick metal films in the infrared range is based on the model of a gas of free charge carriers in the Drude approximation for the dielectric function with parameters depending on the film thickness and frequency. The results of calculations are compared with experimental data on the transmittance of Pb films with a thickness of 0–5 nm in the frequency range 1000–4000 cm$^{-1}$. It is found that the effective mass of charge carriers in the nanometer film noticeably differs from its value in the bulk metal; the frequency dependences of the relaxation rate and plasma frequency are detected.