An improved dispersion law of thin metal film and application to the study of surface plasmon resonance phenomenon

The dispersion law of metal film based on the Drude׳s free-electron theory is improved by employing the Fuchs–Sondheimer theory. In the new law, the thickness and surface roughness are taken into account to describe theoretically the dispersion of thin metal films. Then the improved model is used to analyze the surface plasmon resonance (SPR) of gold films. The results indicate that the thickness and surface roughness of gold film affect the resonance properties significantly. Specifically, when the film thickness is getting close to the electron mean-free-path (MFP), there is no obvious SPR phenomenon. In addition, the surface roughness of metal film can change the resonance angle of SPR. When the surface becomes smooth, resonance angle of SPR will decrease. It means that, for a certain metal the effects of film thickness and surface roughness should be considered in SPR technique.