Verification of the Anomalous-Skin-Effect Theory for Silver in the Infrared

Abstract

The measured infrared reflectance of silver films prepared by rapid evaporation in ultrahigh vacuum was found to be in excellent agreement (0.1%) with values predicted by the anomalous skin effect theory in the wavelength region from 4-24 \ensuremath{\mu} (values of $\ensuremath{\omega}\ensuremath{\tau}$ between 15 and 2, where $\ensuremath{\tau}$ is the relaxation time). If a small correction term was included for electron-electron collisions, the agreement could be extended to 1 \ensuremath{\mu} ($\ensuremath{\omega}\ensuremath{\tau}\ensuremath{\simeq}50$). The theoretical curves were determined from values of dc conductivity and Hall constant measured on silver films prepared in the same evaporation as the optical samples. No optical data were used to fit the calculated curves to the experimental data. Silver films of varying degrees of roughness were prepared by evaporating silver onto supersmooth fused-quartz optical flats which had been roughened with calcium fluoride films. It was found that there was no difference between the infrared reflectance of rough and smooth silver samples for roughnesses up to 45 \AA{} rms. Thus $p\ensuremath{\simeq}1$, a condition usually interpreted as specular reflection of the conduction electrons, for surfaces about an order of magnitude rougher than the value predicted by simple diffraction theory. For rougher surfaces, $p$ dropped rapidly to 0 and, for the roughest surfaces studied (\ensuremath{\sim}100 \AA{} rms), the reflectance was somewhat lower than that predicted theoretically.