Abstract

The thermal transport properties of compositionally modulated materials are currently of interest. These materials are deposited as thin films onto substrates, thereby complicating conventional thermal transport measurements. For thin metallic films, transient thermoreflectance (TTR) is a technique which permits transport measurements perpendicular to the film plane and independent of the substrate.^1’2 A transient thermoreflectance measurement is initiated with the absorption of a short optical heating pulse by the metal electrons. The electrons rapidly thermalize with the metal lattice and diffuse distances on the order of $\ell \approx \sqrt{kt}$ where k is the thermal diffusivity and t is the time after the arrival of the heating pulse. This ultra-fast heating and diffusion produces a change in reflectivity which is linearly proportional to the temperature for small deviations (~ 10 K). This change in reflectivity is measured with a weaker laser pulse which is delayed with respect to the heating pulse. For a typical metal, k ≈ 1.5 × 10⁻⁵ m²/sec, and after 200 psec the surface heat has diffused a distance of only ℓ ≈ 55 nm. The penetration depth of visible light in a metal is approximately 20 nm, and for film thicknesses of approximately 100 nm or greater, the TTR measurement can be completed before substrate effects become important. Since the optical heating pulse is focussed to a diameter of ~ 20 μm, on the surface and only heats to a depth of ~ 20 nm, the rather large aspect ratio of the heated volume permits a one dimensional treatment of the heat flow for times corresponding to diffusion out of the optical skin depth.

© 1986 Optical Society of America