Thermal conductivity of thin film-substrate systems from two-side scanning photothermal deflection measurements: Theoretical model and validation

Abstract

Photothermal deflection (PTD) has been frequently utilized to measure the thermal properties of thin solid films on a substrate. In the models commonly used to interpret PTD data, the substrate is assumed to be an ideal thermal insulator. This assumption poses important restrictions on the reliability of these thermal measurements and limits the possibility to use PTD for also measuring the specific heat of the samples. Simultaneous knowledge of specific heat and thermal diffusivity is necessary to determine the thermal conductivity of thin solid films. In this work, we calculated the phase and amplitude of the PTD signal at the two opposites sides (film-side and substrate-side) of a thin-film substrate system. We find that, on both sides, the phases of the PTD signal primarily depend on the thermal diffusivity of the thin film, while the amplitudes primarily depend on the specific heat. By using the phases and amplitudes at the two sides, we show that the accuracy of thermal conductivity measurements by PTD can be dramatically improved. We validate our theoretical model by measuring, in a scanning PTD apparatus, the thermal properties of gold thin films, which are in excellent agreement with, and improve on, existing data from the literature.