On the Steady-State Temperature Rise During Laser Heating of Multilayer Thin Films in Optical Pump–Probe Techniques

Abstract

In this study, we calculate the steady-state temperature rise that results from laser heating of multilayer thin films using the heat diffusion equation. For time- and frequency-domain thermoreflectance (TDTR and FDTR) that rely on modulated laser sources, we decouple the modulated and steady-state temperature profiles to understand the conditions needed to achieve a single temperature approximation throughout the experimental volume, allowing for the estimation of spatially invariant thermal parameters within this volume. We consider low thermal conductivity materials, including amorphous silicon dioxide (a-SiO2), polymers, and disordered C60, to demonstrate that often-used analytical expressions fail to capture this temperature rise under realistic experimental conditions, such as when a thin-film metal transducer is used or when pump and probe spot sizes are significantly different. To validate these findings and demonstrate a practical approach to simultaneously calculate the steady-state temperature and extract thermal parameters in TDTR, we present an iterative algorithm for obtaining the steady-state temperature rise and measure the thermal conductivity and thermal boundary conductance of a-SiO2 with a 65-nm gold thin film transducer. Furthermore, we discuss methods of heat dissipation to include the use of conductive substrates as well as the use of bidirectional heat flow geometries. Finally, we quantify the influence of the optical penetration depth (OPD) on the steady-state temperature rise to reveal that only when the OPD approaches the characteristic length of the temperature decay does it alter the temperature profile relative to the surface heating condition.