Upper limit to the thermal penetration depth during modulated heating of multilayer thin films with pulsed and continuous wave lasers: A numerical study

In this study, we present a method to calculate the temperature and heat flux profiles as a function of depth and radius for bulk, homogeneous materials and samples with layered thin-film structures, including geometries supporting bidirectional heat fluxes, during pulsed and continuous wave (CW) laser heating. We calculate the temperature profiles for both modulated and unmodulated heating events to reveal that the thermal penetration depth (defined as the depth at which temperature decays to 1/e of the surface temperature) for a pulsed laser is highly dependent on time and repetition rate. In the high repetition rate limit, the temperature profile relaxes to that of a CW source profile, while in the opposite extreme, a single pulse response is observed such that the concept of the thermal penetration depth loses any practical meaning. For modulated heating events such as those used in time-and frequency-domain thermoreflectance, we show that there is a limit to the thermal penetration depth obtainable in an experiment, such that simple analytical expressions commonly used to determine thermal penetration depth break down. This effect is further compounded in samples with multiple layers, including the case when a similar to 100 nm metallic transducer is deposited onto a bulk substrate, revealing that many recent studies relying on this estimation significantly over-predict the thermal penetration depth. Considering a bidirectional heat flow geometry (e.g., substrate/metal film/liquid), we find that heating from an unmodulated source results in an asymmetric heat flux about the plane of laser absorption to preserve a symmetric temperature profile when interfacial thermal resistance is negligible. However, the modulated case reveals a temperature asymmetry such that the thermal penetration depths in each side fall in line with those resulting from an insulated boundary condition. Published by AIP Publishing.