Toolbox for modeling frequency-domain photothermal experiments on multilayers

Abstract

A general expression (master equation, ME) is derived for the thermal impedance in photothermal experiments in a multilayer system, based on one-dimensional (1D) periodic heat diffusion. The ME in a compact form benefits from newly defined generalized, higher-order thermal reflection and transmission coefficients. The modeled system comprises seven layers among which a semitransparent sample and a transducer that integrates the temperature field within it (e.g., a pyroelectric sensor). The ME can be adapted to various experimental cell structures used in photopyroelectric, photoacoustic, photothermal radiometry, or thermoreflectance methods using volume- or surface-temperature detection, in view of spectroscopic applications or thermophysical properties determination. The derivation of special cases is facilitated by applying simple contraction rules to dimensionless quantities. Modeling multiple heat sources in the system is done by superposition of individual solutions. The possible extension of the 1D model to 2D geometry is demonstrated, in general, and practical criteria are discussed.