Modeling for thermal conductivity measurements of thin films using photothermal deflection with obliquely crossed configuration

A three-dimensional theoretical model has been developed to calculate the normal probe-beam deflection of obliquely crossed photothermal deflection configuration in samples including thin films and substrates, which is applied to thermal conductivity measurements of thin films deposited on the substrates. From the dependence of the normal component of probe beam deflection on the cross-point position of the excitation and probe beams, the thermal conductivity of the thin film can be extracted from the ratio of the two maximum normal deflection amplitudes, which occur when the cross-point is located near the two surfaces of the sample. The effects of other parameters, including the intersect angle between the excitation and probe beams in the sample, the modulation frequency of the excitation beam, the thickness and absorption of the thin films, the thermal properties of substrates, on the measurement of the thin-film thermal conductivity are discussed. The obliquely crossed photothermal deflection technique seems to be well suited for thermal conductivity measurements of thin films with high thermal conductivity, such as diamond or diamond-like carbon films deposited on substrates with relatively low thermal conductivity, at relatively low modulation frequency.