Optical Depth Profiling of Thin Films by Impulse Mirage Effect Spectroscopy. Part I: Theory

Abstract

Impulse mirage effect/photothermal deflection spectrometry may be used to detect depth-dependent optical absorption in materials, through the time dependence of the probe beam deflection signal occurring in response to sample irradiation with a short excitation pulse. In this work a theoretical expression was derived for the normal and transverse photothermal deflection signals which occur in a sample with homogeneous thermal properties but where optical absorptivity varies with depth from the surface. An analytical solution of moderate simplicity is obtained for several cases of experimental interest, with three-dimensional heat conduction effects included. The depth profile resolution obtained with the mirage effect method is critically dependent on the distance between the sample layer probed and the offset position of the probe beam in the fluid layer above the sample. Saturation conditions and conditions for obtaining optimal depth resolution of continuous and discrete optical profiles are examined in detail.