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Inverse problem theory in the optical depth profilometry of thin films

2002; American Institute of Physics; Volume: 73; Issue: 12 Linguagem: Inglês

10.1063/1.1517054

1527-2400

J. F. Power,

Optical measurement and interference techniques

The problem of nondestructive measurement of composition with depth on the scale of ∼0.1–500 μm, in polymers and related materials, has many applications in traditional and recent areas of thin film processing. This article reviews the optical depth profilometry techniques operating on this scale based on optical absorption, photoluminescence, elastic, and inelastic scattering. These methods include photoacoustic and photothermal imaging (including pulsed laser opto–acoustic profiling), attenuated total reflectance infrared, integrated optical spectroscopy methods (based on excitation of planar waveguide structures), confocal scanning microscopy, and the recent technique of light profile microscopy. The profiling of planar structures is emphasized. A common element of all of these methods is that depth mapping requires the solution of a linear inverse problem, where a map of the sample properties is mathematically reconstructed from a set of experimental measurements. This problem is to some extent ill conditioned in some or all regimes of measurement, with the result that depth maps may show sensitivity to data errors. A method is presented for assessing performance of the above experimental depth profilometry techniques in terms of ill conditioning as indicated by: spatial resolution, sensitivity to data errors, and apparent multiplicity of solutions. This method is applied a priori given a knowledge of the linear response theory and measurement parameters Application is made to individual profiling techniques, the performance of each in applications is reviewed, and an inter-comparison is made based on the conditioning of the inverse problem.