|
Optical measurements provide a useful tool for indirect measurements of various parameters (thicknesses, refractive indices) of thin films. Parameters are established by fitting the performance of the thin film model to the measured values. There are several methods used for this purpose, e.g. spectrophotometric and ellipsometric measurements in various arrangements. To get sufficiently precise values of the parameters we need sufficient amount of information. More information can be acquired by varying the experimental setup, e.g. wavelengths of the incident light or angles of incidence, we can perform measurements in immersion liquids, on various substrates or in series of specially prepared samples. Many such methods have been already reported in literature but the choice of the proper method for the specific problem is done rather intuitively until now. The common feature of all these methods is a need for numerical processing of the data. Fitting is done usually by the least squares method, minimizing a merit function. This approach enables also the statistical error analysis. The precision of the computed parameters is estimated from the measurement errors. What is important is that provided we know parameters of the system and accuracy of the measurement, we can compute the resulting precision of parameters in advance. In conclusion suppose we can reasonably estimate the thicknesses and refractive indices of the layers and measurement errors before the measurement, we can test various experimental setups for the best resulting precision of parameters with minimum effort. This idea has already ben formulated e.g. for the special case of ellipsometrical analysis in . In this paper I would like to document its usefulness and power in a more general context.
|
