Extrapolating the actual quantities based on findings: a case for mathematicians

If the guilt of the accused cannot be proven directly, then evidence can help. Experts of accurate measurement also must similarly proceed indirectly more and more often: If it is not possible to measure a measurand directly, then other quantities must be measured and the actual quantity of interest extrapolated with the aid of intelligent computer programmes. Scientists of the Physikalisch-Technische Bundesanstalt (PTB) are proceeding in this same manner, together with partners in a joint project of the Bundesforschungsministerium (BMBF - Federal Ministry of Research). The matter involved is the measurement of increasingly smaller computer components and other industrial structures which are only nanometer-sized and thus can no longer be examined with the classic light-microscopic method. A new method for examining such structures is by using scatterometry. Light is scattered thereby at periodic nanostructures and the dimensions of the specimen are extrapolated from the characteristics of the scattered light. The project partners have now developed a mathematical model and a so-called inverse method which enable such measurements to be carried out with great accuracy.