Forward Diffraction Modelling: Analysis and Application to Grating Reconstruction

The semiconductor industry uses lithography machines for manufacturing complex integrated circuits (also called ICs) onto wafers. Because an IC is built up layer by layer it is very important to align the wafer each time it enters the machine. Today, gratings are used for this alignment step. Gratings are tiny periodic structures printed on a wafer and are even smaller than ICs. These gratings are illuminated with a laser and by measuring the scattered field one can get information on the position of a wafer. In a similar way gratings can also be used for various other lithographic metrology tasks such as overlay metrology and CD metrology which give additional information on the production process. All in all it becomes increasingly more important to develop and use a rigorous mathematical model that solves optical diffraction problems for periodic gratings.