Gratings studied with SESANS

In the figure we show SESANS measurements on a silicon line-grating with a period of 12 mm, a ridge height of 40 mm and a ridge width of 4 mm. For the measurement of such a one-dimensional structure we expect the autocorrelation function of the density profile of the grating. This is the auto-convolution of a rectangular grid, which results in a triangular grid with the same period and with a base-width that is twice the width of the rectangular ridges. This is indeed in rather good agreement with the measured polarisation curve.  However, the edges in the measurements are seen to be rounded, but assuming a trapezoidal shaped density profile provides an excellent description of the data. The dashed curve is a (mis)fit with a rectangular shaped ridge. The drawn curve is a fit where the density profile has sloped edges on the ridges. Inserted in the graph are the density profiles of the ridges according to the two models. In electron microscopic pictures of the grating effects of etching erosion are seen that give rise to a significant slope in the density profile.

 Analysis of artificial silicon microstructures by ultra-small-angle and spin-echo small-angle neutron scattering, M. Trinker, E. Jericha, W.G. Bouwman, R. Loidl, H. Rauch, Nuclear Instruments and Methods in Physics Research A 579 1081–1089 (2007),