Novel scheme for the ultraprecise and fast measurement of the nanotopography of large wafers

The measurement of the topography or the nanotopography of large wafers up to 450 mm in diameter with satisfactory lateral resolution and nanometer uncertainty is still an unsolved problem. The topography of wafers covers a relatively large measurement range as wafers have surfaces with a so-called "slightly unflat" topography which mostly exceeds the measurement capabilities of interferometers. For the ultraprecise and traceable measurement of the slope and topography of slightly unflat optical surfaces, a novel scanning deflectometry principle has been developed. An uncertainty of the topography in the nanometer range will be achieved, as this principle minimizes error influences and allows a highly precise calibration of the angle measuring device. The main goal is to use this principle for the ultraprecise measurement of the nanotopography of large wafers. The measurement principle is based on the analysis of differences of reflection angles obtained at surface points which are separated by large lateral shears. It does not rely on external reference surfaces of matched topography and in first and second order is independent of any stage errors and the whole-body motion of the specimen. The measurands are directly traced back to the base units of angle and length. The specific idea of wafer measurement is to combine rotational and linear scanning with the measurement of slope difference vectors and to arrive at an unambiguous solution for the topography and nanotopography. The equations with the slope difference vectors are solved to reconstruct the slope vectors, as newly developed mathematical algorithms allow the surface slope to be reconstructed from slope differences for two different shears. This is reached by applying natural extensions and shearing transfer functions by a mathematically exact method over the whole surface area. Further the differential equations for the slope vectors are solved to unambiguously reconstruct the topography. With this method it is possible to achieve nanometer uncertainty and at the same time a high lateral resolution, short measurement times and the possibility of mastering the large measurement range necessary for slightly unflat wafer surfaces.