Scatterometry—fast and robust measurements of nano-textured surfaces

Scatterometry is a fast, precise and low cost way to determine the mean pitch and dimensional parameters of periodic structures with lateral resolution of a few nanometer. It is robust enough for in-line process control and precise and accurate enough for metrology measurements. Furthermore, scatterometry is a non-destructive technique capable of measuring buried structures, for example a grating covered by a thick oxide layer. As scatterometry is a non-imaging technique, mathematical modeling is needed to retrieve structural parameters that describe a surface. In this review, the three main steps of scatterometry are discussed: the data acquisition, the simulation of diffraction efficiencies and the comparison of data and simulations. First, the intensity of the diffracted light is measured with a scatterometer as a function of incoming angle, diffraction angle and/or wavelength. We discuss the evolution of the scatterometers from the earliest angular scatterometers to the new imaging scatterometers. The basic principle of measuring diffraction efficiencies in scatterometry has remained the same since the beginning, but the instrumental improvements have made scatterometry a state-of-the-art solution for fast and accurate measurements of nano-textured surfaces. The improvements include extending the wavelength range from the visible to the extreme ultra-violet range, development of Fourier optics to measure all diffraction orders simultaneously, and an imaging scatterometer to measure area of interests smaller than the spot size. Secondly, computer simulations of the diffraction efficiencies are discussed with emphasis on the rigorous coupled-wave analysis (RCWA) method. RCWA has, since the mid-1990s, been the preferred method for grating simulations due to the speed of the algorithms. In the beginning the RCWA method suffered from a very slow convergence rate, and we discuss the historical improvements to overcome this challenge, e.g. by the introduction of Li's factorization rules and the introduction of the normal vector method. The third step is the comparison, where the simulated diffraction efficiencies are compared to the experimental data using an inverse modeling approach. We discuss both a direct optimization scheme using a differential evolution algorithm and a library search strategy where diffraction efficiences of expected structures are collected in a database. For metrology measurements two methods are described for estimating the uncertainty of the fitting parameters. The first method is based on estimating the confidence limits using constant chi square boundaries, which can easily be computed when using the library search strategy. The other method is based on calculating the covariances of all the free parameters using a least square optimization. Scatterometry is already utilized in the semiconductor industry for in-line characterization. However, it also has a large potential for other industrial sectors, including sectors making use of injection molding or roll-2-roll fabrication. Using the library search strategy, the comparison can be performed in ms, making in-line characterization possible and we demonstrate that scatterometry can be used for quality control of injection molded nano-textured plastic samples. With the emerging methods of highly parallel manufacturing of nano-textured devices, scatterometry has great potential to deliver a characterization method for in-line quality control and metrology measurements, which is not possible with conventional characterization techniques. However, there are some open challenges for the scatterometry techniques. These include corrections for measuring on non-ideal samples with a large surface roughness or line-edge roughness and the path towards performing traceable scatterometry measurements.