The goal of this work is to describe a simulatively designed scatterometry approach for the in-line characterization of
sub-wavelength sinusoidal gratings, which are formed on a transparent foil in a roll-to-roll procedure. The challenge is to
acquire the 3D information of the workpiece, i.e., to measure the grating height in addition to the grating period with nm
precision. The grating period is obtained straightforward from the position of the first order diffraction maxima in the
reflection and the transmission region. For determining the grating height, the inverse problem is solved, i.e., the relation
between the scattered intensities of the diffraction maxima and the grating height is extracted from light scattering
simulations. The measurement uncertainty is evaluated for different instrumentation and simulation parameters, such as
the detection and incidence angle, the laser wavelength as well as the input parameters of the simulation. As a result, the
measurement uncertainty for the grating period and the height is estimated to 0.3 nm and ≤8 nm, respectively, when
using laser light in the visible wavelength range. Large area scanning measurements performed offline using the setup
parameters derived from simulations verify the sensitivity of the presented measurement approach for identifying local
variations of the spatial surface properties. Depending on the chosen detection system, sampling rates up to the MHz
range are feasible meeting the requirements of in-line process control of the roll-to-roll production procedure.
This paper deals with an efficient computation method for scattered light intensity distributions, which occur, if a nanostructured surface is illuminated with a monochromatic laser beam of several millimeters in diameter. The minimization of the computational amount is an essential precondition in connection with the development of powerful design tools for laser optical surface measuring methods, which derive structure characterizing attributes from structure dependent scattering effects.
The presented approach differs from concepts based on near-field solutions of the Maxwell equations (finite element methods (FEM), finite difference time domain methods (FDTD)) or approximation methods for the near-field (Discrete Dipole Approximation (DDA), Generalized Multipole Technique (GMT)) as the near-field is not computed. Instead, an electrically equivalent model based on pre-computed radiation sources like Huygens point sources, dipoles, quadrupoles, etc. is used, which for standard geometrical nanostructures (cylindrical holes, spheres and ellipsoids) leads to the same far-field distributions as the conventional methods. In order to simulate the scattered light by an arbitrary surface it is divided into subwavelength geometries, which can be substituted by electrically equivalent dipole radiation sources. The far-field is calculated with a numerical scalar method. The computational effort is much smaller compared to algorithms based on the solution of Maxwell's equations.
This paper presents a simulation approach for light scattering from surfaces containing spherical and elliptical nanoparticles. For this approach an electrically equivalent macro model is derived based on the analytical solutions of Maxwell's equations (e.g. Mie's solution of a sphere). These macro models do not necessarily fulfill the boundary conditions or give the correct near-field but they provide a suitable far-field solution. The benefit of this approach is an abstract model for the far-field computation that is much more efficient than known solutions like FEM. The radiation sources at the surface are reduced to a maximum like a single source for a whole particle, which gives the correct far-field but does not fulfill the boundary conditions. For the set of radiation sources used for the macro models the approach presented here reverts to the accurate computation of simple geometries. In this special case of spherical and elliptical particles the solution of the Mie theory can be used. In this paper it is shown that in the case of nanostructures the far-field of a sphere and an ellipse can be replaced by the radiation field from a set of dipoles. Based on these results it is possible to approximate an equivalent macro model of the surface containing spherical and elliptical elements. The presented macro model provides a very reasonable simulation approach with acceptable simulation times for large surface areas of several square millimeters.