Filters

2011 - 20182

More filters

20192
Reset filters

Settings

End date: 2019 × Start date: 2010 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: time-harmonic Maxwell’s equation × WGL Institute: WIAS ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Fast scatterometric measurement of periodic surface structures plasma-etching processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Klesse, Wolfgang Matthias; Rathsfeld, Andreas; Groß, Claudine; Malguth, Enno; Skibitzki, Oliver; Zealouk, Lahbib
    To satisfy the continuous demand of ever smaller feature sizes, plasma etching technologies in microelectronics processing enable the fabrication of device structures with dimensions in the nanometer range. In a typical plasma etching system a plasma phase of a selected etching gas is activated, thereby generating highly energetic and reactive gas species which ultimately etch the substrate surface. Such dry etching processes are highly complex and require careful adjustment of many process parameters to meet the high technology requirements on the structure geometry. In this context, real-time access of the structures dimensions during the actual plasma process would be of great benefit by providing full dimension control and film integrity in real-time. In this paper, we evaluate the feasibility of reconstructing the etched dimensions with nanometer precision from reflectivity spectra of the etched surface, which are measured in real-time throughout the entire etch process. We develop and test a novel and fast reconstruction algorithm, using experimental reflection spectra taken about every second during the etch process of a periodic 2D model structure etched into a silicon substrate. Unfortunately, the numerical simulation of the reflectivity by Maxwell solvers is time consuming since it requires separate time-harmonic computations for each wavelength of the spectrum. To reduce the computing time, we propose that a library of spectra should be generated before the etching process. Each spectrum should correspond to a vector of geometry parameters s.t. the vector components scan the possible range of parameter values for the geometrical dimensions. We demonstrate that by replacing the numerically simulated spectra in the reconstruction algorithm by spectra interpolated from the library, it is possible to compute the geometry parameters in times less than a second. Finally, to also reduce memory size and computing time for the library, we reduce the scanning of the parameter values to a sparse grid.
  • Thumbnail Image
    Item
    Shape derivatives for the scattering by biperiodic gratings
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Rathsfeld, Andreas
    Usually, the light diffraction by biperiodic grating structures is simulated by the time-harmonic Maxwell system with a constant magnetic permeability. For the optimization of the geometry parameters of the grating, a functional is defined which depends quadratically on the efficiencies of the reflected modes. The minimization of this functional by gradient based optimization schemes requires the computation of the shape derivatives of the functional with respect to the parameters of the geometry. Using classical ideas of shape calculus, formulas for these parameter derivatives are derived. In particular, these derivatives can be computed as material derivatives corresponding to a family of transformations of the underlying domain. However, the energy space $H(rm curl)$ for the electric fields is not invariant with respect to the transformation of geometry. Therefore, the formulas are derived first for the magnetic field vectors which belong to $[H^1]^3$. Afterwards, the magnetic fields in the shape-derivative formula are replaced by their electric counter parts. Numerical tests confirm the derived formulas.