WIAS Preprint No. 2564, (2018)

Fast scatterometric measurement of periodic surface structures in plasma-etching processes


  • Klesse, Wolfgang Matthias
  • Rathsfeld, Andreas
  • Groß, Claudine
  • Malguth, Enno
  • Skibitzki, Oliver
  • Zealouk, Lahbib

2010 Mathematics Subject Classification

  • 65N21 35Q61

2008 Physics and Astronomy Classification Scheme

  • 42.40.Lx


  • Scatterometry, inverse problem, time-harmonic Maxwell's equation




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 structure's 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.

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