Physical Modeling

Nova’s Tools employ a model-based approach as their back-bone interpreter. For a given sample, the measured signal is compared to a modeled signal. The latter signal is furnished by an innovative Nova solution to a physical electromagnetic scattering problem (i.e. a solution to Maxwell’s equations). In this solution, both the sample and the system’s components are treated as the scattering object. When measurement and modeled signals are compared, the difference between the two is educatively used to refine the model of the sample until both signals match.

Highlights & Benefits

  • High accuracy: Physical modeling inherently provides accurate sample description, because the scope of possible solutions is limited from the onset of this approach.
  • Unphysical outlier rejection: For the same reason, non-physical results are inherently filtered out.
  • Speed-up: With physical modeling, previous knowledge about the sample can be easily accounted for. This greatly speeds-up the solution.
  • Physical results: Physical modeling allows a straightforward connection to other metrology tools (refer to Hybrid metrology) as the parameters at its output have well-understood physical meaning.

In the “Model-based” approach, the measured signal is compared to a set of modeled signals from a known family of samples. This family of samples are represented by several geometrical parameters, where the range of these parameters is known and is limited by previous knowledge. Both deterministic samples (in which the exact structure is known) and non-deterministic samples (where only structure statistics is known) are encountered with Nova’s metrology tools.

Evaluating the modeled signals involves finding the solution to a highly complicated scattering problem, such as the scattering of electromagnetic off a given sample. Several innovative methods for the solution of this problem were developed in Nova, and these are continuously being improved for better speed and accuracy.

In addition to the bare interaction of the electromagnetic wave with the sample, Nova has also developed sophisticated physical models that account for the other components of the measurement system, such as the sub-system that guides the light from the source to the sample, and the one that guides the scattered light from the sample to the detector. These models dictate the way the light scattered from the bare sample-light interaction combines to give an overall signal at the detector, so that comparing modeled-signal to measured-signal is done at the most accurate reference level.