Effective-medium model for fast evaluation of scatterometric measurements on gratings

Scatterometry is now an accepted technique for linewidth measurement in semiconductor manufacturing. To reduce the evaluation time when using real-time optimization procedures, we introduce an effective-medium approach to simulate the optical signatures of subwavelength line-and-space gratings. Such gratings behaves approximately like uniaxial crystals whose optical properties are completely described by two refractive indices. We propose an algebraic method for their calculation up to second order in pitch/wavelength for the extraordinary index, and up to 4th order in pitch/wavelength for the ordinary index. The formulas are valid for any angle of incidence and can be used with standard matrix formalism to calculate the optical properties of any arbitrary layer stack. We deduce the formul as for the indices. The comparison of effective medium-calculations to rigorous coupled wave simulations for spectral measurements (polarized reflectometer and spectroscopic ellipsometer) shows excellent agreement. The sensitivity of scatterometry to tilt of the structures is very low for all measurement parameters except phase difference. It is shown that left and right tilt cannot be distinguished at all with spectral measurements with non-conical incidence of light.