A practical method for optical dispersion model selection and parameters variations in scatterometry analysis with variable n&k's

• A method to identify suitable dispersion model for the optical constants is proposed.
• The methodology allows determination of most influential model parameters to be floated.
• The method is tested through different kinds of examples to illustrate its performance.
• The sensitivity ratios of the parameters were discussed as quantitative sensitivity measures.
• This method should be useful in many practical situations in the microelectronic industry.

Optical critical dimension (OCD) scatterometry in recent years became a well-accepted and powerful technique to determine the properties and grating profiles of 2D and 3D microelectronic structures (critical dimensions, side-wall angles, grating and underlying thin film thicknesses) in modern semiconductor manufacturing. However, the optical scatterometry, as any model-based metrology technique, relies on the accuracy of the OCD model which highly depends on the optical properties (the n&k's) of the materials in the structure. In practice, even small deviations in material's optical properties (from nominal model inputs) due to process condition variations might significantly affect the scatterometry measurements. A logical way to deal with this problem is to allow some degree of the n&k's variability of the most affected layer(s) in the OCD model describable by relevant dispersion model(s) (floating n&k's). Essentially, one of the largest complications for the end users (process engineers) is to decide which optical dispersion model (Cauchy, Lorentz, Tauc–Lorentz, etc.) needs to be selected to describe a material under production conditions and which parameters are more sensitive and need to be floated in the OCD model. We developed an approach which, we believe, will result in more straightforward and fast development of the OCD models. This approach provides a possibility to automatically select a most proper dispersion model which has been always an ambiguous decision for most of the end users. This methodology will allow determination of most influential model parameters to vary, eliminating potential sources of modeling error at the initial steps of the OCD modeling. A few examples to illustrate the key ideas and practical use of our procedure have been provided.