New dispersion model for band gap tracking

• A new Continuous-Cody–Lorentz dispersion model is proposed.
• The model provides meaningful value for Eg and adequately describes the underlying physics.
• The model gives a way to detect the band-gap without additional references.
• It has enough flexibility to portray the dielectric functions for a variety of materials.
• The model can be used for in-line device process monitoring.

The spectroscopic ellipsometry (SE) is known as the best in-situ non-invasive method suitable for thickness and composition measurements of the Si/oxide gates. However, a composition measurement performed by the SE is indirect and it needs a reference. Moreover, thickness and composition cannot be directly related to the relevant device performance parameters. On the other hand, a dielectric function, another optimized parameter of the SE metrology, has a direct relation to the bandgap parameter which is a major factor determining electrical performance of the Si/oxide gates. In this paper we develop and demonstrate a new optical model suitable for band gap tracking. The optical model developed is based on continuous version of the Cody–Lorentz model. This model can intrinsically define a physically meaningful value of the band gap. We show that developed model can be used for device process monitoring.