Multi-Oscillator, Continuous Cody-Lorentz Model Of Optical Dispersion

摘要

Methods and systems for monitoring band structure characteristics and predicting electrical characteristics of a sample early in a semiconductor manufacturing process flow are presented herein. High throughput spectrometers generate spectral response data from semiconductor wafers. In one example, the measured optical dispersion is characterized by a Gaussian oscillator, continuous Cody-Lorentz model. The measurement results are used to monitor band structure characteristics, including band gap and defects such as charge trapping centers, exciton states, and phonon modes in high-K dielectric layers and embedded nanostructures. The Gaussian oscillator, continuous Cody-Lorentz model can be generalized to include any number of defect levels. In addition, the shapes of absorption defect peaks may be represented by Lorentz functions, Gaussian functions, or both. These models quickly and accurately represent experimental results in a physically meaningful manner. The model parameter values can be subsequently used to gain insight and control over a manufacturing process.

主权项

1. A system comprising:
an illuminator configured to provide an amount of illumination to an unfinished, multi-layer semiconductor wafer across a spectral range; a spectrometer configured to collect an amount of light from the unfinished, multi-layer semiconductor wafer in response to the illumination provided by the illuminator and generate an amount of data indicative of a spectral response of the unfinished, multi-layer semiconductor wafer; and one or more computer systems configured to:
receive the spectral response of the unfinished, multi-layer semiconductor wafer across the spectral range; determine a plurality of parameter values of an optical dispersion model of one or more layers of the multi-layer semiconductor wafer based at least in part on the spectral response, wherein the optical dispersion model includes a continuous Cody-Lorentz model having a first derivative function that is continuous at the Urbach transition energy of the continuous Cody-Lorentz model and at least one unbounded Gaussian oscillator function; and store the plurality of parameter values of the optical dispersion model in a memory.