Multi-oscillator of optical dispersion, continuous coordination Lorenz model

摘要

Methods and systems for monitoring band structure characteristics and predicting the electrical properties of samples early in the semiconductor manufacturing process are presented herein. A high throughput spectrometer produces spectral response data from a semiconductor wafer. In one example, the measured optical dispersion is characterized by a Gaussian oscillator, a continuous-coded Lorentz model. The measurement results are used to monitor band structure characteristics, including defects such as charge trapping centers, exciton states, phonon mode, and band gaps in high-K dielectric layers and embedded nanostructures. Gaussian oscillators, continuous-coded Lorentz models can be generalized to include any number of defect levels. In addition, the shape of the absorption defect peak may be expressed by a Lorentz function, a Gaussian function, or both. These models represent the results of the experiments quickly and accurately in a physically meaningful manner. The model parameter values may subsequently be used to gain insight and control over the manufacturing process.