Research On Instrument Measurement Configuration Optimization In Optical Scatterometry

Compared with SEM and AFM tools, the optical scatterometry tools have been widely applied in semiconductor manufacturing besause of their high throughput, low cost and non-destruction. At present, one of the focus of research is to achieve more precise and faster measurement of the structural parameters in optical scatterometry.As a model-based metrology, the structural parameters obtained by fitting the measured signatures with the calculated ones, the precision of the extracted structural parameters mainly depend on the sensitivity of model parameters and the extraction speed is affected by the number of measured signatures. While the sensitivity of model parameters can be improved by a proper choice of the mesurement configuration, which is defined as a combination of selected wavelengths, incidence, and azimuthal angles. The number of measured signatures usually depends on the number of selected wavelengths. From a theoretical standpoint, in chosen set of data the most linearly independent measured signatures contain all the information needed to resolve the unknown structural parameters in an inverse problem. Therefore, a proper choice of the mesurement configuration should be selected to enhance the measurement precision and speed by improving the sensitivity of structural parameters and less measured signatures.Accordingly, optimization methods of measurement configuration in optical scatterometry are explored in the dissertation. Firstly, the optical model based on the rigorous coupled wave analysis and the extraction method by Levenberg-Marquart algorithm is established. Then, an experimental platform for the nanostructure measurement is developed with the independently developed dual-rotating compensator Mueller matrix polarimeter and the established theory algorithm. Sensitivity analysis performed on a tylical nanostructure shows that more measurement sensitivity can be achieved by a proper choice of mesurement configuration. After that, for single and a set of nanostructures, the optimizations of incidence angle θ and azimuthal angle φ have been deep investigated using the local ang global sensitivity analysis, respectively. On this basis, the optimization of wavelength λ is explored further by the application of linear correlation analysis. The main contents and innovations include:The uncertainty propagation between the structrue parameters and measured signatures is investigated based on local sensitivity analysis, and a first-order error propagating formula is derived by considering the actual measurement, which connect the measuring error with the parameter to be measured. Then, detailed formulation for the estimation of random error that are propagated into the final extracted parameters are further derived. For single nanostructure under test, a novel measurement configuration optimization method based on the minimization of the mean of relative uncertainties is proposed to find an optimum configuration for all the investigated parameters.The formula of total variance is derived to assess the impact of uncertainty in input structural parameters on the variance of optical model output, and then the expression of main effect(a global sensitivity measure) of parapeters are obtained. By combining the main effects of each input structural parameter and the corresponding noise level, we define a metric called the uncertainty index to evaluate the impact of random noise in measured signatures on the precision for each measurement configuration. For a set of nanostructures with various dimensions, a novel measurement configuration optimization method based on the minimization of the uncertainty index is proposed to find an optimum measurement configuration.The independency analysis is performed on the differences between the calculated data according to the parameters true values and the ones obatained at the design values. The conditional inequality is achieved to identify the redundant information corresponding wavelength. Further, the objective function is derived according to the Cauchy inequality and the actual measurement random error. In order to improve the extraction speed with no loss in the solution accuracies, a novel measurement configuration optimization method based on linear correlation analysis is proposed.The proposed methods will provide novel means for the optimization of measurement configuration in optical scatterometry, which will provide theoretical direction also precise and fast measurement of the nanostructures in high-volume nanomanufacturing.