Optical scatterometry has been proven to be a useful tool for the inspection and assessment of lithographic processes. The characteristic signature of the scattergram provides information about the surface relief profile and can be rapidly and non-invasively acquired. Currently, attention is being focused on the inversion of scatterometric data to determine the surface profile of the relief structure. To overcome the highly non-linear relationship between the properties of the diffracting structure and the diffraction measurements, we present a linearized solution based on a least-squared refinement method. This approach relies on the reliability of lithographic processes, which allows us to determine the departures of structural key parameters from a set of expected design values. This linearized inversion, as shown by the mathematical formalism, is independent of the scatterometric measurement configuration. Hence it can be applied whether, for example, the incident angle or wavelength of the light is varied to acquire either irradiance of phase information. This is validated in this paper by various examples handling the retrieval of three geometrical parameters (groove depth, line width, and sidewall angle) from reflectance data simulated using the rigorous coupled-wave theory (RCWT) for both angular and wavelength scans. An additional benefit of the proposed linearized solution is the ability to examine mathematically the significance of measurement errors. An analytical propagation of error is presented, connecting measurement noise to the soughed parameter precisions and uncertainties. We applied this formalism to the cases mentioned above, where we simulated the retrieval of three parameters from measurements containing various levels of noise. This studies allows us to draw preliminary conclusions on the sensitivity of scatterometry with respect to the number and types of structural parameters to be retrieved, but also to the technique employed to gather the measurements.
As progress in ultra-large scale integration (ULSI) continues to lower the critical dimension (CD) requirements, measurement science is regularly witnessing changes in the monitoring techniques for the development and control of semiconductor fabrication processes. Microscopy, reflectometry and ellipsometry are examples of optical techniques constantly adjusted in attempts to provide mask and wafer state monitoring with non-invasive, rapid and in situ schemes. In the past years special attention has been devoted to optical diffraction as a potential method to satisfy those requirements, yielding the field of scatterometry. A linearized method was introduced to represent the relationship between parameters that describe a surface relief profile and the resulting scattering geometry data. An advantage of this approach is that describe a surface relief profile and the resulting scatterometric data. An advantage of this approach is that large databases containing profile information are not needed to process the scatterometric dat, resulting in a technique that is more versatile to process changes. In this paper, studies on the effect of changing profile parameters as well as measurement variables on the accuracy of retrieved parameter values using the linearized inversion method are presented.
Optical diffraction is an attractive process with which to non-invasively examine materials and structures. Waves diffracted by a periodic structure carry information about geometrical characteristics of the diffracting structure as well as intrinsic properties of the material comprising the structure. These features make optical diffraction from surface relief gratings appealing as a monitor for lithographic processes. Considering that lithographic processes are usually quite stringently controlled, a search for 'departures' from a set of expected design values can linearize the highly non-linear relationship between parameter values and diffraction measurements, and hence permits analyses using classical linear methods. We therefore propose a linear inversion technique to determine key parameters of a periodic structure from an analysis of diffraction data that seeks to determine the departures from a set of expected design values. The approach is validated for the retrieval of three geometrical parameters (groove depth, line width, and sidewall angle) based on simulations performed using the rigorous coupled-wave theory (RCWT). The results obtained are very encouraging and highlight the potential of a linear inversion technique in scatterometry.