KEYWORDS: Nanostructures, Electron microscopy, Scattering, Diffraction limit, Diffraction, Optical microscopy, Near field optics, Near field, Multilayers, Modeling
Dimensional optical microscopy allows for the rapid inspection of devices at the cost of limited accuracy. Introducing a model-based approach that includes diffraction effects allows for increased accuracies. The model needs to be efficient and accurate to evaluate the measurements in an acceptable time frame.
We present an overview of the illumination model and different incidence-pupil sampling techniques. Furthermore, we will demonstrate strategies for efficiently calculating the near-field scattering response from structures using the finite element method.
Using these aspects, we demonstrate a significant increase in the accuracy of dimensional estimates for a range of structures.
In this contribution, we present a technique for the determination of optical aberrations, which is based on measurements of the point spread function and a Bayesian optimization of rigorous simulations. The measuring system is a UV-microscope in a reflected light configuration with a 200x magnification, unpolarized light, and an illumination and imaging NA of 0.44 and 0.55, respectively. The PSF is measured by imaging a small quadratic chrome dot (side length ≈ 180 nm) on a glass substrate. We investigate the impact of different adjustment states, different dot locations and different optical microscopes.
A reliable tool for simulations of confocal microscopes shall be developed to enable improved model-based dimensional metrology. To simulate measurements on rough surfaces the boundary element method (BEM) simulation tool SpeckleSim, developed by the ITO of the University of Stuttgart, is combined with a Fourier optics based image formation. SpeckleSim, which calculates the light-structure interaction by solving the Maxwell equations, is compared with the well-known FEM based solver JCMsuite and the FDTD based solver Ansys Lumerical. As an example, a rectangular shaped line is used as an object. Due to different boundary conditions the results show as expected small deviations, which require further investigations. First comparison results and the general concept of the image formation method will be presented.
In many industrial sectors, dimensional microscopy enables non-destructive and rapid inspection of manufacturing processes. However, wave-optical effects and imaging errors of the optical system limit the accuracy. With modelbased approaches it is possible to measure the physical position of edges and corners with submicron uncertainty. This requires an accurate model for phase aberrations of the optical system. We present a method to model and quantify those phase aberrations by an efficient inverse measurement.
A model-based edge detection is always required when quantitatively evaluating the bidirectional measurements of micro- and nanostructures in optical microscopy. For example, the accurate determination of the width of a structure requires the knowledge of the location of the real physical edges in the measured profile. The interpretation of the measured edge profile cannot be performed intuitively due to distortion which is caused by diffraction and refraction. We advise a model-based edge detection algorithm which is based on rigorous simulations of the microscope’s imaging. The intensity level which corresponds to the position of the real physical edge is called the threshold and it is determined in the simulations. For these optical simulations we employ the JCMsuite, which is a software application of the finite-element-method (FEM). Since numerical and semi-analytical methods for the calculation of electromagnetics in optical systems rely to some degree on approximations, their results may vary even when the input parameters are identical. We apply a test suite of input parameters for the purpose of comparing numerical simulation tools regarding the resulting thresholds for measurements on line-shaped nanostructures in a periodic grating. The test suite maintains the illumination and imaging parameters of a transmitted light UV-microscope while the object parameters of a binary line grating are varied. There are 25 grating configurations with different line-to-space ratios, where the line width ranges from the resolution limit up to almost 10 µm. The illumination pupil is discretized in a cartesian grid with 113 grid points in total. We introduce different pupil samplings, after calculating the threshold values of the original test suite. We obtain a high agreement of the thresholds results and the related linewidth values when comparing with already performed results of two additional rigorous applications. Furthermore, we showcase the threshold variation for different samplings of the illumination pupil.
In light microscopy, optical aberrations always affect the performance of the employed microscope. They can emerge from imperfect optical components of the microscope, like lenses, or from misalignments of such optical components, which may even change over time. In our contribution, we retrieve the optical aberrations in form of Zernike polynomials from measurements of small point structures by applying the extended Nijboer-Zernike approach. Subsequently, we include the expression for these optical aberrations in rigorous simulations of the microscope’s imaging process. Finally, we will compare the simulations with measurements to demonstrate optical bidirectional measurements on aberrant imaging systems.
Optical microscopy is widely used for the characterization of micro- and nanostructures in the field of unidirectional and bidirectional dimensional metrology. Despite the general high recognition in the metrological community, the inherent difficulties which are bound to optical bidirectional measurements using commercial vision-based metrology tools are not sufficiently investigated, yet, and require additional insight, which we intend to provide here. We demonstrate the need for sophisticated analysis methods to find a threshold value which locates the correct physical edge position within the microscopical image. The common assumption for the threshold to be at 50% of the intensity level of the edge signal is in essentially any imaging configuration wrong and leads to large systematic measurements errors. For example, the correct threshold values for transmission light microscopy using high NA objectives on chrome on quartz photomasks, are within 15% and 35% of the intensity level in the simulated images. For other measurement configurations the threshold variation can be even much larger. Since the correct threshold values depend on the illumination and imaging parameters of the imaging system as well as on the geometrical and optical parameters of the measurement object, we showcase a selection of them and their respective influence on the determination of the threshold values. Rigorous simulations are the key feature for this analysis since they require all the relevant parameters to be included in the simulation of a microscopical image which enables the correct threshold determination and to extract the correct bidirectional quantities out of the optical images.
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