Mueller matrix ellipsometry has been demonstrated as a powerful tool for nanostructure metrology in high-volume manufacturing. Many factors may induce depolarization effect in the Mueller matrix measurement, and consequently, may lead to accuracy loss in the nanostructure metrology. In this paper, we propose to apply a Mueller matrix decomposition method for the Mueller matrix measurement to separate the depolarization effect caused by the MME system. The method is based on the polar decomposition by decomposing the measured depolarizing Mueller matrix into a sequence of three matrices corresponding to a diattenuator followed by a retarder and a depolarizer. Since the depolarization effects will be only reflected in the depolarizer matrix, the other two matrices are used to extract the structure parameters of the measured sample. Experiments performed on a one-dimensional silicon grating structure with an in-house developed MME layout have demonstrated that the proposed method achieves a higher accuracy in the nanostructure metrology.
Dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) has been designed and applied as a powerful tool for the characterization of thin films and nanostructures. The compensators are indispensable optical components and their performances affect the precision and accuracy of DRC-MME significantly. Biplates made of birefringent crystals are commonly used compensators in the DRC-MME, and their optical axes invariably have tilt errors due to imperfect fabrication and improper installation in practice. The axis tilt error between the rotation axis and the light beam will lead to a continuous vibration in the retardance of the rotating biplate, which further results in significant measurement errors in the Mueller matrix. In this paper, we propose a simple but valid formula for the retardance calculation under arbitrary tilt angle and azimuth angle to analyze the axis tilt errors in biplates. We further study the relations between the measurement errors in the Mueller matrix and the biplate axis tilt through simulations and experiments. We find that the axis tilt errors mainly affect the cross-talk from linear polarization to circular polarization and vice versa. In addition, the measurement errors in Mueller matrix increase acceleratively with the axis tilt errors in biplates, and the optimal retardance for reducing these errors is about 80°. This work can be expected to provide some guidences for the selection, installation and commissioning of the biplate compensator in DRC-MME design.
Optical scatterometry, also referred to as optical critical dimension (OCD) metrology, has been introduced for critical dimension (CD) monitoring and overlay metrology with great success in recent years. Forward modeling to calculate the optical signature from the measured diffractive structure is one of the most important issues in OCD metrology. To simplify the forward modeling approach, such as rigorous coupled-wave analysis (RCWA), the incidence and azimuthal angles are usually assumed to be constant. However, since some focusing elements, such as focusing lens or parabolic mirrors with finite numerical aperture (NA), are always used to gain a sufficient small spot size onto the sample, this assumption is not true in the whole exit pupil of the focusing elements, leading to a modeling error in forward modeling, and finally leading to a fitting error in OCD metrology. In this paper, we propose a correction method with consideration of the effect of NA to decrease the modeling error in the forward modeling. The correction method is an average integral method based on Gaussian quadrature in two dimensions inside a circle, and is performed on forward modeling with varied incidence and azimuthal angles over the exit pupil. Experiments performed on silicon gratings with a Mueller matrix polarimeter have demonstrated that the proposed correction method achieves a higher accuracy in OCD metrology.
The random noise and the systematic errors caused by azimuthal errors of the optical elements, i.e., the polarizer, the analyzer, or the compensator, would lead to measurement errors in the Mueller matrix ellipsometer (MME). In this paper, we develop the two-channel MME of the optical configuration PCr1SCr2Wp by replacing the analyzer with a Wollaston prism. In the two-channel MME, two intensity spectra would be acquired simultaneously due to the separation and orthogonal polarization of two light beams by the Wollaston prism and are combined to deduce the Mueller matrix. Two figures of merit are derived to evaluate the effects of random noise and systematic errors on the Mueller matrix measurement, and numerical simulations demonstrate that the two-channel MME can give access to higher accuracy by reducing measurement errors due to random noise and systematic errors.