# Metrology of Nanostructures by Tomographic Mueller-Matrix Scatterometry
## 4 Results and Discussion
### Measurement of Grating Structural Parameters
As an example, Figure 6 presents the fitting result of the measured and calculated best-fit Mueller matrices of the photoresist grating at the wavelength of 633 nm, the incidence angles varied from 50\({}^{\circ}\) to 65\({}^{\circ}\) at an interval of 1\({}^{\circ}\), and the azimuthal angles of 50\({}^{\circ}\) and 60\({}^{\circ}\). Good agreement can be observed from Figure 6. As can also be observed, the TMS-measured results exhibit good agreement with those measured by MME. Some deviations  
Figure 5: Mueller matrix representation of the zeroth-order diffracted field of the photoresist grating collected at the wavelength of 633 nm. The incidence angles varied from 0\({}^{\circ}\) to 65\({}^{\circ}\) at interval of 1\({}^{\circ}\), and the azimuthal angles from 0\({}^{\circ}\) to 90\({}^{\circ}\) at interval of 5\({}^{\circ}\). The panel associated with each Mueller matrix element (normalized to \(m_{11}\)) consists of three sectorial parts. The lower right part corresponds to the TMS-measured data, the upper left part corresponds to the calculated best-fit data, and the lower left part presents the difference between the measured and calculated best-fit data. For each sectorial part, the polar coordinate system is set as shown in the inset with the radial coordinate being the sine of the incidence angle sin\(\theta\) and the angular coordinate being the azimuthal angle \(\varphi\). between the TMS- and MME-measured data may be induced by measurement errors. Still, the different sizes and locations of illumination spots between TMS and MME may induce an unequal number of grating periods and different areas detected by the systems, bringing about little disparity in the measured results. Table 1 presents the comparison of fitting parameters of the photoresist grating extracted from TMS, MME, and SEM measurements. For TMS measurements, we present both the fitting parameter values before and after the pitch correction. For MME measurements, we only present the fitting parameter values after the pitch correction. As can be seen, after the pitch correction, the TMS measured parameters \(x_{1}\) and \(x_{3}\) match well with their nominal values and MME and SEM results. As for the parameter \(x_{2}\), the TMS-measured result exhibits a discrepancy with its nominal value and SEM result, but shows good agreement with the MME measured result. The top corner rounding \(x_{4}\) also matches well with the MME result. This discrepancy is probably due to sample denaturation. We analyzed areas with structures and the assumption was supported by variations in the refractive index and extinction coefficient of the photoresist in comparison with our previous analysis [35]. A changed mixing layer existing between the resist and BARC layers could have introduced the measurement error. In addition, a possible modification of the structural cross-section due to the slicing process in SEM measurement (typically the focused ion beam), as well as the different testing areas of TMS and SEM on the sample, may be other reasons for the discrepancy. Even so, a noticeable improvement in accuracy of the extracted parameters can be recognized from the TMS-measured parameters before and  
Figure 6: Fitting result of the measured and calculated best-fit Mueller matrices of the photoresist grating at the wavelength of 633 nm. The incidence angles varied from 50\({}^{\circ}\) to 65\({}^{\circ}\) at interval of 1\({}^{\circ}\), and the azimuthal angles of 50\({}^{\circ}\) and 60\({}^{\circ}\). The red solid lines represent the calculated best-fit data, the blue rectangles and blue triangles represent the TMS-measured data at the azimuthal angles of 50\({}^{\circ}\) and 65\({}^{\circ}\), respectively. The green circles represent the corresponding MME-measured data for a comparison. after the pitch correction. It is thereby necessary to acquire accurate pitch value before the extraction of other grating structural parameters, as it affects the results greatly.