In this paper, we report on Muller Matrix (MM) based scatterometry (aka. optical critical dimension or OCD) simulation strategies for two sub-7nm fin structures: one with a SixGe1-x/Si/SixGe1-x/Si/SixGe1-x/Si nanosheet structure and its comparison with a hypothetical Si-only fin structure of similar dimensions at sub-7nm semiconductor technology nodes. Si-fins are providing the performance improvements necessary for the transistors used in current generation integrated circuits. Development of sub-7nm technology nodes requires further performance improvements including advanced structures including new materials. This demand for improved performance has created the need for new fabrication processes such as extreme ultraviolet lithography, self-aligned quadruple patterning etc., along with new metrology challenges for adequately monitoring the semiconductor process control during fabrication of these advanced nanostructures.1 New materials and structures, such as, Si/Si1-xGex (0≤x≤1) stacked nanosheet structures have recently been developed as one of the potential replacement for Si-based FinFETs.2,3 We have simulated two fin structures: one with Si-fins and another with 3 alternating stacks of Si1-xGex/Si (x=0.3). We have used Rigorous Coupled Wave Approximation (RCWA) to simulate OCD spectra for 0° – 360° azimuthal angles in 10° steps by keeping the fin pitch fixed at 24nm while systematically changing (1) the fin critical dimension (CD) from 5.0–7.5nm in 0.5nm steps, (2) thickness of the Si and Si1-xGex (x=0.3) nanosheets (NST) from 8.0–1.5nm in 0.5nm steps, (3) the fin bending angle (FBA) from 0°–2.5° in 0.5° steps, and (4) the undercut angle (ED) of the Si1-xGex NSTs from 0°–10° in 2° steps. Difference in etch-rate of Si and Ge could give rise to non-zero ED during NST formation. Both the fin structures possess mirror symmetry about two orthogonal planes perpendicular to the substrate and with one of the planes along the fin long-axis. For angles 0°, 90°, 180°, and 270°, this mirror symmetry leads to absence of the cross-polarization terms in the simulated OCD spectra such that off-diagonal MM elements are zero over the simulated wavelength range. The broken mirror symmetry in other azimuthal angles leads to cross-polarization of the electrical field vectors which is seen in the off-diagonal MM elements becoming non-zero. Additionally, the off-diagonal MM elements show increased sensitivity and reduced correlation between the parameters under study which leads to a powerful metrology means for studying the critical fin-parameters for fast and reliable semiconductor process control in sub 7-nm technology nodes. All the non-zero MM-elements are found to be sensitive to changes in CD and NST with the off-diagonal elements showing greater sensitivity to the changes. At azimuthal angles <15°, MM23, MM31, and MM34 are highly sensitive to changes in etch undercut and fin bending angle defects.
 D. Dixit et al., “Advanced applications of scatterometry based optical metrology,” Proc SPIE 10145, 101451H (2017).
 N. Loubet et al., “Stacked nanosheet gate-all-around transistor to enable scaling beyond FinFET,” VLSI Technol. 2017 Symp., T230–T231, IEEE (2017).
 R. Muthinti et al., “Advanced in-line optical metrology of sub-10nm structures for gate all around devices (GAA),” Proc SPIE 9778, 977810 (2016).
Sonal Dey, Alain Diebold, Nick Keller, and Madhulika Korde, "Mueller matrix spectroscopic ellipsometry based scatterometry simulations of Si and Si/SixGe1-x/Si/SixGe1-x/Si fins for sub-7nm node gate-all-around transistor metrology," Proc. SPIE 10585, Metrology, Inspection, and Process Control for Microlithography XXXII, 1058506 (Presented at SPIE Advanced Lithography: February 26, 2018; Published: 6 June 2018); https://doi.org/10.1117/12.2296988.
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