Reduced basis method for computational lithography

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times for different values of geometrical parameters. The reduced basis method allows to split up the solution process of a parameterized model into an expensive offline and a cheap online part. After constructing the reduced basis offline, the reduced model can be solved online very fast in the order of seconds or below. Error estimators assure the reliability of the reduced basis solution and are used for self adaptive construction of the reduced system. We explain the idea of reduced basis and use the finite element solver JCMsuite constructing the reduced basis system. We present a 3D optimization application from optical proximity correction (OPC).Comment: BACUS Photomask Technology 200

Rigorous Simulations of 3D Patterns on Extreme Ultraviolet Lithography Masks

Simulations of light scattering off an extreme ultraviolet lithography mask with a 2D-periodic absorber pattern are presented. In a detailed convergence study it is shown that accurate results can be attained for relatively large 3D computational domains and in the presence of sidewall-angles and corner-roundings.Comment: SPIE Europe Optical Metrology, Conference Proceeding

FEM investigation of leaky modes in hollow core photonic crystal fibers

Hollow-core holey fibers are promising candidates for low-loss guidance of light in various applications, e.g., for the use in laser guide star adaptive optics systems in optical astronomy. We present an accurate and fast method for the computation of light modes in arbitrarily shaped waveguides. Maxwell's equations are discretized using vectorial finite elements (FEM). We discuss how we utilize concepts like adaptive grid refinement, higher-order finite elements, and transparent boundary conditions for the computation of leaky modes in photonic crystal fibers. Further, we investigate the convergence behavior of our methods. We employ our FEM solver to design hollow-core photonic crystal fibers (HCPCF) whose cores are formed from 19 omitted cladding unit cells. We optimize the fiber geometry for minimal attenuation using multidimensional optimization taking into account radiation loss (leaky modes).Comment: 8 page

Fast simulation method for parameter reconstruction in optical metrology

A method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate the sensitivity of a scatterometric setup with respect to geometrical parameters of the scattering target. The method can significantly improve numerical performance of design optimization, parameter reconstruction, sensitivity analysis, and other applications

Time-optimal polarization transfer from an electron spin to a nuclear spin

Polarization transfers from an electron spin to a nuclear spin are essential for various physical tasks, such as dynamic nuclear polarization in nuclear magnetic resonance and quantum state transformations on hybrid electron-nuclear spin systems. We present time-optimal schemes for electron-nuclear polarization transfers which improve on conventional approaches and will have wide applications.Comment: 11 pages, 8 figure

Metrology of EUV Masks by EUV-Scatterometry and Finite Element Analysis

Extreme ultraviolet (EUV) lithography is seen as a main candidate for production of future generation computer technology. Due to the short wavelength of EUV light (around 13 nm) novel reflective masks have to be used in the production process. A prerequisite to meet the high quality requirements for these EUV masks is a simple and accurate method for absorber pattern profile characterization. In our previous work we demonstrated that the Finite Element Method (FEM) is very well suited for the simulation of EUV scatterometry and can be used to reconstruct EUV mask profiles from experimental scatterometric data. In this contribution we apply an indirect metrology method to periodic EUV line masks with different critical dimensions (140 nm and 540 nm) over a large range of duty cycles (1:2, ..., 1:20). We quantitatively compare the reconstructed absorber pattern parameters to values obtained from direct AFM and CD-SEM measurements. We analyze the reliability of the reconstruction for the given experimental data. For the CD of the absorber lines, the comparison shows agreement of the order of 1nm. Furthermore we discuss special numerical techniques like domain decomposition algorithms and high order finite elements and their importance for fast and accurate solution of the inverse problem.Comment: Photomask Japan 2008 / Photomask and Next-Generation Lithography Mask Technology X