SHORT DESCRIPTION

Finite-element solver for Maxwell's electromagnetics equations for optical modeling.

OVERVIEW

EMFlex is a time-domain finite-element program for solving Maxwell's equations. To date, it has been applied mainly to computational optics simulations. It is used in electromagnetic wave propagation studies for computational domains no larger than 100x100 wavelengths in 2-D or 10x10x10 wavelengths in 3-D. Although frequency domain results are typically of interest, large advantages in speed and problem-size are obtained by integrating to steady state in the time domain, then extracting amplitude and phase quantities via a discrete Fourier transform.

Currently, EMFlex is used by prominent academic institutions and foreign and domestic commercial corporations, including semiconductor manufacturers, instrument makers, chemical suppliers, and research labs.

The accuracy of the program has been verified through analysis of standard benchmark problems for which analytic solutions are known (e.g., Mie scattering). Code results have also been compared with those from other computer programs and with experimental data. The numerical errors resulting from spatial and temporal discretization have been quantified by solving the discrete equations analytically.

Fields of application include:

Scattering
      Particles in free space
      Particles in or on a layered half-space

Photolithography
      Phase-shift mask simulations
      Conventional mask simulations
      Intensity distributions within photoresist
      Alignment-mark simulations

IC Metrology
      Scattering from features

Integrated optics
      Waveguides
      Grating couplers
      Resonators

Applications also include related FLEX piezoelectric, elastic, and heat codes modeling: thermal diffusion, index changes, elastic waves from absorbed light; piezoelectric transducers and surface acoustic waves (SAWs); and 3-D SAW-induced index modulation for acousto-optical studies.

CAPABILITIES

EMFlex has a wide range of modeling capabilities in 2-D, 2.5D, and 3 D. In 2-D, it can be used to model both TE and TM polarizations, and in 2.5-D, 2-D geometry and arbitrary illumination.

The materials are assumed to be isotropic or anisotropic dielectrics (including those with isotropic or anisotropic partial conductivity). A Drude model is included for modeling metals or dielectrics with k > n. Perfectly conducting material is also supported as a useful approximation for metals. Time-domain analyses are performed using an explicit time-integration technique that avoids the difficulties of manipulating large assembled matrices for the model. This approach restricts the computational time-step to satisfy the Courant stability criteria.

EMFlex uses cartesian isoparametric finite elements to model a continuum. 2-D models use 4-noded quadrilateral elements, and 3-D models use 8-noded hexahedron elements. The adoption of single-point integration, although optimal in terms of solution accuracy, processing speed, and required storage, can result in unresisted modes of deformation (hourglass modes) that must be suppressed. The approach adopted therefore includes hourglass suppression (stabilization). A large portion of the EMFlex development effort has been spent on implementing robust and accurate boundary conditions, which contribute significantly to its modeling power.

ADDITIONAL INFORMATION

Output includes time histories and/or snapshots of field variables, such as electric field, amplitude, phase, and intensity. Total, reflected, and scattered steady-state quantities are available. The data are saved during analysis for post-processing at a later time. The EMFlex package also includes REVIEW, a postprocessor that can be used to plot results. It also implements Fourier optics for imaging through a lens system (including NA, magnification, primary aberrations, and partial coherence), and Kirchhoff extrapolation for continuing to the far field.

The structures of the various data output files were purposely kept simple so that the data are easy to manipulate for integration with the user’s graphics capabilities. In addition, EMFlex provides its own graphics options for plotting time histories, creating plots, and displaying field quantities such as electric field amplitude and phase in color. The graphics options use X-windows graphics protocols to run across a network and produce Postscript image files for Grayscale or color hardcopy devices. The graphics option also allows the creation of on-screen movies.

Reports and Papers

"Ultra High Confinement Waveguides for Very Large Scale Integrated Optics (VLSIO) with Three Dimensional Packaging," by West, Roberts and Piscani, Optical Society of America, Integrated Photonics Research Technical Digest, 1996 (download pdf)

"Highly Compact Optical Waveguides with a Novel Pedestal Geometry," by Chaudhari, West, Roberts and Lu, IEEE Photonic Technology Letters, Vol. 7, 526-528, 1995 (download pdf)

"Non Uniform Grating Couplers for Coupling of Gaussian Beams to Compact Waveguides," by West, Roberts, Dunkel, Wojcik and Mould, Jr., Optical Society of America, Integrated Photonics Research Technical Digest, 1994 (download pdf)

"Some Imaging Modeling Issues for I-line, 5x Phase Shifting Masks," by Wojcik, Mould, Jr., Ferguson, Martino and Low, SPIE Microlithography Proceedings, Optical Laser Microlithography VII, 455-465, 1994 (download pdf)

"Time-Domain Finite Element Modeling of 3D Integrated Optical Devices," by Wojcik, Mould, Jr. and West, Optical Society of America Technical Digest Series, Integrated Photonics Research, Vol. 10, 112-115, 1993 (download pdf)

"Numerical Reference Models for Optical Metrology Simulation," by Wojcik, Mould, Jr., Marx and Davidson, SPIE Microlithography Proceedings, IC Metrology, Inspection, and Process Control I, Vol. 1673-06, 1992 (download pdf)

"Laser Alignment Modeling Using Rigorous Numerical Simulations," by Wojcik, Vaughan, Mould, Jr., Leon, Qian and Lutz, SPIE Microlithography Proceedings, Optical Laser Microlithography IV, Vol. 1463, 1991 (download pdf)

"Numerical Simulation of Thick Line Width Measurements by Reflected Light," by Wojcik, Mould, Jr., Monteverde, Prochazka and Frank, SPIE Microlithography Proceedings, IC Metrology, Inspection, and Process Control V, Vol. 1464, 1991 (download pdf)

"Calculation of Light Scatter from Structures on Silicon Surfaces," by Wojcik, Vaughan and Galbraith, SPIE Microlithography Proceedings, Lasers in Microlithography Vol. 774, 1987 (download pdf)

More information can be obtained about this product by emailing flex_support@wai.com.