An experimental technique for quantitatively characterizing edge effect contributions in transmission through thick
photomasks is described and evaluated through electromagnetic simulation. The technique consists of comparing the 0<sup>th</sup>
order transmission for various duty cycles to the expected experimental behavior from a thin mask model. The real
electric field component from the edges is proportional to the shift in the position of the minimum energy in the 0<sup>th</sup> order
field away from the expected thin mask location. The square root of the minimum 0<sup>th</sup> order diffraction energy
normalized to a clear mask gives the imaginary edge contribution. The results indicate that Alternating Phase Shifting
Masks (ALT-PSM) and Attenuating Phase Shifting Masks (ATT-PSM) technologies have significant edge effects on the
order of 0.1λ to 0.2λ per edge respectively, as well as polarization dependence. For periods of 2 wavelengths and larger
these edge contribution values are nearly independent of pitch. The existence of an imaginary (or quadrature) phase
component is shown to result in an additive linear variation of line edge shortening through focus. This tilt can be
interpreted as a focus shift of the normal parabolic behavior and is about 0.5 Rayleigh units (RU). This focus shift
depends to some extent on the surrounding layout as well as the feature itself.
Exploratory prototype DfM tools, methodologies and emerging physical process models are described. The examples
include new platforms for collaboration on process/device/circuits, visualization and quantification of manufacturing
effects at the mask layout level, and advances toward fast-CAD models for lithography, CMP, etch and photomasks. The
examples have evolved from research supported over the last several years by DARPA, SRC, Industry and the Sate of
California U.C. Discovery Program. DfM tools must enable complexity management with very fast first-cut accurate
models across process, device and circuit performance with new modes of collaboration. Collaborations can be promoted
by supporting simultaneous views in naturally intuitive parameters for each contributor. An important theme is to shift
the view point of the statistical variation in timing and power upstream from gate level CD distributions to a more
deterministic set of sources of variations in characterized processes. Many of these nonidealities of manufacturing can be
expressed at the mask plane in terms of lateral impact functions to capture effects not included in design rules. Pattern
Matching and Perturbation Formulations are shown to be well suited for quantifying these sources of variation.
Contact holes represent one of the biggest <i>critical dimension</i> (CD) mask metrology challenges for 45nm technology mask development. The challenge is a consequence of both wafer and mask sensitivities. Large mask error factors and the small process windows found when contact holes are imaged on wafers impose very tight mask specifications for CD uniformity. The resultant CD error budget leaves little room for mask metrology. Current advanced mask metrology deploys a CD-SEM to characterize the mask contact hole CD uniformity. Measuring a contact hole is complex since it is inherently two-dimensional and is not always well-characterized by one-dimensional x- and y-axis measurements. This paper will investigate contact metrics such as <i>line edge roughness</i> (LER), <i>region of interest</i> (ROI) size, area, and CD sampling methods. The relative merits of each will be explored. Ultimately, an understanding of the connection between what is physically measured on the mask and what impacts wafer imaging must be understood. Simulations will be presented to explore the printability of a contact hole's physical attributes. The results will be summarized into a discussion of optimal contact hole metrology for 45nm technology node masks.
Direct imaging and characterization of exo-solar terrestrial planets require coronagraphic instruments capable
of suppressing star light to 10<sup>-10</sup>. Pupil shaping masks have been proposed and designed<sup>1</sup> at Princeton
University to accomplish such a goal. Based on Princeton designs, free standing (without a substrate) silicon
masks have been fabricated with lithographic and deep etching techniques. In this paper, we discuss the
fabrication of such masks and present their physical and optical characteristics in relevance to their
performance over the visible to near IR bandwidth.
Stray-light sources from pupil plane masks that may limit Terrestrial Planet Finder Coronagraph (TPF-C) performance are characterized<sup>1,2</sup> and mitigation strategies are discussed to provide a guide for future development. Rigorous vector simulation with the Finite-Difference Time-Domain (FDTD) method is used to characterize waveguiding effects in narrow openings, sidewall interactions, manufacturing tool-marks, manufacturing roughness, mask tilt, and cross-wavelength performance of thick Silicon mask structures. These effects cause stray-light that is not accounted for in scalar thin-mask diffraction theory, the most important of which are sidewall interactions, waveguiding effects in narrow openings, and tilt. These results have been used to improve the scalar thin-mask theory used to simulate the TPF-C with the Integrated Telescope Model.<sup>3</sup> Of particular interest are simulations of 100m thick vertical sidewall openings that model features typically found on Ripple masks<sup>4</sup> fabricated by Reactive Ion Etching (RIE) processes.<sup>5</sup> This paper contributes fundamental data for systematically modeling these effects in end-to-end system simulation.
Leakage straight through the mask material varies greatly with wavelength, especially in Silicon (an attractive mask material due to the precision manufacturing techniques developed by the IC industry). Coating Silicon with 200nm of Chrome effectively mitigates the leakage without causing additional scattering. Thick-mask diffraction differs from the predictions of scalar thin-mask theory because diffraction spreading is confined by the mask's sidewalls. This confinement can make a mask opening look electro-magnetically larger or smaller than designed, by up to 3λ per vertical sidewall on a 50μm thick mask yet this can be reduced an order of magnitude by undercutting the sidewalls 20°. These confinement effects are sensitive to mask tilt (if light reaches the sidewalls) which can lead to an imbalance in stray-light sources and an extra wavelength of effective opening change on the illuminated sidewall.
The edge generated stray-light from corner boundary conditions, interactions with the lower mask structure, and surface plasmon polaritons that may limit Terrestrial Planet Finder Coronagraph performance are characterized. Previously a number of stray light sources, unaccounted for by the ideal thin mask theory used to design the pupil-plane masks, were identified. In this paper we illustrate and quantify the most important outstanding stray-light sources in the near-field in order to improve the model of pupil-plane mask transmission used by the Integrated Telescope Model.
Corner spikes, caused by the need to bring the ideal top-hat field into compliance with the boundary conditions set forth by Maxwell's equations, form the strongest source of stray-light, accounting for up to a 1λ shift in the effective opening width per edge. Undercutting mask edges by 20<sup>°</sup> reduces this source of stray-light by more than a factor of five. Interactions between light and the lower mask structure, a secondary effect, account for only a few percent of the stray-light in the TE polarization but account for up to 50% of the stray-light in the TM polarization due to surface plasmon polaritons. Surface plasmon polaritons, surface waves that run for tens of microns and radiate at corners, form the final stray-light source. On thin masks they may account for up to a 1λ shift in the effective opening width; however, their effects can be easily mitigated by choosing a poor surface plasmon material, such as Chrome. The results presented here are being used to facilitate end-to-end system modeling through the Integrated Telescope Model.
The Terestrial Planet Finder (TPF) mission to search for exo-solar planets is extremely challenging both technically and from a performance modeling perspective. For the visible light coronagraph (the C) approach, the requirements for 1e10 rejection of star light to planet signal has not yet been achieved in laboratory testing and full-scale ground testing provides additional challenges to overcome. Therefore, end-to-end performance modeling will be relied upon to fully predict system performance. One of the key technologies developed for achieving the rejection ratios uses shaped pupil masks to selectively cancel starlight in planet search regions by taking advantage of the diffraction. Modeling results published to date have been based upon scalar wavefront propagation theory to compute the residual star and planet images. This ignores the 3D structure of the mask and the coupled EM fields resulting when light interacts with matter. Secondly it ignores a most important engineering question which is how well the proposed wavefront control system can correct any effects introduced by mask/ light interactions.
To address this problem we incorporate results from vector propagation through the masks. These fields, computed by the Finite Difference Time Domain (FDTD) method, are coupled into a TPF coronagraph integrated model and propagated end-to-end through the optical system. In this paper we build upon two recently published papers (refs 1,2) and evaluate this additional disturbance to the far field image, discuss the interface with surface-to-surface propagators and set up the formulism for polarization effects. A follow-on paper, part II, results will be presented with a surface-to-surface Fourier-based propagator coupled to the difference field models which include corrections from a wavefront control system.
Rigorous finite-difference time-domain electromagnetic simulation is used to simulate the scattering from proto-typical pupil mask cross-section geometries and to quantify the differences from the normally assumed ideal on-off behavior. Shaped pupil plane masks are a promising technology for the TPF coronagraph mission. However the stringent requirements placed on the optics require that the detailed behavior of the edge-effects of these masks be examined carefully. End-to-end optical system simulation is essential and an important aspect is the polarization and cross-section dependent edge-effects which are the subject of this paper. Pupil plane masks are similar in many respects to photomasks used in the integrated circuit industry. Simulation capabilities such as the FDTD simulator, TEMPEST, developed for analyzing polarization and intensity imbalance effects in nonplanar phase-shifting photomasks, offer a leg-up in analyzing coronagraph masks. However, the accuracy in magnitude and phase required for modeling a chronograph system is extremely demanding and previously inconsequential errors may be of the same order of magnitude as the physical phenomena under study. In this paper, effects of thick masks, finite conductivity metals, and various cross-section geometries on the transmission of pupil-plane masks are illustrated. Undercutting the edge shape of Cr masks improves the effective opening width to within λ/5 of the actual opening but TE and TM polarizations require opposite compensations. The deviation from ideal is examined at the reference plane of the mask opening. Numerical errors in TEMPEST, such as numerical dispersion, perfectly matched layer reflections, and source haze are also discussed along with techniques for mitigating their impacts.
The TPF mission to search for exo-solar planets is extremely challenging both technically and from a performance modeling perspective. For the visible light coronagraph approach, the requirements for 1e10 rejection of star light to planet signal has not yet been achieved in laboratory testing and full-scale testing on the ground has many more obstacles and may not be possible. Therefore, end-to-end performance modeling will be relied upon to fully predict performance. One of the key technologies developed for achieving the rejection ratios uses shaped pupil masks to selectively cancel starlight in planet search regions by taking advantage of diffraction. Modeling results published to date have been based upon scalar wavefront propagation theory to compute the residual star and planet images. This ignores the 3D structure of the mask and the interaction of light with matter.
In this paper we discuss previous work with a system model of the TPF coronagraph and propose an approach for coupling in a vector propagation model using the Finite Difference Time Domain (FDTD) method. This method, implemented in a software package called TEMPEST, allows us to propagate wavefronts through a mask structure to an integrated system model to explore the vector propagation aspects of the problem. We can then do rigorous mask scatter modeling to understand the effects of real physical mask structures on the magnitude, phase, polarization, and wavelength dependence of the transmitted light near edges. Shaped mask technology is reviewed, and computational aspects and interface issues to a TPF integrated system model are also discussed.