Daniel P. Ceperley

Self-Organized Silver Nanoparticles for Three-Dimensional Plasmonic Crystals

Metal nanostructures that support surface plasmons are compelling as plasmonic circuit elements and as the building blocks for metamaterials. We demonstrate here the spontaneous self-assembly of shaped silver nanoparticles into three-dimensional plasmonic crystals that display a frequency-selective response in the visible wavelengths. Extensive long-range order mediated by exceptional colloid monodispersity gives rise to optical passbands that can be tuned by particle volume fraction. These metallic supercrystals present a new paradigm for the fabrication of plasmonic materials, delivering a functional, tunable, completely bottom-up optical element that can be constructed on a massively parallel scale without lithography.

Fabrication and characteristics of free-standing shaped pupil masks for TPF-coronagraph

Direct imaging and characterization of exo-solar terrestrial planets require coronagraphic instruments capable of suppressing star light to 10-10. Pupil shaping masks have been proposed and designed1 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 mask edges and mitigation techniques for the TPF Coronagraph

Stray-light sources from pupil plane masks that may limit Terrestrial Planet Finder Coronagraph (TPF-C) performance are characterized1,2 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.3 Of particular interest are simulations of 100m thick vertical sidewall openings that model features typically found on Ripple masks4 fabricated by Reactive Ion Etching (RIE) processes.5 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 masks 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.

Modeling and simulation for nanometricsa)

Nanoscale phenomena and especially surface plasmon-based optical devices are playing important roles in historical and emerging applications of photography, instrumentation, imaging, and signal processing. Simulation of these devices is synergistic with invention, and commercial computer-aided design infrastructure will eventually follow to cope with design and manufacturing. Devices based on source-free solutions to Maxwell’s equations, such as plasmons and guided waves, are emphasized. They include the Daguerrotype and plasmon scattering from topographical features. A more general survey of the applications of simulation to optical nanodevices is also included. For finite-difference time domain using up to 250 million nodes, the major computational challenges are associated with the nm-level detail of large distributed structures, the small real part of the refractive index, and the necessity to accurately compute phases.

Wavelength and polarization dependent absorbtion effects in millisecond annealing of metal gate structures

Finite difference time domain simulation of the electromagnetic coupling in millisecond radiation heating is used to explore how the energy couples, where it goes in the device structure, and wavelength dependencies. Millisecond annealing is advantageous for improving IC device characteristics; however, the application of short time scale annealing requires very careful control over the localized heating that can be pattern, device structure, and material dependent. The presence of metal gate structure introduces extra complexity. This paper considers the case of tungsten gates on poly-silicon pedestals with or without silicon nitride caps. Rigorous finite difference time domain techniques are used to compute the fields throughout the device structure as a function of polarization, angle of incidence, wavelength, CD, and pitch. One of the dominant effects is that a grating formed by a metal gate array acts like a polarizer. Thus the coupling changes with grating orientation. The coupling is the strongest when the incident plane is perpendicular to the gate and the electric field is p-polarized. In the case of laser light with a 10 μm wavelength incident near silicon’s Brewster angle, the absorptivity approaches 100% just as if the tungsten metal gates do not exist. Data from similar studies at shorter wavelengths is also presented as well as a comparison with experimental measurements.

Engineering surface plasmon grating couplers through computer simulation

Surface plasmon grating couplers are optimized by separately characterizing the collection efficiency, rescattering, and transmission effects of isolated grating elements with finite difference time domain methods and then using signal flow graph methods to assess the performance of arrays of N identical elements. Small bars, ridges, and trenches on silver at a wavelength of 700nm are shown to have different coupling patterns and efficiencies from near zero to the physical width of the element. The overall efficiency requires a suitable trade-off of coupling and surface wave transmission and an example structure exhibiting an equivalent 100% capture length over ten wavelengths is shown.

Characterizing edge-generated stray light sources for TPF Coronagraph pupil masks

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 Maxwells 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° 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.

Simulating novel EM effects

Numerical simulation is a useful tool for evaluating new technologies. In order to analyze new plasmonic and photonic band-gap devices we have re-written and extended our finite-difference time-domain (FDTD) simulator, TEMPEST, into a guided-wave analysis system. We illustrate our new simulation capabilities with investigations into two devices: 1) a sub-wavelength grating mirror, and 2) plasmon-enhanced Daguerreotype photographs.

Characterization and monitoring of photomask edge effects

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 0th 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 0th order field away from the expected thin mask location. The square root of the minimum 0th 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.

Vector Scattering Analysis of TPF Coronagraph Pupil Masks

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.