# Simulation Framework for Electromagnetic Effects in Plasmonics, Filter Apertures, Wafer Scattering, Grating Mirrors, and Nano-Crystals

### Daniel Peter Ceperley

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2008-146

December 2, 2008

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-146.pdf

This thesis presents a Finite-Difference Time-Domain simulation framework as well as both scientific observations and quantitative design data for emerging optical devices. These emerging applications required the development of simulation capabilities to carefully control numerical experimental conditions, isolate and quantifying specific scattering processes, and overcome memory and run-time limitations on large device structures. The framework consists of a new version 7 of TEMPEST and auxiliary tools implemented as Matlab scripts. In improving the geometry representation and absorbing boundary conditions in TEMPEST from v6 the accuracy has been sustained and key improvements have yielded application specific speed and accuracy improvements. These extensions include pulsed methods, PML for plasmon termination, and plasmon and scattered field sources. The auxiliary tools include application specific methods such as signal flow graphs of plasmon couplers, Bloch mode expansions of sub-wavelength grating waves, and back-propagation methods to characterize edge scattering in diffraction masks.

Each application posed different numerical hurdles and physical questions for the simulation framework. The Terrestrial Planet Finder Coronagraph required accurate modeling of diffraction mask structures too large for solely FDTD analysis. This analysis was achieved through a combination of targeted TEMPEST simulations and full system simulator based on thin mask scalar diffraction models by Ball Aerospace for JPL. TEMPEST simulation showed that vertical sidewalls were the strongest scatterers, adding nearly 2λ of light per mask edge, which could be reduced by 20◦ undercuts.

TEMPEST assessment of coupling in rapid thermal annealing was complicated by extremely sub-wavelength features and fine meshes. Near 100% coupling and low variability was confirmed even in the presence of unidirectional dense metal gates.

Accurate analysis of surface plasmon coupling efficiency by small surface features required capabilities to isolate these features and cleanly illuminate them with plasmons and plane-waves. These features were shown to have coupling cross-sections up to and slightly exceeding their physical size. Long run-times for TEMPEST simulations of finite length gratings were overcome with a signal flow graph method. With these methods a plasmon coupler with over a 10λ 100% capture length was demonstrated.

Simulation of 3D nano-particle arrays utilized TEMPEST v7’s pulsed methods to minimize the number of multi-day simulations. These simulations led to the discovery that interstitial plasmons were responsible for resonant absorption and transmission but not reflection.

Simulation of a sub-wavelength grating mirror using pulsed sources to map resonant spectra showed that neither coupled guided waves nor coupled isolated resonators accurately described the operation. However, a new model based on vertical propagation of lateral Bloch modes with zero phase progression efficiently characterized the device and provided principles for designing similar devices at other wavelengths.

**Advisor:** Andrew R. Neureuther

BibTeX citation:

@phdthesis{Ceperley:EECS-2008-146, Author = {Ceperley, Daniel Peter}, Title = {Simulation Framework for Electromagnetic Effects in Plasmonics, Filter Apertures, Wafer Scattering, Grating Mirrors, and Nano-Crystals}, School = {EECS Department, University of California, Berkeley}, Year = {2008}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-146.html}, Number = {UCB/EECS-2008-146}, Abstract = {This thesis presents a Finite-Difference Time-Domain simulation framework as well as both scientific observations and quantitative design data for emerging optical devices. These emerging applications required the development of simulation capabilities to carefully control numerical experimental conditions, isolate and quantifying specific scattering processes, and overcome memory and run-time limitations on large device structures. The framework consists of a new version 7 of TEMPEST and auxiliary tools implemented as Matlab scripts. In improving the geometry representation and absorbing boundary conditions in TEMPEST from v6 the accuracy has been sustained and key improvements have yielded application specific speed and accuracy improvements. These extensions include pulsed methods, PML for plasmon termination, and plasmon and scattered field sources. The auxiliary tools include application specific methods such as signal flow graphs of plasmon couplers, Bloch mode expansions of sub-wavelength grating waves, and back-propagation methods to characterize edge scattering in diffraction masks. Each application posed different numerical hurdles and physical questions for the simulation framework. The Terrestrial Planet Finder Coronagraph required accurate modeling of diffraction mask structures too large for solely FDTD analysis. This analysis was achieved through a combination of targeted TEMPEST simulations and full system simulator based on thin mask scalar diffraction models by Ball Aerospace for JPL. TEMPEST simulation showed that vertical sidewalls were the strongest scatterers, adding nearly 2λ of light per mask edge, which could be reduced by 20◦ undercuts. TEMPEST assessment of coupling in rapid thermal annealing was complicated by extremely sub-wavelength features and fine meshes. Near 100% coupling and low variability was confirmed even in the presence of unidirectional dense metal gates. Accurate analysis of surface plasmon coupling efficiency by small surface features required capabilities to isolate these features and cleanly illuminate them with plasmons and plane-waves. These features were shown to have coupling cross-sections up to and slightly exceeding their physical size. Long run-times for TEMPEST simulations of finite length gratings were overcome with a signal flow graph method. With these methods a plasmon coupler with over a 10λ 100% capture length was demonstrated. Simulation of 3D nano-particle arrays utilized TEMPEST v7’s pulsed methods to minimize the number of multi-day simulations. These simulations led to the discovery that interstitial plasmons were responsible for resonant absorption and transmission but not reflection. Simulation of a sub-wavelength grating mirror using pulsed sources to map resonant spectra showed that neither coupled guided waves nor coupled isolated resonators accurately described the operation. However, a new model based on vertical propagation of lateral Bloch modes with zero phase progression efficiently characterized the device and provided principles for designing similar devices at other wavelengths.} }

EndNote citation:

%0 Thesis %A Ceperley, Daniel Peter %T Simulation Framework for Electromagnetic Effects in Plasmonics, Filter Apertures, Wafer Scattering, Grating Mirrors, and Nano-Crystals %I EECS Department, University of California, Berkeley %D 2008 %8 December 2 %@ UCB/EECS-2008-146 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-146.html %F Ceperley:EECS-2008-146