dependence of waveguide loss on lower oxide cladding...
TRANSCRIPT
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Dependence of Silicon-On-Insulator Waveguide Loss on Lower Oxide Cladding Thickness
Adam Mock and John O'Brien
University of Southern CaliforniaMicrophotonic Device Group
July 16, 2008IPNRA - IWG4
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Optical Loss Due to High Index Substrate
400 nm
Thermal Conductivity
Si 1.5 W / (cm K) SiO
2 0.015 W / (cm K)
- A thermally insulating SiO2 layer may not be compatible with the heat
dissipation requirements of VLSI circuits
- A sufficiently thick SiO2 layer is required for optical confinement
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Presentation Outline
Simple model for estimating substrate leakage
Compact FDTD method for the numerical analysis of leaky waveguides
Dependence of waveguide loss on SiO2 thickness
Bending loss analysis using FDTD formulation for cylindrical symmetry
Alternative waveguide cross sections that reduce substrate leakage
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Estimating Substrate Losses for Rectangular Waveguides Using the Effective Index Method
P z =P0 e− z=P0−P substrate
Assume evanescent field becomes propagating field in Si substrate to obtain P
substrate
Use effective index method to obtain the propagation constant and field profile assuming infinite SiO
2 substrate
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Estimating Substrate Losses for Rectangular Waveguides Using the Effective Index Method
y
x
TE-like Polarization(dominant electric field along x)
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Finite-Difference Time-Domain Method for Dielectric Waveguides Uniform Along Propagation Direction
Compact FDTD: Six vector components on a 2-d gridAssume functional form F(x,y,z) = F(x,y)e-iβz for 6 field components
with β specified by user
∂ Dxi , j1 /2
∂ t= 1
yH z
i , j1−H zi , j−−i H y
i , j1 /2
∂ D yi−1 / 2, j1
∂ t=−i H x
i , j1 /2− 1 x
H zi , j1−H z
i−1, j1
∂ Dzi , j1
∂ t= 1
xH y
i , j1 /2−H yi−1, j1 /2− 1
yH x
i−1 /2, j 1−H xi−1 /2, j
∂ Bxi−1 /2, j1
∂ t=−i E y
i−1 /2, j 1− 1 y
E zi−1 /2, j 3/2− E z
i− 1/2, j1 /2
∂ B yi , j1 /2
∂ t= 1 x
E zi1 /2, j1 /2−E z
i−1 /2, j1/2−−i Exi , j1 /2
∂ B zi , j1
∂ t= 1
yEx
i , j3 /2−Exi , j1 /2− 1
xE y
i1 /2, j1−E yi−1 /2, j1
{{{
x-components
y-components
z-components
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Numerical analysis method
- Broadband initial condition to excite all waveguide modes
- Propagate the fields in time for 70,000 FDTD time steps
- 15 layers of PML on all boundaries to absorb leaky radiation from the waveguide
- Padé interpolation to resolve spectral widths due to substrate loss
DFT of time sequence Padé interpolation
Q=f 0 f
=0vgQ
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Six field components for TE-like mode of a rectangular wavguide
500 nm
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Six field components for TM-like mode of a rectangular wavguide
500 nm
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Propagation loss calculated numerically and using effective index method
TE-like Polarization TM-like Polarization
Gray curves correspond to estimated loss using effective index model
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Propagation loss for different rectangular waveguide cross sections with a 500nm SiO
2 layer
500 nm SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
TE-like Polarization TM-like Polarization
Consistent with experimental reportsXiao et al. Opt. Expr. 15 10553 (2007)Vlasov et al. Opt. Expr. 12 1622 (2004)
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SOI waveguide loss as a function of SiO2
thickness
TE-like Polarization TM-like Polarization
SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
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FDTD for cylindrical symmetry: estimation of bending loss from SOI ring resonators
∂Dri , j1 /2
∂ t= 1 z
Hi , j−H
i , j1−mr 0H zi , j1/2
∂Bri , j1 /2
∂ t= 1 z
Ei , j1−E
i , j−mr1E zi , j1 /2
∂Di1 /2, j1/2
∂ t= 1 r
H zi , j1 /2−H z
i1, j1 /2 1 z
H ri1 /2, j1−H r
i1 /2, j
∂Bi1/2, j1/2
∂ t= 1r
E zi1, j1 /2−E z
i , j1/2 1 z
Eri1/2, j−E r
i1 /2, j1
∂D zi1 /2, j
∂ t=2r2r22−r1
2 Hi1, j−
2 r1r22−r1
2 Hi , j2mr
r22−r1
2 H ri1/2, j
∂B zi1/2, j
∂ t=2 r2r 22−r1
2 Ei , j−
2r1r22−r1
2 Ei1, j2m r
r22−r1
2 Eri1 /2, j
{{{
r-components
φ-components
z-components
Assume functional form F(r,φ,z) = Fμ(r,z)e+imφ + F
ν(r,z)e-imφ
for 6 field components with integer m specified by user
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Bending loss calculated from FDTD ring resonator losses with 500 nm SiO
2
SiO2
Si
Si
SiO2
Si
Si
TE-like Polarization TM-like Polarization
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Bending loss calculated from FDTD ring resonator losses with 500 nm SiO
2
TE-like Polarization TM-like Polarization
SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
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Bending loss dependence on lower oxide thickness
SiO2
Si
Si
SiO2
Si
Si
TE-like Polarization TM-like Polarization
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Bending loss dependence on lower oxide thickness
TE-like Polarization TM-like Polarization
SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
SiO2
Si
Si
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Waveguide geometries for reducing substrate loss
TE-like Polarization TM-like Polarization
y
x
-
TE-like Polarization TM-like Polarization
SiO2
Si
Si
SiO2
Si
SiO2
Si
Si
SiSi
Dependence of loss on SiO2 thickness
400 nm
400 nm400 nm400 nm
400 nm
300 nm
300 nm
100 nm
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Dependence of loss on SiO2 thickness
TE-like Polarization TM-like Polarization
SiO2
Si
Si
SiO2
Si
Si
Si
waveguide losstotal bend loss
waveguide losstotal bend loss
waveguide losstotal bend loss
waveguide losstotal bend loss
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Summary
Method for estimating substrate loss in SOI waveguides
FDTD numerical method for leaky wave analysis
Investigated loss as a function of SiO2 thickness
- 300nm to 400nm required for α < 5 cm-1 - not limited by bending loss even for r = 1μm
Alternative waveguide geometries that reduce substrate loss
AcknowledgementsDefense Advanced Research Projects Agency (DARPA)
National Science Foundation (NSF)
University of Southern California Center for High Performance Computing and Communications (USC HPCC)