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

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

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

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

Estimating Substrate Losses for Rectangular Waveguides Using the Effective Index Method

y

x

TE-like Polarization(dominant electric field along x)

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

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

Six field components for TE-like mode of a rectangular wavguide

500 nm

Six field components for TM-like mode of a rectangular wavguide

500 nm

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

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)

SOI waveguide loss as a function of SiO2

thickness

TE-like Polarization TM-like Polarization

SiO2

Si

Si

SiO2

Si

Si

SiO2

Si

Si

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

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

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

Bending loss dependence on lower oxide thickness

SiO2

Si

Si

SiO2

Si

Si

TE-like Polarization TM-like Polarization

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

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

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

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)