Silicon-on-Insulator Slot-waveguide Design Trade-offs

Patrick Steglich

1,2

, Claus Villringer

, Silvio D

umecke

, Yazmin Padilla Michel

1,2

, Mauro Casalboni

and Sigurd Schrader

Faculty of Engineering and Natural Sciences, University of Applied Sciences Wildau, Wildau, Germany

Department of Industrial Engineering, University of Rome ”Tor Vergata”, Rome, Italy

Keywords:

Slot-waveguide, Silicon-organic Hybrid Technology, Optical Field Conﬁnement, Effective Nonlinear Area.

Abstract:

Silicon-on-insulator slot-waveguide structures are designed and analysed numerically. We present our theoret-

ical investigation of ﬁeld conﬁnement factors and effective nonlinear areas for different waveguide structures

in order to ﬁnd optimized geometrical dimensions. It is shown that a slot-waveguide with a height of 220 nm,

a slot width of 180 nm and a silicon rail width of 180 nm provides a ﬁve times higher ﬁeld conﬁnement in

the cladding region compared to conventional strip-waveguides which explains the high sensitivity of slot-

waveguide based label-free bio-sensors.

1 INTRODUCTION

The major advantage of slot-waveguides is the fact

that the guided light is conﬁned in-between two sil-

icon rails (Almeida et al., 2004). Consequently, the

light is forced to interact directly with the surrounding

material. Figure 1 shows a detailed cross-sectional

view and compares the guided optical ﬁeld in a strip-

waveguide to the one of a slot-waveguide. The reason

for this high conﬁnement in-between the silicon rails

is the large-index contrast of the high-index silicon

and the low-index surrounding material. At the inter-

face the normal electric ﬁeld, which is according to

Figure 1 the E

ﬁeld, undergoes a large discontinuity.

This results in a ﬁeld enhancement in the low-index

region which is proportional to the ratio of the dielec-

tric constant of the surrounding material to that of sil-

icon.

The high conﬁnement inside the slot is of special

beneﬁt for sensing and electro-optical applications.

The so called silicon-organic hybrid (SOH) technol-

ogy uses organic materials with exceptional high lin-

ear electro-optical coefﬁcients as surrounding mate-

rial (Vivien and Pavesi, 2013). Current electro-optic

modulators are based on semiconductors like silicon.

In silicon photonics, fundamental speed limitations

are related to carrier injection and removal (Vivien

and Pavesi, 2013). Therefore, parametric processes

are impaired by nonparametric processes like two-

photon absorption and become to the main speed lim-

iting factor. Additionally, silicon has a lack of lin-

ear electro-optical coefﬁcients. All this can be over-

come by using organic materials with nonlinear opti-

cal properties as active material.

Slot-waveguides are the key element in order to

integrate organic materials into silicon photonics. Be-

cause the organic materials offer high linear electro-

optical coefﬁcients once can generate advanced mod-

ulation formats (Korn et al., 2013). The reason for

that is that organic materials have less free-carrier

dispersion which normally leads to an intrinsic cou-

pling of amplitude and phase. For that reason, slot-

waveguides have been employed in order to develop

high-speed modulators for telecommunication inter-

connects (Weimann et al., 2014).

In the last decade integrated optical sensors

based on slot-waveguides have also been proposed

(Dell’Olio and Passaro, 2007) and developed (Bar-

Figure 1: Cross-sectional view of a SOI strip-waveguide

(left) and a SOI slot-waveguide (right). The pictures below

show the optical ﬁeld amplitude distribution. Both waveg-

uide structures are on top of a buried oxide (BOX) substrate.

Steglich P., Villringer C., Dümecke S., Padilla Michel Y., Casalboni M. and Schrader S..

Silicon-on-Insulator Slot-waveguide Design Trade-offs.

DOI: 10.5220/0005336200470052

In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2015), pages 47-52

ISBN: 978-989-758-093-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

rios et al., 2007). In case of label-free bio-sensors it

has been shown that the sensitivity of slot-waveguides

is more than three times higher compared to conven-

tional silicon strip-waveguides (Claes et al., 2009).

This fact is due to the high interaction between guided

light and the surrounding material.

The most challenging issue of SOH technology based

slot-waveguides is the compatibility with common

complementary-metal-oxide-semiconductor (CMOS)

fabrication processes since such integrated photonic

devices need a high integration rate and a cost efﬁ-

cient mass production environment.

For that reason, in this work we present design trade-

offs and an approach in order to improve SOI slot-

waveguide structures for a CMOS-like production en-

vironment. Typical ﬁgures of merit like the ﬁeld con-

ﬁnement factor and the effective nonlinear area are

calculated and discussed in detail.

There are several publications about ﬁeld conﬁnement

factors of slot-waveguide structures. These structures

consist of vertical silicon rails (Robinson et al., 2008)

or multiple nanolayers (Feng et al., 2006). However,

none of them consider SOI slot-waveguides with typ-

ical geometrical dimensions for CMOS-like produc-

tion processes using 200 mm SOI wafers with 220 nm

high SOH slot-waveguides.

In this work we present to our best knowledge a ﬁrst

comparison of common SOI strip-waveguides with

SOI slot-waveguides by the meaning of modal ﬁeld

conﬁnement inside the region of interest.

2 SILICON-ON-INSULATOR

SLOT-WAVEGUIDES

A SOI slot-waveguide consist of two silicon rails with

a ﬁxed height of 220 nm due to common CMOS-like

production restrictions. As it can be seen in Figure 1

both silicon rails are located on top of a buried oxide

(BOX) substrate and are separated from each other by

a slot width s and have a rail width w.

Lithographically fabricated slot-waveguides have due

to the side-wall roughness relatively high optical

losses of 10 dB/cm (Baehr-Jones et al., 2005) which

is ﬁve times higher compared to common strip-

waveguides (Vivien and Pavesi, 2013). Figure 2

shows one scanning electron microscopy picture of

three slot-waveguides with different slot widths from

the top view and one slot-waveguide in the cross-

sectional view recorded with a focused ion beam.

They are fabricated in a 130 nm SiGe BiCMOS pro-

duction line at the Institute of High-Performance

Microelectronics (IHP) in Frankfurt (Oder) using

200 mm SOI wafers and 248 nm DUV lithography.

Figure 2: Slot-waveguides with different slot widths fabri-

cated with a 248 nm DUV lithography.

Assuming a wavelength of 1550 nm, the refractive in-

dex for the silicon is n

= 3.48 and for the BOX sub-

strate n

box

= 1.444 (Palik, 1997; Tsang et al., 2002).

The refractive index of the surrounding material n

is variable because it can be air, gas, ﬂuid or an opti-

cal nonlinear material, depending on the application.

In the following we will use n

clad

as cladding refrac-

tive index instead of n

because we will consider

an organic cladding material. We choose n

clad

= 1.8

which corresponds to a commercially available and

reliable organic material named M3 (commercialized

by GigOptix Inc.). M3 is successfully used for several

slot-waveguide based electro-optical modulators like

in (Palmer et al., 2013a; Leuthold et al., 2013; Korn

et al., 2013; Palmer et al., 2013b).

3 SIMULATION OF

SLOT-WAVEGUIDES

For the calculation of waveguide eigenmodes we em-

ployed a commercial full-vectorial 2D ﬁnite element

method (FEM) based mode solver from COMSOL

Multiphysics

. Doing this we swept several parame-

ters like the silicon rail width and slot width whereas

the height is ﬁxed to 220 nm and the wavelength is

assumed to be 1550 nm. Triangular vector-elements

with a maximum and minimum element size of 8 nm

and 6 nm, respectively, have been adopted for mesh-

ing the proﬁle. We have always used over 12 · 10

mesh elements. For our simulations we consider a

total domain of D

tot

= 3 µm

which is illustrated in

Figure 1.

In order to yield the mode ﬁeld distribution and effec-

tive refractive index, the refractive index distribution

n(x,y) for the structure shown in Figure 1 need to be

declared to calculate eigenvalues and eigenfunctions

of the wave equation

∇ × (∇ × E) − k

E = 0, (1)

where k

is the wave number in free space. By do-

ing this we get the optical ﬁeld distribution for the

quasi-TE and quasi-TM mode as shown in Figure 3.

In the following we will neglect the quasi-TM mode

because it is over two times of magnitude smaller than

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

the quasi-TE mode. However, it should be mentioned

that the cross-section capture area for the surface is

typically greater for the quasi-TM mode in biosensing

applications due to the difﬁculty in functionalising the

interior of the slot.

Figure 3: Optical ﬁeld distribution for the quasi-TE and

quasi-TM mode of a SOI slot-waveguide.

3.1 Field Conﬁnement Factor of

Slot-waveguides

In order to design, develop and improve slot-

waveguides for applications in the ﬁeld of biopho-

tonic or high-speed modulators it is necessary to cal-

culate characteristic values which describe the con-

ﬁnement and therefore the interaction of light with

the surrounding material. One ﬁgure of merit of how

well the guided modal ﬁeld is conﬁned in a certain

region is the so-called ﬁeld conﬁnement factor. The

ﬁeld conﬁnement factor is usually deﬁned as the ra-

tio of the time averaged power ﬂow in the domain of

interest (D

int

) to the time averaged power ﬂow inside

the total domain (D

tot

)

Γ =

Z Z

int

Re{[E × H

∗

] · e

} dxdy

Z Z

tot

Re{[E × H

∗

] · e

} dxdy

. (2)

E and H are the electric and magnetic ﬁeld vectors,

respectively, and e

is the unit vector in z direction

(Chuang, 2009). There are three different cases in

order to choose the domain of interest. In case of

common strip-waveguides the domain of interest is

equal to the core region, D

int

core

. In contrast to

that, for bio-sensing applications the region of the

cover medium is considered to be the domain of in-

terest, D

int

cover

, which is valid for strip- and slot-

waveguides as well. Considering slot-waveguides for

electro-optical modulators the domain of interest is

equal to the slot region, D

int

slot

. All possible do-

mains of interest are illustrated in Figure 4. In case

of low-index-contrast waveguides, Equation 2 can be

simpliﬁed using the linear relationship between the

electric and magnetic ﬁeld for a plane-wave

Figure 4: Domains of interest: core D

core

, cladding D

clad

and slot D

slot

regions are highlighted in green. Please note

that the substrate is not included in the cladding region.

Z Z

Re{[E × H

∗

] · e

} dxdy =

ωµ

Z Z

|E|

dxdy,

(3)

which leads to

Γ =

Z Z

int

|E|

dxdy

Z Z

tot

|E|

dxdy

. (4)

However, for high-index-contrast waveguides and

especially for slot-waveguides this linear relation-

ship does not apply since they must satisfy different

boundary conditions (Robinson et al., 2008). Conse-

quently, in this work all conﬁnement factors are cal-

culated according to Equation 2.

3.2 Effective Nonlinear Area of

Slot-waveguides

A ﬁgure of merit of how well the waveguide geome-

try supports the nonlinear interaction is the so called

effective nonlinear area (Koos et al., 2007). The

smaller the effective nonlinear area provided by the

waveguide structure the higher the nonlinear interac-

tion which is important for electro-optical modula-

tors.

For the analysis of low-index-contrast systems, it

is usually assumed that the gradient of the dielectric

constant is approximately zero in the entire cross sec-

tion. But this approximation is not valid for high-

index-contrast material systems. Therefore, Koos et

al. derived the effective nonlinear area for high-index-

contrast waveguides in 2007 by using the slowly vary-

ing envelope approximation (Koos et al., 2007). The

Silicon-on-InsulatorSlot-waveguideDesignTrade-offs

effective nonlinear area results then from the nonlin-

ear Schr

odinger equation

e f f

clad



Z Z

tot

Re{[E × H

∗

] · e

} dxdy



Z Z

int



dxdy

, (5)

with the free-space wave impedance Z

/ε

≈

377 Ω. In our case is the domain of interest equal

to the cladding domain, D

int

= D

slot

. Equation 5

counts for high-index-contrast material systems. In

case of low-index-contrast material systems it can be

assumed that n

core

≈ n

clad

≈ n

box

≈ n

int

, and the lon-

gitudinal ﬁeld becomes negligible (Koos et al., 2007).

Furthermore, the transverse components of the elec-

trical ﬁeld E and the magnetic ﬁeld H can be ap-

proximated by a scalar function F with the condi-

tion E ≈ F · e

and H ≈ (n

int

)F · e

where e

and

are the unit vectors in x and y direction, respec-

tively (Koos et al., 2007). Further it can be stated that

int

= D

tot

if the nonlinearity is homogeneous in D

tot

Now Equation 5 becomes simpliﬁed to

e f f



Z Z

tot



dxdy



Z Z

int



dxdy

, (6)

which is similar to the common deﬁnition of an effec-

tive area (Agrawal, 2012).

4 RESULTS AND DISCUSSION

Calculated effective refractive indices n

e f f

as a func-

tion of the slot width s of SOI slot-waveguides are

shown in Figure 5. It can be seen that the effective

refractive index becomes higher by increasing the rail

width w and by decreasing the slot width s.

Figure 6 shows the obtained ﬁeld conﬁnement fac-

tor Γ

strip

for a silicon strip-waveguide. The domains

of interest are the core and the cladding. Please note

that the substrate is not included in the cladding do-

main. Therefore, the sum of core and cladding ﬁeld

conﬁnement factor is not equal to unity. As it can be

seen there is a high light conﬁnement in the core re-

gion. These results are in good agreement with the

literature (Vivien and Pavesi, 2013). In order to

maximize the sensitivity of SOI slot-waveguide based

label-free sensors it is necessary to maximize the ﬁeld

conﬁnement factor of the cladding Γ

clad

. From Figure

7 it can be seen that the conﬁnement in the cladding

region is increased by decreasing the rail width w and

increasing the slot width s. For w = 180 nm the high-

est conﬁnement in the cladding region is obtained in

Figure 5: Calculated effective refractive indices n

e f f

of SOI

slot-waveguides as function of the slot width s and with the

rail width w as parameter.

Figure 6: Field conﬁnement factor Γ

strip

of conventional

SOI strip-waveguides for the core and cladding region as a

function of the waveguide width wg.

the parameter range of our simulation. This result

is in good agreement with (Dell’Olio and Passaro,

2007). For the slot-waveguide with w = 180 nm and

s = 180 nm we obtain a ﬁeld conﬁnement factor of

clad

= 0.69. This is an enhancement of about ﬁve

times compared to a conventional strip-waveguide

with a typical waveguide width of wg = 500 nm.

With that result, the high sensitivity of slot-waveguide

based label-free sensors as stated by Claes et al. can

be explained (Claes et al., 2009). However, due to the

difﬁculty in functionalising the interior of the slot the

sensitivity can be smaller than expected.

In order to improve SOI slot-waveguides for

electro-optical applications it is necessary to ﬁnd the

highest conﬁnement in the slot region. Figure 8 de-

picts the obtained ﬁeld conﬁnement factors for the slot

region Γ

slot

as a function of the slot width s and the

rail width w as parameter. It can be seen that there

is one maximum of the highest ﬁeld conﬁnement of

slot

= 0.216 at a slot width of s = 116 nm and a

rail width of w = 200 nm. This is about four times

smaller compared to a SOI strip-waveguide. How-

ever, in this case it is more convenient to relate the

ﬁeld conﬁnement factor Γ

slot

to the area where the

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

Figure 7: Field conﬁnement factor Γ

clad

of a SOI slot-

waveguide for the cladding region in dependence on the slot

width s.

Figure 8: Field conﬁnement factor Γ

slot

of a SOI slot-

waveguide for the slot region as a function of the slot width

s and the rail width w as parameter.

Figure 9: Calculated effective nonlinear area A

e f f

of SOI

slot-waveguides in dependence on the slot width s. The rail

width w was varied as parameter.

light is conﬁned as ﬁgure of merit, FOM = Γ

slot

and FOM = Γ

strip

. In our case A

slot

is equal

to D

slot

and A

strip

is equal to D

core

. With that we

can show for our example that the FOM for a SOI

slot-waveguide (s = 116 nm, w = 200 nm) is about

four times higher compared to that one of a strip-

waveguide (wg = 500 nm) which conﬁrms our results

for the cladding ﬁeld conﬁnement and other publica-

tions like (Almeida et al., 2004).

Furthermore, it is necessary to minimize the effec-

tive nonlinear area A

e f f

in order to improve SOI slot-

waveguides for third order nonlinear effects. Figure

9 indicates that there is a minimum in the parameter

range of our simulation of A

e f f

= 0.032 µm

for a slot

width of s = 80 nm and a rail width of w = 225 nm.

Our results are in good agreement with (Muellner

et al., 2009).

5 CONCLUSION

Simulation and analysis of SOI slot-waveguides have

been carried out and ﬁeld conﬁnement factors and

effective nonlinear areas have been thoroughly cal-

culated with the Finite Element Method. Field con-

ﬁnement factors have been calculated in the slot and

cladding region. According to our simulation, SOI

slot-waveguides provide about ﬁve times higher ﬁeld

conﬁnement in the cladding region compared to con-

ventional SOI strip-waveguides. These results can be

used for design optimization in order to achieve op-

timal SOI slot-waveguide dimensions for sensing ap-

plications. For the slot region we have found a maxi-

mum conﬁnement of Γ

slot

= 0.216 which is compared

to a SOI strip-waveguide about four times smaller.

However, relating it to the area there the light is con-

ﬁned it is four times higher compared to a SOI strip-

waveguide. For the effective nonlinear area we have

found a minimum of about A

e f f

= 0.032 µm

for our

simulated parameter range. In total, we have demon-

strated design trade-offs and an approach in order to

improve SOI slot-waveguide structures.

ACKNOWLEDGEMENTS

The authors would like to thank the German Federal

Ministry of Education and Research (BMBF) for the

ﬁnancial support under contract no. 03FH086PX2,

the University of Applied Sciences Wildau (THWi),

Germany, and the Ministry of Science, Technology

and Culture of the federal state Brandenburg, Ger-

many, for ﬁnancial support. The authors would also

like to thank Fr. Nanni, P. Prosposito, F. De Matteis,

and R. De Angelis from the University of Rome Tor

Vergata, Italy, St. Meister and A. Al-Saadi from the

Technical University Berlin, Germany, and L. Zim-

mermann, D. Knoll, D. Stolarek, J. Katzer, St. Lis-

chke, H. Silz, B. Tillack and W. Mehr from the In-

stitute of High-Performance Microelectronics (IHP),

Germany, for their encouragement and support in the

framework of the Joint-Lab IHP-THWi.

Silicon-on-InsulatorSlot-waveguideDesignTrade-offs

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