Circular Grating Resonators as Candidates for Ultra-SmallPhotonic Devices

Sophie Schonenbergera, Nikolaj Molla, Thilo Stoferlea, Thorsten Wahlbrinkb, Jens Boltenb,Stephan Gotzingerc, Thomas Mollenhauerb, Christian Moormannb, Rainer F. Mahrta, and

Bert J. Offreina

a IBM Research, Zurich Research Laboratory, Saumerstrasse 4, 8803 Ruschlikon, Switzerland

b Advanced Microelectronic Center Aachen (AMICA), AMO GmbH, Otto-Blumenthal-Strasse25, 52074 Aachen, Germany

c Nano-Optics Group, Laboratory of Physical Chemistry, ETH Zurich, 8093 Zurich.Switzerland

March 11, 2008

ABSTRACT

We investigate circular grating resonators (CGR) with a very small footprint. Photonic devices based on cir-cular grating resonators are computationally designed, optimized and studied in their functionality using finite-difference time-domain (FDTD) method. A wide variety of critical quantities such as transmission and reflection,resonant modes, resonant frequencies, and field patterns are calculated. Due to their computational size someof these calculations have to be performed on a supercomputer (e.g. parallel Blue Gene machine). The de-vices are fabricated in SOI using the computational design parameters. First they are defined by electron-beamlithography. Then the pattern transfer is achieved by an inductively coupled reactive-ion etch process. Finally,the devices are characterized by coupling light from a tunable laser with a tapered lensed fiber. As predictedfrom the simulations the measured transmission spectra exhibit a wide range of different type of resonances withquality factors exceeding 1000.

1. INTRODUCTION

For future applications in telecommunication networks, such as chip-to-chip or on-chip optical interconnects,a high physical integration density is necessary. Exploiting integrated micro-cavities could lead to such highlydense and novel optical devices.1–4 Microcavities could lead to the development of advanced silicon-on-insulator(SOI) based nano-photonic devices. They are clearly beyond state of the art in terms of functionality, size, speedand integration density.

This paper reports on a specific type of integrated micro-cavities, namely circular grating resonators (CGR).5, 6

Even at low refractive index contrasts, CGRs offer full two-dimensional light confinement. They can have a verysmall footprint of a few micrometers, which essentially corresponds to one of the smallest optical resonators.Because the volume in which the light is confined is so small, also the refractive index change which has tobe induced for switching can be very small. Therefore, it is expected that the use of CGRs will enable high-speed electro-optical modulators to be built. This makes CGRs a very promising candidate for future integratedphotonic devices.

The design of such a CGR is illustrated in Fig. 1. It is fabricated in silicon-on-insulator (SOI) technology bylithography and etching. Finally, it is cladded with SiO2. It consists of concentric rings of silicon with a perioda and a thickness h surrounding the center defect with a radius rc. The circular grating around the center discacts as a Bragg mirror and imposes a photonic band gap, i.e. stop band, which prevents lateral leakage of lightfrom the cavity. The resonance frequency of such a cavity is then mainly determined by rc. Waveguides whichpenetrate the circular grating act as in- and out-coupling waveguides. The partial penetration of the circulargrating improves the coupling from the waveguides to the defect in the center. Light which does not propagatefrom the defect into the direction of the waveguides will be reflected back and trapped in the center of the device.

Silicon Photonics and Photonic Integrated Circuits, edited by Giancarlo C. Righini, Seppo K. Honkanen, Lorenzo Pavesi,Laurent Vivien, Proc. of SPIE Vol. 6996, 69960A, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.780176

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SiO2

Si

Figure 1. A CGR consisting of a central defect and concentric rings of silicon with in-coupling and out-coupling waveguides.

2. DESIGN OF THE CIRCULAR GRATING RESONATORS

To achieve a small cavity volume, which is imperative for high switching speeds, we optimize the geometricparameters of the circular grating to maximize the band gap. A larger band gap leads to a larger reflectivityR of the circular grating for the same number of gratings. Therefore, the light decays faster inside the circulargrating and decreases the spatial extension of the cavity mode.

The band gap of the circular grating can be approximated by the corresponding linear grating which inprinciple is the cross section of the circular grating, see Fig. 2. The duty cycle D = q/a is defined as the ratiobetween the width of the gap q and the grating period a. The height h of the Si structure, the duty cycle D,and the lattice constant a are three free parameters for the mirror structure. These parameters are varied toobtain the largest possible band gap centered around the wavelength λ = 1550 nm, which is commonly used intelecommunication applications.

The band structure of this linear grating is computed using a simulation tool called MIT Photonic Bands(MPB7), which is based on a frequency-domain technique. It performs a direct computation of the eigenstatesand eigenvalues of the full Maxwell’s equations in a plane wave basis. We calculate the upper and lower edgesof the band gap ν2 and ν1, respectively. Thus, the band gap center frequency νm = (ν1 + ν2)/2 as well as therelative width υ = (ν2 − ν1)/νm of the band gap can be obtained.

In this paper we will focus on TM polarization. Therefore, the electric field compontent is in the z-direction.7

However, our procedures can also be applied to the TE polarization.

z

r

Si

SiO2SiO2

h

q

a

Figure 2. The radial cross section of the linear grating of a 3D CGR in silicon with a height h, a lattice constant a and aduty cycle D = q/a. The hole structure is cladded with SiO2.

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0 100 200 300 400 500 600 700 800height [nm]

0

0.1

0.2

0.3

0.4

band

gap

340nm

Figure 3. Band gap of the linear grating centered around λ =1550 nm as a function of the Si thickness h. Each of thecircles represents one configuration with a certain duty cycle D = q/a, lattice constant a and height h.

0 0.2 0.4 0.6 0.8 1duty cycle

0

0.05

0.1

0.15

0.2

band

gap

0 0.2 0.4 0.6 0.8 1200

300

400

500

600

latti

ce c

onst

ant (

nm)

lattice constant

band gap

Figure 4. Band gap and the grating period centered around λ =1550 nm as a function of the duty cycle D for a Si thicknessh = 340 nm.

The results of our calculations are shown in Fig. 3. There is a maximum relative band gap width of 16% fora thickness h ∼= 320 nm. For larger thicknesses, even larger band gaps can be achieved.

Because later the fabrication of the device will be made using SOI wafers with a Silicon thickness of 340 nm,we chose this height for our device design. In Fig. 4 the band gap and the lattice constant are plotted as afunction of the duty cycle for a silicon thickness of 340 nm. The linear grating which maximizes the band gapfor a Si thickness of 340 nm has a duty cycle of 0.65 and a lattice constant of 467 nm.

To achieve the target specification of switching on a picosecond timescale, we designed a CGR with a quality-factor Q of a few thousands. This gives us a target reflectivity R of the circular gratings of 85%, which correspondsto 6 to 8 grating periods around the defect.

To build an electro-optical modulator in silicon it is necessary to study the quality factor and the confinementfactor of such devices. Typically charge carrier injection is applied to change the refractive index8 by about∆n = 1.5 10−3. From theoretical studies a confinement factor of 80% can be obtained. These leads to an opticalswitching speed of about 15 ps or 70 GHz,9 which corresponds to a quality factor of about 2800.

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2pnH-H2 µm

Figure 5. SEM picture of a CGR device fabricated in Si.

3. CHARACTERIZATION OF THE FABRICATED DEVICES

The CGR devices are fabricated on SOI substrates consisting of a 2 µm buried oxide layer and a 340 nm devicelayer. The devices have been defined by electron-beam lithography (EBL) using hydrogen silsesquioxane (HSQ)as negative tone resist. Then pattern transfer has been achieved in a HBr-chemistry-based inductively coupledreactive-ion etch process. A two-step process has been used. First, in the main etch step, pure HBr has beenused. The etching time for this step is set to stop at a residual top-Si thickness of 20 nm. Then the etchconditions were changed to the second or overetch step. For this part a mixture of HBr and O2 is used. Theoveretch step exhibits an excellent selectivity between the top-Si and the buried oxide. The entire process flow,including both lithography and etching, has been optimized to minimize the surface roughness of the CGRs. Ascanning electron microscope (SEM) picture of a CGR device is shown in Fig. 5.

The CGRs have been characterized as passive devices. To characterize the CGR devices polarized light froma tunable continuous wave laser source is coupled into the device by using tapered lensed fibers near the cleavedwaveguide facets. The output light is collected again with a tapered lensed fiber and analyzed in a power meter.The measured transmission spectrum of a CGR with a duty cycle of 0.65 and a lattice constant of 467 nm with10 outer and 6 inner circles is shown in Fig. 6. The defect radius varies between 770 nm and 790 nm. Foreach defect radius the transmission spectrum shows a couple of sharp resonances with quality factors of a fewthousands and a contrast on/off ratio (corresponding to peak height) of approx. 10 to 15 dB. Varying the defectradius shifts these resonances to shorter wavelengths regularly increasing defect size. Some other features of thetransmission spectra of the CGRs, however, remain the same when varying the defect radius. These features arenot due to transmission through the defect.

Looking at the polarization dependency of the device we note different transmission spectra for TE andTM. As expected, this dependency vanishes outside the band gap. To obtain the absolute transmission of thedevice the transmission spectrum must be normalized to straight waveguides. When measuring different straightwaveguides we observe that most of them have qualitatively the same spectral shape of the transmission. Theabsolute transmission however varies around 5 dB due to variations in the input coupling efficiency or variationsin the waveguides. Thus, we inherit this uncertainty to the absolute transmission.

Because variations on the order of a few nanometers can significantly affect the device performance, weevaluate the reproducibility of the fabrication process from chip to chip by measuring the same CGR deviceon different chips. The spectrum shape and relative positions of the resonant features are nicely reproduced.However, we observe a 5 nm shift in absolute wavelength for all resonances, which is about 0.3% of the wavelength.

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Figure 6. Measured transmission spectra of CGR devices with a duty cycle D = 0.65, a lattice constant a = 467 nm anddefect radii rc from 810 nm to 830 nm.

For such a shift, the radius of central defect size has to be changed by 3 nm. This agrees very well with theexpected tolerances of the fabrication process.

The measured transmission spectra of the CGRs show a large number of resonances. Not all of them canbe assigned to resonances found in the simulations. For a working modulator at a certain wavelength a reso-nance should be chosen for which most of its intensity is located in the central defect. To analyze the spectraldistribution of the modes further measurements, for example scanning near field optical microscopy (SNOM)measurements.10, 11

4. CONCLUSIONS

We designed circular grating resonator (CGR) devices computationally and studied their functionality. Using thecomputational design parameters the CGR devices were fabricated in SOI. The measured transmission spectraexhibit different types of resonances with Q-factors exceeding 1000 and a transmission up to 40%.

The high confinement factor of the optical mode in the high refractive index Si allows electro-optical modulatorwith optical switching speed of about 15 ps or 70 GHz.

Acknowledgments

The authors would like to acknowledge the support by the EU-Project ”Circles of Light”.

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