Low-Loss Grating-Coupled Silicon Ridge Waveguides and Ring Resonators for OpticalGain at Telecommunication Frequencies

J. P. Balthasar MullerScience Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavık, Iceland

Ryan M. Briggs and Harry A. AtwaterCalifornia Institute of Technology, Pasadena, California 91125, USA

(Dated: October 17, 2009)

Low-loss grating-coupled ridge waveguides and ring resonators have been modeled and fabricatedon silicon-on-insulator wafers. Theoretical models were developed and used to determine propertiesof the waveguides, and an optimized fabrication process has been employed to minimize loss. Theresonators exhibit an intrinsic quality factor as high as Q = 537, 000, corresponding to propagationloss of 1.23dB/cm. We also discuss modal gain as a function of bulk gain for active materialsintegrated with waveguide structures. This represents a significant step towards a C-band emittingCMOS compatible light source.

Recent advances in the dense integration of silicon-based passive photonic components have highlighted thepossibility of complex optical devices for computation,sensing, and telecommunications technology on the samechip as conventional CMOS electronics. Silicon-based de-vices exhibiting optical gain at frequencies below the sil-icon band gap would constitute critical components, buthave yet to be demonstrated. The development of such alight source is hindered by the weak emission propertiesof suitable emitters, such as erbium-doped glass, in com-bination with relatively high propagation losses in siliconwaveguide structures.3

High index-contrast silicon-on-insulator (SOI) ridgewaveguide structures can be fabricated on pre-existingCMOS fabrication lines and have been demonstratedwith very low losses.6 7 We believe that quasi-planar lightsources may be constructed by integrating ridge waveg-uide ring resonator structures with a suitable gain ma-terial. Using wafer bonding, the ridge waveguides canfurthermore be combined into slot waveguide structures(Fig. 1) which are capable of drastically improving theproperties of emitters in the narrow slot region throughenhanced radiative emission, which may enable an effi-cient light source that can be pumped electrically throughthe silicon.1 2 3 4 As a gain material covering the ridgewaveguides, we here consider erbium-doped yttria films.As gain material in the slot region of slot waveguides weconsider erbium-doped silica glass.

In the following, we discuss the main loss mechanismsin high-index-contrast single-mode ridge waveguides aswell as the modal gain as a function of the bulk activematerial gain. Furthermore, we demonstrate fabricatedlow-loss grating coupled ridge waveguides and ring res-onators in SOI. Fig. 2 shows an optical microscope imageof the fabricated structures.

Using single-crystalline silicon, the main source ofpropagation loss in the waveguides is due to roughness-induced scattering at the material boundaries. This losscan be shown to scale with the third power of the refrac-tive index difference and therefore constitutes a major

FIG. 1: Cross-sections of SOI a) ridge and b) slot waveguideswithout upper cladding.

FIG. 2: Optical micrograph of a fabricated grating-coupledridge waveguide and ring resonator with the electron-beamresist mask still in place.

challenge in the design and fabrication of silicon waveg-uides.9

In quasi-transverse-magnetic (TM) mode operation,losses also arise due to leakage of the guided TM-polarized mode into the transverse-electric (TE) modesupported by the silicon slab. This is due to mode con-version at the vertical ridge sidewalls creating quasi-TEpolarized radiation of higher effective index than the slabTE mode. This loss cannot be reduced through opti-mized fabrication processes but has been shown to bedrastically reduced for certain widths of the ridge, atwhich some of the leaking radiation interferes destruc-tively. These ”magic” widths, W , are, for single modeoperation, given by equation Eq. (1) below:

2

W =�√

n2TE,core − n2

TM,guided

(1)

Here, � represents the wavelength in free space, nTE,core

the effective fundamental guided TE mode index of a sili-con slab with thickness equivalent to the thickness of thecore of the ridge waveguide, and nTM,guided the effectivemode index of the fundamental guided quasi-TM modesupported by the ridge waveguide.15 The effective modeindex of the quasi-TM mode is thus weakly dependenton the ridge width, such that an iterative scheme has tobe employed to solve Eq. (1).

The guided mode indices are found using COMSOLMultiphysics, a commercially available finite-elementmode solver, as well as an effective index method. Theeffective index method reduces the ridge waveguide geom-etry into an analytically solvable one-dimensional three-layer slab waveguide problem by assuming the core andslab regions of the waveguide to be of continuous refrac-tive index (refer to inset in Fig. 3). This equivalent indexis assumed as the guided fundamental TE or TM modeindices of the three-layer slab waveguide with refractiveindex profile identical to the the index distribution inthe core or slab region. 11 12 13 When solving for indicescorresponding to TE- and TM-polarized modes, the cal-culations have to be consistently based on mode indicesfound for the respective polarization. All simulations arefor an excitation free space wavelength of 1550 nm andassume the refractive indices of silicon and glass to be3.476 and 1.444 respectively. Both methods are used toensure single mode operation of all considered waveguidegeometries.

The third major loss mechanism is bending loss in thering resonator structures. This loss mechanism also ex-ists independent of fabrication-induced defects and willvary over many orders of magnitude depending on thecross-section and bending radius of the waveguides. Us-ing the effective index method and diffraction theory, thebending loss coefficient, �, can be approximated as:14

� =�2 2e W

�(1 + W2

)(�2 + 2)

exp

(−2 3

3�2R

)(2)

where � and are defined as:

� =√n2

eff,corek20 − �2 (3)

=√�2 − n2

eff,slabk20 , (4)

and k0 is the free space wavelength, � is the propaga-tion constant of the guided mode, and R is the bend-ing radius of the waveguides. Furthermore, neff,core andneff,slab represent the effective index of the core region

FIG. 3: Bending loss of the guided TE and TM modes of a SOIridge waveguide with bending radius of 200�m and a ridgewidth of 700 nm in 220 nm SOI as a function of normalizedslab thickness r = slab thickness

core thickness. For high r, when the silicon

in the core region is only barely thicker than the surroundingslab, the bending loss can reach values of � ≥ 102dB/cm. Theinset illustrates the effective index method approximation.

and slab region respectively. W represents the width ofthe ridge. Figure 3 shows the bending loss of the funda-mental guided TE and TM modes supported by a ridgewaveguide in 220 nm SOI as a function of normalizedslab thickness.

The bending loss becomes quickly negligible for bothguided TE and TM modes as the ridge height increases.Narrow ridges can however help reduce scattering loss asthey reduce the modal overlap with the material bound-aries.

The other defining factor is the interaction of a guidedmode with the active layer. The modal gain coefficient�mode of a mode supported by the structure is relatedto the bulk material gain coefficient �bulk of the activematerial by the confinement factor, Γ, which is given by:3

Γ =�mode

�bulk(5)

Γ =

nAc"0

∫∫A

∣E∣2dxdy∫∫∞Re{E×H∗}dxdy

(6)

where nA is the refractive index of the gain material andthe surface integral in the denominator is over the areaA in which the gain material is located. Eq. (6) showsthat the modal gain scales with the electric field in theactive region in relation to the total power flow. Thesefield quantities can be determined using COMSOL Mul-tiphysics. Fig. 4 shows representative solutions for aridge waveguide covered in erbium-doped yttria and aslot waveguide with erbium-doped glass in the slot re-gion. The refractive index of yttria is taken to be 1.9.

Fig. 5 depicts simulation results for the confinementfactors of the fundamental guided TE and TM modes in

3

FIG. 4: Electric energy density distributions calculated usingCOMSOL Multiphysics (arbitrary units). The first row de-picts solutions for a silicon ridge waveguide with ridge height40 nm and ridge width 650 nm in 220 nm SOI that was cladwith a 200 nm yttria layer. The fundamental a) TE and b)TM modes. The second row depicts solutions for a silicon slotwaveguide with a ridge height of 30 nm, a ridge width of 700nm and a slot layer thickness of 25 nm. The core thicknessof the upper silicon slab as well as the thickness of the lowersilicon slab is 220 nm. The fundamental c) TE and d) TMmodes. The slot layer consists of SiO2.

yttria-clad ridge waveguides as a function of upper slaband cladding thickness. As high-quality erbium-dopedyttria films are fabricated using atomic layer deposition,only thin films are practical, such that we limited the do-main to a maximum cladding thicknesses of 200 nm. Thesparse local minima in the density plots corresponding tothe TM-polarized modes are due to non-convergence ofthe finite-element solver which plagued certain waveg-uide geometries. The general trends in these plots reflectwell-converged solutions and are thus believed by the au-thors to be an accurate representation of the physicalmodes. The data suggest an optimal slab thickness forthe ridge waveguides depending on the thickness of theyttria cladding. In TE-mode operation, the ideal siliconslab thickness is on the order of a few nanometers, how-ever in TM-mode operation around 150 nm. Accordingly,efficient devices will have to be designed specifically forTE- or TM-mode operation. Peak confinement factorsof 50% and 60% were achieved for TE and TM polariza-tions, respectively. As waveguides designed to operatein TE mode are not required to match the magic widthcriterion, the ridge width represents another parameterto be optimized.

Fig. 6 shows the confinement factors of the funda-mental guided quasi-TM modes of a slot waveguide witherbium-doped glass in the slot layer. The increase of theconfinement factor with the slot width indicates that thestrong enhancement of the electric field in the slot layeris outweighted by the relatively smaller area over whichthe numerator in Eq. (6) is integrated. However, it isdesirable to have slots as thin as possible with respect tothe exhibited gain in order to be able to pump the activematerial electrically, which would represent a great ad-

FIG. 5: Confinement factor of the fundamental quasi-TE (up-per plot) and TM (lower plot) modes of a yttria clad ridgewaveguide as a function of silicon slab and cladding thickness.The ridge height is 40 nm and the ridge width is 650 nm.

vantage over optical pumping as no auxiliary pump lightsource is required. Furthermore, the strong electric fieldin the slot region of TM-polarized slot modes enhancesthe efficiency of the gain material.4 2 The slot waveguidemodes can be described as the coupled modes of twoclosely spaced silicon slab waveguides. For a core thick-ness of 220 nm, these modes will decouple for slot thick-nesses greater than about 80 nm. The simulations show,however, that the confinement factor for TM-polarizedslot modes can well surpass 40%.

Some of the lowest loss ridge waveguides have beenformed by anisotropic reactive ion etching and selectiveoxidation.7 6 While both methods yield smooth side-walls, the oxidation will additionally passivate the sili-con which further reduces loss.10 To fabricate our waveg-uides, negative electron beam resist is first patternedon 220 nm SOI using the electron pattern generator ofthe Kavli Nanoscience Insitute (KNI). The structures arethen formed using a C4F8/O2 etch in the KNI’s induc-tively coupled reactive ion etching chamber. The sam-ples are then cleaned in O2 plasma to remove remainingpolymer from the surface. Finally, an oxide passivationlayer is grown using dry oxidation. Fig. 7 shows SEMand AFM micrographs of a waveguide, revealing a meansquare surface roughness below 1.8 nm.

4

FIG. 6: Confinement factor of the fundamental quasi-TMmode of a slot waveguide with silica glass in the slot layeras a function of upper slab and slot thickness. The ridgeheight is 40 nm and the ridge width is 700 nm.

The fabricated waveguides have a ridge height of 30nm and a ridge width of 720 nm. The ring resonatorshave a diameter of 400 �m and are seperated from thewaveguides by a coupling gap of 1 �m. The gratings areoptimized for operation at 1550 nm.

Light from a New Focus 6428 Vidia Swept tunablediode laser is coupled into the structures using a lensedfiber focuser with an estimated working distance of12.4 mm and a spot size of 8 �m. The TE and TM modesare selectively adressed by adjusting the angle of inci-dence of the light onto the gratings. The laser is then setto sweep over wavelengths around 1550 nm at a constantspeed of 1 nm/s. The outcoming light is picked up usingan identical lensed fiber focuser aimed at the through- ordrop port and measured using a InGaAs photoreceiver.The drop port intensities transmitted in quasi-TE andTM modes as a function of input wavelength are shownin Fig. 8. They show a clear intensity drop off at the ringresonator resonances. The resonances are spaced 0.508nm apart in TE- and 0.516 nm in TM-like mode oper-ation. From this free spectral range the group indicesof the guided TE and TM resonator modes can be exs-tracted as 3.76 and 3.66, respectively. The linewidth ofthe resonators in TE-mode operation is 8.65pm and inTM mode operation 26.5pm. This corresponds to propa-gation losses of 1.23dB/cm and 3.71dB/cm respectively.The loaded quality factor Q is then 179, 000 for TE and58, 000 for TM.11 As there are identical through- anddrop port couplers, the intrinsic Qs of the resonators arethen 537, 000 and 174, 000, as given by the equation:

1

Qloaded=

1

Qintrinsic+

2

Qcoupler

=3

Qintrinsic(7)

where Qintrinsic = Qcoupler for a critically coupled re-sonator. The 15dB extinction at resonance in TE-modeoperation justifies the assumption of critical coupling,

FIG. 7: a) SEM and b) AFM micrographs of a C4F8/O2

etched waveguide with a 30-nm ridge height.

FIG. 8: The upper row depicts the through port intensitiesas a function of wavelength measured in quasi-TE- and TM-mode operation, displaying the free spectral range. The lowerrow depicts individual resonances in quasi-TE- and TM-modeoperation.

but the assumption is more dubious for TM-mode opera-tion. The signal in TM-mode operation is overall noisier,because the gratings work less efficiently for this polar-ization.

Conclusively, considering the high possible confine-ment factors and assuming no significant further loss inthe gain materials, light emitting devices based on thefabricated ridge waveguide devices should be possible.The demonstrated theoretical methods can be used tooptimize the design of such structures.

Acknowledgments

The authors gratefully acknowledge the rest of theAtwater group at Caltech as well as the KNI staff fortheir help. J. P. B. Muller thanks the Caltech - Uni-versity of Iceland Exchange Program as well as theKavli Nanoscience Institute for his undergraduate re-search fellowships. J. P. B. Muller thanks his co-mentorR. M. Briggs and his mentor H. A. Atwater for a fantasticsummer in California!

5

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