DTIC ADA518370: Enhanced Electro-Optic Phase Shifts in Suspended Waveguides

0.92 MB·English

by  Defense Technical Information Center

Enhanced Electro-Optic Phase Shifts in
Suspended Waveguides
T.H.Stievater,1 D.Park,1 W.S.Rabinovich,1 M.W.Pruessner,1,
S.Kanakaraju,2 C.J.K.Richardson,2 andJ.B.Khurgin3
1NavalResearchLaboratory,Washington,DC20375
2LaboratoryforPhysicalSciences,CollegePark,MD20740
3JohnsHopkinsUniversity,Baltimore,MD21218
Email:[email protected]
Abstract: We demonstrate enhanced electro-optic phase shifts in sus-
pended InGaAs/InGaAsP quantum well waveguides compared to attached
waveguides. The enhancement stems from an improved overlap between
the optical mode and the multiple quantum well layers in thin waveguides
when the semiconductor material beneath the waveguide is selectively
etched.Themeasuredvoltagelengthproductis0.41V-cmandthemeasured
propagationlossis2.3±0.7dB/cmfortheTEmodeintheopticalL-band.
© 2009 OpticalSocietyofAmerica
OCIS codes: (160.6000) Semiconductors, including MQW; (230.3990) Microstructure de-
vices;(160.2100) Electro-opticalmaterials
Referencesandlinks
1. T. H. Stievater, W. S. Rabinovich, P. G. Goetz, R. Mahon, and S. C. Binari, “A Surface-Normal Coupled-
Quantum-WellModulatorat1.55Microns,”IEEEPhoton.Technol.Lett.(16),2036–2038(2004).
2. E.Kunkee,C.-C.Shih,Q.Chen,C.-J.Wang,andL.J.Lembo,“ElectrorefractiveCoupledQuantumWellMod-
ulators:ModelandExperimentalResults,”IEEEJ.QuantumElectron.(43),641–650(2007).
3. J.Shin,S.Wu,andN.Dagli,“BulkUndopedGaAs–AlGaAsSubstrate-RemovedElectroopticModulatorsWith
3.7-V-cmDriveVoltageat1.55μ m,”IEEEPhoton.Technol.Lett.(18),2251–2253(2006).
4. J.Shin,Y.-C.Chang,andN.Dagli,“0.3VdrivevoltageGaAs/AlGaAssubstrateremovedMach–Zehnderinten-
sitymodulators,”Appl.Phys.Lett.(92),201,103–201,105(2008).
5. T.H.Stievater,W.S.Rabinovich,D.Park,J.B.Khurgin,S.Kanakaraju,andC.J.K.Richardson,“Low-loss
suspendedquantumwellwaveguides,”Opt.Express(16),2621–2627(2008).
6. D.Park,T.H.Stievater,W.S.Rabinovich,N.Green,S.Kanakaraju,andL.C.Calhoun,“Characterizationof
hydrogensilsesquioxaneasaCl2/BCl3 inductivelycoupledplasmaetchmaskforair-cladInP-basedquantum
wellwaveguidefabrication,”J.Vac.Sci.Technol.B.(24),3152–3156(2006).
7. R.J.DeriandE.Kapon,“Low-lossIII-Vsemiconductoropticalwaveguides,”IEEEJ.QuantumElectron.(27),
626–640(1991).
8. S.Pogossian,L.Vescan,andA.Vonsovici,“Thesingle-modeconditionforsemiconductorribwaveguideswith
largecrosssection,”J.Lightwave.Technol.(16),1851–1853(1998).
9. T.Ikegami,“Reflectivityofmodeatfacetandoscillationmodeindouble-heterostructureinjectionlasers,”IEEE
J.QuantumElectron.(8),470(1972).
10. P.C.Kendall,D.A.Roberts,P.N.Robson,M.J.Adams,andM.J.Robertson,“Newformulaforsemiconductor
laserfacetreflectivity,”IEEEPhoton.Technol.Lett.(5),148–150(1993).
11. E.M.Skouri,P.Martin,L.Chusseau,C.Alibert,C.Coriasso,D.Campi,andC.Cacciatore,“Measurement
oftherefractiveindexofGaInAs/InPquantumwellsbyagratingcouplingtechnique,”Appl.Phys.Lett.(67),
3441–3443(1995).
12. S.Nishimura,H.Inoue,H.Sano,andK.Ishida,“ElectroopticeffectsinanInGaAs/InAlAsmultiquantumwell
structure,”IEEEPhoton.Technol.Lett.(4),1123–1126(1992).
13. J.E.Zucker,PropertiesofLattice-MatchedandStrainedIndiumGalliumArsenide,inEMISDatareviews(IN-
SPEC,1993).(andreferencescontainedtherein).
14. S.Adachi,PhysicalpropertiesofIII-Vsemiconductorcompounds:InP,InAs,GaAs,GaP,InGaAs,andInGaAsP
(Wiley-VCH,1992).
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 885
Report Documentation Page Form Approved
OMB No. 0704-0188
Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and
maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,
including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington
VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it

does not display a currently valid OMB control number.
1. REPORT DATE 3. DATES COVERED
2010 2. REPORT TYPE 00-00-2010 to 00-00-2010
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Enhanced Electro-Optic Phase Shifts in SuspendedWaveguides
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
Naval Research Laboratory,Washington,DC,20375 REPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)
11. SPONSOR/MONITOR’S REPORT
NUMBER(S)
12. DISTRIBUTION/AVAILABILITY STATEMENT
Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES
14. ABSTRACT

15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF
ABSTRACT OF PAGES RESPONSIBLE PERSON
a. REPORT b. ABSTRACT c. THIS PAGE Same as 8
unclassified unclassified unclassified Report (SAR)
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
15. J.Mendoza-Alvarez,L.Coldren,A.Alping,R.Yan,T.Hausken,K.Lee,andK.Pedrotti,“Analysisofdepletion
edgetranslationlightwavemodulators,”J.Lightwave.Technol.(6),793–808(1988).
16. Q.Lu,W.Guo,D.Byrne,andJ.F.Donegan,“DesignofLowVπHigh-SpeedGaAsTravelling-WaveElectrooptic
PhaseModulatorsUsingann-i-p-nStructure,”IEEEPhoton.Technol.Lett.(20),1805–1807(2008).
1. Introduction
Compound-semiconductor-based electro-optic modulators are poised to displace lithium nio-
bate(LiNbO3)asthematerialofchoiceforapplicationsthatrequiremodulationvoltages(the
so-calledVπ)(cid:2)1V.Suchapplicationsincludesystemsformicrowavephotonics,on-chipin-
terconnects,andultra-highfrequencymodulators.Forexample,inmicrowavephotonics,arrays
ofmodulatorshavebeenproposedtosimultaneouslyencodemultiplemicrowavesignalsonto
an optical carrier. RF power scaling dictates that these systems use modulators that operate
at the lowest possible Vπ, ideally much less than one volt. To reduce Vπ, compound semi-
conductor heterostructures such as coupled quantum wells [1, 2] enable the enhancement of
electro-optic coefficients at wavelengths near the material bandedge. In addition, compound
semiconductorheterostructuresenablethedesignofwaveguidesthatconfinetheopticalmode
between two closely spaced electrode layers, reducing the voltage needed to achieve a large
electric field. This second advantage can be further extended by removing the semiconductor
materialfromaboveandbelowthewaveguide,providingthetightestpossibleout-of-planeop-
ticalconfinementbymaximizingtheindexcontrastinthatdimension.Infact,suchasubstrate
removaltechniquehaspreviouslybeenreported[3,4]intheGaAs/AlGaAssystem,withare-
porteddrivevoltagelengthproductof0.21Vcm.Thesubstrateremovalwasachievedusinga
low-index transfer substrate that allowed complete etching of the GaAs substrate beneath the
waveguide.
(a) 1 - 4 µm top (b)
contact
70 nm
165 nm n-InGaAsP (3 -10 x1017 cm-3) 10 µm InGaAs/
InGaAsP
408 nm i-InGaAs/InGaAsP MQW
air gap
235 nm p-InGaAsP (1- 3 x1017 cm-3)
[011] 1 µm InP
1600 nm
p-InAlAs (1x1018 cm-3)
bottom
(sacrificial layer) contact [011]
50 nm p-InGaAs (5x1018 cm-3) (etch stop)
p-InP (5x1018 cm-3)
Fig.1.(a):Theepitaxiallayerstructureandwaveguideribdimensions(nottoscale).(b):
Afalse-colorSEMimageofasuspendedquantumwellwaveguidecomprisedofashallow
ribboundedbyetchholes,priortothedepositionofthemetalcontacts.Inset:thefacetof
a2μ mwiderib.
Inthiswork,wereportonanovelprocessthatusessurfacemicromachiningtoremovethe
semiconductormaterialbeneathInGaAs/InGaAsPmultiplequantumwell(MQW)waveguides
grownonanInPsubstrate[5].BygrowingthequantumwellwaveguidesonaInAlAssacrificial
layer,asimpleselectiveetchsuspendsthewaveguidesinairforhigh-indexconfinementinthe
out-of-planedirection.SincetheInAlAssacrificiallayerhasalowerrefractiveindexthanthe
waveguide,wecancomparetheelectro-opticphaseshiftbeforeandafterthislayerisselectively
etched.ThiscomparisondemonstratesthatsuspendingtheMQWwaveguidesresultsintighter
opticalmodeconfinementandenhancedelectro-opticphaseshifts.
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 886
2. Fabrication
The waveguides are comprised of a 32-period In.48Ga.52As/In.82Ga.18As.40P.60 MQW that is
grown between two partially doped 235 nm thick InGaAsP layers, forming a p-i-n diode. A
structureschematicisshowninFig.1.Thefirst20nanometersofthebottomInGaAsPlayerim-
mediatelybelowtheMQWisundoped,followedbyp-dopingthatisgradedfrom1×1017cm−3
to3×1017 cm−3 atthesacrificiallayer.Similarly,thefirst20nanometersofthetopInGaAsP
layer is undoped, followed by n-doping that is graded from 3×1017 cm−3 to 10×1017 cm−3
at the waveguide top. This 880 nm thick waveguide layer is grown on a p-InAlAs sacrificial
layerusingmolecularbeamepitaxy.TheMQWisdesignedtohaveaheavy-holebandedgeat
approximately1475nm,allowingforoperationintheopticalL-band[5].Thewaveguidesare
designedtohaveaphosphorusfractioninanylayerbelow0.65topreventetchingduringexpo-
suretotheHCl:H2O(3:1)selectiveetch.Thesampleisetchedforapproximately15minutes,
whichresultsinlateraletchingoftheInAlAsofapproximately20 μ m.Inaddition,thewave-
guide alloy fractions were chosen such that the waveguide would have a small amount of net
tensilestraintoensureflatnessuponreleasefromthesacrificiallayer:toomuchtensilestrain
andthematerialcracks,whereasevensmallamountsofcompressivestraininducebucklingin
thesuspendedmaterial.
The1-4μ mwidewaveguideribsarefabricatedinboththe[011]and[01¯1]directionsusing
electron-beam lithography and plasma etching [6]. As shown in Fig. 1, the rib is etched to
a depth of approximately 70 nm, enabling operation at the fundamental waveguide mode for
both TM and TE polarized light. A second lithography step is used to etch holes alongside
the waveguides to a depth that penetrates into the InAlAs sacrificial layer. These holes are
spaced either 5 μ m or 10 μ m from the waveguide edge, a distance chosen to enable release
of the waveguides from the sacrificial layer upon exposure to the selective HCl etch without
degrading the waveguide transmission. Finally, metal contacts are deposited on both the top
n-InGaAsPlayerandonthep-InGaASetchstoplayersothatareversebiasresultsinavertical
(out-of-plane)electricfieldacrosstheMQW.Thewaveguides arecleaved tolengthsbetween
2.4mmand7.2mmandthefacetsareleftuncoated.
3. OpticalLoss
Optical loss and electro-optical phase shift measurements are made for the waveguides both
priortoandaftertheselectiveetchstep.Fig.1showsoneparticularwaveguideaftertheselec-
tiveetchstep,clearlyshowingthatthewaveguidesaresuspendedinair.Tunablepolarizedlaser
lightiscoupledintoandoutofthewaveguidesusingahighnumerical-aperturenanoposition-
ingsystem.TheFabry-Perotfringesformedbyreflectionsfromthewaveguide end-facetsare
analyzed to provide a measurement of the fringe contrast (K), phase shift (Δ φ(FP)), and free-
spectral-range (FSR) as a function of reverse bias, polarization, and wavelength for a given
waveguide.ThecontrastoftheFabry-Perotfringesisusedtoestimatethelossesincurreddur-
ing propagation between the end facets [7]. The change of the fringe phase as a function of
reverse bias is a measurement of the strength of the electro-optic effect. Last, The FSR is a
measurementofthegroupindex,whichprovidesacheckthatonlythefundamentalmodefora
givenpolarizationisexcited.Infact,widerwaveguides(4μ mandabove)doshowevidenceof
propagationofhigher-ordermodes,consistentwithourmodalcalculations[8].Thesewaveg-
uidesarenotusedinourlossanalysisorelect√ro-opticanalysis.
Fig. 2 shows a plot of the quantity ln(1− 1−K2)−ln(K) vs. the waveguide length, for
wavelengths of 1600 nm and 1620 nm. The data points represent an average found across a
rangeofwaveguidesofequallengthatthesetwowavelengths,andtheerrorbarsrepresentthe
standarderrorassociatedwiththisaverage.Plottedinthisway,they-interceptisln(R)where
Risthefacetreflectivity,andtheslopeisthepropagationloss,α,incm−1.Aleast-squaresfit
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 887
tothedatagivesaTEpropagationlossof2.3±0.7dB/cm,aTEfacetreflectivityof0.36±0.02,
aTMpropagationlossof1.8±1.7dB/cm,andaTMfacetreflectivityof0.18±0.02.Thepolar-
izationdependenceofthefacetreflectivityisduetotheasymmetryofthesubwavelengthmode
[9,10],andcanbeestimatedfrom
RTE(TM) = R(cid:2)0(1+(−)(ky2−kx2)+(ky4+kx4)) (1)
ln2/n λ
k = eff
i πa
i
whereR istheFresnelreflectivity(here0.28),λisthewavelength,n istheeffectivemodal
0 eff
index,anda isthefull-width-at-half-maximumofthemodeinthatdimension.Forthefunda-
i
mentalTEmode,thecalculatedfacetreflectivityis0.39,whereasforthefundamentalTMmode
thecalculatedreflectivityis0.23,inqualitativeagreementwithourmeasurements.Inaddition,
comparisonoflossamong waveguides ofvariouswidthswiththesamelengthshowsthatthe
lossisindependentofwaveguidewidthforwidthsassmallas1.5 μ m,implyingthatsidewall
roughness is not a dominant source of loss within this waveguide width range. In addition,
above 1580 nm, the loss is independent of wavelength, which indicates that near-bandedge
absorption is also not a limiting loss factor in this wavelength range. We do observe a much
largerlossinthesewaveguidesbeforethesacrificiallayerisremoved:approximately15dB/cm
for both polarizations. Since the sacrificial layer is p-doped at ∼ 1×1018 cm−3, we believe
thatfree-carrierabsorptionateventhismoderatep-dopinglevelcontributessignificantlytothis
propagationloss.
Fig.2.Fabry-Perotmethodformeasuringpropagationlossinthesuspendedwaveguides.
Thelinesareleast-squarefitstothedata.
4. Electro-opticalproperties
Theelectro-opticeffectinawaveguidegeometryinducesachangeintheopticalphase,Δ φ:
Δ φ=2πLΔ n/λ (2)
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 888
where L is the waveguide length, Δ n is the change in the refractive index, and λis the free-
spacewavelength.Inazinc-blendesemiconductor,Δ niscomprisedofcontributionsfromboth
thelinear(Pockels)effectandthequadratic(Kerr)effectfortheTEmode,whereasfortheTM
modeitarisesexclusivelyfromthequadraticeffect:
Δ n = −n3s E2Γ /2 (3)
TM 11 TM
Δ n[011] = −n3(s E2+r E)Γ /2 (4)
TE 12 41 TE
Δ n[01¯1] = −n3(s E2−r E)Γ /2 (5)
TE 12 41 TE
Δ n[001] = −n3s E2Γ /2 (6)
TE 12 TE
where n is the refractive index, r is the linear electro-optic tensor component, s is the di-
41 11
agonal component of the quadratic electro-optic tensor (which here arises primarily from the
light-hole quantum-confined Stark effect), s is the off-diagonal component of the quadratic
12
electro-optictensor(whichherearisesprimarilyfromtheheavy-holequantum-confinedStark
effect),E istheelectricfield(negativeforourdefinitionofcoordinateaxes),andΓistheover-
lapfactorbetweentheelectricfieldorthesquareoftheelectricfieldandtheopticalmode.In
this work we use the abrupt-junction approximation to estimate the depletion width and thus
theelectricfieldstrength.Notethattheelectricfieldisthesumofthebuilt-injunctionvoltage
andtheexternalreversebias.Separatemeasurements(notshown)confirmthattheTMelectro-
optic effect is independent of the waveguide direction, whereas the TE effect is strongest in
the [011] direction and weakest in the [01¯1] direction. The quadratic effect is significant for
ourmeasurementssinceweoperateclosetotheMQWbandgap,wherethequantum-confined
Starkeffectisstrongest.NotethatitistheΓtermsthataccountforthebulkoftheenhancement
of the phase shift when the waveguides are suspended; a suspended waveguide has a smaller
out-of-plane optical mode than an attached waveguide, which improves the overlap with the
thinMQWlayer.
Theelectro-opticphaseshiftismeasuredbymonitoringtheFabry-Perotfringesformedby
reflectionsfromtheendfacetswhileareversevoltageisappliedtothewaveguide.Thephase
shiftmeasuredinthiswayisequivalenttoapush-pullphaseshiftinaMach-Zehnderelectro-
opticmodulatorwitharmsoflengthequaltoourwaveguidelength.Thus,themeasuredFabry-
Perotphaseshiftforagivenwaveguidelength,Δ φ(FP),istwicethephaseshiftofEq.2,Δ φ.
ThephaseoftheseFabry-Perotfringes(withrespecttothephaseat0Vbias)for1600nm
and1620nmina4.8mmlong[011]-orientedwaveguidepriortoandafterreleaseisplottedin
Fig.3aforTEpolarizedlightandinFig.3bforTMpolarizedlight.Similarresultsareobserved
forotherwaveguidesonthesample.Asexpected,theTEphaseshiftislargerthantheTMphase
shift.Bothpolarizationsshowaclearenhancementinthephaseshiftofsuspendedwaveguides
comparedtoattachedwaveguidesforvoltagesupto1V.Forvoltagesabove1V,thep-doped
InGaAsPcontactlayerbeginstofullydeplete,andthefieldacrosstheMQWinthewaveguide
saturates. The inset in Fig. 3 shows the Fabry-Perot fringes from transmission spectra at 0 V
and 0.85 V that are used to measure the phase shift at 1620 nm. The phase shift is measured
forwavelengthsbetween1580nmand1640nm.Withinthiswavelengthrange,theadditional
propagationlossincurredduetotheappliedvoltageissmall(<1.5dBat1Vreversebiasat
1580nm).However,thisadditionallossduringreversebiasfortheTEmodeforwavelengths
below1580nmbecomessignificantduetothered-shiftofthebandedge.
For wavelengths between 1580 nm and 1640 nm, the overall measured TE phase-shift en-
hancementfactoraverages1.19withamaximumvalueof1.28at1640nm.ThemeasuredTM
enhancement is between 1.41 and 1.52, with an average of 1.44. This enhancement factor is
almost entirely due to the increase of the overlap factors before and after waveguide release,
Γsuspended/Γattached,withonlyasmallcontribution fromchanges tothemodalindex. Theen-
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 889
Fig.3.MeasuredFabry-Perotphaseshiftvs.reversebiasforTE(a)andTM(b)lightinthe
opticalL-band.Inset:TheTEFabry-Perotfringesforreversebiasesof0Vand0.85V.
hancement islargerfortheTMmodethanfortheTEmodebecause theboundary conditions
fortheTMmodeallowtheopticalfieldtobediscontinuousacrosstheupperandlowerwave-
guide boundary. This permits more of the TM field to be confined within the waveguide in
high-index-contraststructuresthatare∼λthick.
Tocalculatethisenhancement,weuseawavelength-dependentrefractiveindexfunction[11]
for an InGaAs-based MQW that has only two free-parameters: the light-hole and heavy-hole
band edges. This refractive index is combined with a finite-element mode solver to estimate
the integrated TE and TM mode power confined between the waveguide contact layers, for
waveguides on a material with n=n (attached) or n=1 (suspended). This technique
InAlAs
has previously been used to accurately compare our measured group velocity with the calcu-
latedgroupvelocityintightlyconfinedsuspendedMQWwaveguides[5].Ourmodelpredicts
an average TE enhancement of 19% between 1580 nm and 1640 nm, which agrees with our
measuredenhancement,andisprimarilyduetoimprovedmodaloverlapwiththeMQW(e.g.
Γsuspended/Γattached =0.74/0.63at1620nm).Thepredictedaverage TMenhancement is37%
TE TE
(e.g.Γsuspended/Γattached =0.79/0.60at1620nm),onlyslightlylowerthanouraveragemeas-
TM TM
uredvalue.
Fig4showstheTEFabry-Perotphaseshiftinthesuspended[011]-orientedwaveguidesfor
wavelengthsfrom1580nmto1640nm.Thephaseshiftisrelativelyconstantandlinearwithin
this wavelength range, even though the wavelength is only 100 nm to 160 nm from the band
edge.Thisismostlikelyduetothefactthatatexternalvoltageslessthan1V,thecontributionto
thephaseshiftfromthelinearelectro-opticeffect(whichislargelywavelength-independent)is
largerthanthatofthequadraticeffect.Infact,anexpansionofEq.4showsthatthelargestcon-
tributionfromthes termatthesevoltagesisactuallylinearintheexternalfieldandsmaller
12
than the r term: s E2 <2s E E <r E [12]. In addition, for the wavelength range
41 12 ext 12 bi ext 41 ext
1580nmto1640nm,theVπvariesbetween0.85Vand0.91V,whichcorrespondstoamini-
mumvoltagelengthproductof0.41V-cminasuspendedwaveguide.Thisvaluerepresentsan
orderofmagnitudeimprovementovertypicalLiNbO3devices,andisonly2timeslargerthan
theequivalentvaluereportedinRef.[4],despitethefactthatourwaveguidesareabout3times
thicker.
BycomparingthephaseshiftvaluesfortheTEmodeforwaveguidesorientedinthe[011]
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 890
Fig.4.MeasuredFabry-Perotphaseshiftvs.reversebiasinasuspended[011]waveguide
fortheTEmode.
direction to those oriented in the [01¯1] direction, Eq. 4 and Eq. 5 can be used to estimate the
valuesofr ands asafunctionofwavelength.Eq.3canalsobeusedtoestimates fromthe
41 12 11
measuredTMphasechange.Thevoltage-dependenceofthedepletedregion,whichisnecessary
toestimatetheexactelectricfieldatthequantumwells,isestimatedfromC-Vmeasurements.
Thesevaluesoftheelectro-opticcoefficientsareshowninFig.5.Notethattheerrorbarsshown
inthisplotaredominatedbytheuncertaintyintheexactdepletionlayerthickness,whichwe
approximate using the abrupt-junction approximation. Our measured r is in the range of -
41
1.0 pm/V to -1.8 pm/V, which is similar to previously reported values [12, 13, 14], which
alsorangefrom-1.0pm/Vto-1.8pm/VforInGaAs/InGaAsP-basedstructures.Theapparent
wavelength dependence of our measured r is likely an artifact that arises from our analysis
41
technique: r is found from subtracting the phase shift data from two different samples, so
41
thatsmallabsoluteerrorsinthemeasuredphasebecomelargerelativeerrorsforr .Thiserror
41
would be the largest for wavelengths that show the largest overall phase shift (closest to the
bandedge),implyingthatourmostaccurater valueisobtainedfurthestfromthebandedge.
41
Ourvaluesfors ands ,-2.8×10−19 m2/V2 and-5.1×10−19 m2/V2 at1580nm,respec-
11 12
tively,arelowerthanthosepreviouslyreportedforanInGaAsMQW[12]:-6.2×10−19m2/V2,
and-15×10−19 m2/V2,respectively.However,ouranalysisofthedatapresentedinRef.[12]
using their reported values of Vπ and their Eq. 1 (equivalent to our Eqs. 3 and 4) shows an
errorintheircalculations.Thecorrectedvaluesofs ands at1580nmfromthatworkare
11 12
-2.1×10−19 m2/V2 and-5.8×10−19 m2/V2,whicharenearlyidenticaltoourvalues.Itshould
be noted that in p-i-n semiconductor waveguide modulators, effects other than the linear and
quadraticelectro-opticeffects,suchasthoserelatedtoachangeinfree-carrierdistributionwith
voltage [15], can play an important role. Since these free-carrier based effects are direction-
independent and approximately linear, they would be expected to appear in our analysis as
linearcontributionstoEqs.3through6.However,ourfittingtoEq.3(fors )andtothesum
11
ofEqs.4and5(fors )showsexcellentagreementwithamodelbasedonapurelyquadratic
12
effect, and the agreement of our values of s and s with that of previous reports together
11 12
indicatethatfree-carriereffectsdonotplayanimportantroleinourmeasuredphase-shifts.
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 891
Fig.5.Measuredelectro-optictensorcoefficientsasafunctionofwavelength.
5. Conclusions
In this work, we have demonstrated that suspending electro-optic semiconductor waveguides
reducesthevoltageneededtoachieveaπphaseshift,resultinginavoltage-lengthproductas
lowas0.41V-cm.Thinnerwaveguideswillresultinanevenlargerelectro-opticphaseshiftby
furtherincreasingtheelectricfieldstrengthforagivenvoltage,withonlyasmalldecreasein
themodaloverlapfactor.Suchwaveguidesneedtobecarefullydesigned,however,tomaintain
low resistivity in the thin doped layers. Since p-doped layers have a significantly lower mo-
bility and higher optical loss than n-doped layers (for the same doping level), future designs
are focused on the use of an n-p-i-n [16] junction instead of a p-i-n. Such layers also offer
thepossibilitytoincorporatehigh-electron-mobilitylayers,tofurtherdecreasethecarriermo-
bility and improve the RF performance. In such a device, the net waveguide thickness could
bedecreasedtoafewhundrednanometers,resultinginasignificantlylowermodulationvolt-
age.Whencombinedwithcoupledorasymmetricmultiplequantumwells,suspendedquantum
wellwaveguidesshouldenablewidebandelectro-opticmodulatorsintheopticalC-bandwith
Vπ(cid:2)1V.
#119157 - $15.00 USD Received 27 Oct 2009; revised 17 Dec 2009; accepted 17 Dec 2009; published 6 Jan 2010
(C) 2010 OSA 18 January 2010 / Vol. 18, No. 2 / OPTICS EXPRESS 892