DTIC ADA470952: Introducing Defects in 3D Photonic Crystals: State of the Art

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Materials, 18, 2665–2678 Journal Reprint, September 2006

(2006).

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Introducing defects in 3D photonic crystals: State of the art DAAD190310227

6. AUTHOR(S)
P. V. Braun, S. A. Pruzinsky, and F. Garcia-Santamaria

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
University of Illinois-Urbana-Champaign REPORT NUMBER
109 Coble Hall
801 S. Wright Street
Champaign, IL 618206242

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U. S. Army Research Office
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Department of the Army position, policy or decision, unless so designated by other documentation.

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13. ABSTRACT (Maximum 200 words)

3D photonic crystals (PhCs) and photonic bandgap (PBG) materials
have attracted considerable scientific and technological interest. In order
to provide functionality to PhCs, the introduction of controlled defects
is necessary; the importance of defects in PhCs is comparable to that of dopants in semiconductors.
Over the past few years, significant advances have been achieved through a diverse
set of fabrication techniques. While for some routes to 3D PhCs, such as conventional lithography,
the incorporation of defects is relatively straightforward; other methods, for example, selfassembly
of colloidal crystals (CCs) or holography, require new external methods for defect
incorporation. In this review, we will cover the state of the art in the design and fabrication of
defects within 3D PhCs. The figure displays a fluorescence laser scanning confocal microscopy
image of a y-splitter defect formed through two-photon polymerization within a CC.

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DOI:10.1002/adma.200600769
Introducing Defects in 3D Photonic Crystals:
State of the Art**
By Paul V. Braun,* Stephanie A. Rinne,*
and Florencio García-Santamaría*
3D photonic crystals (PhCs) and photonic bandgap (PBG) materials
have attracted considerable scientific and technological interest. In or-
der to provide functionality to PhCs, the introduction of controlled de-
fects is necessary; the importance of defects in PhCs is comparable to that of dopants in semi-
conductors. Over the past few years, significant advances have been achieved through a diverse
set of fabrication techniques. While for some routes to 3D PhCs, such as conventional lithogra-
phy, the incorporation of defects is relatively straightforward; other methods, for example, self-
assembly of colloidal crystals (CCs) or holography, require new external methods for defect
incorporation. In this review, we will cover the state of the art in the design and fabrication of
defects within 3D PhCs. The figure displays a fluorescence laser scanning confocal microscopy
image ofay-splitterdefect formedthroughtwo-photonpolymerizationwithinaCC.
1.Introduction arenaturallyclassifiedbythedimensionalityoftheirperiodic-
ity,andinordertorigorouslypreventthepropagationofPBG
Photonic crystals (PhCs) are materials that possess spatial frequencies in all directions, a 3D PhC with an omnidirec-
periodicity in their dielectric constant on the order of the tional,orcompletePBG(cPBG)isrequired.
wavelength (k) of light. These materials can strongly modu- cPBG materials have been fabricated and well character-
late light[1] and, with sufficient dielectric contrast and an ap- ized for operation at microwave and radio frequencies, how-
propriate geometry, may exhibit a photonic bandgap (PBG). ever,operationinthevisibleandIRrequiresthecharacteris-
This concept was first proposed in 1975 by Bykov[2] but re- tic length scales of these structures to be scaled down by
mained relatively unknownuntil the seminal work of Yablo- several orders of magnitude, necessitating 3D fabrication
novitch[3] and John.[4] In a rough analogy to semiconductors, techniques capable of defining structures with sub-microme-
whichpossessanelectronicbandgap,aPBGmaterialprohib- ter-tomicrometer-scaleperiodicityandnanometer-scalereso-
its the existence of photons with energies in the PBG. PhCs lution.Additionally,cPBGstructuresmustbefabricatedfrom
opticallytransparentmaterialswithahighdielectricconstant.
Intheopticalregime,thereisalimitedsetofmaterialssatisfy-
–
ing these conditions, largely ruling out organic and metallic
[*] Prof.P.V.Braun,Dr.S.A.Rinne,Dr.F.García-Santamaría
materials, most oxides, andmany semiconductor-basedstruc-
DepartmentofMaterialsScienceandEngineering
tures. Because of the materials restrictions and stringent 3D
BeckmanInstituteforAdvancedScienceandTechnologyand
FrederickSeitzMaterialsResearchLaboratory fabricationrequirements,thereareonlyasmall,butgrowing,
UniversityofIllinoisatUrbana-Champaign numberofcPBGmaterialsthathavebeenconstructedinthe
1304WestGreenSt.,Urbana,IL61801(USA)
visible or IR. A review of PBG fabrication methods can be
E-mail:[email protected];[email protected];[email protected]
foundintheliterature.[5]Thedevelopmentofefficient,practi-
[**] The authors thank the following for support: the U. S. Army Re-
search Laboratory and the U. S. Army Research Office grant caltechniquesamenabletothefabricationofcPBGmaterials
DAAD19-03-1-0227;theNationalScienceFoundation;andtheU.S. operating in the visible to IR remains a vibrant area of re-
Department of Energy, Division of Materials Sciences grant
search,withnewapproachesregularlybeingintroducedinthe
DEFG02-91ER45439,throughtheFrederickSeitzMaterialsResearch
LaboratoryattheUniversityofIllinoisatUrbana-Champaign. literature.
Adv.Mater.2006,18,2665–2678 ©2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 2665
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materials, including low-threshold lasers,[3] low-loss wave- create embeddedoptical cavities. Suchcavities containing an
guides,[6–8] on-chip optical circuitry,[9] and fiber optics.[10,11] emitting material could be usedto inhibit spontaneousemis-
The majority of these applications not only require a PBG sion.
material,butalsotheprecise,controlledincorporationofpre- Thisreviewwillfocusontheincorporationofdefectsin3D
engineered defects. These defects disrupt the periodicity of PhCs that operate at optical wavelengths and it is organized
thecrystal,creatingopticalstateswithintheotherwiseforbid- bythetypeofdefectandthetechniqueusedtofabricatethe
den bandgap frequencies. Therefore, light coupling to these PhC lattice. Defect fabrication techniques will be evaluated
statescanbelocalizedwithinthedefectregionsandmanipu- ontheirpotentialresolution,accuracyofregistrationwiththe
latedbyengineeringthedefectgeometryandplacement.For underlyingPhClattice,flexibilityindefiningcomplicatedem-
example, a complicated 3D defect with sharp bend radii bedded3D structures, andtheir potential to incorporatema-
(ca.k) may be engineered to guide light along its complex terialsthatmightimpartadditionalfunctionality.Ifavailable,
pathwithoutlossif definedwithina cPBG material.[12] Simi- opticalcharacterizationandtheoreticalmodelingofthesede-
Paul V. Braun is an Associate Professor and Willett Faculty Scholar in Materials Science and
Engineering,theFrederickSeitzMaterials ResearchLaboratory,andtheBeckmanInstitutefor
AdvancedScienceandTechnology,attheUniversityofIllinoisatUrbana-Champaign(UIUC).
Prof.Braunhasauthoredfourbooksoreditedvolumes,55publications,andmultipleproceed-
ings and abstracts. He is the recipient of a Beckman Young Investigator Award (2001), a 3M
NontenuredFacultyAward,the2002RobertLansingHardyAwardfromTMS,giventooneout-
standingmaterialsscientisteachyear,theXeroxAwardforFacultyResearch(2004),andmulti-
pleteachingawards.ProfessorBraunreceived hisB.S.degreefromCornellUniversityin1993,
and his Ph.D. in Materials Science and Engineering from UIUC in 1998, both in Materials
Science and Engineering.Following a one year postdoctoral appointment at Bell Labs, Lucent
Technologies,hejoinedthefacultyatUIUCin1999.
StephanieRinne(née Pruzinsky)wasa National Science Foundation(NSF)graduatefellowin
the Department of Materials Science and Engineering at the UIUC. Her Ph.D. thesis work in
Prof. Braun’sgroupfocusedonthetwo-photonpolymerizationandoptical characterization of
embedded features within self-assembled photonic crystals. Upon completion of her Ph.D.
Stephanie began a postdoctoral fellowship at the Beckman Institute for Advanced Science and
TechnologyatUIUCinJuly,wheresheisworkingintheareaofbiomedicalimaging.Stephanie
received her B.S. in Materials Science and Engineering at Rensselaer Polytechnic Institute in
2000. As an undergraduate, she participated in NSF summer research projects in surface and
interfacialscienceattheUniversityofMassachusettsatAmherstandStanfordUniversity.
Florencio García-Santamaría is a postdoctoral scientist in Prof. Braun’s group in the Depart-
mentofMaterialsScienceandEngineeringatUIUC.Hismajorresearchinterestshavebeenthe
opticalcharacterizationandfabricationof3Dphotoniccrystals.FlorencioreceivedhisB.S.de-
greeintheoreticalphysicsfromtheUniversidadAutonomadeMadrid(UAM)in1998.Hisdoc-
toratewasconductedattheInstituteofMaterialsScienceofMadrid(ICMM-CSIC)wherehein-
vestigated self-assembled artificial opalsand developed a method to fabricate photonic crystals
withdiamondsymmetry,workingwithProfs.CefeLopezandFranciscoMeseguer.Heobtained
his M.S. (2001) and Ph.D. (2003) degrees from the UAM; his work as a graduate student was
namedthe‘Outstandingdissertationof2003–2004’atthesameuniversity.
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fectswillbeincluded.Wecategorizedefectsintwotypes:in- removing a line of cylinders from the initial design, linear
trinsicandextrinsic.Intheformercasedefectformationdoes waveguides can be introduced into a 2D PBG material
not require any special processingaside from that needed to (Fig.1).[18,19] Point defects, formed by removing or reshaping
form the PhC itself (e.g., conventional photolithography and air cylinders, serveasresonantcavities thatcan trapphotons
direct writing). In the latter case, the PhC fabrication tech- of certain frequencies.[18] Through proper engineering, very
niquelacksaninherentmeansfortheincorporationofdefects highQcavities(upto600000)havebeenreported(Fig.2).[20]
(e.g.,holographiclithographyandself-assembly)andtheyare Furthermore,variousdefectdesignshavebeenproposedand,
introducedbeforeorafterformationofthePhC. in some cases, realized for low-loss waveguides containing
sharp bends,[8] channel drop filters,[21,22] and T-shaped
branches.[23] By introducing active materials (e.g., quantum
2.Defectsin2DPhCs wellsordots)inthedesignofthePhCthepossibilityofusing
point defects as resonant cavities for lasing action has also
Initially 2D PhCs did not generate as much excitement as beendemonstrated.[24–26]
their 3D counterparts since they cannot rigorously confine
lightinalldimensions.However,duetothesubstantialfabri-
cation and modeling advantages in two dimensions, the ex- 3.Defectsin3DPhCs
perimental and theoretical work on defect-containing 2D
PhCsissignificantlyadvancedoverthaton3DPhCs.Thecon- Although 2D PhCs containing exquisitely designed defects
finementoflightwithintheplaneofa2DPhCisachievedby haveexhibitedpowerfulopticalproperties,itremainstruethat
sandwiching the 2D PhC between Bragg reflectors,[13] 3D
PhCs,[14]orlower-indexmaterials,includingair,toutilizetotal
internalreflection.[15]
2DPhCsthatoperateatopticalwavelengthshaveaperiod-
icityofca. 100nm–1lmwithfeaturetolerancesinthenano-
meter range. Typical 2D PhCs consist of triangular arrays of
aircylindersinadielectricmaterial,asthisgeometrycanyield
a 2D PBG foranypolarization,providedthedielectric hasa
refractive index over 2.7.[16] With state of the art lithogra-
phy,[13,17]followedbyreactive-ionorelectrochemical etching,
high-resolution2DPhCscanbedefinedinhigh-refractive-in-
dexmaterialsincludingsiliconandIII-Vsemiconductors.
Theadditionofdefectstothesestructuresiscarriedoutsi-
Figure1.Scanningelectronmicroscopy(SEM)imageofamacroporous
multaneously with the fabrication of the 2D PhC, affording silicon2DPhCcontainingalinedefect.Theporepitchis1.5lmandthe
excellent registration between the defects and the lattice. By PhCis100lmdeep.Reproducedfrom[19].
Figure2.a)SEMimageandb)spectrafromaphotonicdoubleheterostructurenanocavity.Theinsetsin(b)showanear-fieldimageandhigh-resolu-
tionspectrumoftheresonance.Alinewidthof2.8pmandaQ-factorof600000wereobserved.Reproducedwithpermissionfrom[20].Copyright
2005Macmillan.
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be achieved by extending the PBG into
the third dimension. From a fabrication
and materials standpoint, 3D systems
containingdefineddefectstructurespres-
ent a difficult set of challenges. For a
cPBGatopticalwavelengths,ahigh-reso-
lution3Dfabricationtechniqueandhigh
dielectricconstantmaterialsarerequired,
significantlylimitingbothpossiblemate-
rials and processing routes. Still, several
processing routes to cPBG materials
have been identified. Those that are
amenable to defect fabrication will be
coveredinthissection.Importantconsid-
erations will be discussed, including po-
tentialresolution,accuracyofdefectreg-
istration with the PhC lattice, ability to
definecomplicatedstructures,andpoten-
tial for incorporation of materials with
advanced functionalities. Although still
limited,opticalcharacterizationandthe-
oretical modeling of these defects will
alsobereviewed.
Figure3.SEMimages:a,b)sideandtopviewsof3DPhCsbuiltusingconventionallithographic
techniques((a)reproducedwithpermissionfrom[30].Copyright1998Macmillan).b)Thestruc-
turecontainsasharpbenddefectformedbyleavingoutrodportionsduringPhCfabrication.Re-
3.1.IntrinsicDefects producedwithpermissionfrom[12].Copyright2000AAAS.c)SchematicofaPhCcontainingpoint
defectsfabricatedusingsimilartechniques.d)Simulatedandmeasuredopticalspectraobtained
3.1.1.ConventionalLithography fromthestructurein(c);thedefectstatecanbeobservedinboth.Reproducedwithpermission
from[31].Copyright2004Macmillan.
As the microelectronics industry has
demonstrated, top-down lithography
cancreateextraordinarilycomplexmultilayerstructures.Such waveguidestructureswithsharpbends(Fig.3b).[12]Transmis-
layer-by-layer processing routes have now been exploited to sion and reflection through such a bend was simulated
create3DPBGmaterialscontainingdefineddefectstructures. through a finite difference time domain (FDTD) method.[29]
On one hand, lithographic approaches have a number of Thelayer-by-layerapproachpioneeredbyLinetal.followsa
shortcomings,fromcostandpractical limitationstothenum- classical device-fabrication process with repeated cycles of
beroflayers.Forexample,formingmultilayerstructuresiste- photolithography, wet and dry etching, chemical mechanical
diousanddifficult,requiringstate-of-the-artprocessingequip- planarization,andsequentialgrowthofSiN,Si,andSiO thin
2
ment to overcome layer-to-layer registration issues. On the films (Fig. 3a).[30] Following a related layer-by-layer proce-
other hand, the infrastructure for lithographic approaches is dure, Qi etal. successfully fabricated a 3D cPBG structure
extraordinarily well developed and, for some device applica- containing defined point defects (Fig.3c).[31] Optical charac-
tions, will probably be the method of choice for integrating terization showed the presence of defect states in agreement
3DPCswithmicroelectronics. with theoretical simulations performed with a FDTD meth-
The lithographic methods reported in the literature follow od[32](Fig.3d).
conventional2Dlithographyandpattern-transfertechniques,
andvaryprimarilyintheprocedureusedtostackthemultiple 3.1.2.ElectrochemicalEtching
layers to create a 3D PhC (Fig.3). Lithographic approaches
arehighlysuitableforformingwoodpilestructuresconsisting Theformationofperiodicarraysofmicrometer-sizedpores
of high-dielectric-constant rods assembled such that the con- inn-typesiliconthroughanodicetching[33]isanapproachthat
tact points form a diamond lattice.[27] Noda and co-workers has greatly advanced over the past decade and now enables
developed a ‘wafer-fusion’ method in which multiple layers the fabrication of Si-based 3D PhCs containing defined de-
arecreatedonseparatesubstratesandthenalignedandfused fects(Fig.4).Asubstrateisfirstpatternedwithpyramidalpits
together.[28]Leavingoneormorerodsoutoftheoriginalpat- through standard lithography followed by an isotropic wet
tern yields defects in the final 3D structure, for example, etch.WhenthesubstrateisthenplacedinaHFacidsolution
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3.1.3.GlancingAngleDeposition
Glancingangledeposition(GLAD)isarelativelynewtech-
niqueamenabletothelarge-areamicrofabricationof3Dtetrag-
onalsquarespiralPhCs,[42]structureswhicharetheoreticallyca-
pable ofpossessing a large and robust cPBG.[43,44] GLADhas
beenusedtogrowmaterialsofinterestforPhCs,includingSiO ,
2
Si,Ge,TiO ,andMgF .First,aflatsubstrateispatternedwitha
2 2
regulararrayofshortseedpostsviaelectron-beam(e-beam)or
photolithography.Then,thesubstrateisexposedtoacollimated
vaporfluxatalargeincidentangle,suchthatself-shadowingoc-
cursduringnucleation.Throughshadowingandthelimitedada-
tomsurfacediffusion,nucleationandgrowthonlyoccuronthe
top surface of the seed posts and oriented pillars emerge and
growtowardthesourceoftheincidentvaporflux.Byappropri-
ately rotating the substrate during deposition, the growth and
shapeofthesestructurescanbecontrolled,enablingthegrowth
ofcircular,square,orpolygonalspiralsandtheincorporationof
Figure4.SEMsideviewimageofa3DPhCcontainingaplanardefect
fabricatedbyelectrochemicaletching.Thedefecthasawidthof2.65lm. embeddedplanartwistandspacinglayerdefects(Fig.5).[45]Ad-
ReproducedwithpermissionfromG.Mertens[39].Copyright2005Amer- ditionally,byeliminatingpointsorlinesintheinitialseedpat-
icanInstituteofPhysics. tern,siliconorair2Dpointorlinedefectsthatextendthrough
the thickness of the crystal have been defined.[46,47] Photonic
bandstructure calculations have been performed for homoge-
under an electrical bias, the enhanced current density at the neous3DGLADstructures,[43,44]however,thereisonlylimited
tips of the pyramidal pits drives selective etching and propa- opticalcharacterizationofeitherhomogeneousanddefect-con-
gates cylindrical holes through the substrate creating a 2D tainingGLADstructures.Transmissionsimulationshavebeen
structure.[34] The method can be used to create 3D PhCs by performed on heterostructures composed of two tetragonal
modulating the light intensity during the etching with HF, squarespiralPhCsthatsandwicha2DPhCcontainingpointand
varyingthenumberofchargecarrierswhichinturnmodifies line defects.[14] The optical properties of ambichiral TiO thin
2
thedissolutionoftheSi.Thus,bymodulatingtheillumination filmswithvariouspolygonalheliceshavebeeninterrogated.By
intensity,theinternalmicrostructure,andthuslocalrefractive comparing right- and left-handed circularly polarized trans-
indexofthesampleiscontrolled.[35–37] mitted light, the defect mode arising from an embedded twist
Thisfabricationtechniquepresentsseveraladvantages,per- layer defect was identified.[45] Although considerable work
haps the most significant of which is that the structure is remains, and complex arbitrary embedded defects can not be
formedfromsilicon, whichhasa high refractive index andis directly formed by GLAD, for applications that require only
verywellunderstood.Thereisthepossi-
bility for excellent control of the pore
shape,[38] since the structure in the z-
axiscanbecontrolledindependentlyof
the other two axes. This feature makes
theintroductionofplanardefectstrivial
since the structure in the z-axis is di-
rectlycontrolledbytheilluminationin-
tensity (Fig.4).[39] Also, linear defects
normal to the surface are possible by
modifyingtheinitial patternofthepyr-
amidal pits. There are two significant
shortcomingswiththisfabricationtech-
nique. First, the introduction of arbi-
trarilyshapeddefectspresentsanunre-
solved problem. Second, structures
createdthiswayshowatbestaverynar-
rowcPBG[40]unlesstheprocessiscom-
bined with focused-ion-beammilling of
Figure5.a)GLADschematic.b)SEMsideviewimageofa3DPhCcontaininga150nmplanarde-
channels,[41] which significantly reduces
fectfabricatedwithGLAD.ReproducedwithpermissionfromA.C.vanPopta[45].Copyright2005
thesimplicityofthismethod. AmericanInstituteofPhysics.
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therapid,andrelativelylowcost,fabricationofPhCstructures manipulate 3D arrays of colloidal microspheres.[52] Introduc-
overlargeareas. tion of defects should be possible by simple modification of
thetraparray.Unfortunately,sincethismethodrequiresaliq-
3.1.4.Micromanipulation uidmediumandthetrapscannotbeallowedtooverlap,itwill
bedifficulttodirectlyformclose-packed,mechanicallystable
Micromanipulation is an intriguing approach for the crea- structures that retain their structure upon solvent removal.
tion of nearly arbitrary 3D structureswithout the limitations Perhaps,throughnewchemistriesandassemblyroutes,itwill
ofconventionallithography. Here,thePhC isbuiltin a com- becomepossibletocreatestructuresthatcansurvivethedry-
pletely serial fashion from building blocks. For PhCs operat- ing process. To date, monolayers containing limited numbers
ing in the visible ornear-IR regime the buildingblocksneed of colloids have been formed through optical trapping fol-
tocontainsub-micrometerfeatures, andthustheuseofopti- lowedbysupercriticaldrying.[53]
cal tweezers or high-resolution robots attached to scanning Despitethemanyadvancesinopticaltrappingandrobotics,
electron or optical microscopes are ideal candidates for ma- including automatic image recognition[54] that will eventually
nipulatingthebuildingblocks. improve and accelerate the process of fabrication, the use
Throughtheuseofananorobot,[48]thefirstdiamondstruc- of micromanipulation assembly techniques seems to be re-
ture formed out of colloidal microspheres was fabricated strictedtosmallsamplesforscientificresearch.
(Fig.6a).[49] Aglassprobenanomanipulatorwasfirstusedto
assemble polystyrene and silica microspheres into a body- 3.1.5.DirectWriting
centeredstructure;subsequentremovalofthesacrificialpoly-
styrene spheres led to a diamond structure of touching silica DirectwritingofPhCshasbeengrowingininterestdueto
microspheres.[50]Throughtheappropriateplacementofpoly- boththeeaseofincorporationofdefects,andanumberofre-
cent successes in 3D PhCs, including promising optical spec-
troscopy.[55,56] In principle, direct writing involves nothing
morethanconvertinga3Dcomputeraideddesignintoatar-
getmaterial.Becausetherequireddimensionsareonthemi-
crometerscale,traditionalfabricationtechniques,suchasrap-
id prototyping, are not suitable and new approaches have
been required. The most promising to date appear to be ro-
boticinkwriting[55,57,58]andlaserwritingbytwo-photonpoly-
merization(TPP)[56,59](Fig.7).
Figure6. SEM image of PhCs fabricated with the aid of a nanorobot.
a)Topviewofadiamondstructureof1lmsilicacolloids.Reproduced
from[49].b)Sideviewofalayer-by-layerstructure.Reproducedwithper-
missionfrom[51].Copyright2003Macmillan.
styrene microspheres, point defects could be embedded into
theresultingstructure.Thesamenanorobotwasalsousedto
fabricatewoodpilestructurespresentinga cPBG (Fig.6b).[51]
Individual InP plates were fabricated by conventional inte-
grated circuit processing, and then robotically stacked and
aligned with the nanorobot to form structures of up to
20layers. An advantage of using microfabricated InP plates
overmicrospheresisthatthestructurewasbuiltonelayerata
time rather than one particle at a time. The inclusion of de-
fects was straightforward, simply requiring that one of the
plates contained a pre-designed defect. Transmission spectra
at varying angles were taken from an eight-layer structure
Figure7.SEMimagesofPhCsfabricatedbydirectwriting.a,b)Layer-by-
containing an embedded defect formed by varying the pitch layerstructurescreatedbyink-polymerwriting[55,58];b)showsalinear
within two of the central layers. Comparison to calculations defect from a missing rod; c,d)Slanted-pore and layer-by-layer struc-
suggestedthataresonantguidedmodewasbeingexcitedand tures, respectively, fabricated using TPP [78, 79]. (a) reproduced from
[55],(b)courtesyofG.GratsonandJ.Lewis,(c)reproducedwithpermis-
transmittedthroughthesample.
sion from Markus Deubel [79]. Copyright 2004 American Institute of
LaseropticaltrappinghasnotyetbeenusedtocreatePhC-
Physics.(d)Reproducedwithpermissionfrom[78].Copyright2004Mac-
containing defects, but the potential is certainly present. millan.
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Robotic ink writing consists of the fabrication of 3D mi- 3.2.ExtrinsicDefects
croperiodic polymer scaffolds via direct-write assembly of a
concentrated engineered polyelectrolyte ink that is ex- 3.2.1.HolographicLithography
truded through a micrometer-diameter orifice.[60] If the ink
rheology is properly designed, the deposited filaments TheconceptofholographiclithographyforPhCfabrication
maintaintheircylindricalshapewhilespanningunsupported wasfirstdemonstratedbyBergeretal.andisdeceptivelysim-
regions in the structure, yet adhere to both the substrate ple.[84]Inherently,itconsistsofrecordingthehologramcreat-
and the underlying layers. By means of this method, layer- edbytheinterferenceofmultiplebeamsoflightintoaphoto-
by-layer[27] and woodpile[61] structures have been ob- resist.TheirfirstholographicPhCwasa2Dtriangularlattice
tained.[55] The introduction of line defects can be easily obtained from the interference of three beams in a photore-
achieved by modifying the computer design to move or re- sist;thestructurewassubsequentlyreplicatedinGaAs.Inho-
move individual lines (Fig. 7b). To date, the minimum rod lographic lithography, the minimum number of beams re-
diameter is ca. 1 lm and consequently the stop band lies quired to form an n-dimensional lattice is n+1, thus four
between 3 and 5 lm. As is the case for PhCs made of poly- beamswererequiredtoobtainthefirst3DPhCwiththistech-
mers,therefractive-indexcontrastisnotsufficienttogener- nique.[85]Thephotoresistusedinthatstudy,andinmostsub-
ate a cPBG, so conversion of the polymer template to a sequentstudies,wasSU-8,aresistthathasproventobevery
high-refractive-index material is necessary. In a recent pub- useful due to its low intrinsic absorption and capability for
lication we demonstrated this conversion and characterized formingsub-micrometerfeatures.[86]
the resulting optical properties.[55] Theoretical and experi- Therearetwokeyreasonswhyholographiclithographyhas
mental optical studies on structures containing defects are thepotentialtobecomealeadingmethodfor3DPhCfabrica-
yettobeperformed. tion.First,holographyishighlyamenableforlarge-scalepro-
Direct laser writing through multiphoton polymerization duction. Second, addition of optically active defects into the
(MPP)isanotherpowerfulrouteto3Dfabrication.MPPwas photoresist prior to development via laser direct writing is
first developed by Strickler and Webb,[62] and has now been possible. The direct writing of features in holographic PhCs
usedtocreatearangeofhigh-resolution3D free-formstruc- has now been demonstrated in both 2D[87] and 3D[88] struc-
tures, including microchannels,[63–65] cantilevers,[66–68] micro- tures(Fig. 8).Todate,theopticalpropertiesofdefectsinho-
gears,[69,70] sub-micrometer oscillators,[71] hydrophobicatomic lographically definedPhCshavenotbeen studied,butthis is
forcemicroscopytips,[72]andPhCs.[59,67,73–81]Briefly,MPPuti- likelytohappensoon.
lizes the nonlinear nature of the multiphoton excitation pro-
cess to only excite dye molecules in a very small volume
around the focal point, with dimensions on the order of the
resolutionlimit.Theseexciteddyemoleculeslocallyinitiatea
polymerization.Byscanningthislocalizedexcitationthrough-
outa definedvolume, a monomercanbe polymerizedintoa
robustintricate3Dpolymerstructure.Thistechniquehasalso
beenusedtowriteembeddedfeatureswithinholographicand
self-assembledPhCs,seeSections3.2.1and3.2.3,respectively.
Inmostcases,MPPisatwo-photonprocess,inwhichcasewe
willrefertoitasTPP.
TPPisapromising,flexible3D fabricationtechniquethat
Figure8. a)SEM image of PhCs fabricated using holographiclithogra-
can be used to form both the PhC and, in principle, to
phy. b)Confocal microscope image of a feature embedded within the
embed arbitrarily complex defects. To date, PhC structures
PhCwrittenusingTPP.Reproducedfrom[88].
with layer-by-layer and slanted pore[82] geometries, present-
ing stop bands in the IR, have been fabricated (Fig. 7c and
d).[59,78,79] Similar to robotic ink writing, the PhC is often There remain, however, several serious issues before the
fabricated in a polymer, and thus a similar replication ap- potentialofholographicstructurescanbe realized. Theopti-
proach is necessary to create a high-refractive-index con- calpropertiesof3DPhCsformedviaholographyareweaker
trast structure.[56] Alternatively, there are certain high- thanexpectedforreasonsthatarenotobvious.Thereareonly
refractive-index chalcogenide glasses such as As S that limited reports on the optical response of these structures[89]
2 3
undergo solubility changes upon exposure to light and are and although a direct comparison is difficult, to date, it ap-
therefore amenable to direct laser writing.[83] To date, there pearsthatcolloidalcrystals(CCs)presentbetteropticalprop-
are no reports of optically active defects incorporated with- erties.Theopticalresponseofholographicstructurescouldbe
inTPPPhCs,howevertheprocessisstraightforward. improvedbybetterlasers,photoresists,andprocessingparam-
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P.V.Braunetal./IntroducingDefectsin3DPhotonicCrystals
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come even more important as the number of interfering with a 120° rotation between exposures. Since the refractive
beamsisincreasedtoformmorecomplexstructures(e.g.,dia- indexofPMMAisinsufficienttoopenacPBG,theinterstitial
mond or chiral lattices).[90,91] An equally significant issue is space was filled with TiO ormetals.[97] Transmissionand re-
2
thattherefractiveindicesofcommonphotoresistsaretoolow flection spectra revealed the presence of a stop band at
to open a cPBG, regardless of the structure, thus, replicating 2.4lm, which is in agreement with transfer matrix method
thestructureswithhigh-refractive-indexmaterialsisessential. simulations.Defectscanbeincorporatedintothesestructures
Advancesintemplatingsiliconwithpolymericstructures[55,56] via multiple exposure and multilayer resist schemes
indicatepossibleroutestocreatestructureswithenhancedre- (Fig.9).[100–102] Additional X-ray or e-beam exposures have
fractive-index contrast.Also,veryrecently,Summersandco- beenproposedforthedefinitionof2Ddefectsinonelayerof
workers[92]demonstratedtheuseofatomiclayerdepositionto a multilayer resist, possibly enabling the incorporation of a
replicatethestructureofaholographicPCintoTiO ,ahigh- plane of embedded 2D defects within PBG structures fabri-
2
refractive-indexmaterialwhichistransparentinthevisiblere- cated using LIGA.[100,102] The fact that synchrotronradiation
gion.Finally,sincetheexposurewavelengthisdirectlypropor- isrequired,coupledwithissuesinuniformityforsub-microm-
tionaltothelatticeparameterofthecrystal,thechemistryof eter structures, probably limits the general applicability of
the photoinitiating system may need to be changed to tune LIGAforPhCsoperatingatlongerwavelengths.
the spectral position of the optical features. Although possi-
ble, this not a trivial task.[93] Even given these issues, holo-
graphic lithography coupled with direct laser writing is cer-
tainlyanareaofgreatpotential.
Avariant to holographiclithographyin which the interfer-
ence is created from a phase mask, as opposed to multiple
beaminterference,wasdemonstratedbyRogersandco-work-
ers.[94]Thephasemaskisfirstdefinedina‘master’,fabricated
through photolithography. This master is used to create a
poly(dimethylsiloxane) (PDMS) flexible phase mask. The Figure9.SEMimageofmetallicYablonovitestructuresfabricatedusing
PDMSphasemaskisplacedindirectcontactwiththesurface LIGA.Linearresist-baseddefectscanbeseenwithinthestructure.Repro-
ofaphotoresist(SU-8)andilluminatedwithUVlight,result- ducedwithpermissionfrom[102].Copyright2005IOPPublishing.
ing in a complex 3D intensity distribution in the photoresist.
Apart from the simplicity of this method, a very interesting
featureofthisfabricationtechniqueisthatitallowstheintro- 3.2.3.ColloidalSelf-Assembly
ductionofbothintrinsicandextrinsicdefects.Theformerare
obtained by creating defects in the original 2D master tem- Self-assembled CCs have been widely studied as routes to
plate.[94]Itshouldbepossibletoformthelatterviadirectlaser PhCsandPBGmaterials,insubstantialpartduetotheirease
writing,asdemonstratedinPhCsobtainedbymultibeamho- offabricationandlowcost,butalsoduetotheirexcellentop-
lographiclithography.Opticalcharacterizationofthesestruc- ticalproperties.TypicalcolloidalPhCsconsistof3Dface-cen-
tureshasyettobepublished. teredcubic(fcc)arrays,self-assembledfromhighly monodis-
perse silica or polystyrene microspheres with diameters
3.2.2.X-RayLithography,Electroforming,Molding(LIGA) rangingfromca. 200nmto2lm.[103]Mostearlyresearchfo-
cusedonimprovingCCqualityandinvertingtheminhigh-re-
LIGA is a deep-etch X-ray lithography microfabrication fractive-index materials.[104] This is necessary because only a
processwhichcombinesX-raylithography,electrodeposition, high-refractive-index contrast inverse-fcc geometry can pos-
and/or molding to circumvent the layer-to-layer registration sessacPBG.[105]ToutilizeCCsformostcPBGapplications,it
and multistep processing issues found in conventional layer- isadditionallynecessarytoincorporatedesigneddefectswith-
by-layer lithographic approaches.[95,96] Through LIGA, high- inthem.Sincethecontrolledadditionofwell-definedintrinsic
aspect-ratio PhCs up to six crystal periods thick have been defects is not compatible with the self-assembly process, the
fabricated with sub-micrometer precision and low surface viabilityofCCsformanyPBG-basedapplicationsreliesona
roughness.Synchrotron-baseddeepX-raysareusedtoexpose compatible external-defect fabrication technique. Substantial
poly(methylmethacrylate)(PMMA)throughapatternedab- strideshavebeenmadeoverthelastfiveyearsinthedevelop-
sorbermask.TheexposedPMMAisremoved,andtheresult- mentofnovelprocessesfortheincorporationofpoint,linear,
ingstructurecanserveasamoldthatisfilledbyelectrodepo- planar,and3Ddefectswithinself-assembledPhCs.
sition or casting, forming a template of the PMMA mold in Substitutional Doping: Although well-defined defects in
metal,ceramic,orcomposites.[97] CCs may have the greatest long-term potential, significant
This technique enabled micrometer-scale fabrication of in- strides in understanding the impact of defects can be deter-
verseYablonovite[98]or“threecylinder”structures.[99]PMMA minedthroughtherandomplacementofdefects.Thefirstin-
was exposed through a triangular array of holes via three tentionalincorporationofopticaldefectstatesinaCCwasac-
2672 www.advmat.de ©2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim Adv.Mater.2006,18,2665–2678
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complishedintrinsicallyviasubstitutionaldoping.Watsonand thedepositionofanintermediatelayerandperhaps2Dlitho-
co-workersdopedcolloidal suspensionswithmicrospheresof graphic patterning of this layer, and is concluded with the
differentsizesordielectricconstants,andusedthismixtureto growthofanoverlyingCC.Additionalstepsmayincludefill-
growCCswithsubstitutionalimpurities.[106]Near-IRtransmis- ing the interstitial space of the CC and template removal. In
sionspectroscopywasusedtoprobetheopticalpropertiesof thisfashion,embeddedfeaturesoflimiteddimensionalitycan
thewetcrystalsdopedwithbothdonorandacceptorimpuri- bedefinedwithincolloidalPhCs.
ties.Defectmodesaswellasasignificantwideningoftheopti- Through e-beam and nanoimprint lithography extrinsic
cal stop band were observed (Fig. 10). Spectra simulated pointdefectscanbedefinedinoronCCs(Fig.11).E-beamli-
usingthetransfermatrixmethod[107]qualitativelyagreedwith thographywasusedtoindividuallyexposeanarrayofspheres
experimental results, though a quantitative comparison was on the top layer of a CC and it was proposed that an addi-
notpossible.AnotherdopingstudybyGatesandXiaandlat- tional CC could be grownbeforedevelopmentto embed the
erbyLopezandco-workersobservedareductioninattenua- defects.[110] Nanoimprint lithographywas used to introducea
tionoftransmittancewithintheopticalstopbandwithincreas- plane of point defects between two colloidal multilayers.[111]
AlignmentofdefectswiththeCClatticewasnotpossibleand
multiple additional processing steps were required to embed
the layer of defects; however, since nanoimprint lithography
isaparallel,lesstime-consumingprocessthane-beamlithog-
raphy, it may still find application. It will be interesting to
comparetheopticalpropertiesofa2Dembeddedlayerofex-
trinsic point defects with those from randomly three-dimen-
sionallydistributedintrinsicpointdefectsintroducedviasub-
stitutionaldoping(seeprevioussection).
It is straightforward to extend e-beam and nanoimprint
techniques to define linear and other 2D defects in CCs.[111–
114] A similar approach to define embedded linear extrinsic
defects is to use conventional photolithography to pattern a
photoresistdepositedonaCC(Fig.12).Followingtheassem-
bly of another crystal on this structure and removal of the
photoresist,buried linear air defects have been incorporated
within CCs.[115,116] While these linear defects have been sug-
gestedforuseaswaveguides,opticshaveonlybeenmeasured
Figure10. Near-IR transmission spectra for CCs containing intrinsic normalto theirlong axis.[115] Thereis a reportthat measures
polystyrenedonorimpurities (10% numberfraction) expressed in nor- transmission through “opal-clad” waveguides, however, in
malizedfrequencyunits(c/a).Thehostcolloiddiameteris173nm,the thatcase thewaveguideis notcompletely surroundedby the
dopant colloids have diameters of 204, 214, and 222nm. The dotted CC.[117]
curveiscollectedfromanundopedCC,theothercurvesarefromdoped
Anothertechniqueusedtodefineextrinsiclineardefectsin
CCs.Reproducedwithpermissionfrom[106].Copyright1996theAmeri-
canPhysicalSociety. CC-based PhCs is laser microannealing, which was used to
write micrometer-scale defects on the surface of silicon in-
verse opals by inducing a localized phase transition from
ing impurity concentration in dried CCs, however
distinguishable defect modes within the gap were
notobserved.[108,109]
Substitutionaldoping doesnot afford control of
defectplacementandcanthereforeonlybeusedto
create randomly distributed point defects. For the
fabrication of more complex defect structures, re-
quiredformanyadvancedfunctionalities,anexter-
nalfabricationtechniqueisnecessary.
2DEmbeddedDefects viaMultistep Procedures:
Severalmultistepprocedureshavebeendeveloped
for the fabrication of extrinsic point, linear, and
planar defects within self-assembled PhCs. These
Figure11.a)SEMimagepresentingarectangularlatticeofpointdefectsdefinedon
approaches generally incorporate a 2D plane of
thesurfaceofaPMMACC(latticeparameteris498nm).b)Proposedprocessforem-
defects sandwiched between two CCs. The proce-
beddingdefects:1.e-beamexposure,2.growthofsecondCC,3.developmentofex-
dure begins with the growth of a CC, followed by posedregions.Reproducedwithpermissionfrom[110].Copyright2005Elsevier.
Adv.Mater.2006,18,2665–2678 ©2006WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.advmat.de 2673