InP-based photonic crystals : Processing, Material properties and Dispersion effects

Pro essing, Material properties and

Dispersion ee ts

AUDREYBERRIER

TRITA-ICT/MAPAVH Report2008:7

ISSN 1653-7610

ISRNKTH/ICT-MAP/AVH-2008:7-SE

ISBN 978-91-7178-969-3

Mi roele troni sandAppliedPhysi s

KungligaTekniskahögskolan

Ele trum229

SE-16440Kista

AkademiskavhandlingsommedtillståndavKunglTekniskahögskolanframlägges

till oentliggranskningföravläggandeavTeknologiedoktorsexamenfredagenden

30maj 2008kl.10:00iN1,Ele trum3,KunglTekniskahögskolan,Sto kholm.

Contents iii

A knowledgments vii

Listofpapers ix

A ronyms xiii

1 Introdu tion 1

1.1 Ba kgroundandMotivation . . . 1

1.2 AimandOverviewoftheoriginalwork. . . 4

1.3 Outlineofthethesis . . . 5

2 Photoni rystals: general on epts 7 2.1 Lightpropagationinperiodi media . . . 7

2.2 Two-dimensionalPhClatti e . . . 8

2.3 PlanarPhotoni Crystals . . . 8

Highindex ontrastsystem . . . 9

Lowindex ontrastsystem . . . 9

2.4 Lightpropagationinplanarphotoni rystals . . . 10

2.5 Computationalmethods . . . 13

PlaneWaveExpansion . . . 13

FiniteDieren eTimeDomain . . . 14

2.6 Leaky modes . . . 15

3 Fabri ation steps forphotoni rystals 17 3.1 Epitaxy . . . 17

3.2 Maskdeposition . . . 17

3.3 Ele tronBeamLithography . . . 18

Ebeamresists . . . 18

TheRaith150E-beamlithographysystem. . . 19

3.4 Maskopening-Rea tiveIonEt hing . . . 22

3.6 Post-et hingpro esssteps . . . 23

4 Chemi ally Assisted Ion Beam Et hing of InP-based photoni rystals 25 4.1 Chemi allyAssistedIonBeamEt hing . . . 25

4.2 Featuresize dependen e oftheet hing . . . 27

APhysi o- hemi almodelforInPet hing . . . 27

Experimental hara terizationofthelag-ee t. . . 29

Roughnessdevelopment . . . 32

Impa tontheopti alproperties . . . 33

4.3 Briefoverviewofsomedry-et hingpro esses. . . 33

4.4 Con lusion . . . 35

5 Opti alpropertiesofthe fabri atedphotoni rystal mirrorand avities 37 5.1 Internal LightSour e method . . . 37

Des riptionoftheinvestigatedPhCstru tures . . . 39

5.2 Opti allosses . . . 40

Intrinsi lossparameter . . . 41

Extrinsi lossparameter . . . 42

Optimization ofverti alheterostru turewaveguide . . . 43

5.3 Impa t ofthe featuresize dependen e oftheet hing ontheopti al propertiesofPhCs . . . 45

5.4 Con lusion . . . 47

6 Carrierlifetimesin et hedphotoni rystals 49 6.1 Surfa e/Interfa eStates . . . 49

6.2 Carrierdynami sinsemi ondu tormaterials . . . 50

6.3 Timeresolvedphotolumines en espe tros opy . . . 51

6.4 Modi ationof arrierlifetimes . . . 52

Sampledes ription . . . 52

Inuen eofthemaskmaterial . . . 52

Eviden efora umulatedsidewalldamage. . . 52

Non-radiativesidewallre ombinationvelo ity . . . 53

6.5 Modelingofthea umulateddamageinCAIBE . . . 54

Sputteringtheoryappliedto photoni rystalet hing . . . 54

Inuen e oftheholeshape. . . 56

6.6 Con lusion . . . 57

7 Lateral ele tron transport through photoni rystal elds 59 7.1 Ele trontransportthroughaphotoni rystaleld . . . 59

Modelingthe arriertransport . . . 59

Sample fabri ation . . . 64

Current-Voltagemeasurements . . . 65

Thermalee tsdue to arrierheating . . . 65

7.3 Et hing indu edmodi ationofsurfa epotential . . . 66

Inuen e of dry et hing on ele tri al properties of semi ondu tor surfa es . . . 67

7.4 Con lusion . . . 69

8 Some sele ted dispersion properties of photoni rystal based devi es 71 8.1 Blo hmodesintwo-dimensionalphotoni rystals . . . 71

8.2 Negativerefra tioninPhotoni rystals . . . 75

Negativerefra tionintwo-dimensionalInPbasedphotoni rystals . 76 8.3 End-re hara terization . . . 77

8.4 Experimentalinvestigationsofnegativerefra tion . . . 78

Lightfo using. . . 78

LightColle tionusingNegativeRefra tion. . . 79

8.5 FourierOpti s. . . 80

Experimentalset-up: prin ipleofmeasurement . . . 81

Auto- ollimation . . . 82

Visualizationoftheex itedBlo hmodesinthe2DPhCeld . . . . 83

8.6 Groupvelo itydispersioninphotoni rystalwaveguides. . . 83

PhC waveguides . . . 84

Slowlight . . . 85

Coupled avitywaveguides. . . 85

Phase-shift te hnique. . . 87

Measurementresults . . . 88

8.7 Con lusion . . . 89

9 Summary, on lusions and future work 91 9.1 A hievements . . . 91

9.2 Futurework . . . 92

10Guide to the papers 95

Abstra t

Photoni rystals (PhCs) are periodi diele tri stru tures that exhibit

aphotoni bandgap, i.e., arange ofwavelengthfor whi hlight propagation

is forbidden. The spe ial band stru turerelated dispersion properties oer

a realmof novel fun tionalities and interesting physi al phenomena. PhCs

havebeen manufa turedusing semi ondu torsand other material

te hnolo-gies. However, InP-basedmaterialsare themain hoi efora tivedevi esat

opti al ommuni ation wavelengths. Thisthesisfo uses ontwo-dimensional

PhCsintheInP/GaInAsP/InPmaterialsystemandaddressestheir

fabri a-tion te hnology and their physi al properties overing both material issues

andlight propagationaspe ts.

Ar/Cl

2

hemi allyassistedionbeamet hingwasusedtoet hthephotoni rystals. Theet hing hara teristi sin ludingfeaturesizedependentet hing

phenomenawereexperimentallydeterminedandtheunderlyinget hing

me h-anismsareexplained. Fortheet hedPhCholes,aspe tratiosaround20were

a hieved,withamaximumet hdepthof5

µ

mforaholediameterof300nm. Opti al losses in photoni rystal devi es were addressed both in terms of

verti al onnementandholeshapeanddepth.Theworkalsodemonstrated

thatdryet hinghasamajorimpa tonthepropertiesofthephotoni rystal

material. Thesurfa eFermilevelat theet hedhole sidewallswasfound to

be pinned at 0.12eV below the ondu tion bandminimum. This is shown

to haveimportant onsequen es on arrier transport. It is alsofound that,

for anInGaAsPquantumwell, the surfa ere ombinationvelo ity in reases

(non-linearly)by morethanoneorder ofmagnitudeas the et hduration is

in reased,providingeviden efora umulationofsidewalldamage. A model

basedonsputteringtheoryisdevelopedtoqualitativelyexplainthe

develop-mentofdamage. Thephysi sofdispersivephenomenainPhC stru turesis

investigatedexperimentallyandtheoreti ally. Negativerefra tionwas

experi-mentallydemonstratedatopti alwavelengths,andappliedforlightfo using.

Fourier opti s was used to experimentally explore the issue of oupling to

Blo h modes insidethe PhCslaband to experimentallydetermine the

ur-vature of the band stru ture. Finally, dispersive phenomena were used in

oupled- avitywaveguidestoa hieveaslowlight regimewithagroupindex

ofmore than180 andagroupvelo ity dispersion upto 10

7

times that ofa

onventionalber.

Keywords:Photoni rystals,indiumphosphide, hemi allyassistedion

beamet hing,lagee t, avities,opti allosses, arriertransport, arrier

The a omplishment of a PhD thesis is a long journey. Many people made this

workpossibleandhelpedmegothrougheventhemostdi ultmoments. Iwould

liketothankthemall:

Gunnar Landgren, for a epting me as a PhD student at the department of

Semi ondu torMaterials,

SebastianLourdudoss,foralwayshavingtimeto listentomy on ernsand for

sharinghis onstantgoodmood aswellas forhis areandsupport,

Srinivasan Anand, my thesis supervisor, my main support through all those

years. It is animpossible taskto express the fullextent of mygratitude towards

him. Iwouldliketo thankhimherefortheimmensityofknowledgehetransfered

to me on the way to be ome a good s ientist and to grow as a person (what a

omplextask!). Alwaysfor ing me to think along dierent paths, he guided me

byindi atingthepresen eofdoors butallowingmetotakethene essarystepsto

openthem. Keepinganeyeonmyprogresses,hehasalwaysbeenreadytoredire t

mewhen ne essary. I would also liketo thank himfor alwaystaking the timeto

put meba k ontherighttra kwhen I myselfsaw onlydead-endsin front ofme.

His ontinuoussupport,boths ienti allyandmorally,ishighly a knowledged.

The ollaboratorsfromotherlabsIhadthepleasureto loselyworkwithwithin

theframeworkoftheEuropeanNetworkofEx ellen eonPhotoni Integrated

Com-ponents and Cir uits, and from whom I learned a lot: Anne Talneau from the

LaboratoryofPhotoni sandNanostru tures,Mar oussis,Fran e;RolandoFerrini,

Ni olas Le Thomas and Romuald Houdré from E ole Polyte hnique Fédérale de

Lausanne,Switzerland,

DavidHavilandandAndersLiljeborgfromtheNanophysi sLaboratory(KTH)

forprovidinga esstotheele tronbeamlithographysystem,

BozenaJaskorzynskaforprovidinga ess totheend-resetupat KTH,

My former olleagues, and nowadays lose friends: Olivier Douhéret for his

spe ial humor and his onstantpresen e when times were di ult; Mikaël Mulot

fortea hing me so mu h aboutpro essesand methods in my rstyearas aPhD

studentandforthenumberdis ussions,s ienti ornot,westillhave. Thememory

ofhiss ienti rigorandpre iseknowledgehasbeenamodelformeallalongthese

Allthepeoplehelping meoutin the leanroom. Inparti ularGunnar

Anders-son, Sven ValerioandPeterGoldmanfor theire ientte hni alsupport, and for

alwaystakingtimeto sharetheirknowledgewithme,

MarianneWidingforher onstant areande ientadministrativesupport,

JesperBerggrenforalwaysbeingreadytohelp,

WoutervanderWijngaartforintrodu ingmetoresear h,

The olleagues and friends I had the pleasure to work with: Yao heng Shi,

Mar inSwillo,Ri haTyagi,ShaguftaNaureen,NaeemShahid,JörgSiegert,Saulius

Mar inkevi ius,HenrikJohansson,JoakimStrandberg,GunnarMalm,

All my olleagues and friends from the Mi roele troni s and Applied Physi s

Department,A reoand ReplisaurusIhadthepleasure tosharemomentsand

dis- ussionswith. Inparti ular,ThomasAggerstam,NadeemAkram,SussiAlmqvist,

Ce ilia Aronsson,YohannesAssefaw-Redda,XavierBadel,JesperBerggren, Hans

Bergkvist,StefanoBonetti,MarekCha inski,SilviaCorlevi,MatteoDainese,

Beat-rizEspinoza,RezaFatehnia,Ming-HongGau,Os arGustafson,MattiasHammar,

Julius Hållstedt,Carl Junesand, StephaneJunique, Sören Kahl,Joo-HyungKim,

Magnus Lindberg, Kestutis Maknys, Ri kard Mar ks von Württemberg, Fredrik

Olsson, Min Qiu, Henry Radamson, IsabelSainz Abas al, Yan-Ting Sun, Petrus

Sundgren, IlyaSy hugov, Qin Wang, Ma iej Wolborski, Le h Wosinski, Xingang

Yu, Zhenzhong"Andy"Zhang,Zhi-BinZhang,

All my friendsin Sto kholm and in therest of theworld,for forgivingme for

mylongperiodsofsilen e andforoeringmetheirsupport,

Myparentsfor their onstant are andsupport, and forallowingmeto follow

myownpath.

Publi ations in luded in the thesis

A A.Berrier ,M.Mulot,A.Talneau,R.Ferrini,R.Houdré,andS.Anand

Cha-ra terizationofthefeaturesizedependen einAr/Cl

2

hemi allyassistedion

beamet hingof InP basedphotoni rystaldevi es, J. Va . S i. Te hnol.

B.25(1)1-10(2007).

B R.Ferrini, A.Berrier , L.A.Dunbar, R.Houdré, M.Mulot, S.Anand, S.de

Rossi, A.Talneau Minimization of out of plane losses in planar photoni

rystals by optimizing the verti al waveguide, Appl. Phys. Lett. 85(18),

3998-4000(2004).

C A.Berrier ,R.Ferrini,A.Talneau,R.Houdré,andS.Anand,Impa tof

fea-ture size dependen e on theopti al properties of two-dimensional photoni

rystaldevi es, J. Appl. Phys.,103(9)(2008).

D A.Berrier , Y.Shi, J.Siegert, S.Mar inkevi ius, S.He, and S.Anand,

Evi-den eofa umulatedsidewalldamageindry-et hedInP-basedphotoni

rys-tals, submittedto Appl. Phys. Lett. (2008).

E A.Berrier ,Y.Shi,S.Mar inkevi ius,S.He,andS.Anand,Developmentof

damageanditsimpa tonsurfa ere ombinationvelo itiesindry-et hed

InP-basedphotoni rystals,,manus ript(2008).

F A.Berrier ,M.Mulot,G.Malm,M.ÖstlingandS.AnandCarriertransport

throughadry-et hedInP-basedtwodimensionalphotoni rystal, J. Appl.

Phys,101,123101(2007).

G A.Berrier ,M.Mulot,M.Swillo,M.Qiu,L.Thylén,A.TalneauandS.Anand,

Negative refra tionat infra-red wavelengths in a two-dimensional photoni

rystal, Phys. Rev. Lett.,93(7),073902(2004).

H A.Berrier ,M.Swillo,N.LeThomas,R.Houdré,andS.Anand,Blo hMode

Ex itationinTwo-DimensionalPhotoni CrystalsImagedbyFourierOpti s,

I A.Talneau,G.Aubin,A.Uddhammar,A.Berrier ,M.Mulot,andS.Anand,Highly

dispersivePhotoni Crystal-basedguidingstru tures, Appl. Phys. Lett. 88,

201106(2006).

Other journal publi ationsand onferen e pro eedings not

in luded in the thesis

J1 P.El-Kallassi,R.Ferrini,L.Zuppiroli,N.LeThomas,R.Houdré,A.Berrier ,

S.Anand, A.Talneau Opti al tuning of planar photoni rystals inltrated

withorgani mole ules, J. Opt. So . Am. B 24(9), 2165-2171(2007).

J2 L.Prkna,A.Talneau,M.Mulot,A.Berrier ,S.AnandEviden eofthe

Pho-toni Gap ontributiontotheguidingme hanismforstrongly onnedmodes

inthe"refra tive-like"domain, Opt. Lett. 31,2139(2006).

J3 M.J.Martin,T.Benyattou,R.Orobt houk,A.Talneau,A.Berrier ,M.Mulot,

S.Anand,Eviden e ofBlo h wavepropagation within photoni rystal

wa-veguides, Appl. Phys. B-LasersandOpti s 82(1)(2006).

J4 T.Benyattou,M.Martin, R.Orobt houk,A.Talneau,A.Berrier ,M.Mulot,

S.AnandOpti al Blo h wavesstudied by near opti aleld mi ros opy, J.

ofthe KoreanPhys. So . 47S72-S75Suppl. 1,(2005).

J5 S.deRossi,I.Sagnes,L.Legratiet,A.Talneau,A.Berrier ,M.Mulot,S.Anand,

J.L.Gentner Longitudinal Mode Sele tion in Constri tedPhotoni Crystal

GuidesandEle tri allyInje tedLasers,IEEEJour. Lightwave Te h. 23(3),

1363(2005).

J6 A.Talneau,J.L.Gentner,A.Berrier , M.Mulot, S.Anand,S.Olivier,High

externale ien yinamonomodefullphotoni rystallaserunder ontinuous

waveele tri alinje tion, Appl. Phys. Lett. 85(11),1913-1915(2004).

J7 M.Qiu,S.Xiao,A.Berrier ,S.Anand,L.Thylén,M.Mulot,M.Swillo,Z.Ruan,

S.He,Negativerefra tionintwo-dimensionalphotoni rystals,Appl. Phys.

A00,1-6(2004).

J8 W.vanderWijngaart,A.Berrier ,G.StemmeAmi ropneumati -to-vibration

energy onverter on ept, Sensorsand A tuatorsA: Physi al 100(1) 77-83

(2002).

J9 A.Berrier ,Y.Shi,J.Siegert,S.Mar inkevi ius,S.HeandS.Anand"Impa t

ofdry-et hing indu eddamage in InP-basedphotoni rystals" Pro . SPIE

Vol.6989,Photoni CrystalsMaterials andDevi es,p.698930(2008).

J10 A.Berrier , M.Mulot,A.Talneau,R.Ferrini,R.HoudréandS.Anand

"Fea-turesizeee tsin hemi allyassistedionbeamet hingofInP-basedphotoni

J11 A.Berrier ,M.Mulot,G.Malm,M.ÖstlingandS.Anand"Ele tri al

ondu -tionthrougha2DInP-basedphotoni rystal",Pro . SPIEVol.6322,Tuning

the Opti al Response ofPhotoni Bandgap Stru turesIII p.63220J(2006).

J12 A.Berrier ,M.Mulot,A.TalneauandS.Anand"Featuresizeee tsinAr/Cl

2

hemi ally assisted ion beam et hing of InP-basedphotoni rystals" IEEE

Pro . InternationalConferen eonIndiumPhosphide andRelatedMaterials,

Vol.2006,pp.340-3(2006).

J13 G.Aubin,A.Talneau,A.Uddhammar,A.Berrier ,M.MulotandS.Anand,"

Highlydispersivephotoni rystal-based guidingstru tures"Quantum

Ele -troni sandLaserS ien e Conferen e,Vol.2,pp.972-4(2005).

J14 B.Jaskorzynska,M.Qiu,A.Berrier ,M.Dainese,S.Anand,L.Wosinski,L.Thylén,

Z.J.Zawistowski"Appli ations of wavelengthdispersionin 1D and2D

pho-toni rystals" Pro . SPIE Vol.5959, Photoni Crystals and Fibres, pp.1-9

(2005).

J15 M.Qiu,Z.C.Ruan,ABerrier ,S.S.Xiao,M.Mulot,S.Anand,S.He,L.Thylén

"Negativerefra tioninsemi ondu torphotoni rystals"Pro . SPIEVol.5624

345-A ronyms

1D,2D,3D One-,two-,three-dimensional

BZ Brillouinzone

CAIBE Chemi allyassistedionbeamet hing

CBM Condu tionband minimum

CCW Coupled- avitywaveguide

EFC Equi-frequen y ontour

FDTD Finitedieren etimedomain

FIB Fo usedionbeam

FP Fabry-Pérot

FSDE Featuresizedependentet hing

FT Fouriertransform

FWHM Fullwidthat halfmaximum

GVD Groupvelo itydispersion

ICP Indu tively oupledplasma

ILS Internallightsour e

IV CurrentVoltage

LED Lightemittingdiode

MOVPE Metalorgani vaporphaseepitaxy

PhC Photoni rystal

PECVD Plasma-enhan ed hemi al-vapor deposition

PL Photolumines en e

PMMA Polymethylmetha rylate

PWE Planewaveexpansion

RIE Rea tiveionet hing

RF Radiofrequen y

SEM S anningele tronmi ros ope

TE Transverseele tri

TM Transversemagneti

QW Quantum well

Notations

a

PhC latti eperiod

c

Lightvelo ityin va uum

d

Holediameter

~

E

Ele tri eld

f

Air-llingfa tor

~

H

Magneti eld

h(t)

Depth ofthestraightportionofthehole

J

Iondensity

~k

Waveve tor

k

x

Propagation onstantinaPhC waveguide

L(λ)

Mirrorloss

L(t)

Holedepth

L

decay

De aylengthoftheele tri eldin thesubstrate

L

p

Opti alpenetrationdepthinsideaPhCmirror

n

Refra tiveindex

n

core

Refra tiveindexinthe orelayer

n

clad

Refra tiveindexinthe laddinglayer

n

eff

Ee tiverefra tiveindexoftheplanarwaveguide

n

g

Groupindex

Q

Qualityfa torofaresonant avity

q

Elementary harge

R

Mirrorree tion

~r

Positionve tor

t

TransmissionofaPhCstru ture

T

Mirrortransmission

u

Normalizedfrequen y(

= a/λ

)

u

~

_k

Blo hfun tion

W

Mirrorspa ingofa1D avity

v

g

Groupvelo ity

V

bias

Self-indu ed biasin RIE

V

₋

,

V

+

Ele tri potentialsofthegridsoftheCAIBE system

Y

Sputteringyield

Symbols

θ

c

Coneangleof aPhChole

α, α

i

Opti alabsorption oe ient

α

c

Clausing'sfa tor

δ

DepletionregionwidtharoundthePhCholes

ǫ

,

ǫ

′

Diele tri onstant

ǫ

′′

Lossparameter(imaginarypartof omplex

ǫ

ǫ

′′

int

Intrinsi lossparameter

ǫ

′′

ext

Extrinsi lossparameter

Γ

core

Connementfa torinthe orelayer

λ

Opti alwavelength

µ

′

Magneti permeability

η

in

Couplinge ien y

η

out

Colle tione ien y

ω

Opti alfrequen y

φ

,

φ

i

Phaseshift

σ

Ele tri ondu tivity

ζ

Verti aleldprole

τ

P L

Photolumines en ede aytime

τ

nonrad

, τ

Carrierlifetime(non-radiative)

ν

S

Surfa ere ombinationvelo ityattheholesidewalls

θ

Cl

Surfa e overage(probability)forClattheet hplane

Introdu tion

1.1 Ba kground and Motivation

Themajorappli ationareasforphotoni saredisplays,lighting,health are

in lud-ingmedi aldiagnosis/therapy,sensing,and ommuni ationtonameafew. The

Eu-ropeanroadmapforphotoni sandnanote hnologies,MergingOpti sand

Nanote h-nologies(MONA)aresultofdis ussionsamongEuropeana ademi andindustrial

organizationsandreleasedearly2008[1℄,identiesnineeldsinwhi h

nanophoton-i swill haveamajor impa tin the omingyears: sensors, data and tele om,

data storage, at panel displays, imaging, instrumentation, LEDs and

lighting, opti al inter onne ts and photovoltai s. Ontheroad towardsthe

developmentofnovelte hnologiesin these appli ationareas,astrongresear h

ef-fort is devoted to new promising materials su h as semi ondu tor quantum dots

and wires, metalli nanostru tures, arbon nanotubes, fun tionalized

nanoparti- les,metamaterialsand high index ontrast nanostru tures. Inthis last material

type,photoni rystalsarehighlypromising andidatesfortheiropti alproperties.

Photoni rystals(PhCs)arediele tri stru tureswithaperiodi ityinthe

die-le tri onstantoftheorderofthewavelengthoflight. One-dimensional(1D)PhCs

arehistori ally alledBragggratings/mirrorsandhavebeenstudiedformanyyears

[2, 3℄, e.g., as mirrors in laser designs [4, 5℄ or for their dispersiveproperties [6℄.

Later the on ept of periodi variation of the diele tri onstant was extended

to two and three dimensions. Subsequent to the rst proposals of PhCs for

in-hibition of spontaneous emission [7℄ and photon lo alization [8℄, several types of

two-dimensional(2D)andthree-dimensional(3D)PhCshavebeensu essfully

fab-ri atedand hara terized. Insu h stru tures,theperiodi diele tri potential an

giverisetoaphotoni bandgap,similartothesituationforele tronsina

semi on-du tor rystalinwhi h asetheperiodi potentialisthatoftheatoms onstituting

the rystal. ItisforthisreasonthatsometimesPhCsarealsoreferredtoas

photo-ni bandgapmaterials. Theexisten eofabandstru turemodiesthedispersionof

theowoflight. Inanotherwiseperfe t rystalthelo almodi ationofthe rystal

latti eorbasiswillintrodu e"defe ts"inthe rystal,givingrisetothepresen eof

new statesin the bandgap. Line or point defe tresonators an be reatedin the

rystal. Su hanengineeringofdefe ts inthePhClatti eoersnewwaysto guide

and onnelightbytheformationofwaveguides[911℄,or avities[12,13℄.

Figure 1.1: a) GaAs-based 1D PhC stru ture; Courtesy of F.Raineri (LPN); b)

GaAs-based 1D PhC mirror in GaAs; Reprinted bypermission from Elsevier [5℄,

Copyright2001; ) InP-based2DPhCstru turefabri atedatKTH;d)Si3DPhC

stru ture; Reprinted by permission from Ma millan Publishers Ltd:Nature [14℄,

Copyright1998;e)GaAs-based3DPhCstru ture;Reprintedwithpermissionfrom

[10℄,Ameri anInstitute ofPhysi s,Copyright2006.

Photoni rystalshave thepotentialto play animportant role in most of the

domains identiedbytheMONAroadmap. They an bring ompa tnessand

im-proved sensitivity to sensors ( hemi al [1517℄, biologi al[18℄). Quantum as ade

lasers withPhCsare sour esofmid-infraredradiation whi h willallowintegrated

terahertz spe tros opy for hemi al and biologi alsensing [1921℄. For data and

tele omappli ations,e ientand ompa twaveguides,lightsour esand

photode-te tors among others are required. Dispersion engineering an enable new

fun -tionalities su h as dispersion ompensation, slow light, et . PhC-based designs

allowimprovedperforman esforlightemittingdevi es: LEDs an makeuseofthe

bright-displays. Similarly,tele omwavelengthlasers anbemademore ompa t[24℄with

lowpower onsumption -lowthreshold-[25, 26℄. Photodete torsusephotoni

rys-talbaseddesignstoimprovetheirquantume ien yinthevisible[17℄,atinfra-red

wavelengths[2729℄.

PhCdesignsarepotentiallyinterestingforintegrationandfornewfun tionality

in omponentsused in opti al inter onne tsfor lo al areanetworks and Fiber To

TheHomes hemes[30℄,withwavelengthmultiplexingandre ongurabilityas

ad-vantages. SlowlightmodesinPhCs anbeawaytoobtainopti aldelaylines. The

signi antmodedispersion losetobandedgesor losetomode ut-osof

oupled- avitysuper-modes an slowdownlight, whi h is interesting foropti al buering

andpro essing [31℄ andalso forenhan inglight-matter intera tions[32, 33℄. The

steadyin reaseofthestoragedensityofdatawill soonrequiretobeatthe

dira -tion limit of light to perform memory read-out. New ways to improve imaging

apabilities,whi harenotdira tionlimitedwouldbevaluabletowardsthatgoal.

Even thoughplasmoni materialshaveverygood prospe ts, tailoredPhC designs

antoyieldsuper-resolution[34℄.

Figure1.2: S hemati drawingofatwo-dimensionalphotoni rystalindi atingthe

typeofverti allight onnementa)lowindex ontrast,verti alheterostru ture;b)

high index ontrast,membrane. The orientationof the

x

,

y

and

z

axisas used in thisthesisarealsoshown.

The te hnology for manufa turingphotoni rystalsfor operationat infra-red

wavelength or in the visible spe trum is hallenging, requiringhigh pre ision

na-nofabri ationtools. Eventhoughsomesu essfulattemptswerereportedbasedon

top-down[35℄orbottom-upapproa hes[36℄,3DPhCstru turesarefarfrom

realis-ti appli ationsdue tothehighlevelof omplexityoftheirfabri ation. Therefore,

2DPhCswithin-planeperiodi ity ombinedwitha onventionalslab onnement

in the third dire tion are nowadays the dominant te hnologi al solution. Figure

1.2showsas hemati drawingofaplanar2DPhCeldwithlowindex ontrastor

highindex ontrastverti allight onnement.

Whenthisthesisworkwasinitiated,theinterestforphotoni rystalswasmainly

fo used ondefe t engineering anddevi es operatingin thebandgap; examples of

ap-interest, espe ially for un onventional light propagation phenomena, su h as

su-perprism ee t [37℄ or negativerefra tion [38℄. Re ently, it hasbeen shown that

modi ationsofthePhClatti e[39,40℄oralo alalterationofthebasisby,e.g.,a

variationoftheholeradius

r

[41℄of thephotoni rystal an enhan e greatlythe opti alpropertiesofPhClasersand avities.

For the broadrange of appli ations mentioned earlier, the main driving for e

is thesteadily in reasingintegration levelof omponentsand fun tionalities. The

integration of a tive fun tionalities still relies on III-Vmaterials. InP-based

ma-terials are the main hoi e for operation in the 1.3 to 1.7

µ

m range. Resear h on onventional InP-based devi es has now rea hed a ertain degree of maturity

and te hnologyplatforms/foundriesare beingstarted. However,nanophotoni

de-vi es in luding photoni rystals are still far from maturity. The hallenges are

even higher onsidering that most appli ations require devi es with high quality,

low loss, high ompa tness, robustness, and ompatibility with ele tri al a ess.

Fun tionaldevi eswouldideallybeopti allya tive,beele tri ally ontrollableand

enableintelligentpro essingoflight. Towardstheseobje tivesanin-depth

under-standing oftheopti al, ele tri al anddispersionpropertiesofphotoni rystalsis

indeedhighlyvaluable. Atthesametime,knowledgeand ontroloffabri ation

pro- essesare loselylinkedto theperforman esofnanophotoni sdevi es. Thusthere

is aneed to understand and ontrol fabri ation te hniques for a mature

te hnol-ogyyieldingdevi eswithhighreprodu ibilityandquality. Fabri ationofphotoni

rystalstru turesis hallengingintermsofpro essa ura yandreprodu ibility

af-fe tingtheopti alpropertiesofthedevi esin ludingpropagationloss. Con erning

waveguiding andother passivewaveguidefun tions,sili onnanowires haveshown

better performan es. However, for a tive fun tionalities (light emission, opti al

signal pro essing, non-linear pro esses, et ) III-V materials are parti ularly well

suited.

1.2 Aim and Overview of the original work

Theawarenessand ontroloffabri ation andofthematerialpropertiesare

ne es-saryforhighperforman ePhCdevi esandintegrationofthese,in ludingele tri al

a ess. It iste hnologi ally ru ial for devi e performan eto understand the

im-pa t of pro essing on opti al losses, on the ele tri al propertiesof thematerial

-relevant in the ontext of ele tri ally a tivedevi es -, and on the opti al

proper-ties of thematerial -relevant foropti ally a tivedevi es. Further, theknowledge

of the dispersion properties of PhCs and how to engineer them is important for

novel fun tional devi es. Therefore there is aneed forunderstanding the physi s

of fabri ation-relatedissues, andhow theyae tlossesand materialpropertiesin

order to ontrolandpredi tpro essout omes.

Thepresentthesisaddressestheabovementionedissuesinthe ontextofplanar

Theperforman esofthe hemi allyassistedionbeamet hing (CAIBE)should

be evaluated in terms of a hievable aspe t ratios, feature size dependen e of the

holeshapeanddepth. Knowledgeaboutthephysi o- hemistryoftheet hingand

amodelfortheet hing hara teristi sarene essarytounderstandthe apabilities

ofthepro essandoriginsofitslimitations. Thisisthesubje tmatterofPaperA

andthe obtainedresultsaredire tly relevantfor optimizingdevi e performan es.

The impa t of the et hing hara teristi s on the opti al properties of photoni

rystalsu haslosses,ree tivityandqualityfa torfordevi esoperatinginsidethe

bandgap,areaddressedinPaper B and C

Dry-et hing, a ne essarypro ess stepin PhC devi e manufa turing, is known

tointrodu edamageintheet hedmaterial [42,43℄. Pro essindu eddamageand

itsimpa t on the ele tri al and opti al properties of PhCs need to be evaluated.

Further, theextentandnature of the reateddamage depends ontheet hed

ma-terial,theet hing te hniqueandpro essparameters. Inlightofthis,amethodto

assesstheee tofsidewalldamageontheele tri al ondu tioninPhCsisproposed

( PaperF).Theopti alpropertiesofthePhCmaterialwillalsobeae tedbythe

typeofet hing. Paper DandE presenttheexperimental hara terizationofthe

variationof the arrierlifetime of InGaAsP quantum wellsin PhCs as afun tion

ofthe et h parameters. Theoriginfor material damageis identiedand amodel

isdevelopedtopredi tthepro essdependentdefe t reationandthendingshave

importantimpli ationsfora tivePhCdevi es.

ThepotentialofdesigningdispersioninPhCstru turesisexperimentally

demon-stratedwithexamplessu hasnegativerefra tion,atlensingandauto- ollimation.

Theunderstanding of the oupling to PhC Blo h modes is bene ial in order to

de idehowtomakethebestuseofPhCstru turesbothinthegapandinthe

trans-mission bands. Band stru ture related dispersionee ts in PhC are investigated

in Papers G, H and I.Paper G gives anexperimental demonstration of light

fo usingusingnegativerefra tion. Thispaperalso showsitspotentialappli ation

forlight olle tion. PaperHisatheoreti alandexperimentalanalysisofthe

ex i-tationofBlo hmodesinaPhCeldoperatingabovethebandgap. InPaperItwo

designsof PhC-based oupled- avitywaveguidesare opti ally hara terizedin the

slowlightregime. Groupvelo itydispersionandthegroupindexaredetermined.

1.3 Outline of the thesis

Therest of the thesisis organizedas follows. The following hapter givesa

gen-eral introdu tion to the on epts used to des ribe the opti al properties of

two-dimensionalphotoni rystalsin ludinganoverviewofsomerelevant omputational

methods. Chapter3presentsthepro essstepsusedinthisworkforthefabri ation

of2Dphotoni rystals, andin ludes abriefdes riptionof themethods involved.

Chapter4givesadetailed des riptionof hemi allyassistedionbeamet hingand

sults on the evolution of PhC losses as a fun tion of the verti al onnement or

the PhC hole shape and depth. The results onthe inuen e of the PhC et hing

onthe arrierlifetimemeasuredbytime-resolvedphotolumines en earepresented

in Chapter6. Chapter7detailstheresultsobtainedontheele tri al propertiesof

PhC elds whi hprovidesanin-depth understandingof theele trontransport as

wellasthepro essindu edmodi ationoftheele tri alpropertiesofthePhC

ma-terial. Chapter8des ribesthenature andbehaviorof Blo hmodesaswellas the

anomalousdispersionregimesin2DPhC elds. This hapter alsosummarizesthe

resultsonnegativerefra tion,theobservationofBlo hmodesbyFourieropti sand

experimental measurementsofslowlightmodes. Finally,Chapter9givesthemain

Photoni rystals : general on epts

Photoni rystals(PhCs)areele tro-magneti stru tures hara terizedbythe

spa-tialperiodi ityofthediele tri onstant

ǫ(~r)

. Theperiodi ityallowsa mathemat-i aldes riptionbyintermsofalatti ewhi hbringstheanalogywiththeperiodi

arrangement of atoms in a rystalline material, hen e the name " rystal". The

periodofthelatti ein PhCsisoftheorderofmagnitudeofthewavelengthofthe

"light", hen ethe term"photoni ". Most ommonly in PhCs, likein the present

work,

ǫ(~r)

is aperiodi repetitionofpo ketsofamaterialwithdiele tri onstant

ǫ

m

in aba kgroundmaterialwith diele tri onstant

ǫ

b

. One ouldimaginesome stru tureswithmore ompli atedfun tionsforthepermittivity

ǫ(~r)

orpermeability

µ(~r)

.

2.1 Light propagation in periodi media

Maxwell's equationsdes ribethe behaviorof ele tro-magneti wavesin any given

medium. For an ele tri ally polarizable, non-magneti , lo ally ma ros opi ally

isotropi andlosslessmaterialwherewenegle tfree hargesand urrentswehave,

inSIunits,in thelinearregime[44℄:

∇ · (ǫ

0

ǫ(~r) ~

E) = 0

(2.1)

∇ × ~

H − ǫ

0

ǫ(~r)

∂ ~

E

∂t

= 0

(2.2)

∇ · ~

H = 0

(2.3)

∇ × ~

E + µ

0

∂ ~

H

∂t

= 0

(2.4)

where

E(~r)

~

istheele tri eld,

H(~r)

~

isthemagneti eld,

ǫ

0

isthepermittivityin va uum,

µ

0

thepermeabilityin va uumand

ǫ(~r)

isthelo al relativepermittivity.

Byintrodu ingtimedependen eoftheeldsasanharmoni os illatingfun tion,

intoequations2.1to2.2weobtainaftersomealgebrathefollowingmasterequations

forthe

E

~

-eldand

H

~

-eld,respe tively,

ˆ

Ξ ~

E

ω

(~r) = (

ω

c

)

2

_E

_~

ω

(~r)

(2.5)

ˆ

Θ ~

H

ω

(~r) = (

ω

c

)

2

_H

_~

ω

(~r)

(2.6)

where

ω

is the y li frequen y,

c

the light velo ity,

Ξ =

ˆ

1

ǫ(~

r)

∇ × ∇×

and

Θ =

ˆ

∇ ×

1

ǫ(~

r)

∇×

.

2.2 Two-dimensional PhC latti e

Thefo usofthisthesisisontwo-dimensional(2D) airholephotoni rystals. We

will provide herethe on eptsneededto des ribe2DPhCs. We onsider here2D

PhCs made from a triangular latti e of airholes in adiele tri material, i.e., an

InP-basedheterostru ture. Thelatti e onstant

a

and thediameter oftheholes

d

are dened on Fig. 2.1. Theair llfa tor

f

, usually expressed in %,is the ratio betweenthesurfa eo upiedbyairtothetotalsurfa eofthePhC.Itis al ulated

from aunit ellandisgivenby

f =

π

2

√

3

(

d

a

)

2

≈ 0.907d

2

/a

2

.

The re ipro al latti e is generated by the basis ve tors

b

~

1

and

b

~

2

onstru ted from thereal spa e basisve tors

a

~

1

= (a, 0)

and

a

~

2

= a(

1

2

,

√

3

2

)

and are given by

~

b

1

=

2π

a

(1, −

1

√

3

)

and

b

~

2

=

2π

a

(0,

2

√

3

)

. Figure 2.1 shows the real and re ipro al spa easso iatedwiththetriangularlatti e2DPhC,aswellasthemainsymmetry

dire tions

Γ

Mand

Γ

K,andtherstBrillouinzone.

Introdu tion of simple defe ts in a 2D PhC latti e in the form of removed

holes (or holes lled with a material dierent from the host matrix) allows the

formation ofwaveguides[9℄, resonators[12, 45℄. Re ent works haveshown that a

lo almodi ationofthelatti e(modi ationof

a

toformphotoni heterostru tures [39℄, shift in position of latti e points [46℄) or of the basis ([40, 47, 48℄) of the

photoni rystal anenhan etheopti alpropertiesgreatly.

2.3 Planar Photoni Crystals

By denition, two-dimensional rystals extend innitely in the dire tion normal

(verti aldire tion) to the plane of periodi ity. Thus for opti al devi es based on

PhCs, a onnementintheverti aldire tionisne essary. This onnementis

ob-tained by aplanar waveguide with the light onned in the ore layerof higher

refra tiveindex. Several solutionsfor this material sta kingare possibleand are

generally lassiedintohighorlowindex ontrastsystemsa ordingtothe

surround-Figure2.1: a)S hemati ofa2DPhCinrealspa e. The ir lesrepresentthebasis

(hole) repeated at ea h latti e point.

a

~

1

and

a

~

2

are theprimitivelatti e ve tors. Thelatti e onstant

a

and hole diameter

d

are also shown; b) s hemati s of the re ipro al spa e orrespondingto thelatti eshownin a).

b

~

1

and

b

~

2

are thebasis ve torsof the re ipro allatti e. The rst Brillouin zone is shown, as well as the

symmetrypoints

Γ

,KandM.

ingmaterial(s). Itistobenotedherethattheindex ontrastreferstotheverti al

stru tureandnotto theindex ontrastbetweenba kgroundandPhCholes/rods.

Highindex ontrast system

The high index ontrast domain is ommonly dened by the ondition

∆n ≥ 2

. Thematerials aboveandbelowthe orelayermaybemadeofdierent materials.

Examplesinthis ategoryaremembranes[12, 49,50℄, semi ondu tor-on-insulator

stru tures where the ore layer is asymmetri ally bounded by air and a low

in-dexdiele tri layerwhi h ouldbeoxides [51, 52℄, polymers[53, 54℄ or lowindex

substrates(e.g., sapphire[55,56℄).

Low index ontrastsystem

Themost ommonwaytofabri atePhC devi esinthelowindex ontrastsystem

makes use of semi ondu tor heterostru tures to onne the light in the verti al

sket hofthisverti alstru tureindi atingtherespe tivevaluesofrefra tiveindex

(at 1.55

µ

m) as well as themodeprole

ζ(z)

ofthe thefundamental modeof the ele tri eld

E(z)

~

in the waveguidefor TE polarization. The small dieren e in

Figure 2.2: S hemati diagram of the verti al stru ture omposed of

InP/InGaAsP/InPas wellastheverti alproleoftheTEfundamental mode

refra tiveindi esdoesnotallowforastrongverti al onnement,i.e.,

ζ(z)

extends deepinto thesubstrate. Thisweak onnementofthemodeprolehassigni ant

impli ations on the fabri ation of PhC devi es and on their opti al properties.

These issueswill begivenattentionin Chap.5.

2.4 Light propagation in planar photoni rystals

In asesforwhi hwe andenetwodistin tpolarizationstatesTE(E

z

=H

x

=H

y

=

0

) and TM(H

z

=E

x

=E

y

= 0

) the master equations for the z- omponent of the respe tiveeldsaregivenby:

∂

∂x



₁

ǫ(~r)

∂

∂x

H

z



+

∂

∂y



₁

ǫ(~r)

∂

∂x

H

z



+

ω

2

c

2

H

z

= 0

(2.7)

1

ǫ(~r)

 ∂

2

∂x

2

+

∂

2

∂y

2



E

z

+

ω

2

c

2

E

z

= 0

(2.8)

We annowintrodu etheperiodi ityofthediele tri fun tion:

ǫ(~r) = ǫ

m

h

1 + C exp(−j ~

G · ~r)

i

(2.9) with

G

~

are ipro allatti eve torsu has

G =

~

P

n

i=1

m

i

b

~

i

with

n

beingthenumber of dimensionsofthe onsidered problem,

m

i

anintegerand

b

~

i

thebasisve torsof

theoremtodealwithlineardierentialequationswith periodi oe ientsin

one-dimension,andmu hlaterasimilar on eptwas developedbyFélixBlo h [59℄in

threedimensions(3D) tosolvetheproblemofthemotionofele tronsinaperiodi

potential. Therefore,solutionsoftheMaxwell'sequationsdes ribingthe

propaga-tionofele tro-magneti wavesin aperiodi diele tri mediumareoftenreferredto

as "Floquet-Blo h waves" (FB waves) or simply "Blo h waves". Mathemati ally

aFB wave, for examplefor TM polarization for whi h theele tri eld in the

~z

dire tionis

E = E~z

~

, an beexpressedas,

∞

X

n=−∞

V

n

(~k) · exp(−j ~

k

n

· ~r)

(2.10)

with

~k

n

= ~k

0

+ ~

G

n

where

~k

n

is thewaveve torofthe

n

-th omponent of theFB wave,

~k

0

thewaveve torof therst harmoni ,

G

~

n

are ipro al latti eve tor,and

V

n

(~k)

theFourier oe ientfun tion.

The dira tion properties of one- or two-dimensional gratings and the opti s

oftheFB wavessupportedin su h stru tureswereanalyzedin thelate80's [2, 3℄

using thepowerful framework of waveve tordiagrams. Su h diagrams havebeen

appliedto anisotropi rystalsand laterto photoni rystalstru tures. Theywill

be used in Chap.8 to explainthe physi sof the dispersionrelated ee ts seenin

2DPhC stru tures.

The eigenvaluesof the masters equations 2.7 and 2.8 givethe band stru ture

ω(~k)

of the PhC and is also alled the dispersion relation [60℄. It is ommon to onsider the band stru ture in the rst Brillouin zone either in the full zone

or along the main symmetry dire tions (

Γ

MK) only. Figure 2.3 displays an exampleshowingthebandstru tureforatriangular-latti e2DPhCindi atingthe

bandgap (sometimes alled stopgap) and the rst three bands are labeled. The

masterequations 2.7and 2.8 arewavelength s alable. Thepropertiesof thePhC

stru turesdonotdependontheabsolutewavelengthofthelightbutratheronthe

ratioofthewavelengthto thelatti eperiodi ity. Thus itismeaningfulto usethe

normalizedfrequen y

u = a/λ

, as in Fig.2.3 to des ribethe opti alproperties of PhCs.

In the rst band lose to the

Γ

point the waveve tor of the light inside the stru tureismu h smallerthanthelatti e onstant: weareinthelongwavelength

limit(i.e.,

λ

is mu h largerthan the PhC period). Thelight doesnot "feel" the periodi diele tri perturbationandthepropagationissimilartothatinanisotropi

medium of refra tive index

n

ef f

, the ee tive refra tive index of the stru ture. Awayfromthislongwavelengthlimit,as

λ

de reasesthewaveseestheperiodi ity: weentertheregimeofBraggree tion. Dependingonthestrengthofthediele tri

"potential"(that anbe alled"photoni strength"),theenergyofthewavewillbe

moreor lessdistributed in between theFourier omponents of theex ited mode.

Fig.2.3 omparesthebandstru turesforTEandTMpolarizedlightforaPhC

stru ture of

f

= 30%,airholesinaba kgroundof refra tiveindex

n = 3.24

. The bandstru tureforTEshowsthepresen eofabandgapwhereasthereisnobandgap

forTM.Anotherdieren eisthat forTM theseparationbetweenthese ondand

thethird bandsislarger.

Figure2.3: Bandstru tureforTEmodesina2Dtriangularlatti ealongthemain

symmetrydire tionswithairllfa tor

f = 30%

;b)Bandstru tureforTMmodes. Theairlightlineisshowninthe

Γ

Mdire tion.

Therelationshipbetweenthewavelengthoflightanditswaveve torinairorin

theba kgroundmaterialisgivenby:

u =

a.k

2πn

(2.11)

where

n = n

mat

or

n

air

istherefra tiveindexoftheba kgroundmaterialorofair (=1), respe tively. These linearrelations are alled thelightlines. OnFig.2.3b,

thelightline orrespondingtoairisindi atedinthe

Γ

Mdire tiononly. Lightlines areoftenusefulto identifyguidedand leakymodes. Amoredetaileddis ussionis

givenin Se .2.6.

Fig.2.3alsosuggeststhatforagivenPhCthebandstru ture anbeinvestigated

byvaryingthewavelengthoflightand/orthelatti eperiod

a

. Inpra ti e,thelatter an beusefulwhentheavailablewavelengthrangeofthesour eislimited. Thisis

alled lithographytuning, andisappliedin Chap.5.

Modelingoftheopti alpropertiesof2DPhCdevi eswiththeInP/GaInAsP/InP

verti alheterostru tureis usuallyperformedwith2Dmodelingtools. The

refra -tiveindexoftheba kgroundmaterialis giventhevalueoftherefra tiveindex for

theheterostru ture

n

ef f

andisobtainedfromtheee tiveindexapproximation. Deningthepolarizationofmodesinaplanarphotoni rystalisnota

straight-forwardissue. Firstofall,the onventionsusedinthe"waveguideapproa h"andin

the"2DPhC"aredierent. Fromthepointofviewoftheverti alwaveguideaeld

axisof theholes. Itis thereforeimportantto statewhi hdenitions areused. In

this thesis the 2D PhC denition is applied. There is an added ompli ation 

areal 2D PhC isstri tly a 3Dobje t andthe Blo h oe ientsof the eld have

omponentsinthethreedire tionsandthestri tdenitionsforTEandTMmodes

given above do nothold anymore. An a epted way is to dene an approximate

polarizationstatein thePhC alled TE-likeandTM-like. Howeverthisdenition

holdsonlyifone andeneasymmetryplaneintheverti alstru ture(atthe

sym-metryplane,polarizationisstri tlyTEorTM).Inthelowindex ontrastsystem,

this is not valid and results in polarization mixing. We refer to the polarization

statesaspseudo-TEandpseudo-TM.Keepingthisinmind,intherestofthethesis

thepolarizationmodesinthePhCwill besimplyreferredtoas TEorTM.

3D al ulationtoolsarerequiredtosimulatePhCsbasedonhigh-index ontrast

stru tures. However, in the ase of low-index ontrast system, even though 2D

simulations give a reasonable agreement with experiments more a urate results

anbea hievedby3D al ulations. Dieren esinwavelengthshiftortransmission

levelsbetween2Dand3Dsimulationshavebeenreported[61℄.

2.5 Computational methods

Dierentmethodshavebeensu essfullyusedtosolvetheMaxwell'sequationsand

tomodeltheopti al hara teristi sofphotoni stru tures. Hereonlyalistofafew

(most ommon)methodsisgiven. Inasket hypi ture,themethods anbedivided

intwomain ategoriestreatingMaxwell'sequationseitherinrealspa easafun tion

oftime (where Finite-Dieren eTime-Domain (FDTD) isthe dominantmethod)

orin re ipro alspa e (frequen ydomain). Inthefrequen ydomain, methods are

distinguishedbythebasis usedfor theexpansionof theeld. Therstand most

straightforwardmethodisthePlaneWaveExpansionmethod(PWE)usingabasis

of plane waves. It is a parti ularly su essful method to obtain the PhC band

stru ture. To address simple defe ts in PhC stru tures it is possible to use the

super ell method. Howeverothermethodsare morepowerfultosimulate omplex

stru tures. For instan e, the MultipleMultipole Expansion method using abasis

ofspatialBessel/Hankelfun tions[62℄,orWannierfun tionsisespe iallyusefulin

the ase oflo alizedelds (i.e., avities) [63℄. S attering/transfer matrixmethod

isa widelyused omputational method for photoni s. This method and has also

been appliedto photoni rystals, sometimes together witha modalexpansion of

theeld. Modal methods an expand theeigenmodeson aBlo h mode basis(as

in the freely available software CamFR [64℄ or on a Fourier basis (e.g., Fourier

modalmethod[65℄). Inthisthesis,PWEandFDTDareused,andamoredetailed

dis ussionofthosetwomethodsisgivenbelow.

Plane Wave Expansion

stru -majorimplementationsare available: afull ve torial al ulationusedbythe MIT

program MPB [66℄, or a more omputationally ee tive method proposed by Ho

[67℄. Whenwe introdu e theperiodi ity ofthe latti ewe an expandthe eld in

termsofBlo hmodes

ϕ

~

k

(~r) = exp(j~k · ~r) ~

u

k

(~r)

with

u

~

k

(~r)

ave torialfun tionwith the same periodi ity as the PhC latti e. Owing to this periodi ity, we an now

expand

u

~

k

(~r)

into aFourierseries. Inorderto solvethemasterequations2.7and 2.8numeri allyoneneedstoexpandallthe oe ientsandtrun atetheseriestoa

nite number

N

ofplanewaves. Onepossibilityistoexpand

1/ǫ(~r)

. However,for reasonsofimproved onvergen eHo'smethodrst al ulatestheFouriertransform

of the diele tri map

ǫ(~r)

, trun ates it to the number of onsidered plane waves

N

, andthen inverts it. In thisthesis, the2DPWE resultswereobtainedusing a MatlabimplementationofHo'sPWEmethod [67℄.

In thePWE method the simulatedPhC elds are innite in the2D plane of

periodi ityandtranslationinvariantalongtheverti aldire tion(i.e.,innitelylong

holes). Itispossibletosimulatestru tureswithsimpledefe tsinthe rystallatti e

(su has avities,waveguides)usingthesuper ellapproa h. Wedeneaunit ellfor

the rystal(mu hlargerthantheoriginalunit ellofthePhClatti e)in ludingthe

defe tthatwe all"super ell"andthenrepeatthisunit ellto overthefullspa e.

In order to avoid artifa ts arising from arti ial oupling between the repeated

defe ts the super ell should be su iently large. One understands immediately

that thismethodissuitabletoverysimplegeometriesonly.

Finite Dieren e Time Domain

In theFDTD method Maxwell'sequations aresolved in time domainusing nite

dieren e operatorsto approximate thedierentials. Itis apowerfulmethod,

al-beitoften des ribedas a"brute for e"method, and is ableto simulate anygiven

geometry anddoesnotrelyontheperiodi ityofthestru ture. Itisawidespread

omputational method to solve a large variety of ele tro-magneti problems. It

has been proposed in 1966 by Yee [68℄. A grid (Yee's grid) is used to dis retize

spa e. Atea hpointofthegridtheele tri omponentoftheeld attime t+1/2

is al ulatedfromthevalueofthemagneti eldattimet,thenthemagneti eld

at time

t

+1 is obtained from the ele tri eld value at

t

+1/2, and so on. The dis retizationintimedependsonthespatialgridsize. Forinstan e,in2Dthetime

stepisexpressedas:

∆t = β

1

c

a

q

1

∆x

2

+

1

∆y

2

(2.12)

where

∆x

,and

∆y

arethegridstepsizes,

a

isthelatti e onstant(usuallysetto1),

c

thelightvelo ityand

β

a oe ient. Theeld anbeex itedbydierentsour es su haspointsour es,planewavesorwaveguidemodes. The omputationaldomain

is surrounded by Perfe tly Mat hed Layers(PML) [69℄ that are absorbinglayers

towards zero over a boundary layer. FDTD al ulations are very demanding in

termsof omputationalpower,espe iallyforsimulationof3Dstru tures.

In this thesis, only 2D al ulationswere performed with an innitestru ture

inverti aldire tion(i.e.,innitelylong ylindri alholes)and anite geometryin

the2Dplane. TheFDTD method anprovidethespatialeld distributionatany

giventime stepfor mono hromati ex itation,or the spe tral energydistribution

(transmission, ree tion, ...) by al ulating the value of the Poynting ve tor at

agiven position in thestru ture ex ited by a pulse. It is possibleto indu e loss

in thestru ture by theintrodu tion ofan imaginarypartin the denition of the

refra tiveindexof oneor moreof theregions. For amoregeneralreferen eabout

the FDTD method see Ref.[70℄. In this work, we have used the freely available

FDTDprogramF2P[71℄.

2.6 Leaky modes

Figure 2.4: Comparison of the in-plane waveve tor with the out-of-plane sphere

denedbythewaveve torinair

ModessupportedbyaPhCslab ansuerfromlossesifsomeBlo hharmoni s

arelo atedinside thelight ones. For a2DPhC,modes anbeguided intheslab

orleakyintothe laddinglayers. Inthe aseofthelowindex ontrastsystem,leaky

modesareradiativemodesinairorin thesubstrate,whi hbydenitionintrodu e

energy losses. If the in-plane wave-ve tor

k

~

in

of a given Blo h harmoni in the PhCslabisshorterthan thenormofthe orrespondingwaveve torin air

~k

0

,it is possibleforlightto oupleintoradiativemodesin air. Theverti al omponentof

the

p

th

Blo hmode omponentisexpressedas:

~

k

p

z

=

q

n

layer

~k

0

− ( ~

k

in

+ p ~

G)

(2.13)

where

n

layer

isthe refra tiveindex of airor ofthe substrate. From this equation one an see that ifthere exists aninteger

p

su h that

~k

in

+ p ~

G < n

layer

~k

0

the

waveve tor

~k

p

z

will be real and this omponent of theBlo h modewill leak. The groupofve torsin

k

-spa e,normsofwhi hareequalto





n

layer

~k

0







denethelight one. In order to nd theleaky modes of the stru ture one should ompare the

position ofthe ex itedBlo h modesin

k

-spa ewithrespe tto thelight ones for airand forthesubstratematerial. OnFig.2.4, themodeof waveve tor

~k

in−1

an ouple into radiativemodesin air, whereasthemodeof waveve tor

~k

in−2

will be evanes entin air. Theinuen e of leaky modes onthe opti alpropertiesof PhC

Fabri ation steps for photoni

rystals

The fabri ation of semi ondu tor-based 2D PhCs involves several pro ess steps,

typi ally in lean room environment, and dierent pro ess equipments are used.

Ea h ofthepro essstepsshouldbepre isely ontrolledand alibratedin orderto

obtainstru turesofdesiredquality. Inthis haptertherelevantpro essstepsthat

were used for PhC devi e fabri ation are des ribed, followingtheir sequen e in a

typi alpro essow.

3.1 Epitaxy

TheInP/GaInAsP/InPverti alwaveguideisgrownbymetal-organi vapor phase

epitaxy(MOVPE)onanInPsubstrate. Thegrowthpre ursorsaretrimethylindium,

trimethylgallium,arsineAsH

3

andphosphinePH

3

andthegrowthis ondu tedat

atemperatureof 680

o

C. Thethi kness ofthe topInP ladding is200nm (unless

otherwisestated). The orelayerismadeofGa

x

In

1−x

As

y

P

1−y

with

x = 0.24

and

y = 0.52

latti emat hedtotheInPsubstrate. Therefra tiveindexofthismaterial at

λ

=1.55

µ

mis

n

=3.35anditsabsorption edgeat

λ

edge

=1.22

µ

m. Somesamples hada10-nmInGaAsPquantumwell(QW)for arrierlifetimemeasurements,with

anemission wavelength of

λ

=1.14

µ

m. Thethi knessof the orelayeris 420nm, unless otherwise spe ied. All the layersare undoped. For internal light sour e

measurements ( hap.5), twoQW with emission wavelengths around 1.47

µ

m and 1.55

µ

mareembedded intotheInGaAsP orelayer.

3.2 Mask deposition

The SiO

2

mask is deposited by Plasma Enhan ed Chemi al Vapor Deposition

Table3.1: Pro essparametersforthePECVD pro essesforSiO

2

deposition Pro essC Pro essP Substrate temperature 230

o

C 300

o

C Plasmapower 15W 20W Pressure 700mT 800mT Depositionrate 1nm/s 1.2nm/s Refra tiveindex 1.47-1.49 1.51-1.52

Gasesandows 5%SiH

4

in He: 2%SiH

4

in N

2

:

40SCCM 740SCCM

N

2

O:200SCCM N

2

O:425SCCM

Chemi alvapor deposition (CVD) is apro ess in whi h gaseous spe ies rea t

onasubstratetoformathinsolidlm[72℄. Inplasmaenhan edCVD mostofthe

energyrequiredto generate hemi allyrea tivespe iesisprovided by theplasma.

ThusPECVDallowsdepositionofthinlmsatrelativelylowpro esstemperatures.

Theplasma isgenerated at afrequen y of13.56 MHz. Inthis thesiswork we

used twotypesofdepositionpro essesas listedonTable3.1. The onformalityof

thedepositedlms anbetailoredtosomeextendbyadaptingenergyandangular

distributionoftheions. ThegasesweusedtoformSiO

2

thinlmsaresilane(SiH

4

)

and dinitrogen oxide ("laughing gas") N

2

O.Details aboutthe PECVD pro esses

used inthisthesisarefoundinTable3.1.

3.3 Ele tron Beam Lithography

Thepatterndenitionofnanostru turesisa riti alstepfordevi egeneration.

Al-thoughalternativemethodshavebeenproposed(deep-UVlithography[73℄,

nanoim-printlithography[74℄,selfassembly[75℄),ele tronbeam(e-beam)lithographyisstill

by far the dominant method owingto its exibility. Inthe presentwork,two

e-beam systems were used: a Raith 150 e-beam system at the KTH Nanophysi s

departmentandaLEICAe-beamsystemattheLaboratoryforPhysi sand

Nano-stru tures(CNRS-LPN,Mar oussis,Fran e).

Ebeam resists

Thedoseistheamountofele tri al hargesre eivedbytheresistperunitarea. It

isusuallyexpressedin

µ

C/ m

2

. The riti aldose orrespondstotheminimaldose

requiredbytheresistinorderfortheexposedregionstoberemoved ompletelyby

thedeveloper. Whenele tronspenetrateintoamaterial,theyaresubje tedto

for-wardandba kwards attering. Thesedependonthematerial(natureofsubstrate

fortheexposureoftheresistinareasawayfromthea tualbeamposition. This is

alledtheproximityee t(PE)denedaspatternspe i linewidthvariations[76℄.

The magnitude of this ee t depends on the a eleration voltage  an operation

at100keVallowsadiminution ofthePEdue toalargerpenetrationdepth ofthe

ele tronsin the substratematerial. Inthis ase, thelargeangle s atteringo urs

furtherawayfrom thesubstrate/resistinterfa eand theprobabilitythat theyget

s attered/absorbedinthematerialbeforerea hing theresist ismu h higher. This

isnotthe aseforlowera elerationvoltages,at25keVforinstan e,forwhi h ase

thePE an beveryimportant. Workat verylowbeamenergies an beasolution

toredu es atteringbutitsuersfromamaindrawba kintermsoftheresistresist

thi kness.

Figure3.1: a)Chemi alstru ture ofPMMA;b) Chemi alstru tureofZEP.

Manye-beamresistsareavailable,dieringintermsofresolution,sensitivityor

resistan eto dry-et hing. Howeversome of them are predominantly used due to

theirhighsensitivityor theirresistan etodryet hing. Inthiswork,twotypesof

positiveresistswereused: PMMAandZEP 520-A.

Poly-methyl-metha rylate(PMMA)(Fig.3.1a)is onventionallyadoptedforits

highsensitivityallowingverynestru turestobepatterned. ZEP-520A,provided

by Nippon ZeonCo, hasthestru ture presentedin Fig.3.1b[77℄. It onsistsof a

virtual1:1 opolymerof

α−

hlorometha rylateand

α

-methylstyrenewhi hexhibits apositiveresistbehavioruponele tronbeamexposure. Thehigh-sensitivityis

at-tributedtothe

α

- hlorometha rylategroups,whereastheresistan etodry-et hing isdueto the

α

-methylstyrenegroups. Theglasstransition temperatureof ZEP is 145

o

C.We hose hereto hardbaketheresist at 180

o

C and p-xylenewas used as

thedeveloper.

The Raith 150 E-beam lithography system

Ane-beamlithographysystemis a omputer- ontrolledS anningEle tron

Mi ro-s ope(SEM)providedwithabeamblankerandapatterngeneratorunit. Insome

asesan interferometri stage forexposureof patternsoveralargesample areais

also available [76℄. A s hemati drawingof the Raith 150e-beamsystem is

pro-videdon Fig.3.2. TheSEM hamberismaintained under highva uum(range of

Figure3.2: S hemati sfortheRaith150system. Reprodu edwithpermissionfrom

The SEM olumn is aGemini olumn, spe ially builtto provide high

perfor-man eatlowa eleratingvoltages. The olumnisequippedwithaS hottky

eld-emissionele tronsour eofthehot- athodetype(atungstentip withazir onium

oxide ollar). Theva uum in theele trongun hamber("gun va uum")is in the

10

−9

mBarrange. Thepatterngeneratorisaunit ontrollingthebeamblankerand

thedee tionofthebeambysendingvoltagesignalstothes an oils. The

displa e-mentofthesamplewithrespe ttothe olumnisadjustedbyalaser-interferometer

ontrolledstage,whi hintheRaithsystemweusedhasaresolutionof5nm. The

movementofthestage allowsstit hing ofwritingeldswhen exposinglargeareas

(i.e.,largerthanwhatisa hievablebydee tion ofthee-beam). IntheRaith150

system, the writingeld length is limited to the range 60

µ

m to 1400

µ

m. How-ever,atrade-oshould bemadedependingontherequirementsinthea ura yof

patterning. Alargewritingeldareaallowstoexposeextremelystit hingsensitive

patterns (su h as PhC areas) without moving the stage. However, large writing

eld areas should be avoided if distortion sensitive patterns are present far from

the entral area. In the ase of stit hing, smaller writingelds will also provide

betterresults.

Thewritingspeeddepends onseveral parameterssu h astheavailable e-beam

urrent (dose), the maximum frequen y of operation of the DAC ontrolling the

beam dee tion (10MHz, step displa ement) and the settling time whi h is the

timethee-beamneedsea h timeit movestoanewposition onthesample(5 ms

in the Raith systemwe use). The pattern designneeds to be divided into small

re tangularandtriangularunitsthatthesystemwillexposefollowingparallellines.

Thisisaproblemfor ir ularfeatures;thustheholesareapproximatedbypolygons.

Typi alholediameters forPhC operatingat near infrared(

λ

around1.5

µ

m) are intherangeof100toafew100nm.

TheparametersoftheexposuresperformedwiththeRaith150systematKTH

are ana eleration voltage of 25keV, apertures of 7.5

µ

m for PhC holes (e-beam urrent

≈

10-20pA)and of20to60

µ

mforlargeareas(ebeam urrent

≈

3nA),a workingdistan e ofapproximately5mm,awritingeld sizeof100

µ

mandastep sizeofafewnm.

Beforeexposureoneshould orre tforfo us,astigmatismandbeamalignment,

as in any onventional SEM system. In the ase of exposure over large areas, a

writingeld alignment(WFA) pro edure has to be performed. It is a"learning"

pro edureaimedat alibratingtheorthogonalityands alingfa torofthedee tion

axis to the high pre ision sample stage. The stage is assumed orre t and the

dee tion systemis adjusted to it. One hooses asmall feature that is pla edat

the enterofthegivenwritingeld(WF) orrespondingtothe enterofthe olumn

forzerodee tion. Thenthesystemmovesthestageinordertopositionthefeature

atoneoftheWF orners. Thesystemthendee tstheele tronbeamtos anover

anareaattheWF orner(seeFig.3.3),thegeneratedimageisusedtoindi ateto

thesystemthea tualpositionofthefeaturewithinthes anarea. Thisisrepeated

at regularintervalsthat thefeature isstillatthe enterofthewritingeld. Ifthe

dee ted beamdoesnotndtheexa tpositionitwillresultsinstit hingerrors.

3.4 Mask opening - Rea tive Ion Et hing

Rea tiveionet hing(RIE)isawidespreadte hniqueusedinmi roele troni s.

Gen-erally a apa itively oupledradio-frequen y(RF) plasmais omposedofasour e

operating at 13.56MHz and two planar ele trodes in a va uum hamber. The

system is self-biased, whi h means that the ion energy annot be independently

ontrolled. It depends on the RFpower,the operatingpressure and gas

ompo-sition. The et hing of the SiO

2

mask is performed by Fluorine based RIE. The

rea tivegasis usuallyCHF

3

. CF

4

analso beused, howeverin this asetheet h

sele tivityoftheSiO

2

overtheresistisrather poor. Onesolutionisto addH

2

to

theCF

4

plasma. Thepresen eofhydrogenin reasesthepolymerizationpro esses

(C-Hbonds)thusin reasingthesele tivity. Theparametersofthepro essusedin

this thesis are apowerof 45 W, abias

V

bias

of -300V,and apro ess pressureof 15mT.Thegas ompositionwasH

2

(10SCCM)/CF

4

(28SCCM).

3.5 Et hing of the semi ondu tor material

Thepatternsdenedbye-beamlithographyandtransferedtothehardmaskneed

to be now transfered to the semi ondu tor material by highly anisotropi et h

pro esses. Dry-et hing methods are ideally suited for this purpose. All the PhC

stru turespresentedinthisthesiswereet hedusingAr/Cl

2

CAIBE.The

implemen-tationofthisparti ularet hingte hniqueaswellasthestudyofits hara teristi s

and impli ations on the properties of the fabri ated PhC represent a signi ant

partin thisthesiswork. Adetailed presentationof CAIBEandits hara teristi s

ispresentedin thenext hapter.

Mostofthealternativete hniquesforPhCfabri ationarealsodry-et hingbased

andarelistedonTable3.2. Anequipment-spe i omparisonofthemaindryet h

te hniquesusedinthe ontextofPhCet hingispresentedinthenext hapter. Wet

hemi alet hing is ex luded in most of the ases due the isotropy of theet hing

and theimpossibilitytoobtainhighaspe tratioforthePhCholes. Howeverhigh

aspe tratios anbeobtainedbyanele tro- hemistrymethodofporeet hing[97℄.

Table3.2 lists outmostofthe reportedInP et hing te hniques forPhC

fabri- ationand omparestheirreportedperforman es. Thevaluesfortheaspe tratios

giveninTable3.2refertothetotaldepthoftheholesdowntothetaperedbottom.

Depending on the hole shape the aspe t ratio of the straight portion of the hole

will besmallerthanthat givenin thetable. Typi allytheapproximatelystraight

portion orrespondsto about70%of thetotal depth. However, thisestimate has

to betaken autiously. RIE ismorelimitedin a hievableaspe tratiosthanother

pro esseswithmoredenserplasmassu hasICP.HighestreportedARareprovided

manu-Table3.2: Comparisonofet hing te hniques forInP-basedPhCfabri ation

Te hnique Chemistry Performan e Referen e

RIE CH

4

AR

≈

2 [79℄

CH

4

/Ar/H

2

AR

≈

2 [80, 81℄

ECR-RIE Cl

2

/Ar AR=8 [82℄

ylindro- oni al

Cl

2

AR

≈

2 [83℄

ICP-RIE SiCl

4

(/Ar) AR=14 [84℄, [85℄

ylindro- oni al Cl

2

AR

≈

10 [86℄ Cl

2

/O

2

AR=16 [87℄ 250

o

C ylindro- oni al ylindri al Cl

2

/N

2

AR

≈

8 [88℄

Cl

2

/Ar/N

2

(/He) AR=16 [89℄

oni al Cl

2

/Xe AR

≈

5 [90℄ ones swelled ylinders Hi/Xe AR=13 [91℄, [92℄ oni al CAIBE Ar/Cl

2

AR

≈

18-20 [81, 93,94℄ ylindro- oni al FIB  lowAR [95, 96℄

fa turinga tivedevi es. It is reasonable to expe t that high bombarding energy

will reatemore damage. However thenature of the reateddefe ts will also

de-pend onthe typeof dry-et h hemistry. Themostmaterial damagingfabri ation

te hniqueis Fo usedIon Beamet hing, whi h bombardsthe samplewithgallium

ionsa eleratedtoahighenergy(typi ally15to30keVforsputtering,oftheorder

of100keVforimplantationregimes).

3.6 Post-et hing pro ess steps

AfterthePhCiset hed,dependingonthedevi esandmeasurement onguration,

additionalpro essstepsareusuallyne essary. Ifoneneedstoa essthePhC

stru -turesele tri ally( aseoflateral ondu tion(Chap.7)),oneshoulddeneele tri al

onta ts. Weuse onventionalopti allithographytopatternareasforthe onta ts,

thenweevaporateametallayer(Ni/AuGe/Ni/Aufor

n

- onta ttoInP)andusea lift-ote hniqueto isolate the onta t pads. An annealing step in neutral

atmo-sphere(N

2

) around450

o

themetallayerandthesemi ondu torbyalloying. Ifthephotoni rystaldevi es

aretobemeasuredbyanin-plane ouplingte hnique,su hastheend-remethod

des ribedinSe .8.3,otherpro essstepsareusuallyne essary. Theopti al oupling

viathe leavedfa etofthesamplerequiresgoodopti alquality. Inordertoa hieve

this it ispreferableto thin down thesubstrate toathi knessofabout100

µ

m by a lapping te hnique. Then the samples are be leaved at a suitable length and

Chemi ally Assisted Ion Beam

Et hing of InP-based photoni

rystals

Severalte hniques havebeenused foret hing PhCsin InP-basedmaterialsas

de-s ribedinthepre eding hapter. Argon- hlorine hemi allyassistedionbeam

et h-ing(Ar/Cl

2

CAIBE) isone ofthe mostsu essful pro essesfor high aspe t ratio

et hing. Theawareness and ontrol of fabri ation and understanding of the

ma-terialissuesforphotoni rystalsarene essaryforhighperforman ePhCdevi es.

The hara terization of theet hing is thereforene essary. The quality of et hing

ofphotoni rystalsisvery riti alasitdire tly inuen estheiropti alproperties

in termsof losses. Inaddition, et hing hara teristi ssu h as et h depth,

rough-nessand shape invariablydepend onthe feature size. This hapter presents the

results obtained in Paper A. We introdu e the CAIBE te hnique, present the

experimental resultson thefeature size dependen e of theet hing and developa

physi o- hemi al model forthe et hing me hanism. The phenomenon behind the

featuresizedependen e oftheet hingisexplainedanditsimpli ationsintermsof

theopti alpropertiesofPhCsisdis ussed.

4.1 Chemi ally Assisted Ion Beam Et hing

CAIBE is an et hing te hnique relying on the bombardment of a sample with

a hemi ally inert ion beam under a rea tive gas atmosphere in a high-va uum

hamber. Intheexperimentsreportedhere,theneutralgasisargonandtherea tive

spe iesCl

2

. Chlorineisinje tedviaagasringoverthesampleandargonionsare

extra tedfromaremoteplasma. Itallowsindependentvariationsoftheionenergy

anddensity. CAIBEwasperformedwithaNordiko3000ionbeamet hingsystem,

equippedwithatwo-gridiongun(Fig.4.1). Inthissystem,theplasmaisgenerated