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NANOEXPRESSOpenAccessTheroleofdislocation-inducedscatteringinelectronictransportinGaxIn1-xNalloysOmerDonmez1,MustafaGunes1,AyseErol1,CetinMArikan1*,NaciBalkan2andWilliamJSchaff3AbstractElectronictransportinunintentionallydopedGaxIn1-xNalloyswithvariousGaconcentrations(x=0.
06,0.
32and0.
52)isstudied.
Halleffectmeasurementsareperformedattemperaturesbetween77and300K.
Temperaturedependenceofcarriermobilityisanalysedbyananalyticalformulabasedontwo-dimensionaldegeneratestatisticsbytakingintoaccountallmajorscatteringmechanismsforatwo-dimensionalelectrongasconfinedinatriangularquantumwellbetweenGaxIn1-xNepilayerandGaNbuffer.
ExperimentalresultsshowthatastheGaconcentrationincreases,mobilitynotonlydecreasesdrasticallybutalsobecomeslesstemperaturedependent.
CarrierdensityisalmosttemperatureindependentandtendstoincreasewithincreasingGaconcentration.
Theweaktemperaturedependenceofthemobilitymaybeattributedtoscreeningofpolaropticalphononscatteringathightemperaturesbythehighfreecarrierconcentration,whichisattheorderof1014cm2.
Inouranalyticalmodel,thedislocationdensityisusedasanadjustableparameterforthebestfittotheexperimentalresults.
OurresultsrevealthatinthesampleswithlowerGacompositionsandcarrierconcentrations,alloyandinterfaceroughnessscatteringarethedominantscatteringmechanismsatlowtemperatures,whileathightemperatures,opticalphononscatteringisthedominantmechanism.
InthesampleswithhigherGacompositionsandcarrierconcentrations,however,dislocationscatteringbecomesmoresignificantandsuppressestheeffectoflongitudinalopticalphononscatteringathightemperatures,leadingtoanalmosttemperature-independentbehaviour.
Keywords:GaxIn1-xN,In-richGaxIn1-xN,Mobility,ElectronictransportPACS:72.
10.
Fk,72.
20.
FrBackgroundInthelastdecade,aftertherevisionofthebandgapenergyfrom1.
9toapproximately0.
7eV[1],intensiveresearchhasbeencarriedoutonInNandIn-richGaxIn1-xNalloysinordertore-determinethefundamen-talproperties[2-4].
DespitemuchinterestontheopticalpropertiesofInNandGaxIn1-xN[5,6],therehasbeenarelativelysmallnumberofinvestigationstoexplaintemperature-dependentelectronictransportpropertiesinGaxIn1-xNalloys[7,8].
Inthisarticle,wereporttheelectronictransportprop-ertiesofnominallyundopedGaxIn1-xNalloyswithdiffer-entGaconcentrations(x=0.
06,0.
32and0.
52).
Halleffectresultsshowthatallthealloysarehighlyn-type,andthefreecarrierconcentrationsareindependentoftemperature.
MethodsExperimentaldetailsThesampleswithdifferentGaconcentrations(x=0.
06,0.
32and0.
52)weregrownbyaVarianGEN-IIgassourcemolecularbeamepitaxychamberon(0001)c-sapphiresubstrateswitha200-nm-thickGaNbufferlayer.
ThegrowthtemperaturewasvariedfromlowtohighwithincreasingGacomposition[9,10].
Thethick-nessoftheGaxIn1-xNlayerwasdeterminedfromthegrowthparametersandverifiedbybackscatteringspec-trometryatnearly500nm.
TheGaxIn1-xNsampleswerefabricatedinHall-bargeometry,andohmiccontactswereformedbydiffusingAu/Nialloy.
Halleffectmea-surementswerecarriedoutattemperaturesbetween77and300K.
*Correspondence:arikan@istanbul.
edu.
tr1ScienceFaculty,DepartmentofPhysics,IstanbulUniversity,Vezneciler,Istanbul34134,TurkeyFulllistofauthorinformationisavailableattheendofthearticle2012Donmezetal.
;licenseeSpringer.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Donmezetal.
NanoscaleResearchLetters2012,7:490http://www.
nanoscalereslett.
com/content/7/1/490ModellingofcarriermobilityThetemperaturedependenceofcarriermobilityisanalysedusingananalyticmodelwhereallpossiblescatteringmechanismsareindividuallycalculatedusingthematerialparametersgiveninTable1.
Experimentalmobilitycurvesarefittedwiththetheoreticalmobilitycurvesthatareobtainedusingtheanalyticalexpressionsforthemajorscat-teringmechanismsgiveninTable2.
AlthoughGaxIn1-xNlayeristhickenough(500nm)nottobetwo-dimensional(2D),theanalyticmodelconsiderstransportina2Delec-trongas(2DEG).
ThisisbecausetheelectronictransporttakesplaceattheinterfaceofGaxIn1-xN/GaN[11]andon2DGaxIn1-xNsurfacelayer[12].
ResultsanddiscussionsExperimentalresultsFigure1showsthetemperaturedependenceofthecar-rierconcentrationandtheelectronmobilitybetween77and300Kforallthesamplesinvestigated.
Althoughthesamplesarenotintentionallydoped,theHalleffectresultsshowthatallthesampleshaven-typeconductiv-ity,andthefreecarrierdensitiesareindependentofthetemperature;therefore,samplescanberegardedasmetallic-likeoverthewholetemperaturerangeascom-monlyreportedbyusandbyotherresearchgroups[7,8,24-28].
ItisclearfromFigure1athatthefreecarrierconcentrationincreasesbyaboutafactorof3whentheGacompositionincreasesfromx=0.
06to0.
52.
Also,asseeninFigure1b,whenGaconcentrationincreasesfromx=0.
06to0.
52,electronmobilityhasasharpdecreasefrom1,035cm2/VsforGa0.
06In0.
94Nto30cm2/VsforGa0.
52In0.
48Nat77Kthatmaybeassociatedwiththecontributionofbothdislocationsandpointdefectsinthestructure,whichareactingasasourceofdonor-likedefects,inducinghighelectronconcentration.
Inthelow-temperatureregion(≤100K),themobilityisalmostindependentoftemperatureforallthesamples.
How-ever,forthesamplewiththelowestGaconcentration,Ga0.
06In0.
94N,itdecreasesfrom1,035to890cm2/Vswithincreasingtemperaturefrom100to300Kbutdoesnotshowanysignificantchangeintheothertwosam-ples,whichisacharacteristicfeatureofmetallic-likesemiconductors[7,26,27].
Theinsensitivityofcarriermobilitytotemperatureiscommonlyobservedinpolarmaterialswithelevatedcarrierdensitieswherethepolarinteractionsarescreened[19,25,29-33].
ModellingoftemperaturedependenceofmobilityInordertounderstandfullythetemperaturedepend-enceofelectronmobility,wecomparedtheexperimentalmobilityresultswithanalyticaltheoreticalmodelsbytakingintoaccountallthepossiblescatteringmechan-isms.
Atlowtemperatures,thedominantscatteringmechanisminbulksemiconductorsisionizedimpurityscatteringthatchangeswithtemperatureasT3/2.
How-ever,thiskindoftemperaturedependencehasnotbeenobservedinoursamples.
Thesampleshavemetallic-likecharacteristics,confirmingtheformationofahigh-density2DEGatboththeGaN/GaxIn1-xNinterfaceandontheGaxIn1-xNsurface[26,27].
Thedominantmo-mentumrelaxationmechanismistheelectron-opticalphononscatteringinGaxIn1-xNsinceitisahighlypolarmaterialaboveT>150K[34-36].
Inthetheoreticalcalculation,interfaceroughness,alloy,dislocation,opticalandacousticphononscatteringmechanismswiththeappropriateexpressionsgiveninTable2wereconsidered.
ThelateralsizeoftheinterfaceroughnessΔ,correlationlengthΛbetweeninterfacefluctuationsandthedislocationdensityareusedasad-justablefittingparameters,andthevaluesforthebestfitTable1Thematerialparametersusedinscatteringcalculations(adoptedfrom[10,13-15])ParameterInNGaNGaxIn1-xNHigh-frequencydielectricconstantE18:4E15:5E18:42:9xStaticdielectricconstantEs15:3Es8:9Es15:36:4xElectroneffectivemassm0:11m0m0:22m0m0:10:12xm0LO-phononenergy73meV92meV7311:3x12x2meVLA-phononvelocityvs5:17:103ms1vs6:59:103ms1vs5:171:42x:103ms1Densityofcrystalρ6:81:103kgm3ρ6:15:103kgm3ρ6:810:7x:103kgm3ElectronwavevectoratFermilevelkF4:61:108m1kF7:3:108m1kF7:32:69x:108m1TheelectromechanicalcouplingcoefficientK20:028K20:038K20:0280:01xLatticeconstantsa3:5331010mc5:6931010ma3:189:1010mc5:185:1010ma3:5330:344x:1010mc5:6930:508x:1010mOccupiedvolumebyanatomΩ03p.
4a2cΩ03p.
4a2cΩ03p.
4a2cDeformationpotentialΞ7:1eVΞ8:3eVΞ7:11:2xeVAlloypotentialUA2:72x1019VLA-phonon,longitudinalacousticphonon;LO-phonon,longitudinalopticalphonon.
Donmezetal.
NanoscaleResearchLetters2012,7:490Page2of6http://www.
nanoscalereslett.
com/content/7/1/490aregiveninTable3.
Thevaluesthatweusedforthedis-locationdensitiesareingoodagreementwiththetrans-missionelectronmicroscopy(TEM)resultstakenfromGa0.
34In0.
66N[9,25].
Looketal.
[25]determinedthedis-locationdensityforbothInNandGa0.
34In0.
66NusingTEMandfoundthatdislocationdensityinGa0.
34In0.
66NisactuallyhigherthanthatofInN.
ItcanbeseenthatthetrendofthedislocationdensitydependingonGaconcentrationfollowsthecarrierconcentration,whichmeansthatthereisacorrelationbetweendislocationdensityandthecorrespondingcarrierconcentration.
ItisclearfromFigure2thatatlowtemperatures,elec-tronmobilitiesinGa0.
06In0.
94NandGa0.
32In0.
68Naredeterminedbyalloypotential-inducedscattering,interfaceTable2Theformulasofmajorscatteringmechanismsusedin2DEGmobilitycalculationsScatteringmechanismFormulaDefinitionofvariablesAcousticphonon:piezoelectric[15-17]μPEπEs3keK2kBTm21JPEkK,electromagneticcouplingcoefficient;JPE(k),electronwavevectordependentintegral.
JPEkZ2k0F11q4k2qqs21q=2k2qq3dqK2E2LAEscLAE2TAEscTAAcousticphonon:deformation[11,18]potentialμDP16ρev2s33Ξ2kBTm2b1JDPkρ,crystaldensity;vs,longitudinalacousticphononvelocity;Ξ,deformationpotentialconstant;m*,electroneffectivemass;JDP(k),electronwavevectordependentintegral.
b,Fang-Howardexpression;qs,reciprocalscreeninglength;f(0),occupationprobability;F11(q),ground-stateFang-Howardwavefunction.
JDPkZ2k012kπ3qqs21q=2k2qq4dqqse2m2π2EsF11qf0b33e2mn2D8Es21=3Fqb8b29qb3q2=8bq3Polaropticalphonon[17-19]μPO4πEs2eωm2Z0eωLO=kBT1ωLO,polaropticalphononenergy;E1andEs,high-andlow-frequencydielectricconstant;Z0,effectivewidthoftriangularwellformedattheGaxIn1-xN/GaNinterfaceandisgivenintermsofFermiwavevector.
1EP1E11EsZ02πkF2πn2DqInterfaceroughness[11,15,20]μIFR2Esn2DΔΛ23e3m21JIFRkΔ,lateralsizeoftheroughness;Λ,correlationlengthbetweenfluctuations;JIFR(k),correlationlengthandthelateralsize-dependentintegral;n2D,2Delectrondensity.
JIFRkZ2k0expq2Λ2=42k3qqs21q=2k2qq4dqq2ksinθ=2qse2m2πEs2FqAlloydisorder[20]μAlloy16e33bx1xm2Ω0U2Ax,Gafraction;Ω0,thevolumeoccupiedbyoneatom;UA,alloypotential.
Dislocation[21-23]μDis302πpE2c2kBT3=2e3NDisf2λDmpNDis,dislocationdensityperunitareawhichistakenasafittingparameter;λD,Debyescreeninglength;c,latticeconstantofGaxIn1-xN.
f,thefractionoffilledtrapsthatareassumedfullyoccupied.
λDEskBT=e2n2D1=2Donmezetal.
NanoscaleResearchLetters2012,7:490Page3of6http://www.
nanoscalereslett.
com/content/7/1/490roughnessscatteringanddislocationscatteringmechan-isms.
Opticalphononscatteringsbecomesignificantathightemperatures,asdescribedabove.
Figure3showsex-perimentalandcalculatedtemperature-dependentmobil-ityoftheGa0.
52In0.
48N.
ThedislocationdensityincreaseswithGaconcentration;therefore,itseffectonthemobilitybecomesmorepronouncedinthissample.
Atlowtem-peratures,mobilityislimitedbythesamescatteringmechanismsasintheothersamples.
Athightempera-tures,however,interfaceroughnessandalloypotentialre-strictthemobility,buteffectofthedislocationscatteringbecomeslessdominantasaresultofshorteningDebyescreeninglengthduetohighercarrierdensity.
Further-more,inthehigh-carrier-concentrationregime,electron–phononscatteringisheavilyscreened,asdescribedaboveandinreferences[19,25,29-33].
ConclusionsInthispaper,wehaveinvestigatedelectronictransportpropertiesofnominallyundopedIn-richGaxIn1-xNstructureswithdifferentGaconcentrations.
Halleffectresultsshowthat2DEGmobilityinGaxIn1-xNdecreasesandbecomestemperatureinsensitivewithincreasingGaconcentrations.
Thesamplesarenotintentionallydoped,buttheyallhaven-typeconductivity.
ElectrondensityincreaseswithincreasingGacomposition.
Thetemperaturedependenceofelectronmobilityisdeter-minedbytakingintoaccountallthemajorscatteringmechanisms.
ThedecreaseoftheelectronmobilitywithGaconcentrationisexplainedintermsofincreaseddis-locationscattering.
Theweaktemperaturedependence10015020025030012x=0.
06x=0.
32x=0.
52n2D(x1014cm-2)Temperature(K)(a)10015020025030005010090010001100x=0.
06x=0.
32x=0.
52(cm2/Vs)Temperature(K)(b)Figure1Temperaturedependenceof(a)carrierdensityand(b)electronmobility.
Table3ThevaluesoftheparametersusedinthecalculationsSampleΔ(nm)Λ(nm)Dislocationdensity(*1010cm2)Ga0.
06In0.
94N3.
61.
4(fourmonolayer)0.
1Ga0.
32In0.
68N6.
43.
4(tenmonolayer)0.
3Ga0.
52In0.
48N6.
73.
4(tenmonolayer)3.
8(a)1001502002503008x1021x1031x1031x1041x105POACIFRDisAlloyTotalExp.
(cm2/V.
s)Temperature(K)Ga0.
06In0.
94N(b)1001502002503006x1018x101102103104105106IFRAlloyACDisPOTotalExp(cm2/V.
s)Temperature(K)Ga0.
32In0.
68NFigure2Experimentalandcalculatedtemperaturedependenceofmobilitycurvesfor(a)Ga0.
06In0.
94Nand(b)Ga0.
32In0.
68N.
Donmezetal.
NanoscaleResearchLetters2012,7:490Page4of6http://www.
nanoscalereslett.
com/content/7/1/490ofthemobilityathightemperaturesmightbeassociatedwithreducedelectron-opticalphononscatterings.
Alloyandinterfaceroughnessscatteringmechanismsaredom-inantatlowtemperatures.
InsampleswithhigherGafractions,dislocationscatteringbecomesmoresignifi-cant,andathightemperatures,phononscatteringisrestrictedduetoincreaseofdislocationdensity.
Athightemperatures,phononscatteringisonlypronouncedinthesampleswithlowelectrondensities.
AbbreviationsLO-phonon,longitudinalopticalphonon;LA-phonon,longitudinalacousticphonon;2DEG,two-dimensionalelectrongas;TEM,transmissionelectronmicroscopy;IFR,interfaceroughness.
CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterest.
Authors'contributionsODandMGcarriedouttheexperimentsandfittedtheHallmobilitydatawithAEandMCA.
OD,MG,AEandMCAwrotethemanuscriptinconjunctionwithNB.
WJSgrewtheinvestigatedsamples.
Allauthorsreadandapprovedthefinalmanuscript.
AcknowledgmentsThisworkwassupportedbyScientificProjectsCoordinationUnitofIstanbulUniversitywithProjectNumberBYP25027.
WealsoacknowledgethepartialsupportfromRepublicofTurkey,MinistryofDevelopment.
(ProjectNumber:2010K121050).
Authordetails1ScienceFaculty,DepartmentofPhysics,IstanbulUniversity,Vezneciler,Istanbul34134,Turkey.
2SchoolofComputerScienceandElectronicEngineering,UniversityofEssex,Colchester,EssexCO43SQ,UnitedKingdom.
3DepartmentofElectricalandComputerEngineering,CornellUniversity,Ithaca,NY14853,USA.
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doi:10.
1186/1556-276X-7-490Citethisarticleas:Donmezetal.
:Theroleofdislocation-inducedscatteringinelectronictransportinGaxIn1-xNalloys.
NanoscaleResearchLetters20127:490.
Submityourmanuscripttoajournalandbenetfrom:7Convenientonlinesubmission7Rigorouspeerreview7Immediatepublicationonacceptance7Openaccess:articlesfreelyavailableonline7Highvisibilitywithintheeld7RetainingthecopyrighttoyourarticleSubmityournextmanuscriptat7springeropen.
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