A first principles investigation of the effect of aluminum, gallium and indium impurities on optical properties of β-Si3N4 structure

gallium

and

indium

impurities

on

optical

properties

of

␤-Si

3

N

4

structure

P.

Narin

_,

_E.

_Kutlu

_,

_G.

_Atmaca

_,

_S.B.

_Lis¸

_esivdin

_,

_E.

_Özbay

a_{DepartmantofPhysics,FacultyofScience,GaziUniversity,Teknikokullar,06500Ankara,Turkey}

b_{NanotechnologyResearchCenter,BilkentUniversity,Bilkent,06800Ankara,Turkey}

c_{DepartmentofPhysics,BilkentUniversity,Bilkent,06800Ankara,Turkey}

d_{DepartmentofElectricalandElectronicsEngineering,BilkentUniversity,Bilkent,06800Ankara,Turkey}

a

r

t

i

c

l

e

i

n

f

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b

s

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c

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Inthisstudy,effectsofsomeimpurityatomsincludedinIIIAgroupsuchasAl,Ga,and Inontheopticalpropertiesofthe␤-Si3N4structurehavebeendiscussed.The

calcula-tionsweremadeusingDensityFunctionalTheory(DFT)in0–15eVrangeandlocaldensity approximation(LDA)astheexchange-correlation.Usingtherealandtheimaginaryparts ofthecomplexdielectricfunction,thebasicopticalpropertiesof␤-Si3N4suchasdielectric

coefficient,refractiveindex,absorption,reflectioncoefficientshavebeeninvestigated.As aresultofthecalculations,itisdeterminedthatopticalpropertiesofstructurehavebeen significantlychangedwithdoping.

©2017ElsevierGmbH.Allrightsreserved.

1. Introduction

Siliconnitride(Si3N4)duetoitsstrongthermal,dielectricandstructuralpropertiesismostlyusedinelectronic,optical

andindustrialapplications[1,2].Thankstoitsthermalinsulationproperties,siliconnitrideisusedinmanyindustrialfields suchasareasofheatconduction,gasturbines,andautomobileengines,atthesametimeitiswidelyusedasapassivation layerintransistorapplications,lightemittingdiodes(LEDs)andsolarcells[3–7].Inaddition,siliconnitrideisfrequently usedasagatedielectricinhighelectronmobilitytransistors(HEMTs)[8].

Si3N4crystalstructurehasbasicallywell-known␣and␤phases,aswellasphasesindicatedby␥(orc).Wherein␣,␤,

␥arerespectivelyindicatorsoftrigonal,hexagonalandcubicstructures.Underhightemperatureandhighpressure,phase shiftsbetweenthesecrystalsstructuresmayoccur[9].While_␣and_␤phasesshowsimilaritiesintermsofsomeelectronic andopticalproperties,␥phasecanvaryintermsofthesecharacteristics.Forexample,intheliterature,while␣and␤phases demonstrateclosebandgapvaluessuchas∼4.63eVand4.50-5.50,␥phaseisgivenashaving∼3.45eVbandgap[10,11]. Thepropertybasicallyseparating␣and␤phasesarethefactthatclatticeconstantisabout2timeslargerthan␥phase. ␤-Si3N4structurehasa14-atomunitcell,andthiscellhas6siliconand8nitrogenatomsanditisastructurewithP63m

spacegroup.

Singlecrystalsof␤-Si3N4structurecanbegrownwithMolecularBeamEpitaxy(MBE)andChemicalVaporDeposition

(CVD)methods[12–14].Generally,inGaNorGaAs-basedcrystalgrowing,IndiumandAluminumusagearecommon

pro-∗ Correspondingauthor.

E-mailaddress:polatnarin0@gmail.com(P.Narin).

http://dx.doi.org/10.1016/j.ijleo.2017.08.056

Fig.1.ThemoststableatompositionisshownforAl,InandGaimpuritiesthatplacedin␤-Si3N4crystalstructure.

cesses.Duringthesegrowingprocesses,wastegasesremainingfrompreviousgrowthsinthereactororatomssuchasAl,Ga, Incanbefoundinthereactor.Inacrystalgrowth,whichwillbeconductedlater,theseatomscansettleasimpurityatoms withinthecrystalandthissituationmayseriouslyaffectopticalpropertiesofthecrystal[15,16].

Accordingly,itcanbeanimportantstepforgrowingprocessestobeconductedinthefuturetoanalyzeeffectsofAl,Ga andInimpuritiessettledwithinthecrystalduringgrowingprocessonopticalpropertiesofthecrystal.Forthisreason,in thisstudy,changesinopticalpropertiesof␤-Si3N4structurewereanalyzedbymeansofDFTmethodinsituationswhenit

containsAl,GaandInimpurities.Asaresultoftheseanalyses,seriouschangesinbasicopticalpropertiesof␤-Si3N4structure

wereobservedintermsofstaticdielectricconstant,refractiveindex,absorption,reflectioncoefficients.

2. Calculationmethod

Incalculations,todetermineeffectsofimpurityatomssuchasAl,GaandInonopticalpropertiesofthe␤-Si3N4structure,

DFTwithpseudopotentialmethodandLDAasexchange-correlationwereused.ThankstoAtomistix-VisualNanolabToolkit (ATK-VNL)software,theopticalpropertiesof␤−Si3N4structurewithpurityandimpuritywereanalyzedwiththehelp

oftherealandtheimaginarypartsofcomplexdielectricfunction[17–19].While analyzingopticalpropertiesofthe␤ −Si3N4structure,ahexagonal␤−Si3N4structurewith14atomscontaining8nitrogenand6siliconatomsandhavingP63m

spacegroupwasused.Incalculations,latticeconstantsofthestructureweredeterminedasa=7.6015Å,c=2.9061Å,cut-off as280eVandaregularMonkhorst–Pack4×4×10k-pointgridwereused.Intheopticalpropertiescalculations,photon energyrangewasselectedas0–15eV.Inthestudied␤−Si3N4structure,settlementlocationsofAl,InandGaimpurity

atomsweredeterminedbycalculatingformationenergyandbindingenergycalculations[20].Fortheatomplaceswith thelowestformationenergyandbindingenergy,impurityatomswereplaced,andopticalpropertiesofthesenewsystems wereanalyzed.Bycalculatingbindingenergyandformationenergy,themoststableconfigurationspecifiedforeachimpurity atomareshownwithredcircleinFig.1.

3. Resultsanddiscussion

TheopticalpropertiesofastudiedstructurecanbedefinedwiththehelpofthecomplexdielectricfunctiongiveninEq. (1)[21,22].Furtheropticalpropertiescanbedeterminedafterobtainingrealandimaginarypartsofthecomplexdielectric function.

Complexdielectricfunctionisgivenas;

ε(ω)=ε1(ω)+iε2(ω), (1)

TherealandimaginarypartsofthecomplexdielectricfunctionaregivenwiththeKramers-Kronigrelations;

ε1(ω)=1+ 2 p ∞



Here,ε2(ω)istheimaginarypartofthecomplexdielectricfunctionandgivenas;

ε2(ω)= e2h m2_ω2



 

Here,E_iandE_farebindingenergiesinthefirstandthelastconfigurations,andP_if isthemomentummatrixelement[23]. Also,nandkareassociatedwithexpressions␧1(ω)and␧2(ω)therelationshipbetweenthemisgivenas[22];

Fig.2. Fora)pureb)Al-impurityc)Gaimpurity,d)Inimpurityaddedstructures,therealpartofthedielectricfunctionof␤−Si3N4structure.

ε2=2nk (5)

Expressionsgivingthefrequencydependentrealandimaginarypartsofthecomplexrefractiveindexandtheirreflection

coefficientandabsorptioncoefficientaregivenasfollows[24,25];

n(ω)=(1/√2)





_⁄





_⁄

␤-Si3N4structureshowsanisotropicopticalpropertiesduetoitshexagonalstructure.Therefore,z-axis,which

corre-spondstothegrowthdirection,valueswithimportantopticalfeaturesareshowninthestudy.Therefore,fortherestofthe study,thenumericalvalueswillbegivenforz-axis.Table1showsthecalculatedopticalparametersof␤−Si3N4forpure

andwithimpurities.

Fig.2showsthechangesinphotonenergydependentrealpartofdielectricfunctionsafteraddingAl,Ga,Inimpurities separatelyto␤−Si3N4structure.InFig.2a,whilehighlyanisotropicbehaviorisobservedforz-axisforpure␤−Si3N4structure,

itshowsrelativelyisotropicbehaviorforxandy-axesforthedielectricfunctions.Forthepure␤−Si3N4structure,thestatic

Fig.3. Fora)pureb)Al-impurityc)Gaimpurity,d)Inimpurityaddedstructures,theimaginarypartofthedielectricfunctionof␤−Si3N4structure.

Realpartsofthedielectricfunctionsfallingbelowzero,namelywhen_␧1(ω)<0andinenergiesafter9.28eVvalue,␤−Si3N4

showsmetallicbehavior.Withintheenergyrangebeforethisvalue,sincerealpartofthedielectricfunctionisabovezero, namely␧1(ω)>0,thestructureshowsdielectricproperties.

InFig.2b,itwasdeterminedthatthestaticdielectricconstantfor␤−Si3N4structurecontainingAlimpurityis9.12,and

thehighestvalueforthedielectricconstantas13.4isfoundat∼0.19eVvalue.Whileisotropicbehaviorinxandy-axesis notobservedbelow0.4eV,itcanbeseenthatisotropicbehaviorisstartedagainwhileapproachingtowardshighenergies. Asexpectedinallenergyvalues,thehighanisotropicbehaviorisobservedinthez-axis.InFig.2c,fora␤−Si3N4structure

containingGaimpurity,thestaticdielectricvalueisfoundasahugenumberof122.Astaticdielectricconstantsubstantially higherthanthepurestructurehasbeencalculated.

InFig.2d,wehavecalculatedstaticdielectricconstantfor␤−Si3N4containingInimpurityas75.7.Thehighestdielectric

constantwasdeterminedas78.3at0.1eVvalue.Whileisotropicbehaviorinxandy-axisisobservedinlowenergyvalues, theanisotropicbehaviorisseenathighenergyvalues.Inthisregard,itcanbesaidthat,thisbehaviorexhibitssimilar characteristicswiththestructureincludingGaimpurity.

InFig.3,imaginarypartsofdielectricfunctionbasedonphotonenergyareshownforthepure_␤−Si3N4structureand

structureswithimpuritieswithin0–15eVenergyrange.InFig.3a,itcanbeseenthatopticalbandrangevalueforpure ␤−Si3N4iswithin∼5-5.8eVrange.Theopticalbandvalueofthepure␤−Si3N4structureisconsistentwiththeliterature

[10,26,27].Energyvalueswhereopticaltransitionsareatmaximumareseenas7.2eVand9eV.Inthecaseswithimpurities, itcanbeclearlyseenthatstructures␧2(ω)peakvaluesatverylowenergiesdonotrepresentanyopticalbandgap.

InFig.3b,itcanbeseenthatin␤−Si3N4structurewithA1impurity,energyvalueswithmaximumopticaltransitionsare

7.5eVand9eV.Furthermore,sinceitisobservedthatopticaltransitionalsooccursin∼0.45eVand∼1.19energyvalues,it willnotbepossibletomentionaboutopticalbandrangeinA1impurity.Incomparisonwiththepurestructure,forxand y-axes,theisotropicbehaviorispartiallydeteriorated.

InFig.3cand3drespectively,itcanbeseenthatveryhighopticaltransitionsoccuratverylowenergiesin␤−Si3N4

structurewithGaandInimpurities.Inthepresenceofbothimpurities,asecondarypeakwithnotsuchhighopticaltransitions canbeobservedat∼8eV.Forthesetwoimpurityaddedstructures,highlyanisotropicbehavioratlowenergyvaluesand isotropicbehaviorathighenergyvaluesareobserved.

InFig.4,changesinrefractiveindexesofpure␤−Si3N4structureandstructurewithimpuritiesaregivenwithrespectto

photonenergy.Thesechangescanbeactuallyseentochangeinproportiontochangeconnectedwith␧1(ω)intheformula

givenEq.(4).Therefore,ifthedielectriccoefficientofastructureishigh,it’srefractiveindexishighaswell.Inthepure ␤−Si3N4structure,therefractiveindexofthestructurewasdeterminedasn(0)=2.34andresultsclosertotheliterature

Fig.4.Fora)pureb)Al-impurityc)Gaimpurity,d)Inimpurity,therefractiveindexof␤−Si3N4structure.

8.7,respectively.ThestructurewithGa-impurityhasthehighestrefractiveindex,whichisfoundtobe5timeshigherthan thepurestructure.Itisobservedthatrefractiveindexchangeshowinghighanisotropicbehavioralongthez-axisinpure structureandthestructurewithAlimpurity.ForthestructureswithGaandInimpurities,mostlyisotropicbehaviorare observedathigherenergies.However,highanisotropicbehaviorsareobservedatverylowenergies.

Theimaginarypartofthecomplexrefractiveindex,namelyextinctioncoefficientisknowntobeassociatedwith_␧2(ω)

givenbytheEq.(5).Therefore,changeinphotonfrequencydependent␧2(ω)andchangeinphotonfrequencydependent

extinctioncoefficientareshownsimilarbehaviors.Changesinphotonfrequencydependentextinctioncoefficientsofpure ␤−Si3N4structureandstructureswithimpuritiesaregiveninFig.5.Sinceitisdielectricinthepurestructure,itisobserved

thatopticaltransitionsstartaroundabove∼5eV.InthestructureswithAl,GaandInimpurities,thehigherextinction coefficientisobservedatlowerenergies.Anisotropybehaviorsaresimilarwiththerealpartofthecomplexrefractiveindex. Reflectancepropertiesofstructurevaryinconnectionwithwhethertheyshowmetallicbehaviorornot.Since␧1(ω)<0

isconsideredstructureswithmetallicbehavior,negative␧1(ω)representshighreflectivity.Fornegativevaluesof␧1(ω)are

foundtobepossiblewithEq.(4)andk>n.Therefore,highlevelofreflectanceisexpectedforlownandhighkvalues. InFig.6,changesinreflectanceofpure␤−Si3N4structureandstructureswithimpuritiesaregivenwithrespecttophoton

energy.Forpure␤−Si3N4and␤−Si3N4withAl,Ga,Inimpurities,reflectioncoefficientsofstructuresaredeterminedas0.16,

0.32,0.70and0.63,respectively.Forthestructureswithimpurities,behaviorsofreflectancewithenergychangesshow similaritieswitheachother.

Atvalueswhereextinctioncoefficientishigh,itcanbeexpectedabsorptioncoefficienttobehighalso.InFig.7,absorption datashowstheopticalbandgapsuccessfully.Inthestructureswithimpurities,theanisotropicbehaviorispreservedinthe z-axisallalongtheinvestigatedphotonenergies.Neartheopticalband-gapedge,pure␤−Si3N4structureshowsthemost

anisotropicbehavior.

Si3N4isknowntoreducenon-radiativetransitionsinthestructurewhereitisusedasapassivationlayer[30].Inaddition,

incaseswherethepassivationlayercontainsimpuritiessincemoreabsorptionoccursascanbeseeninFig.8.UsingSi3N4

asmuchpureaspossiblebecomessignificantespeciallyinLEDapplications.Fig.8showsabsorptionforpurestructureand structureswithAl,Ga,Inimpuritiesthatchangeatlowenergies,especiallyinthevisibleregion.Whileverylowabsorption isobservedinthevisibleregionforthepurewithimpuritiesstructures,especiallythestructurewithInimpurityshowsvery highabsorptioninthevisibleregion.

Fig.5. Fora)pureb)Al-impurityc)Gaimpurity,d)Inimpurityaddedstructures,theextinctioncoefficientof␤−Si3N4structure.

Fig.7. Fora)pureb)Al-impurityc)Gaimpurity,d)Inimpurityaddedstructures,theabsorptioncoefficientof␤−Si3N4structure.

Fig.8.Fora)pure,b)As-impurity,c)Gaimpurity,d)Inimpurityaddedstructures,absorptionof␤−Si3N4structuresatlowenergies.

4. Conclusion

Inthisstudy,theeffectsofimpurityatomssuchasAl,Ga,andInfoundinIIIAgroupoftheperiodictable,onoptical propertiesofpure␤−Si3N4structurewereanalyzed.ThecalculationswereperformedwithDFTmethodusingLDAapproach

within0–15eVrange.Basedonimpurityatoms,thechangesinbasicopticalpropertiesof␤−Si3N4structuresuchascomplex

dielectricfunction,refractiveindex,extinctioncoefficient,absorptioncoefficient,reflectioncoefficientbasedonphoton energywereanalyzed.Asaresultofcalculations,staticdielectriccoefficientswerefoundforpure␤−Si3N4andstructures

withimpurities,anditwasobservedthatimpurityatomsincreasethedielectricconstanttorelativelyhighervalues.Itis determinedthat,inthepure␤−Si3N4 structure,isotropicopticalpropertiesthatareobservedmostlybetweenxand

y-axes.Andwithaddingimpuritiesthisbehaviortendstowardsanisotropicbehavior.Asexpectedinhexagonalcrystals,it presentshighanisotropicopticalpropertiesinz-axiswithrespecttootheraxes.Duetotheincreasingabsorptionatvisible wavelengths,impuritiesmayresultinunwantedoutcomesinoptoelectronicdevicessuchasLEDs.

Acknowledgement

ThisworkissupportedbytheprojectsDPT-HAMIT,DPT-FOTON,andNATO-SET-193aswellasTUBITAKunderProject Nos.113E331,109A015,and109E301.Oneoftheauthors(EkmelOzbay)alsoacknowledgespartialsupportfromtheTurkish AcademyofSciences.

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