Physical nature of light-emitting centers in spark-processed silicon

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Dedicated to my wife, Angelina Polihronova


ACKNOWLEDGMENTS I would like to express my special gratitude to Dr. Rolf Hummel for being my advisor and chairman of the committee that supervised my work. I am very grateful for his support, encouragement and guidance through the years of my graduate studies. I would like to thank him for providing me the opportunity to study in a world-class university, which has enriched my scientific and research experience. I highly appreciate the knowledge I have received about the art of modern engineering and experimental physics. I am grateful to Dr. Hai-Ping Cheng, Dr. Paul Holloway, Dr. Susan Sinnott, Dr. Robert DeHoff and Dr. Adrian Roitberg for the helpful discussions and for serving on my supervisory committee. Many special thanks are extended to Dr. Magnus Hedstrm for his invaluable contributions to the present work. I appreciate highly the encouragement he has provided and the practical advice for the parameterization and applications of the INDO computer code. I would like to direct thanks to Dr. Nigel Shepherd, who has been a very good colleague and friend. Many thanks also to Thierry Dubroca, Michele Manuel, Dr. Michael Stora, Dr. Matthias Ludwig and Dr. Fabio Fajardo for their friendship and collaboration. I would like to thank David Burton, Kwanghoon Kim, Anthony Stewart, Grif Wise and Shidong Yu for their help and cooperation. My sincere gratefulness is dedicated to my spouse Angelina Polihronova and to my daughter Virginia Polihronova for their immeasurable love, encouragement and support. iii


TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii ABSTRACT.......................................................................................................................vi CHAPTER 1 INTRODUCTION...........................................................................................................1 2 THE MOLECULAR ORBITAL THEORY....................................................................6 The Hartree-Fock Approximation...................................................................................6 Computational Implementation of the Hartree-Fock Approximation..........................11 Further Approximations within Hartree-Fock..............................................................12 Intermediate Neglect of Differential Overlap (INDO)...........................................12 Neglect of Diatomic Differential Overlap (NDDO)..............................................13 Configuration Interaction..............................................................................................14 3 COMPUTATIONAL METHODS.................................................................................17 Background...................................................................................................................17 ZINDO..........................................................................................................................18 MOPAC: AM1 and PM3..............................................................................................20 4 CALCULATIONS AND RESULTS.............................................................................25 Known Facts About Spark-processed Silicon...............................................................25 Research Procedure.......................................................................................................27 Optical Properties of a-SiO 2 based Clusters..............................................................29 Optical Properties of Silicon Rings...............................................................................37 Optical Properties of Other Silicon Clusters.................................................................44 Compound.....................................................................................................................46 Optical Properties of Silicon Particles in an Amorphous SiO x N y matrix.....................49 The Role of N in the Optical Properties of Spark-processed Silicon...........................51 Silicon Spark-processed in Pure Oxygen......................................................................65 Si 6 Clusters in Spark-processed Silicon........................................................................67 5 SUMMARY OF RESULTS..........................................................................................72 6 FUTURE WORK...........................................................................................................75 iv


APPENDIX A SHORT INTRODUCTION INTO DIFFERENTIAL REFLECTOMETRY...............77 B POROSITY AND DENSITY OF SPARK-PROCESSED SILICON [96]...................83 Abstract.........................................................................................................................83 Introduction...................................................................................................................84 Method..........................................................................................................................85 Results and Discussion.................................................................................................94 Density of Spark-processed Si......................................................................................97 Conclusions.................................................................................................................102 LIST OF REFERENCES.................................................................................................103 BIOGRAPHICAL SKETCH...........................................................................................110 v


Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PHYSICAL NATURE OF LIGHT-EMITTING CENTERS IN SPARK-PROCESSED SILICON By Jeliazko G. Polihronov December 2002 Chair: Rolf E. Hummel DEPARTMENT: MATERIALS SCIENCE AND ENGINEERING Spark-processed silicon (sp-Si) is an amorphous, luminescent material that exhibits emission spectra, peaked around 385, 525 and 650 nm. In order to understand the photoluminescence (PL) behavior of sp-Si, UV/visible optical absorption spectra of a large variety of silicon-based molecular clusters were calculated and compared with experimentally measured absorption spectra of sp-Si. All structures in this study were optimized with the AM1 or the PM3 method. The optical absorption spectra were calculated using the quantum-mechanical INDO method together with configuration interaction, which was parameterized for Si. The experimentally measured absorption spectrum of sp-Si exhibits peaks at 245, 277, 325 and 389 nm. In an attempt to reproduce this spectrum computationally, the present work includes a detailed study of the optical properties of silica clusters, Si rings, Si clusters and cages, Si oxides and oxynitrides. vi


While the spectra of silica, Si rings and OH-terminated Si clusters resemble certain features of the experimental absorption spectrum of sp-Si, remarkable agreement is achieved in the case of a Si cluster, surrounded by an amorphous matrix. The agreement improves when the size of the model Si cluster increases from Si 3 to Si 14 2 statistical analysis of the calculated spectra shows that the presence or absence of N influences the optical properties of such complexes. Silicon spark-processed in pure O does not photoluminesce when excited by laser light having a wavelength of 325 nm. The absorption spectrum of this material differs from the one obtained on Si spark-processed in air. The statistical analysis comparing various cluster models to the two spectra shows that certain Si cluster sizes are favored in the case of Si processed in air, while this is not true for Si processed in O. vii


1 CHAPTER1 INTRODUCTION Siliconisamaterialofsubstantialimpor tancefortheelectronicindustry.Ithas beenstudiedinacourseofdecadesandisextensivelyusedintheproductionofelectronic elementsandintegratedcircuits.Siisnon-t oxic,itisreadilyavailableandhasstable oxides,whichareeasilydepositedandpatternedonaSisubstrate.Technologically,Siis extractedfromcommonsand(SiO2)andpurifiedtoelectronic,high-puritygradematerial byvariouscrystalgrowthtechniques. Advancedtechnologyhasthegoaltocreatem iniaturized,high-speedelectronic devices.UtilizingSiforthefabricationofsuchdeviceswouldbehighlybeneficialdueto theadvantagesofthismaterial.Duetothehighspeedoflight,veryhighspeedsof communicationareachievedwhenopticalandelectronicdevicesareintegratedonthe samechip.However,crystallineSihasanindirectbandgapandcannotbeusedforthe productionoflight-emittingdevices. Recentresearcheffortshaveresultedi nthedevelopmentofnovelSi-based materials,containingminiatureSiparticle swithnanometersizes.Thephysicalproperties ofsystemswithsmalldimensionsaregovernedbythelawsofquantummechanics.The bandgapofnanometer-sizedSiparticle sisnolongernarrowandindirect,thereby allowingemissionoflight.Therefore,thema terials,containingSinano-particlesareof specialinterestduetotheopticalpropertiesofthesmallSiclustersembeddedinthem. Researcheffortshavebeendirectedtowardstheunderstandingofthephysicalproperties


2 ofsuchmaterialswiththegoalofachieving detailedknowledgeoftheobservedphysical phenomena,aswellaspreparingthese materialsfortechnologicaluse. In1992,HummelandChang[1]developeda newmethodforpreparationofaSibasedluminescentmaterial.Theso-calleds park-processedSi(sp-Si)photoluminescesin thevisibleregion,havingcharacteristicpeaks[2]near385,525and650nm,as establishedbyLudwig[3](Fig.1-1,thepeakat650nmisseenasashoulderofthe dominantblue/greenpeak).Thephotoluminescen tpropertiesofthematerialexhibithigh stabilityagainstetchinginbufferedhydrofluoricacid,thermalannealingupto11000C andUVirradiation.Duringthepastfewyears,anumberofpapersdescribingand characterizingvariouspropertiesofspSihavebeenpublished.Themainfocusof previousresearchhasbeenontheopticalpropertieswiththegoaltoprovideadescription ofthephotoluminescence(PL)mechanism .Generally,twoapproacheshavebeen applied thefirstapproachrepresentsanefforttonarrowdownthenumberofpossiblePL mechanismsutilizingvariousexperimental techniques;thesecondapproachinvolves experimentstoidentifytheluminescentcentersandthephysicalprocessofemission. Thefirstapproachhasresultedint heeliminationofanumberofproposed mechanisms[4].Nevertheless,thePLphenomenonhasnotbeenidentifiedwithcertainty anddetail.Thesecondapproachisinherentlylimitedsincesp-Si,beingan inhomogeneousmaterial,isverydifficulttocharacterizeatanatomiclevel.The traditionalX-raydiffraction,X-rayabsorp tionandotherrelatedmethodsarenotableto providedefinitivedatainthecaseofinhomogen eous,multi-phasematerialssincetheir resultsareaveragedoverthebulkofthematerial.Theaveragechemicalcompositionof thesp-Sihasbeenstudiedatvariousdepths withsmall-spotX-rayPhotoelectron


3 Figure1-1.Room-temperaturePLof(a)blue-(b)green-lightemittingsp-Si. Spectro-meter(XPS,Fig.1-2).ThematerialpredominantlyconsistsoffourSi-based phasesamorphousSiO2,amorphousandcrystallineSiandSinitrides[3,5]. AmorphousSiO2occupiesmostofthevolumeofthematerial.CrystallineSiand amorphousSiclusterspredominateintheareas,closetotheSisubstrate. Earlierstudieshaveshownthatthepr esenceofNintheambientduringspark processingisessentialfortheopticalprop ertiesofsp-Si[3,6].Sincetheoriginofthe


4 opticalpropertiesofsp-Siis unknown,itisappropriatethatallfourphasesarestudiedby examiningtheopticalpropertiesofmolecu larclustersthatrepresenteachphase. Toachievethisgoal,quantummechani calcalculationshavebeenusedinthe presentworktoprovidethegeometryandopticalspectraofthestudiedmolecules. Comparedwithfirst-principlescalculati ons,thesemethodsarefaster,whichallowsa largenumberofmolecularclusterstobestudiedandtheaveragetrendofthechangeof theirphysicalpropertiestobeidentified.ThecalculatedspectraofoxygenatedSi moleculesinthepresentworkarenotapplicabletosp-Sionly;theopticalcharacteristics ofanySi-orsilica-basedlight-emittingmaterialcanbecomparedtothepresentresults. TheclustersinthisworkcanberelatedtoOH-terminated,Siparticlesonthesurfaceof materials,orinthebulkwhe nSiparticlesareburiedinamorphoussilica;likewisethey candescribeSiparticles,nuc leatinginthegasphaseinthepresenceofoxygenduring laserablationofSiorrelatedgrowthproce ssesofSi-basedmaterialsfromthegasphase. Ourresultsarealsoapplicabletotheinvestigationandcharacterizationofnebulaeand interstellarsilicatedustclouds.Similarstudi eshavebeenpublishedintheliterature[711].


5 Figure1-2.Small-spotXPSdataforsp-Si.(AdaptedfromLudwig[3],Hummeland Ludwig[4],andLudwig etal. [5]).


6 CHAPTER2 THEMOLECULARORBITALTHEORY TheHartree-FockApproximation Ourunderstandingofthenatureoftheelectronicwavefunctionsinamoleculeis basedontheunderstandingoftheelectronicwavefunctionsinanatom.Thetheoryofthe methodsusedinthepresentwork,treatss uchsystemsbyconsideringthevalence electronsonly;thecoreelectronsandthenucleusoftheatomareconsideredtoforman ion,whichinteractswiththevalenceel ectrons.Thus,inallourstudiestheterm electronicwavefunctionwillbeusedtodesc ribeawavefunctionofavalenceelectron. TheproblemfortheelectronicstructureofaH-similaratomiscommonlytreatedin thegeneralcoursesofQuantumMechanic s.Itprovidesknowledge abouttheappropriate mathematicalformofanelectronicwavefunctioninanatom:) ( ) (1 2 1 lm l l n l nlmY L e B+ + +=(2-1) whereBand areconstants;n,landmarethequantumnumbers,LisaLaguerre polynomialandYisasphericalfunction.Thegeneralresultisthattheradialpartofthe wavefunctionofanelectroninanatomcanbeapproximatedasanexponentialfunction:r Ae C r ) (,(2-2) whereCandAareconstants.Sometimes, ( r )isapproximatedasasumofGaussians.In chemistry,theelectronicwavefunctions(2-2)fortheatomarecalledAtomicOrbitals (AO).TheMolecularOrbital(MO)Theoryhasthegoaltoexplainthepropertiesofthe electronicwavefunctionsinamolecule.Suchwavefunctioninamoleculewithn


7 valenceelectronsisacceptedtobeapproximatelyequaltoalinearcombinationofAOs ofthetype(2-2):=n j j ij iC1 b(2-3) withcoefficientsCij.Inchemistry,theabovewavefunctioniscalledaMolecularOrbital (MO). SincetheelectronsareFermions(fromthePauliprincipleforasystemofn undistinguishableparticles),thetotalwavefunctionboftheelectronicsysteminthe moleculemustbeanti-symmetric.Then,itcanberepresentedasaSlaterdeterminant: ) ( ... ) ( ) ( ... ... ... ... ) ( ... ) ( ) ( ) ( ... ) ( ) ( 1 ) ... , (2 1 2 2 2 1 2 1 2 1 1 1 2 1 n n n n n n nr r r r r r r r r n r r rb b b b b b b b b= t (2-4) TheSchrodingerequationforthemoleculebecomes:) , ( ) , ( 2 1 2 1 n nr r r E r r r H t = t (2-5) wheretheHamiltonianoperatorHisnon-relat ivisticandtime-independent.Itassumes fixed-ionsandhasthefollowingforminatomicunits(= e=m =1)[12]: <<+ + n =kiAj iB A AB A ij Ai A kR Z r R Z H 1 2 1 (2-6) A,B,1,2,...designateions;i,j,...designateelectronsand ZKisthecorresponding atomicnumber. Theequation(2-5)canbesolvedusingthevar iationalprinciple.Adetailedsolution hasbeenpublishedbyC.C.J.Roothaan[13].H owever,ifthevariationalprincipleis appliedovertheMOs,thisleadstoasystemof intractabledifferentialequations.Thisis


8 thereasonwhytheMOsareapproximatedaslinearcombinationsofAOs(equation 2-3).Thenthevariationalprincipleisa ppliedovertheAOsandthecoefficients Cij. Substitutingeq.(2-6)into(2-5)andmultiplyingbothsidesoftheresultingequationby b leadsto + =j i ij ij i iK J H E,) ( 2 1(2-7) whereJandKarethetwo-electronCoulombandexchangeoperatoraccordingly: ) 2 ( ) 1 ( 1 ) 2 ( ) 1 ( ) 2 ( ) 1 ( 1 ) 2 ( ) 1 (12 12 i j j i ij j j i i ijr K r J = =.(2-8) Intheexpression(2-7),theion-relatedtermsaremissing,sincethevariationalprincipleis imposedoveratrialwavefunction b ,whichcontainstheioncoordinatesRkas parameters. Nowweintroduceanothermatrix,th eso-calledoverlapmatrixSas j i ijS =.(2-9) Varying(2-7)andtheconditionfororthonormalityoftheMOs bk + =j i ij ij i iK J H E,) ( 2 1 (2-10) 0 ) ( ) ( ) (* *= + = =j i j i j i j iC S C C S C C S C b b andusingthemethodoftheLagrangianmultipliers,weget = + = +j ji j i j j j j ji j i j j jC S C K J H C S C K J Hf f* * *) ( ) ( (2-11)


9 where(fij)aretheLagrangianmultipliers,Jj,Kjaretheone-electronCoulomband exchangeoperatoraccordingly: ) 2 ( ) 1 ( 1 ) 1 ( ) 2 ( ) 1 ( 1 ) 1 (12 12j i j j i j j jr K r J = =,(2-12) andthematricesCiarethecoefficientsfortheMO bifromeq.(2-3).Itcanbeshown, thattheequationsin(2-11)areequivalent,sincetheparticipatingoperatorsare Hermitian. Then,ifwedefinethetotalelectroninteractionoperatorGas =j j jK J G ) (,(2-13) theone-electronoperator H as j B i B B j i ijR Z H 1 2 n = (2-14) andtheFockoperatorasG H F + =,(2-15) theequations(2-11)becomefC S C F =(2-16) inmatrixnotation.ThissystemofequationsisknownasRoothaanequations.Hereone needstodeterminetheMOenergies,whichareinthematrix f ;thematrix C alsoneedsto becalculatedasitcontainsthecoefficientsoftheMOsfromeq.(2-3). Weshallthenproceedasfollowsfirst,the S matrixwillbediagonalizedviathe transformation


10 n diags s s S W S W ... 0 0 ... ... ... ... 0 ... 0 0 ... 02 1= =+,(2-17) where W isthetransformationmatrix. Second,wedefinethematrix S(-1/2)as+ = W S W Sdiag) 2 / 1 ( ) 2 / 1 ((2-18) inwhichthematrix n diags s s S ... 0 0 ... ... ... ... 0 ... 0 0 ... 02 1 ) 2 / 1 (=.(2-19) NowwereturntotheRoothaanequations(2-16)andproceedtocalculating f and C :f f f f f = = = = =+ ' ) ( ' ') 2 / 1 ( ) 2 / 1 ( ) 2 / 1 ( ) 2 / 1 ( ) 2 / 1 ( ) 2 / 1 (C F C C C F C S C S S F S C S C F S C S C F (2-20) Inthelastequation, F isindiagonalformandtheMOenergies ficanbedetermined.The coefficientsmatrix C iscalculatedas ') 2 / 1 (C S C= (2-21) Asacriterionforachievementofself-consis tentfield(SCF),weshallusetheso-called first-orderFock-Diracdensitymatrix P :=k k jk ik ijn C C P ,(2-22) wheren=diag{n1,n2,nn};nkareelectronoccupationnumberswhichare0or2inthe caseofaclosed-shell(zeromagneticmoment )molecule.Afteranumberofthedescribed


11 aboveconsecutiveapproximations,thematrixelements Pijwillreachconvergence.Then wecansaythataself-consistentfield(SCF)hasbeenobtainedandtheHartree-Fock approximationiscomplete.ComputationalImplementationoftheHartree-FockApproximationTheSCF-basedcomputerroutinesnormallyfollowthefollowingprocedure[12]: CalculatetheintegralsnecessarytoformtheFockmatrix F (equation2-15) Calculatetheoverlapoperatorsmatrix S (2-9). Performdiagonalizationof S (equation2-17). Calculate Sdiag (-1/2)andform S(-1/2)(equation2-18). FormtheFockmatrix F as: + n = l k l j k i kl j B i B B j i ijr P R Z F, 12) 2 ( ) 1 ( 1 ) 2 ( ) 1 ( 1 2 ) 2 ( ) 1 ( 1 ) 2 ( ) 1 ( 2 112 j l k ir (2-23) Calculate F (equation2-20). Diagonalize F (thelastequationin2-20)andobtaintheenergyeigenvalues fk. Calculatethecoefficients Cij(equation2-21). Calculatethedensitymatrix P (equation2-22). Check P forconvergence.Ifthedesiredconvergencetolerancehasbeenreached, thenstop. Ifconvergencehasnotbeenreached,extrapolateanewdensitymatrixandrepeat steps510untilSCFisreached. Outputtheresultsitatextformat. Plotthecalculatedabsorptionspectra Optional:calculatetheelectrontransitionamplitudesforallexcitations


12FurtherApproximationswithinHartree-Fock IntermediateNeglectofDifferentialOverlap(INDO)TheINDOapproximationrepresentsfurthersimplificationoftheHartree-Fock method.Certainapproximationsarebeingacce ptedwiththegoaltoincreasecalculation efficiency.DetailedtreatmentoftheINDOmethodhasbeenpublished[12,14-17]. Generally, Sijistheoverlapmatrix(equation2-9).Itisapproximatedsothat productsi(1)j(1) areretainedonlyinone-centerinteg rals.However,thecomputational efficiencyofINDOisachievedmainlydueto theapproximationsofthetotalelectron interactionoperator G (equation2-13). Gijisasumoftwo-,three-,andfour-center integralsofthetype 2 1 12) 2 ( ) 2 ( 1 ) 1 ( ) 1 ( dv dv rl k j i ,(2-24) whicharesettozerounlessi=landj=k.Thosethatremainaresetasparametersand theirvaluesdeterminedfromatomicspectroscopy. Hisapproximatedasfollows: r n A B i B B i i A A i A A iiR Z R Z H 2(2-25) j A A i A A ijR Z H n 2(2-26) ()ij B A ij B A ij B A ijS S H0 0 0 2 1 + =(2-27) where n istheLaplacianoperator,ZAisthecorechargeofatomA,RAisthedistance betweenthei-thelectronandionA.ijisreferredtoasaresonanceintegralandis approximatedviatheparametersAB 0,A 0andB 0.


13NeglectofDiatomicDifferentialOverlap(NDDO)NDDOisdefinedbythesubstitution r d r r r d r rA j A i AB B j A i 3 3) ( ) ( ) ( ) ( ,(2-28) whereAandBdenotetwodifferentatoms(sometimesreferredtoascenters)andisthe Kroneckersymbol.Inthissituation,theFoc kmatrixwillhavethefollowingelements [12]:One-atomdiagonalelements r r + + + n =A B B i B B i B A B l k B i B l B k B i B l B i B k B i kl AA A i A A i AA iiR Z P V R Z F 1 2 2,(2-29) where VAAistheso-calledeffectiveionpotential,beingdeterminedfromexperimental measurements. VAApreventsthevalenceelectronsofatomAfrompenetrationintoits innerorbitals.One-atomoff-diagonalelements r r =A B B i B B i B B j B l B k B i A Bl k A l k kl B l B j B k B i kl AA ijR Z P P F 1 2,,(2-30) Two-atomoff-diagonalelements =A k B l B j A k B l A i kl AB ij AB ijP H F 2 (2-31) where Hij ABisgivenbyequation(2-14).Itisalsoi mportanttonotethatNDDOincludes orbitalanisotropies.


14ConfigurationInteractionTheHartree-Fockapproximationenables ustosolvetheSchrdingerequationfora moleculeandprovidesuswiththemolecularwavefunction(r1,r2,rn) (equation2-5) ofthegroundstateanditsenergy0.Thisenergyisanupperboundtothetrueground stateenergy E0.Thedifferencebetweenthesetwovaluesiscalledcorrelationenergycorr:0 0f = Ecorr.(2-32) Thecorrelationenergyaccountsforintera ctionsbetweenvalenceelectronsinthe moleculeandamountsupto1%of E0.Despitethatthepercentageissmall,itis equivalenttoafeweV.Therefore,theHartree-Fockapproximationcanbefurther improved.Theimprovementwillprovidethevalueofcorr(oratleastpartofit)aswell asimprovedground-statewavefunctionofthemolecule.Inaddition,itwillallowus tocalculatetheenergiesandwavefunctionsoftheexcitedstatesandthusenableusto predicttheopticalabsorptionspectrumofthemolecule. ThecorrectionoftheHartree-Fockapproximationcanbeachievedviatheso-called configurationinteraction(CI),alsoknownasconfigurationmixing.Ithasbeenshownin perturbationtheory[18]thatthemolecula rwavefunctioncontainscontributionsfrom variouselectronicconfigurations.Wes hallexpressthisdependenceasalinear combination[19] < < < < < < < < < < < <+ t + t + t + t + t = r a s r b a t s r c b a u t s r d c b a rstu abcd abcd rstu rst abc rst abc rs ab rs ab r a r aC C C C,...,(2-33) whereistheHartree-Fockwavefunctionofthegroundstate,istheimproved groundstatefunction, Ca rarecoefficientsanda rarecalledexciteddeterminants.The exciteddeterminantsarebuiltfromthefunction,asitsa-thandther-throwhave


15 exchangedplaces(whichis,electronfroma-thMOhasbeenexcitedintother-thvirtual MO).EachoftheseSlaterdeterminantsrepresentsadifferentconfiguration.Thefirstsum inequation(2-33)representssingleexcita tions;thesecond,doubleexcitations;thethird, tripleexcitations,andsoon.Usually,theaboveequationistruncatedandonlysingle excitationsarecalculated: t + t r a r a r aC,,(2-34) knownasCI-S(CI-singles).ForaSi-basedmoleculewith1015atoms,thenumberof theexciteddeterminantsintheabovesum( alsoknownasCIsize)issettobearound65, inordertoprovidegoodapprox imation.IftheCIsizeisincreasedabovethisnumber,the calculatedenergiesdonotimprove. TheapplicationofthevariationalprincipletothecoefficientsCa rleadstothe secularequation0 ) ( det = ES H,(2-35) whereHistheCImatrix,writteninablockform t t t tr a r aH H 0 0 ,(2-36) H isthehamiltonianofthesystem,EisacolumnoftheenergiesoftheCIexcitedstates, andSistheoverlapmatrixfortheCIwavefunctions.TheenergiesEaretheeigenvalues ofH,whileitseigenfunctionst = tr a r a r a CIC,(2-37)


16 arealsocalledCIvectors.ThezeropartsintheCImatrixareduetointegralsofthetype r aH t t ,whichareequaltozeroaccordingtotheBrillouinstheorem[19]. If t isthewavefunctionofthegroundstate, tEXCisthewavefunctionofthe excitedstate(oneoftheCIvectors)and r istheoperatorofdistance,thentheprobability oftransition(alsoknownasoscillatorstrength)isproportionaltothesquareof b bt tr eEXC,(2-38) where t,arethevibrationalwavefunctionsandtheiroverlapiscalledaFrank-Condon factor.Thefirstterm(orrather,itssquare)determinesthetransitionintensity,whilethe secondtermgivestheoverlapofthetwovibr ationalfunctionsanddeterminestheshape oftheline. Inordertojustifytheuseofthecalculatedexcitedstateenergiesfromequation (2-35),oneneedstoapplytheFrank-Condonpr inciple,whichstatesthattheexcitation (absorption)transitionsarevertical,thatis, theelectronsmovefasterthanthenucleiin themolecule. Thecalculatedabsorptionspectrum f(E) containingatotalofNtransitions,has theform = n n =N k E E kke p E f1 773 22 02 355 2 ) (.(2-39) Inthiswork,eachindividualspectrallineisassumedtohaveaGaussianshapewith adoptedfullwidthathalfmaximum n equalto0.4eVandaheightpk,calledanoscillator strength(calculatedasthesquareofequation2-38).


17 CHAPTER3 COMPUTATIONALMETHODSBackgroundThereareseveraldifferentmethodsava ilableforstudyingchemicalandphysical propertiesofmaterialsattheatomiclevel.Themostaccurateisbasedentirelyon quantummechanicswithoutinclusionofadjustableparametersotherthanthequalityof thebasissetexpansionofthewavefunctions.Theotherextremeisclassicalmolecular dynamics,basedonempiricallydeterminedinteractionpotentialsbetweentheatomsthat constitutethematerialormoleculeunderinvestigation.Therearealsovarioustightbindingschemes(TB)thatarequantummechanicalbutrelyheavilyonempiricalfitting andthereforelacktransferabilitytoothersystems,andbondingsituationsandsoon,for whichtheyhavenotbeenparameterized. Sincethegoalofthepresentworkistode scribetheopticalpropertiesofareal material,oneneedsafastandefficientmethodthatallowsalargevarietyofmolecular structurestobeinvestigated.Themostaccu ratemethodsarequiteinsufficientinthat respect,whilethesemi-empiricalquantum-m echanicalmethodsprovidetheefficiencyof calculationandacceptableaccuracy.AsithasalreadybeendescribedinChapter2,the varioussemi-empiricalmethods usetheapproximationofHartree-Fockforcalculationof thegroundstateenergyofthemoleculeandtheenergylevelsofitselectrons.The differencebetweenthevariousmethodsisintheHamiltoniantheyuse,namely: TheHamiltonianoperatorisapproximatedinvariouswayswithinthedifferent methods;


18 TheHamiltonianoperatorisparameterizedwithsemi-empiricalparameters,which arespecificforthegivenZeroDifferentialOverlap(ZDO)method.ZINDOThismethodisknownalsoasINDO/SorINDO/CI[16,17]andhasbeen developedbyProf.MichaelC.ZernerattheQ uantumTheoryProjectattheUniversityof Florida.ThemethodisbasedontheHartree-FockapproximationandusesCIfor calculationofopticalspectra.Theaccuracyofpredictionoftheopticaltransitionenergies is2000cm-1,or0.25eV[12,20]. Themethodhasbeensuccessfullyusedinnum erousstudiesoforganicandorganometalliccompoundsandtheparametersforH,C,NandOinparticularhavebeen previouslyoptimizedtoreproduceopticalabso rptionspectra.Theoreticalparametersfor Si,aswellasthosetakenfromatomicspectroscopy,havebeenimplementedinthe programcode. InZINDO,31theoretical/empiricalparametersareused[21].Thefollowingisa listoftheZINDOparametersandtheirapplicabilityforcalculationsofSimolecular systems: 1,2:s,p:Slaterorbitalexponents accordingtoZerner[12,22,23],theseare takenfromSantryandSegal[24]forSiatoms; 3-6:d1,itscoefficientC1,d2anditscoefficientC2.ItisimportanttonotethatdorbitalsarenotusedinthecalculationforSiatoms; 7-9:Is,Ip,andId ionizationpotentialsforSipublishedbySantryandSegal[24] (atomicdataforSi); 10-12:s,pandd(resonanceintegrals).InthecaseofSi,disneglected,sp= -9eV[25]; 13-20:F2(p,p),G1(s,p),F2(p,d),F2(d,d ),F4(d,d),G1(p,d),G2(s,d),G3(p,d) Slater-Condonfactors,publishedbyBaconandZerner[23]forSi.Theseseven parametersareusedinthemoduleINDO/1forgeometryoptimizations;


19 21,22:Eatom electronicenergyofanisolatedatom;Hatom-heatofformation ofanisolatedatom thesetwoparametersareknownfromexperimentalatomic data; 23-25:Is,a,Ip,a,Id,a secondsetofionizationpotentials,involvingtransitionsto dorbitalsandarethusneglectedinthecaseofSi; 25-28:C1,C2andC3,a fractionalcontributionsofdconfigurationstothecore integral neglectedinthecaseofSi; 29-31:ss,,dd two-electronone-centerCoulombintegrals calculatedfrom theSlaterorbitalsforSi,takenfromSantryandSegal[24]. Otherparametersaresettobeconstants,suchasf=0.585,f=1.267,forsinglets excitations.Thetwo-center,one-electronintegralsareusedtocalculatesomeof theoverlapmatrixelements Sijandaretreatedasparameters. BeforeINDO/Swasusedinthisstudy,therewasaneedtore-optimizetheparameterforSi(Eq.(2-27)).Intheliterature,thereareanumberofpapersthatprovide experimentallymeasuredIRspectraaswe llaUV/visibleabsorptionspectrafor moleculescontainingSi[26-33].Onlymol eculesthatcontainSiandatoms,forwhich theINDO/Shasbeenpreviouslyparameterized,wereselected.Inthechosenstructures, Siparticipatedwithboth-(forinstance,inthecasesofsilabenzeneandH2SiCH2)and-bonding(forinstance,inthecasesofMe6Si2,(Me2Si)5and(Me2Si)6).Thegeometry ofthesemoleculeswasoptimizedwiththeAustinMethod1(AM1),predictingbond lengthwithinafewpercentofthecorrespondingexperimentalvalues.Theabsorption spectrawerecalculatedwiththeINDO/Sforeachmoleculeforvariousvaluesof. LetusconsideratotalofNSi-contai ningcompounds.Theexperimentally measuredabsorptionspectrumofeachcompound willexhibitelectronictransitionswith energiesE1,E2,....EMkwhereMkisthetotalnumberoftransitionsforagivencompound. Ifthecalculatedpredictionofatransitionenergyisdenotedasek(),then


20() = == =N k k N k M j j kM E e Errk1 11 2) ( ) ( (3-1) istheaverageerror,associatedwithagivenvalueof. Thesmallestaveragedeviationwasfoundtobe0.24eV,whichisachievedat(Si) =-9eV.Table3-1showsacomparisonbetweentheoreticalandexperimentalvaluesfora varietyoftransitionsoftendifferentSi-c ontainingcompounds.Ithastobeemphasized, thattheerrorof0.24eVinthecalculatedtransitionenergies,comesasaresultofboth MOPACgeometryoptimizationandINDO/Sspectroscopiccalculation. Inconclusion,ZINDOisanINDO-basedFORTRANcode,whichallowsoneto calculateopticalabsorptionspectra(electronicstructure)ofmolecules,containingthe elementsH,Li,B,C,N,O,F,Si,P,S,Sc,Ti,V,Cr,Mn,Fe,Co,Ni,CuandZnwitha precisionof0.25eV.Otherelementshaveal sobeenparameterizedbyresearchgroups.MOPAC:AM1andPM3Inthe1970s,theMINDO/3andMNDOcodes(Zerner[12]andthereferences therein)havebeenintroduced.TheyrepresentaModifiedversionofINDO, specificallypara-meterizedforpredictionofgeometriesandheatsofformationof molecules.AbriefexplanationoftheFockmatrixelementswithinMINDO/3and MNDOaswellasadiscussionontheirparameterizationcanbefoundintheliterature [12]. BothMINDO/3andMNDOareNDDO-based.Thefirstpracticalprogramthat containedbothapproximationswasthecode MOPAC[34,35].Ithasbeenparameterized forgeometryoptimizationofmolecules,vibrationalfrequencyspectra,heatsof


21 formationsandotherproperties[12].However,theinabilityofMNDOtosuccessfully modelhydrogenbondinghasledtothedevelopmentoftheAustinModel1(AM1)and theParametricMethod3(PM3),thelastbeingthethirdparameterizationofMNDO. Table3-1.Comparisonbetweenexperimentallymeasuredandtheoreticallycalculated transitionenergiesandwavelengthsforvariousSi-containingmoleculesCompoundExperiment[eV]INDO/S[eV] (CH)5SiH[26] 3.88 4.56 5.85 4.28 4.59 5.56 H2SiCH2[28]4.684.68 MeSi(CH)5[29] 4.00 3.85 4.20 4.20 (CH)6(CH2)2MeSi[29]4.724.96 Me2Si(CH)2[30] 4.53 5.12 4.46 5.06 Me(H)SiCH2[31]4.775.15 Me6Si2[32] 6.43 7.52 6.60 7.90 Me2Si[33]2.762.95 Me2Si5[33]4.684.83 Me2Si6[33]5.175.10 ItisimportanttonotethatsinceAM1andPM3arebothNDDO-based,theyare thereforefoundedontheHartree-Fockapprox imation.InAM1andPM3,thevariational principleisappliedtotheAOsandthemolecu larwavefunction,asdescribedinChapter 2.However,thecoordinates{Rk}oftheatomsinthemoleculearealsovarieduntilthe condition 0 = = = k kF U grad R U(3-2) issatisfied,thatis,untiltheforcesactin gonthedifferentatomsarereducedtozero. U representsthepotentialofinteractionbetweentheatomsinthemolecule.


22 TheHartree-Fockmethodandthevariationalprincipleareappliedmultipletimes, whilethecoordinates{rk}arebeingvariedateachstep,searchingforaminimumofthe normofthegradientinequation(3-2).T hecommonmathematicalproceduresfor searchingofthepotentialenergyminimumarethemethodofthesteepestdescent,the methodoftheconjugategradient,Newton-R aphsonandeigenvectorfollowing[21]. Detaileddescriptionofthesemethods canbefoundinanytextbookofnumerical methods. DuringtheHartree-FockNDDOcalculation,va riousempiricalparametersareused, manyofwhichhavebeenlistedinSection2.2.O therparameters,specificallyintroduced inMNDO,andtheirinfluenceonthegeometryca lculationsaredescribedintheliterature [12,34]. MOPACcancalculate32differentmolecu larproperties[34].Thestudyofsp-Si didnotrequiretheuseofall32andthereforeattentionwillbegivenonlytothe quantities,applicabletothepresentresearchwork. TheheatofformationHfofamoleculeiscalculatedasfollows:theHartree-Fock approximationappliedtoasystemof n valenceelectronsinamoleculeresultsina density, P ,andFockmatrix, F .Theone-electronmatrix H ,togetherwiththematrices P and F ,participateintheexpressionforthetotalelectronicenergy ()==+ =nn electronF H P E112 1 .(3-3) Iftheenergyofrepulsionbetweentwonucleiis En pair,thenthetotalenergyof repulsionbetweennucleiinthemoleculewillbegivenby <=AA B pair nucl nuclearB A E E ) (.(3-4)


23 TheenergynecessarytostripallthevalenceelectronsoffatomAwillbedenoted as Eioniz(A)andthetotalenergynecessarytotakeallatomsfromthewholemoleculeto infinitywillbe Eatomiz.Thentheheatofformationofamolecule,calculatedbythesemiempiricalmethodsAM1andPM3atatemperatureof298Kinthegasphaseisgivenby theexpression[35] + + + = natoms all atomiz ioniz nuclear electron fE A E E E H ) (.(3-5) Eioniz(A)iscalculatedusingempiricalparameters.Adetailedprocedureand descriptionoftheseparametershasalread ybeenpublished.[34,35].Theatomization energyfortheatomsinthemoleculeis =atoms all SCF SCF atomizA E E E ) () 0 (,(3-6) E(0)SCF(A) beingthelowesttotalenergyforanisolatedatomAintheself-consistent field(SCF)approximation.Fora cluster,containingatotalof naatoms,onecandefine averageatomizationenergyperatomas ==an k SCF k SCF a atomizE E n E1 ) 0 (1.(3-7) Itdetermineshowstronglyanatomisboundtotheotheratomsandthereforecould beusedasameasureofthestabilityofthemolecule. Inconclusion,MOPACallowsonetocalculate32differentmolecularproperties, betweenwhicharetheoptimalatomiccoordinatesofamolecule(optimizedgeometry), itsheatofformationandgroundstateenergy.nHf,beingaresultoftheabovesemiempiricalmethods,isusefulw hentwomoleculesarecompared.Therelativedifference


24 oftheheatsshowstheenergyexpenditurenecessaryforthetransformationofone moleculetoanother.


25 CHAPTER4 CALCULATIONSANDRESULTSKnownFactsAboutSpark-processedSiliconSpark-processedSi(sp-Si)hasbeent horoughlystudiedsince1992,whenfoundto havevisiblePLatroomtemperature[1].Ho wever,alargesetofitspropertieshave technologicalimportanceonlyandassuchwillnotbeconsideredhere.Someofthe characteristicsofthematerialyieldimportantinformationaboutthelight-emittingcenters asfollows: Sp-SigrowninairhasPLspectra,whichexhibitconsistentlythreepeaks:blue, greenandred(peakingaround385,525and650nmrespectively).Thisfact suggeststhat similarlight-emittingcentersarebeingformedalways,when crystallineSi(c-Si)isspark-processedinair TemperaturebehaviorofthePLsuggest sthatquantumconfinementisnotthe mechanismofemission[3].Therefore, c-Siorc-Siparticlesarenotrequiredinthe modelingofthelight-emittingcenters .However,thepresentstudyincludesa limitednumberofc-Siclustersforthesakeofcompleteness. ThePLofsp-Siishighlyresistantagainstetchinginhydrofluoricacid,aging,UV irradiationandthermalannealingupto11000C.Thisfactsuggeststhat theemitting centersoccupystablemoleculargeometriesupto11000C X-raydiffractionstudies[3,36]showthatsp-Sicontainsamorphousphases.This factsuggeststhattheemittingcenters,althoughsimilarthroughoutthebulk,are posi-tionedindifferentatomicsurroundings.Inotherwords, theemittingcenters belongtothesamefamilyofmolecularclu stersandhavesimilarcharacteristics, butdonothaveidenticalmoleculargeometries Small-spotX-rayelectronicspectrosc opy(XPS)studiesofsp-Sishowthatthe materialconsistsoff ourphases:amorphousSiO2(a-SiO2),a-Si,c-SiandSiNxorSi oxynitrides[3,5].Thisfactsuggeststhat theluminescentcentersarelocatedinone ofthesephasesorataninterfacebetweenthem Earlierstudies[4]onsp-SishowthatitsPLdoesnotoriginatefromSiO2. Therefore, theemittingcentersdonotoriginatefromtheSiO2.


26 Anearlierstudy[3,37]statesthatthePLdecaytimeofsp-Siisintheorderof nanoseconds.Amorerecentstudysuggestsdecaytimesintheorderofpicoseconds [6].Ineithercase,thedecaytimesarefastanditseemsthereforethatchargeor energytransfermechanismsinPLarenotlikely. Theabsorptionandemissionofa photonoccuronthesamecenter. ThisfactisalsoconfirmedbypreliminaryPLE (photoluminescenceexcitation,Figure41)andabsorptionspectraofsp-Si,both showingidenticalpeaks[38].Theabsorptionspectrumofsp-Siwasmeasuredbya differentialtechnique,calleddifferentialr eflectometry.Line-shapeanalysisofthe differentialreflectogram(DR)ispresentedinAppendixA. Sp-Siisadilutedmagneticsemiconductora ndexhibitsferromagneticproperties. Theyareannealedoutataround6000C.ThePLpropertiesareobservedafter thermalannealinguntilatleast11000C.Thisfactsuggeststhatthetwophenomena arenotrelatedand thelightemittingcentersareprobablynon-magnetic,having singletgroundstates(zerospin) Figure4-1.PLE,PLandDR(e.g.,absorptivity,seeAppendixA)characteristicsof Sispark-processedinair.


27 Thesurfaceareaofsp-Siconstitutesmainlyofa-SiO2.However,thereisa populationofSiparticlesi nthematrixofa-SiO2[3,36]. Theemittingcenterscouldbe relatedtoSiparticlesinamatrixofa-SiO2. Theopticalabsorptionspectraofsp-Siprocessedinairandsp-Siprocessedinpure oxygenshowsimilarbandsbetween200and300nm.Howeverinoneofthecases(in pureO)thebandsareresolved(Figure4-2),whiletheyareconvolutedintheothercase (inair).Thisfactsuggeststhat thelight-absorbingcentersinbothmaterialsmightbe related,butwillhaveimportantdifferences .ResearchProcedureSincesp-Siconsistsofa-SiO2,a-Si,c-SiandSinitrides/oxynitrides,thelightemittingcenterswillbemodeledas AmorphousSiO2basedclusterswithandwithoutparticipationofNatoms; AmorphousSibasedclusterswithan dwithoutparticipationofNatoms; Sinitrideandoxynitrideclusters; Clustersofthetypea-SiO2/a-SiNxOyora-SiO2/a-SiNx; Clustersofthetypea-SiNxOy/a-Siora-SiNx/a-Si; C-Siclusterswillbeinclude dforcompleteness:a-SiNxOy/c-Si,a-SiNx/c-Si; Clustersofthetypea-SiO2/a-Sianda-SiO2/c-Si. Forall7familiesofmolecularclustersthefollowingprocedurewasapplied: Withoutexception,theclustergeometri eswerebasedonpreviouslypublished studies,showingsufficientexperimen taland/ortheoreticalsupportfortheir existence; Modificationoftheabovegeometrieswasdonestrictlyfollowingtherulesof bondingforO,N,SiandH; AlldanglingbondswereterminatedwithHatoms; ThestructuresofallclusterswereoptimizedwithAM1/PM3; ZINDO/Sspectroscopiccalculationwasperformedforallclusters,resultingina calculatedopticalabsorptionspectrum; Thecalculatedspectrumwascomparedwiththespectrumofsp-Si.


28 Figure4-2.Differentialreflectogram(e.g.,absorptionspectrum,seeappendixA)of Siliconspark-processedinOatmosphere.Thematerialdoesnotshow PL,whenexcitedwithaHe-Cdlaser(325nm)[39]. Manyofthestudiedcomplexesweretestedforspinstatecontaminationby projectingthemolecularSlater-typewavefunctiontoverwavefunctions,representing thepuremultiplicities(theeigenfunctionsofthespinoperatorS2).Inthecaseof UnrestrictedHartree-Fock(UHF)typeoffield,allmoleculesstudiedinthisworksatisfy theconditionUHF UHFS t t2 ,(4-1) whereisascalarquantity.Therefore,theclustersstudiedinthepresentworkhavebeen consideredtohavesingletgroundstates(close dshellconfigurations )andtheRestricted Hartree-Fock(RHF)implementationoftheINDOcodewasused.


29 ThehightemperaturestabilityofthePLinsp-Sisuggeststheemittingcenters occupyequilibriummoleculargeometries,whichexcludesdefectsfromconsideration. Certaindefectsinthesp-Sibulkarerespons ibleforitsmagneticproperties,whichare annealedoutat~6000C[40],whilethePLpropertiesremainatthistemperature.Toadd moreweighttothisargument,onecanalsopointtothefactthatNatomsinSi-richsilica areproventoimprovethepropertiesofthedi electricbyreducingthedensityofcharged andneutraldefects[41-50]andatthesametimeithasbeenestablishedthatNisofkey importanceforthePLinsp-Si.Still,somehigh-strainstructuresandclusterswith hypercoordinatedatomswereincludedsyst ematicallyinthecalculations,butdidnot provideacceptablepredictions ofthepropertiesofsp-Si. Thecalculationswithclustersfromthevariousclusterfamiliesledtoconsecutive approximationstothespectrumofsp-Siwithincreasingaccuracy.Theyarepresented belowintheordertheoriginalresearchwasconducted.OpticalPropertiesofa-SiO2basedClustersNearly100silicaringclusters(Fig.4-3)wereoptimizedwiththeAM1and modifiedbysubstitutionofOatomswithNato ms[25].Variousschemesofattachment ofclusterswerealsoappliedwiththegoalt oinvokeachangeintheopticalpropertiesof theresultingstructure.Afterthegeometryoptimization,INDO/Sspectroscopic calculationswereperformedforeachindivi dualcluster.Theopticaltransitionsofthe majorityofthestudiedclustersoccurate nergies,higherthan6.2eV(lowerthan200 nm).Someofthestructuresthough,allowopticaltransitionsthatareinclose resemblanceofthoseinsp-Si.Thetwo-memb erringisaplanarstructurehavingtwo doublebondsSi=O[15,51-55].Theringwasmodifiedby SubstitutionofanOatomwithaNatom;


30 SubstitutionofSi=OwithSi-(NH2); Replacingofalldoublebondswithsinglebonds,concomitantwiththeadditionofa Hatom. IfanNatomtakestheplaceofanOatomandifadoublebondSi=Oispresentthen theresultingabsorptionspectraexhibitasinglepeaknear245nm(5.05eV,Fig.4-4).If alloftheOatomsintheclusteraresubstitutedwithNatoms,ornoNatomsarepresent, thepeakvanishes. Figure4-3.Silicaring-shapedclusters.(a)Two-memberring;(b)three-memberring; (c)four-memberring;(d)five-memberringand(e)six-memberring.


31 Thethree-,four-,five-andsix-membersilicaringsarenon-planarstructures[56] thatdonotcontaindoublebonds.SubstitutionofOatomswithNatomsdoesnotresultin absorptionpeaksthatareclosetothoseofsp-Si.However,attachmentofamodifiedtwomemberringmayresultinalterationoftheopticalproperties.Forinstance,ifatwomemberringisattachedtoasix-memberring,anelectrontransitionnear245nm(Fig.45)emergesinitsabsorptionspectrum.Asimilartrendcanbeobservedforsomeclusters thatarestructuredasacombinationofanextendedtwo-memberringandasix-member ring(Figs.4-6and4-7). Furtherunderstandingabouttheprocessofabsorptioncanbeobtainedby consideringsomespecificfeaturesofthemolecularorbitalsinagivencluster.InCI,the absorptionspectrumiscalculatedfromthetransitionsbetweenCIvectors,whichare mathematicallyrepresentedbylinearcombinationsofSlater-typedeterminantalwave functions.IfatransitionispossibleforapairofCIvectors,thentheenergyofthe transitioncanbeidentified.TheTabulatorprogramwithintheCAChecode[57]buildsa three-dimensionalcoordinategridandcalculatesateachpoint,thevalueoftheelectron probabilityamplitudefortheHOMOandtheLUMO.Electronisosurfacesare constructed,usingallpoints,atwhichtheabovecalculatedamplitudeisequalto0.07 atomicunits(a.u.).Theoccupiedandunoccupiedorbitalsurfacesaredisplayedin differentcolors. Fig.4-8isathree-dimensionalimageofsiliconoxynitridemoleculesandthe orbitalisosurfacesforthetransitionat245nmanditsvicinity.Similarplotsweredone forstructureswithdifferentsizes.Iftheseexhibitanabsorptionpeaknear245nm,then alwaystheHOMOandtheLUMOatthisexcitedconfiguration(whichis,theelectron


32 transitionamplitude)arelocatedoverthesmallringstructureswithparticipationofthe oxygenatomintheSi=Obond. 0 7000 14000 21000 28000 35000 220240260280300 Wavelength[nm] (a) (b) (c) (d)Figure4-4.Equilibriumgeometriesandspectraofmodifiedtwo-membersilicaring clusters.


33 Figure4-5.Equilibriumgeometriesandspectraofmodifiedthree-andsix-memberrings viaattachmentoftwo-membersilicaring.


34 Ifthedesiredpeakswerepreservedinthespectraofthetwo-memberringsonlyand nowhereelse,thensuchstructurescannotbe usedtomodelthepropertiesofarealsolidstatematerial.Theabovefactsshow,howev er,thatitispossibletoincorporatethe strainedtwo-memberringsintolargerstructu resandtoimparttheiropticalpropertiesto thewholemolecule.Thus,thesizeoftheclustercanbeincreasedwithoutalterationof thedesiredproperties. However,theprocessofattachmentdoesnotalwaysretainthetransitionofthe smallrings.Ascanbeseenfromtheabovere sults,modifiedtwo-memberringclusters turnouttobealwaysinactivewhenattachedtoafourorfive-memberring.Thisisalso trueinmanycaseswherethree-andsix-membersilicaringsareattached.Mere substitutionofOwithNinthecaseofthree-,four-andfive-membersilicaring-chains doesnotresultinthealterationofopticalpropertieseither. Theseobservationsdemonstratethattherearemanypossibilitiesforincorporation ofNatomsintoamorphousSiO2,butonlyalimitednumberofthemwillresultinan opticalexcitationnear245nm.Theactivecentersarealwaysdependentonthe availabilityofamodifiedtwo-membersilicaringandadoubleSi=Obond. Theprocessofsp-SigrowthrandomlyincorporatesNandOatomsintoan inhomogeneous,disorderedsolidphase.I tisvirtuallyimpossibletocontrolthe microstructureofthematerialduringthesparkprocessing.Inthissituation,thecluster structuresthatcontainNatoms,willhavedissimilargeometriesaccordingly.Thus,a largenumberofNatomswillparticipateinthecompositionofvariousclusters,notbeing abletocontributetotheopticalproperties.Afinitenumberofthemarepossibletotake partintheformationofmodifiedtwo-membersilicarings.Incertaincases,such


35 structureswillinvokealterationoftheopti calpropertiesofthematerial,loweringthe opticalabsorptionthresholdenergyto5. 05eV,whichcorrespondstoawavelengthof 245nm. Figure4-6.Attachmentoftwo-memberringtosix-memberrings.


36 Figure4-7.Calculatedabsorptionspectraof modifiedsix-memberringsviaattachmentof two-membersilicaring.(a),(b)and(c)correspondtotheclustersonFigure 4-6respectively. Figure4-8.Three-dimensionalmolecularorb italsurfaces,correspondingtotheelectron transitionat245nm.


37 Insummary,silicaringsalonecannotaccountfortheopticalpropertiesofsp-Si, sincetheyreproduceonlyonepeakofthesp-Sispectrumthepeakat245nm.However, byreplacingOatomsbyN,aremarkablealterationoftheopticalpropertiesofcertain two-,three-andsix-membersilicaringsisobserved.Theseresultssuggestthatsilica clustersarepotentialparticipantsint heprocessoflightemissionofsp-Si.OpticalPropertiesofSiliconRingsSiandSiO2clustersofdifferentsizesandgeom etriesparticipateintheplasmaassistedvaporizationprocessduringsparkpr ocessingandintheluminescentmaterialas well[3].Thering-shapedclustersareanimportantsubsetofthelargefamilyofthese clusters(Figure4-9).Thereisasubstantia lnumberofcomputationalstudiesonSiring networks,publicationsonwhichcanbetr acedbackto1974[58-70].Thesepublications showthattheoreticalmodelingofa-Siwithnetworkofthreetoeight-memberedSirings successfullypredictsexperimentallymeasuredpropertiesofmaterial(e.g.radial distributionfunctioninX-raydiffraction,densityofstates,infraredspectraetc.). Therefore,thereistheoreticalsupportfortheexistenceofSirings,whicharethe buildingblocksoftherandomnetworkofa-Si.Siringshavealsobeenobserved experimentallyina-Siandoxygenate dSiringshavebeenobservedatSi/SiO2interfaces [71-73].Itisthereforerelevanttostudythe opticalpropertiesofSiringshapedclusters andhowtheycomparewiththemeasuredopticalspectraofsp-SiandsimilarSicontainingmaterials.


38 Figure4-9.OptimizedgeometriesoftheOH-terminatedSirings. Previouslypublishedquantummechanicalca lculationsindicatestablegeometries ofisolatedthree-,four-,five-andsixmemberSiring-shapedclusters.Atroom temperature,theywillnormallyreactwithoxygen,hydrogenornitrogen.Our calculationsindicatethatthisisenergetical lyfavorable.Table4-1containsdataforthe isolatedthree-memberSiringandshowsthetr endinenergeticswhentheringreactswith


39 oxygenandnitrogen.Thesametrendhasbeenobservedinthecasesoffour-,five-and six-memberSirings. TheAM1semi-empiricalcalculationsalsorevealadefinitivetrendinthe energeticsofallstudiedSirings,whenasilicaringisattachedtothem.Inallcases,an increaseoftheaverageatomizationenergyisobservedwhenthistypeofattachment takesplace.TheresultsareshowninTable4-2. AnothercommontrendinthebehaviorofallstudiedhydrogenatedSiringsis observedwhenanOatomissubstitutedbyanNatom.Theaverageatomizationenergy ofsuchclustersdecreasesasthenumberofthesubstituteNatomsincrease. However,iftheheatofformationofthemoleculeisdenotedas n Hf ,thenthedifference| ) ( ) ( |'cluster ring member k isolated H k Hf f n n(4-2) diminishesinallcasesfork=3,4,5and6whenasubstituteNispresent.Inotherwords, ittakeslessenergytoaddtheNH2grouptoanisolatedSiring,comparedtoaddingan OHgroup.ThisfactisillustratedinTable4-3,aswellasinTable4-1. TheopticalabsorptionspectraoftheSiring-shapedclustersconsistentlyshowa numberofdistinctivefeatures.Allspectraexhi bitthreecharacteristicpeaks,positioned Table4-1.Theenergeticsofthethree-memberSiringascalculatedbythesemi-empirical methodAM1.CompoundCalculated,eV CalculatednHf,kcal/mol IsolatedSi3ring-2.30243.6 HydrogenatedSi3ring, Si3H6-3.2049.1 Si3H5(OH)-3.66-17.8 Si3H4(OH)2-4.06-90.2 Si3(OH)6-5.07-365.2 Si3H5(NH2)-3.6322.7 Si3H4(NH2)2-3.94-7.0


40 Table4-2.TheenergeticsofthestudiedSiringswithattachedfour-membersilicaringas calculatedbythesemi-empiricalmethodAM1.CompoundCalculated,eV CalculatednHf,kcal/mol OxygenatedSi3ring, Si3(OH)6-5.07-365.2 Fourmembersilicaring attachedtoSi3ring -5.40-508.4 OxygenatedSi4ring, Si4(OH)8-5.10-474.0 Fourmembersilicaring attachedtoSi4ring -5.40-640.1 OxygenatedSi5ring, Si5(OH)10-5.10-603.9 Fourmembersilicaring attachedtoSi5ring -5.33-769.1 OxygenatedSi6ring, Si6(OH)12-5.10-731.8 Fourmembersilicaring attachedtoSi6ring -5.30-897.3 Table4-3.ThecalculatedenergeticsoftheadditionofNH2andOHgroupstoanisolated Si5ringcluster.CompoundCalculated,eV |nHf -nHf(isolatedSi5ring)|, kcal/mol OxygenatedSi5ring, Si5(OH)10-5.10924.4 Si5(NH2)(OH)9-4.99880.4 Si5(NH2)2(OH)8-4.93837.4 Si5(NH2)3(OH)7-4.86794.8 Si5(NH2)4(OH)6-4.81751.2 between200nmand350nm.Onaverage,thepeaklocatedintheneighborhoodof200 nmhasthehighestintensity,whiletheothertwopeaksat260nmand320nmhave comparablemagnitudeandusuallyoverlap.H owever,thepeakat260nmcoulddominate inintensitymostlyinthecaseswhenlargerclustersarestudied.Inmanyspectra,alowintensitypeakappears,positionedintheintervalbetween400nmand500nm(Figures410and4-11).


41 ThesubstitutionofanOatombyanNatominaSiringclusterdoesnot substantiallyinfluenceitsopticalproperties.Thishasbeentheconclusionfroma comparisonofmorethantwohundredspectraofsuchclusters.Generally,theadditionof anNatomcausesaseparationofthepeaksat260nmand320nm,whichmayotherwise overlap. TheresultsinTable4-2indicatethattheatomizationenergyisfurther increasedinmagnitudewhenasilicaringisattachedtotheSicluster.Thisincreased stabilitysuggeststhatSiring-shapedclusterscouldbeincorporatedinanamorphous silicamatrixwithoutcompromisingthestabilityofthemolecule.Itshouldbenoted howeverthatthisisaqualitativestatementonly,whilethequantitativeinfluenceofonthestructuralpropertieshasnotbeenstudied. TheopticalabsorptionspectraoftheOH-terminatedSiring-shapedclusters consistentlyshowthreepeaksintheneighborhoodof200,260and320nm(Figures4-10 and4-11).Theattachmentofsmallsilicaclustersdoesnotchangetheopticalproperties. Unlikethecaseofafour-memberstrainedsilicaclusterswithdoubleSi=Obond[25], substitutionofanOatomwithanNatomdoesnotleadtoalterationoftheabsorption spectraofoxygenatedSirings.Additionally,theoxygenatedSiring-shapedclusters exhibitasmallpeakintheirabsorptions pectra,locatedbetween400and500nm.The presenceorabsenceofNatomsintheclusterdoesnotinfluencethepeakpositionorits intensity.Thepositionsofthepeakscoincidewiththepositionsofsmallpeaksor shouldersinthespectrumofsp-Si.Thisfact suggeststhatSiringscouldbecontributing tothePLofsp-Si.


42 Figure4-10.Comparisonbetweenanexperimentallymeasuredabsorptionspectrumof sp-Si(DR,seeappendixA)andacalcu latedabsorptionspectrumofthe oxygenatedSi4ringSi4(NH2)(OH)7.ThedarkatomsrepresentO,thegray atomsrepresentSi,thesmallatomsrepresentH.


43 SiOH Figure4-11.Comparisonbetweenanexperimentallymeasuredabsorptionspectrumof sp-Si(DR,seeappendixA)andacalcu latedabsorptionspectrumofthe oxygenatedSi5andSi6ring-shapedclusters.


44OpticalPropertiesofOtherSiliconClustersTheSiring-shapedclustersreproduceanumberoffeaturesoftheoptical absorptionspectrumofsp-Si.Comparedtothespectraofsilicaclusters,theycomemuch closertothespectrumofsp-Si.Sincethisisapointofinterest,thestudyofSiclusters wascontinuedbeyondthefamilyofSirings.T hesubjectofthepresentsectionisfocused onamorphousoxygenatedSiclusterswith2to14Siatoms. ThecalculatedspectraofoxygenatedSimoleculesarenotapplicabletosp-Sionly; theopticalcharacteristicsofanySi-orsilica-basedlight-emittingmaterialcanbe comparedtotheresultsinthisdissertation.Theclustersinthisworkcanberelatedto oxygenated,amorphousSiparticlesonthe surfaceofmaterials,orinthebulkwhen amorphousSiparticlesareburiedinamorphoussilica,orcanrepresentSiparticles, nucleatinginthegasphaseinthepresenceofoxygenduringlaserablationofSiorrelated growthprocessesofSi-basedmaterialsfromthegasphase. Allmolecularstructuresinthissectio narebasedonpreviouslypublished geometriesofisolatedSiclusters,optimizedwith abinitio andDFTcalculationsand widelyacceptedasstable[12,7479].Inthe sp-Simaterial,Siclustersdonotexistas isolatedmolecules,butareratherbondedtooxygenandnitrogenatomsortocrystalline Siparticles.WehavestudiedtheenergeticsofadditionoftheNH2andOHgroupstothe Siclusters.Figures4-12and4-13displaythegeometriesofcertainrepresentative molecules-Si3,Si8,Si10,Si11andSi14.Table4-4containsdatafortheenergeticsofSi3. Themodulusoftheaverageatomizationenergyinthegeneralcaseincreaseswith thehydrogenationandalwaysincreaseswithOH-terminationofanisolatedSicluster.It reachesitshighestvalueswhenNatomsareabsent.Allofthestudiedstructuresinthis workconformtothisrule.IdenticalresultshavebeenachievedforalargevarietyofSi


45 ring-shapedclusters[80].Therefore,theconclusionisimposedthatinSi-based moleculestheattachmentof(OH)groupsleadstostructuralstabilizationwhichismost pronouncedintheabsenceof(NH2)groups.Itshouldbenotedhoweverthatthisisa qualitativestatementonly,whilethequantitativeinfluenceofonthestructural propertieshasnotbeenstudied. Figure4-14displayscalculatedspectrao frepresentativeoxygenatedSimolecules. Thespectraalwaysexhibitatriple-peak featureatoraround205nm,250nmand320 nm.Thevariationofthepeakpositionsiswithin 5nmforthefirstpeak,within 20nm forthemiddlepeakandwithin 30nmforthepeakat320nm.Almostwithout exception,aweakerpeakbetween400nmand500nmisalsoobserved.Inthegeneral casethethreepeaksbetween200and320nmareresolvedandstillcannotreproducea dominantpeakat250nm,asitisinthespectrumofsp-Si. Thebehaviorofthetriplepeakisexplainedbythefollowing:PresenceofNatomsinthemolecule :IfanOHgroupinanoxygenatedSicluster isreplacedwithaNH2group,thisinvokessmallchangesintheopticalspectrum,which donotseemtofollowaspecifictrend.Inthemajorityofcases,uponsuchchangesthe agreementbetweenthecalculatedspectrumoftheclusterandtheobservedspectrumof sp-Sidoesnotimprove.ThespectraofoxygenatedSimoleculesarefarclosertothe spectrumofsp-Si,whencomparedtospectraofSiO2-basedmoleculesandspectraofSi nitrides.Thisconclusionisbasedoncomparisonbetweenmorethanonehundredsilica andmorethanthreehundredSi-basedstructur es.Thus,theabsorptionoflightinsp-Siis highlydependentonSimoleculesratherthanatomicimpuritiesintheamorphousSiO2network.Thestudyoftheelectronictransitionamplitudesforthecalculatedhigh-


46 intensitytransitionspointstowards Siparticleswithin theamorphousSiO2asresponsible forthelightabsorptionofsp-Si. Table4-4.Energeticsoftheadditionofthe(OH)and(NH)2groupstoSi3.Theleft columnshowsthevaluesoftheaverageatomizationenergyineV.CompoundCalculated,eV IsolatedSi3molecule-2.62 HydrogenatedSi3molecule,Si3H8-3.10 OxygenatedSi3molecule,Si3(OH)8-5.18 Si3(NH2)(OH)7-5.10 Si3(NH2)2(OH)6-4.96 Si3(NH2)3(OH)5-4.90 Si3(NH2)4(OH)4-4.81 Figure4-12.GeometriesofOH-terminatedSi3,Si8andSi10molecules.


47 Figure4-13.Geometriesofthecage-shapedoxygenatedSi11andSi14molecules.


48 Figure4-14.CalculatedspectraofoxygenatedSi4andSi6molecules.Thedarkatoms representO,thegrayatomsrepresentSi,thesmallatomsrepresentH.


49 TheroleoftheSiatoms:WehavecalculatedthespectraofhydrogenatedSi2 Si14.Interestingly,thetriple-peakfeatureofthespectrumispreservedinmostof thesecases.Thepeakat205nmisverystrong,whiletheothertwopeaksoverlap. Thelow-energypeakat400nmisabsentinthespectraofsmall,hydrogenatedSi moleculesandreappearsinthespectraofthelargerones(Si10andup),together withneighboringsmallerpeak s.DespitethathydrogenatedSiclustersaremost probablynotpresentinsp-Si,thespecificf eaturesoftheirspectrasuggestthatthe absorptionoflightinhydrogenatedandoxygenatedSimoleculesoccursmainly overtheSiatoms,whiletheH,OandparticipatingNatomshaveminorrole,which couldberelatedtoapossiblelightemissioninsuchmolecules. WithinthesetofcalculatedspectraofoxygenatedSiclustersstudiedinthiswork, wehaveobtainedalimitednumberofoptic alabsorptioncurves,whichshowclose agreementwiththeobservedspectrumofsp-Si.Representativecage-shapedcluster structuresassociatedwiththesespectraareshownonFigure4-13,whileFigure4-15 displaysacomparisonbetweenthecalculate dandobservedabsorption.Theseclusters haveopticalproperties,whichdifferfromt hegeneraltrendofbehaviorofthestudied oxygenatedSimolecules,byexhibitingalargepeakcenterednear250nmand reproducingthelow-energypeaksofsp-Sibetween500and700nm. Sincesp-Siisinhomogeneousandamo rphous,asmallnumberofmolecular structures,howeverclosetheymaymatcht hespectrumofsp-Si,cannotbeexpectedto accountforthepropertiesofthematerial.Thi swouldbeadeterministicapproach,which disagreeswiththerandomnatureofsp-Si.Rather,afamilyofstableclusterswith matchingopticalpropertiesmustberesponsib leforthePLofthismaterial.Nevertheless, theachievedhigherlevelofagreementwiththeobservedspectraofsp-Siatthisstage indicatesthatthepresentstudyhaspoceededinthecorrectdirection.OpticalPropertiesofSiliconParticlesinanAmorphousSiOxNymatrixAsanextstep,Siparticlesinana-SiOxNymatrixwerestudied.Inthiscasethe calculatedabsorptionspectraremarkablywe llreproducedthespectrumofsp-Si.Sicages


50 andclustersweremodeledasbondedtosilicarings.Theagreementbetweentheoretical predictionandexperimentwasachievedfor anySicluster,bondedtosilicarings.The degreeofsimilaritybetweencalculatedandmeasuredspectravariesforthedifferentSi particles,butthespectralfeaturesaresimilar(Figures4-16toFigure4-25). Ourcalculationssuggest,tha ttheSiparticlesina-SiOxNyplayakeyroleinthe processoflightabsorptioninsp-Si.Time-resolvedPLmeasurementswithsp-Sihave shownPLdecaytimesintheorderofnanosecondsorevenpicoseconds[6].Thisfact indicatesthatcharge-orenergytransfermechanismsareunlikelypriortolightemission insp-Si,sincesuchprocessesresultinincreaseddecayPLtimes.Photoluminescence Excitation(PLE)andopticalabsorptionspectraofthematerialshowidenticalpeaks (Figure4-1).Thiscanbeinterpretedtomeanthatabsorptionisfollowedbyemissionon thesamecenter. Si O H Figure4-15.CalculatedspectraofoxygenatedSi11andSi14molecules.


51 ThePLEspectrumshowsthatabsorptiona round320nmmosteffectivelyresultsin emissionofphotonswithawavelengthof380nm.Theabsorptionat245nmisveryhigh, butlessefficientinproducingblueemissi on.Still,laserexcitationat230nmandlower energiesresultsinemissionofbluelight[81].Atthesewavelengths,thePLEexhibitsa non-zerotail(Figure4-1),consistentwithth eabsorptionmeasurements.Itistherefore proposed,thatboththeabsorptionandemissionoflightinsp-SioccurovertheSi particles,embeddedintheamor phousinsulatormatrixofsp-Si.TheRoleofNintheOpticalPropertiesofSpark-processedSiliconIntheconductedexperiments,thePLofsp-SiwasexcitedbyaHe-Cdlaser(325 nm).ItisimportanttonotethatPLwasobserve donlyforsp-Si,processedinmixturesof OandNgases(e.g.air).Firstly,theHe-Cdlaserwasnotabletoexcitesp-Si,processed inpureOatmosphere,whichsuggeststhatsuchmaterialeitherdoesnothavean absorptionbandattheexcitationwavelength,ortheexcitedelectronsloseenergyalong non-radiativepathways.Secondly,theabsor ptionspectrumofsp-Siprocessedinairis differentcomparedtothespectrumofsp-Si ,processedinpureOatmospheres.Forthese reasonsithasbeeninferred,thatNplaysaroleintheopticalpropertiesoflight-emitting sp-Si.Alargenumberofstudiesconsistentlyshowsthatina-SiOxNysystemstheNatoms pileupatthedielectric/Siinterface[42,44,45,47,48,82-91].Ithasbeensuggested thatinsuchsituations,Si2NObondingoccursattheinterface[89,90].The applicationofthesefactstoourcalculations hasresultedinstructuresofthetype,shown inFigures4-19to4-24.Figures4-16to4-18andFigure4-25showgoodagreementas well.


52 Figure4-16.Siparticleinamorphoussilicamatrix.Thegraphdisplaysacomparison betweenthemeasuredDRspectrumofsp-Si(appendixA)andthe calculatedspectrumofthecluster.ThedarkatomsrepresentO,thegray atomsrepresentSi,thesmallatomsrepresentH.


53 Figure4-17.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH.


54 Figure4-18.Siparticleinamorphoussilicamatrix.Thegraphdisplaysacomparison betweenthemeasuredDRspectrumofsp-Si(appendixA)andthe calculatedspectrumofthecluster.ThedarkatomsrepresentO,thegray atomsrepresentSi,thesmallatomsrepresentH.


55 N N N N N N N NFigure4-19.Siparticleinamorphoussilicamatrix.Thegraphdisplaysacomparison betweenthemeasuredDRspectrumofsp-Si(appendixA)andthe calculatedspectrumofthecluster.ThedarkatomsrepresentO,thegray atomsrepresentSi,thesmallatomsrepresentH.


56 NNN N NN NNFigure4-20.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH.


57 N N N N N N N NFigure4-21.Siparticleinamorphoussilicamatrix.Thegraphdisplaysacomparison betweenthemeasuredDRspectrumofsp-Si(appendixA)andthe calculatedspectrumofthecluster.ThedarkatomsrepresentO,thegray atomsrepresentSi,thesmallatomsrepresentH.


58 N N N N N N N N N NFigure4-22.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH.


59 N N N N N N N N N N N N N NFigure4-23.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH.


60 N N N N N N N N N N N N N N N NFigure4-24.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH.


61 Figure4-25.Siparticleinamorphoussilicamatrix.Thegraphdisplaysa comparisonbetweenthemeasuredDRspectrumofsp-Si(appendixA) andthecalculatedspectrumofthecluster.ThedarkatomsrepresentO,the grayatomsrepresentSi,thesmallatomsrepresentH. SincethecalculatedspectraofclusterswithandwithoutNatomslooksimilar (Figure4-26),a2statisticalanalysiswasperformedinordertoverifywhether


62 calculatedabsorptionspectraofstruct ureswithNwouldshowimprovedagreementwith theexperimentalspectrumofsp-Si.2wascalculatedas () =k k kT E n2 2) ( ) ( 1 (4-3) forafamilyof n clusters,eachofthemhavingacalculatedabsorptionspectrumE(). T()representstheabsorptionspectrumofsp-Si,processedinair.Inthisanalysis,5 differentclusterfamilieswerestudied: Siparticleswith3,4,5,6,7,8,10an d14atoms,terminatedwithOHgroups, withoutNatoms; Siringswith3,4,5and6atoms,terminatedwithOHgroups,withoutNatoms; Siparticleswith3,4,5,6,7,8,10 and14atoms,embeddedina-SiO2matrix withoutNatoms; Siparticleswith3,4,5,6,7,8,10 and14atoms,embeddedina-SiO2matrixwith highconcentrationofNatomsaroundth eSiparticlewithbondi ngconfiguration Si2NH; Siparticleswith3,4,5,6,7,8,10 and14atoms,embeddedina-SiO2matrixwith highconcentrationofNatomsaroundth eSiparticlewithbondi ngconfiguration Si2NOH. Eachclustergroupcontained17differentstructures.Theclusterfamiliesshowdifferent average2within10-2.(Thisislargelyduetothefact,thatallspectrawerenormalizedto unitypriortotheimplementationofthestatisticalanalysis).If2isplottedvs.Sicluster size(Figure4-27),onecanseethattheagreementbetweentheoreticalpredictionand experimentimprovesforlargerSiclusters.


63 Figure4-26.CalculatedabsorptionspectraofaSiparticleinanamorphousmatrix withandwithouttheparticipationofNatoms. Atafirstglance,theobtained2valuesarenearlyindistinguishable,becausethey areallveryclosetozero.Itseemsalso,thatthereisnocriterion,basedonwhichsomeof theclusterfamiliesshouldbeexcludedasprovidingunsatisfactory2.Toresolvethis problem,westudiedthedifferencesbetween Theexperimentalabsorptionspectrumofl uminescentSispark-processedinair; Theexperimentalabsorptionspectrumofnon-luminescentSispark-processedinO atmospheres.(Adetailedanalysisofthe setwospectraisprovidedinAppendixA). Theopticalpropertiesofthetwomaterialsaresubstantiallydifferent.Their experimentalabsorptionspectraarealsoqualitativelydifferent.Toquantifythis


64 difference,weevaluatedthe2whenthesecondspectrumisfittedtothefirstone.We achieveda2valueof=0.1.Therefore,anynormalizedcalculatedspectrumfittedto theexperimentalspectrumisconsideredtobeunacceptable,ifthe2ofthefitisinthe orderof0.1(thisincludesall2valuesbetween0.05andinfinity).Ifthe2ofthefitlies below0.05,thereisnoreasontotreatthefitasunacceptable. Theplotof2vs.Siclustersizeshows,thatbestagreementbetweentheoryand experimentisachievedforSi14(Fig.4-27).Letusconsiderforamomentaclustersizeof 14Siatomsonly.Inthiscase,asubstantialdi fferenceisobservedbetweenclusterswith andwithoutNatoms.Theclusters,whereNispresent,liebelowthedividinglineof0.5. Ingeneral,forSiclustersizesbetween6and14,thecomplexesthatcontainNliewithin thelimitofacceptability.Ifthevaluesof2forSi14areextrapolatedtoinfinity(thecase ofalargeSicluster),onecanconcludethat acceptableprecisionofthepredictionis achievedinthecaseswhenNatomsarepresentinthecluster. Anotherissuethatwillbeaddre ssedhereistheprecisionofthe2estimate.The noise-to-signalratiooftheDRis10-5(AppendixA).Therefore,noappreciableerrorin the2willresultfromnoiseintheDRsignal.Theerrorofthecalculationis 0.24eV, comingfromboththeMOPACgeometryoptimizationandtheINDO/Sspectroscopic calculation.Theerrorinthe2valuesatSi14wereestimatedbythefollowingprocedure: TheDRandthecalculatedspectrumwereplottedwithrespecttoenergy; Thecalculatedspectrumwastranslatedwith 0.24eV; Theresulting2valueswerecalculated. Thedeviationinthe2valuesatSi14isestimatedtobe: (OH)-terminatedSiclusters,noN:2=0.08;2 [0.05,0.1] Si/SiO2clusters,noN:2=0.07;2 [0.07,0.1] Si/SiO2clusters,withSi2-N-O-Hbonding:2=0.03;2 [0.03,0.09] Si/SiO2clusters,withSi2-N-Hbonding:2=0.01;2 [0.01,0.04]


65 TheclustersthatdonotcontainNhaveunacceptable2values(largerthan0.05).Si/SiO2clusters,withSi2-N-O-Hbondingprovideanacceptablefit,butthe2confidenceinterval islargeandassumesvalues,beyondtheacceptabilitylimitof0.05.Si/SiO2clusterswith Si2-N-Hbondinghaveacceptable2values.Onceagain,theconclusionisthatacceptable precisionofthepredictionisachievedinthecaseswhenNatomsarepresentinthe cluster.Thistrendwillbefurtherverifiedwhenmorecalculationsareperformed.Itis expectedthattheclusters,containingNwillhave2thatconvergestozerowhenthesize oftheclustersincreasetoinfinity.Ontheopposite,clustersthatdonotcontainNatoms willhave2thatdivergesfromzerowhenthesizeoftheclustersincreases.SiliconSpark-pro cessedinPureOxygenTheexperimentalabsorptionspectrumofthismaterialisshowninFigure4-2.It showsthreeresolvedpeaksbetween200and300nm.Unlikesp-Sipreparedinair,there isnoabsorptionbandat320nminthiscase.Duetothisreason,PLcannotbeexcited withaHe-Cdlaser(325nmexcitationwavelength).A2statisticalanalysiswas performedforthesameclusterfamiliesasabovewiththeonlydifferencethat2was calculatedwithrespecttotheabsorptionspectrumofsp-Si,processedinpureO.Again, allclusterfamiliesshow2within10-2andonlythosehaving2<0.05canbepreferred asagroupthatdescribesbestthepropertie sofsp-SiprocessedinO.Thestructures, containingNwereincluded,sincesomeNatomsmaystillexistintheprocessing atmosphereorcanbeattachedafterthesamplepreparation. Sometrendswereobservedwhen2wasplottedvs.Siclustersize(Figure4-28). Again,agreementbetweentheoreticalpredictionandexperimentimprovesfor largerSiclusters.Whenthevaluesof2forSi14areextrapolatedtoinfinity,onecan concludethatacceptableprecisionofthepredictionisachievedinthecaseswhenN


66 atomsareabsent(Figures4-29to4-31).Sirings,terminatedwithOHgroups,showpoor (higher)2values. Onceagain,theprecisionofthe2estimateneedstobeaddressed.Sincethenoiseto-signalratiooftheDRis10-5(AppendixA),the2willnotbeinfluencedbythenoise intheDRsignal.Theerrorofthecalculationis 0.24eV,comingfromboththe MOPACgeometryoptimizationandtheINDO/Sspectroscopiccalculation.Onceagain, theerrorinthe2valuesatSi14wereestimatedbythefollowingprocedure: TheDRandthecalculatedspectrumwereplottedwithrespecttoenergy; Thecalculatedspectrumwastranslatedwith 0.24eV; Theresulting2valueswerecalculated. Thedeviationinthe2valuesatSi14isestimatedtobe: (OH)-terminatedSiclusters,noN:2=0.05;2 [0.03,0.05] Si/SiO2clusters,noN:2=0.03;2 [0.03,0.07] Si/SiO2clusters,withSi2-N-O-Hbonding:2=0.11;2 [0.07,0.14] Si/SiO2clusters,withSi2-N-Hbonding:2=0.13;2 [0.07,0.18] TheclustersthatcontainNatomshaveunacceptable2values(largerthan0.05).(OH)terminatedSiclustersprovideanacceptablefit,whilethe2confidenceintervalassumes thevalueof0.05,beingtheonlyoneunacceptablevalue.Si/SiO2clusterswithoutNhave2thatoccupiesbothacceptableandunacceptablevalues. Inconclusiononecansaythatbetterprecisionofthepredictioncanbeachievedin thecaseswhenNatomsareabsent.Again,thistrendcanbefurtherverifiedwhenmore calculationsareperformed.Itisexpectedthattheclusters,containingNwillhave2that divergesfromzerowhenthesizeoftheclustersincreasetoinfinity.Ontheopposite, clustersthatdonotcontainNatomswillhave2thatconvergestozerowhenthesizeof theclustersincreases.


67 Figure4-27.Siliconspark-processedinair.Statisticalanalysisforfivedifferentcluster families.Si6ClustersinSpark-processedSiliconTheplotof2vs.Siclustersize(Figure4-27)givesfurtherinsightsaboutthe differencebetweensp-SiprocessedinairandpureOatthemolecularlevel: WhenthenumberofSiatomsisextrapolatedtoinfinity,theagreementisexpected toimprovedependingonthepresenceorabsenceofNatoms; 2exhibitsminimaovercertainSiclustersizes.Thiscanbeinterpretedtomeanthat theprobabilityoftheexistenceofsuchclustersishigher. ThecasesofairandpureOaredistinctlydifferentwithrespecttothesetwofeatures.For sp-Si,processedinair,Si6isafavoredstructureirrespectiveofbondingsituation.Thisis nolongertrueforsp-Si,processedinO.SimilaristhecaseofSi8.Thisstructureisagain, favoredinsp-Siprocessedinair.Suchconclu sionisnottrueforsp-Si,processedinO.


68 OneoftheSi6geometriesisacagestructure[7479].Itcouldbeinferredthat othercagestructuresmightbepreferentiallycreatedintheairatmosphereduringspark processing.Asseenabove,processinginpureOseemstonolongerfavortheSi6clusters. Ithastobenotedalsothatfurtherandexte nsivecomputationalresultsareneededto obtainamuchlargervarietyofSiclustersizes.Aftersuchastudyisaccomplished,a possibletrendintheminimaof2maybemoreclearlyvisible. Figure4-28.Siliconspark-processedinpureO.Statisticalanalysisforfivedifferent clusterfamilies.


69 Figure4-29.Sispark-processedinpureOatmo spheres.Thegraphdisplaysacomparison betweenthemeasuredspectrumandthecalculatedspectrumofthecluster, shownininset.DarkatomsrepresentO,smallatomsrepresentH.


70 Figure4-30.Sispark-processedinpureOatmo spheres.Thegraphdisplaysacomparison betweenthemeasuredspectrumandthecalculatedspectrumofthecluster, shownininset.DarkatomsrepresentO,smallatomsrepresentH.


71 Figure4-31.Sispark-processedinpur eOatmospheres.Thegraphdisplaysa comparisonbetweenthemeasuredspec trumandthecalculatedspectrumof thecluster,shownininset.DarkatomsrepresentO,smallatomsrepresent H.


72 CHAPTER5 SUMMARYOFRESULTS Theresultsofthepresentworkcanbesummarizedasfollows: ThecalculatedabsorptionspectraofSiparticlesina-SiOxNymatrixreproduce remarkablywelltheexperimentalabsorptionspectrumofsp-Si.Further,the similaritiesbetweenthePLEandtheabsorptionspectraoflight-emittingsp-Si,as wellasthepico-secondPLlifetimes,areinterpretedtosuggestthatboththe absorptionandemissionoflightinsp-Siinvolvethesamecenters.Thecalculated absorptionspectrastronglysuggestt hatSiparticlesembeddedintheamorphous insulatingmatrixofsp-Siplayakeyroleintheprocessoflightabsorptionand emissioninthismaterial. Sispark-processedinair:2statisticalanalysiswithalargenumberofSi-based clustersshowsthatagreementbetweentheoreticalpredictionandexperiment improvesforlargerSiclusters.Ifthevaluesof2forthelargestSiclusterinthis studyareextrapolatedtoinfinity,onecanconcludethatacceptableprecision(2< 0.05)ofthepredictionisachievedinthecaseswhenNatomsarepresent. Sispark-processedinpureOatmospheres:Again,2statisticalanalysiswithalarge numberofSi-basedclustersshowsthatagr eementbetweentheoreticalprediction andexperimentimprovesforlargerSiclusters.Ifthevaluesof2forthelargestSi clusterinthisstudyareextrapolatedtoinfinity,onecanconcludethatacceptable precisionoftheprediction(2<0.05)isachievedinthecaseswhenNatomsare absent. TheroleofNintheopticalpropertiesofsp-Si:Thecomputermodelsoftheoptical propertiesofsp-Sishowbestagreementbetweentheoryandexperimentfor molecularclusterswithparticipationofNatoms.TheNatomspileupatthe dielectric/SiinterfacewithbondingconfigurationsSi2NO. Si6clustersinsp-Si:theplotof2vs.Siclustersize(Sispark-processedinair) consistentlyexhibitsminimaatSi6,irrespectiveofbondingc onfigurations.Similar behaviorisobservedinthecaseofSi8.Itcanbeconcluded,therefore,thatSi clusterswithsizes6and8arepreferentiallycreatedduringsp-Sigrowth.The distinctiveminimaintheplotof2arenolongerobservedforSispark-processedin O.Ithastobenoted,though,thatfurtherextensivecomputationalresultsare neededforamuchlargervarietyofSiclustersizes.Aftersuchastudyis accomplished,thetrendintheminimaof2maybemoreclearlyvisible.


73 AmorphousSiO2wasmodeledwith2-,3-,4-,5-and6-membersilicarings.In general,silicaclustersdonotexhibitabsorptionbandsbelow6.2eV(200nm). UponsubstitutionofOatomswithNinthestructure,electronicexcitationswith lowerenergiesarepossible.Suchsubstitutionsinthesmall2-membersilicaring withdoubleSi=Obondresultinabsorptionpeakat5.05eV(245nm).This propertycanberetainedwithattachme ntofthesmallringtoalargerone.The electronictransitionamplitudeat245nmislocatedovertheNatomsinthe2membersilicaring. AmorphousSiwasmodeledwith3-,4-,5-,6-memberringsandwithsmallSi clustershavingbetween2and14Siato ms,terminatedwithOHgroups.Allspectra ofSiringsexhibitthreecharacteristicpeaks,positionedbetween200nmand350 nm.Onaverage,thepeaklocatedintheneighborhoodof200nmhasthehighest intensity,whiletheothertwopeaksat260nmand320nmhavecomparable magnitudeandusuallyoverlap.Inmanyspectra,alow-intensitypeakappearsin theintervalbetween400nmand500nm. ThesubstitutionofanOatombyanNatominaSiringclusterdoesnot substantiallyinfluenceitsopticalproperties.However,ithasacertaininfluenceonits structure.Theaverageatomizationenergyofsuchclustersdecreasesasthenumber ofthesubstituteNatomsincrease.Theatomizationenergyincreaseswhenasilica ringisattachedtotheSiringcluster.Thedegreeofimportanceofthevariationsof hasnotbeenstudied. OH-terminatedSi2Si14havepropertiesverysimilart othoseofOH-terminatedSi rings.Thespectraalwaysexhibitatriple -peakfeatureatoraround205nm,250nmand 320nm.Thevariationofthepeakpositionsiswithin 5nmforthefirstpeak,within 20 nmforthemiddlepeakandwithin 30nmforthepeakat320nm.Almostwithout exception,aweakerpeakbetween400nmand500nmisalsoobserved.InthestudiedSibasedmolecules,theattachmentof(OH)groupsleadstostructuralstabilization,whichis mostpronouncedintheabsenceof(NH2)groups.Thedegreeofimportanceofthe variationsofhasnotbeenstudied.ThepresenceorabsenceofNatomsdoesnot influencesubstantiallytheopti calpropertiesofthisclustergroup.


74 Thepropertiesofsp-Sistronglydepend onthechemicalcontentoftheprocessing atmosphere.WhenNispresentinthegas, certainSigeometriesarecreatedand embeddedinanamorphoussolidphasemate rial.TheNatomspileuparoundtheSi particlesandexertinfluenceontheirstructu ralandopticalpropertie s.Spark-processing ofSiinairisatechniquethatcreatesstable,light-emittingSiparticlesembeddedinan amorphousSiOxNymatrix. Thecalculatedspectraofsilicaring-,Siring-,Sicage-shapedclustersandtheir combinationscanbecomparedwiththemeasuredspectraofSi-orsilica-basedlightemittingmaterials.Theresultsofthepresentworkcanbeusedtoprovidefurtherinsights abouttheroleofSiparticlesintheop ticalpropertiesofsuchmaterials.


75 CHAPTER6 FUTUREWORK Thegraph 2vs.Siclustersize(Figure4-26,Section4)hasadefinedminimumat Si6inthecaseofSispark-processedinair.FurthercalculationswithclustersSi15Si60arenecessary,sincetheycanrevealsimila rminima,positionedoverthemagicnumbers Si20,Si33,Si45andSi60.Also,thegeneraltrendof() n when Sin02(6-1) willbefurtherverified. Theopticalpropertiesofthesp-Simaterialdependonthegeometryofthelightemittingclustersinitsbulk.Furtherworkonthestructuralpropertiescanrevealwhether thisdependenceisvalidonhigh erdimensionalscales.Partofthisstudyhasalreadybeen accomplishedwiththestereologicalstudyoftheporosityanddensityofsp-Si(Appendix B).Itiscurrentlybeingcontinuedwithfractal analysisofsp-Siandotherspark-processed materials.Theaccomplishedstereologic alanalysis(AppendixB)mayprovehelpfulin thecalculationofthefractaldimensionofspark-processedsurfaces.Sofar,ithasbeen visuallyestablishedthatsuchsurfacesexhibi tfractalbehaviorinthecaseofsp-Si,since theyshowrepetitivestructuralfeaturesatvariousscales(Figure6-1). Ithasbeenshownbyexperiment[6],thatNatomsplayanimportantroleinthe opticalpropertiesofvariousspark-processedmaterials.Furthercalculationscanprovide modelsforthelight-emittingcentersinthesesubstancesandgivecluesaboutthe importanceofNintheprocessoflightemission.


76 Figure6-1.Thefractalnatureofthesp-Sisurface.


77 APPENDIXA SHORTINTRODUCTIONINTODIFFERENTIALREFLECTOMETRY Differentialreflectometryisananalyticaltechnique,whichusesUV/visible/IR monochromaticlightforthemeasurementoftheopticalabsorptionspectraofmetalsand semiconductors.Theincomingbeamscanst hesurfaceoftwoadjacentsampleswith reflectivities R1and R2(50100monolayers)andhavingasmalldifferencein compositionX.AschematicrepresentationoftheexperimentalsetupisshownonFigure 7-1.Theoutputsignalfromadifferentialr eflectometeriscalledadifferential reflectogram(DR)andhastheform[92] + = n ,2 / 1 2 2 T TF dX d dX d A R R ,(7-1) where[] 2 1 1 sin ) ( ) ( cos ) ( sin ) (2 1 2R R R s Arc s s s s F + = + = = .isusedtodenotethelifeti mebroadeningfrequency,Tistheelectronictransition frequency,A,sandareparametersandXdenotesthechemicalcompositionofthe studiedmaterial.DetailedtreatmentontheDRexperimentalprocedureanddescriptionof theDRline-shapeanalysishasbeenpublished[93 95].Thesignal-to-noiseratioofthe DRis10-5.ThelineshapeoftheDRspectrumisdeterminedbythefunction F .


78 FigureA-1.Aschematicrepresentationofadifferentialreflectometersinstrumentation setup.


79 FigureA-2. F(s,) forselectedvaluesof[94].


80 Dependingonthevaluesoftheparameter,thedifferentpeaksintheDRspectrum willhaveshapes,asshownonFigure7-2. Sinceinthecrystallinematerialtheelec tronictransitionsoccurbetweenwelldefinedenergybands,theDRspectruminthiscasecanbethoroughlyanalyzed,byfitting alimitednumberof F functionstoit.Eachofthefunctionsisanalyzed,thevalueofis determinedandfinally,theprecisetransitionenergyiscalculated. Inthecaseofamorphousmaterials,avari etyofelectronictransitionstakeplace. Onlyinoneofthecalculatedspectrainthiswork,tensofelectronictransitionsare observed.TheexperimentalDRofsp-Siisaresultofalltheexcitationsfromthevariety ofclustersinthematerialandwillthereforecontainaverylargenumberoftransitions.In suchsituations,apreciseline-shapean alysisoftheDRspectrumisimpossible. Therefore,theanalysisoftheDRcharacteristicofsp-Si(Figure7-3)willbebased oncertainassumptions.First,theDRbands positionedbetween200and450nmwillbe consideredtohaveaparameter=90o.Therefore,theelectronictransitionenergies withinthesebandsdonotneedtobecorrected.Thebandsbetween450and800nm obviouslyhavecomponentswith90o.Theywerenotcorrected,butitwasrather assumedthatenergybandsdoexistinthisregioninthevicinityoftheobservedpeaks (thecorrectionfactorsareusuallyaround10-2eV). TheDRsignalcanbeexpressedintermsoftherealandimaginarycomponentsof thedielectricconstant[92]: n dX d R Rkf,(7-2)


81 FigureA-3.DifferentialReflectogramofSispark-processedinair. wherekiseitherRe()orIm().Therefore,theDRspectruminfactrepresentsthe absorptionspectrumofthestudiedmaterialsinceisproportionaltotheabsorption coefficient. Inthepresentwork,theDRspectrumofsp-Siwascomparedtocalculated absorptionspectraofvariousSi-basedclusters.Thecomparisonwasdonevisuallyanda goodfitwasconsideredtobeone,whichr eproducedcloselytheDRenvelope.The2analysis,describedinSection4wasperformedalwaysbetween200and450nm,since therestoftheDRspectrumwasnotcorrected.Thepeaksbetween450and800nmdonot shownegativeabsorption,butcorrespondtoDRabsorptionpeakswith90o,see Figure7-2.


82 TheDRspectrumofSispark-processedinpureOisplottedinFigure7-4.As shownabove,itrepresentstheabsorptionspectrumofthematerial.Again,similarlyto theabovecase,thisspectrumwasanalyzedbasedontheassumptionthattheenergy bandsbetween200and450nmhave 90o,whilethebandsbetween450and800nm havecomponentswith90o.Thelatterwerenotcorrected,butitwasassumedthat energybandsdoexistinthisregioninthevicinityoftheobservedpeaks.The2analysis tothisspectrum(Section4)wasperformedalwaysbetween200and450nm,where 90o. FigureA-4.DifferentialReflectogramofSispark-processedinpureOatmospheres.


83 APPENDIXB POROSITYANDDENSITYOFSPARK-PROCESSEDSILICON[96]AbstractSpark-processedSi(sp-Si)isaporoussolid-statematerial.Duetothenatureofits structureandmorphology,thetraditionalm ethodsforporositymeasurementsarenot applicable.UsingtheMeasureTheoryandtheexpectedvaluetheoremsofstereology,we havecalculatedtheporosityofsp-Sitobe43% .StereologicalanalysiswasappliedtospSispecimen,preparedwithinafixedsetofgrowthparameters.Over60cross-sectional scanningelectronmicrographsofthespecimenwereutilizedinthiswork.Thesp-Si samplehasacharacteristiccylindricalsymmetryduetotheuniformsurfaceresistanceof theSisubstrateandtotherandomnatureofsparkprocessing.Howeversp-Siisnot isotropic,uniformandrandom(IUR),butrath erexhibitsradialandaxialanisotropyof porosity.Toavoidbiasinthecalculation,we choserandomareasofthecross-sectional surfaceofsp-Siandcalculatedtheirporosities.Thecalculatedvaluesenteredintoa weightedstatisticaldistribution,inwhichthestatisticalweightsweredeterminedfromthe symmetrypropertiesofthesamp le.Thestatisticalapproachandthefactthatvolumeisan additivequantity,allowedustousea2-dimensionalpopulationofpointsinthe calculationofthe3-dimensionalporevolume fractionandtosatisfytherequirementfor IURsample.Small-spotX-rayphotoelectrons pectroscopystudiesofsp-Siwereusedin thecalculationofitsdensity.Inthecaseo finhomogeneousmaterials,thedensityisa weighted(withrespecttovolume)averageofthedensitiesofallparticipatingphases.


84 Takingintoaccountthealreadycalculatedp orosity,wehaveestimatedthedensity ofsp-Sitobe1.36g/cm3.Themaincontributiontothisvaluecomesfromamorphous SiO2,whichoccupiesmostofthevolumeofsp-Si.IntroductionThereareavarietyofSi-basedmaterials,whichofferavarietyofphysical propertiesrangingfrominsulatingtohighlyc onductive.Asubclassofthesematerialshas light-emittingpropertiesandhasbeenanobjectofincreasinginterestinthepastdecade. However,thephysicalnatureofthelightemittingSi-basedmaterialshaspresentedsome challengesintheattemptstostudytheirlocalatomicstructureandotherphysical propertiescloselyrelatedto it.Thereasonforthatistheinhomogeneousstructureofsuch materials.Light-emittingSiachievedbylaserablation[97],porousSi[98]andavariety ofporoussilica[99104]havelight-emittin gpropertiesandareinhomogeneousinmost cases.Thebulkofthesematerialsusuallycontainsmixturesofphases-crystalline, amorphous,surfaceoxidelayersandthefrequentlypresentvoids(pores). Technologicalapplicationoftheabovema terialsrequiresdepositionofmetal contactsorotherthinfilmsontheirsurface.Insuchprocedures,surfaceandvolume porosityoftheunderlyingmaterialisquiteimportant,sinceitcanallowordisallow smoothandcontinuoussurfacecoverage.T hus,structuralcharacterizationand understandingofmorphologyarevitalifoneis todevelopasuccessfulcontactdeposition process. Thepresentworkrepresentsastudyoflight-emitting,spark-processedSi(sp-Si, Figure8-1)anditstopologicalandstructuralproperties.Sp-Sihasstable photoluminescence(PL)[1],whichishighlyr esistantagainstaging,UVirradiationand thermalannealingupto11000C[3].Inaddition,sp-Sibasedelectroluminescentdevices


85 havesuccessfullybeenbuilt[105107]andarecurrentlyundergoingaprocessof optimization.Electroluminescentsp-Sidevicesareusuallypreparedinair,utilizingshort sparkprocessingtimes(1020seconds).Thematerialusedinthepresentworkwas preparedunderidenticalconditions. Thebulkofsp-Siishighlyinhomogeneousandporous.Itsmorphologyand structurehavenotbeenstudiedsofar.Unders tandingofthesepropertieshasvaluefroma physicalpointofview;itcanbealsousedtopr ovidefurtherinsightsforimprovedmetal contactdepositiontechniques.MethodThestudyofsp-Siporositypresentsaseriouschallenge.Thetraditionalmethods forporositymeasurementscannotbeappliedduetothenatureofsp-Sigrowthand morphology.Surfaceatomadsorptiontechni quesarenotapplicable,sincesp-Sicontains alargeportionofinternallyembedded,closedpores(Figure8-2).Thetechniquesthat involveporefillingareexcludedforthesamer eason.Inaddition,thebulkcontainspores withdimensionsintheorderofnanometers.Fillingofsuchporeswithliquidmaynotbe completeandwouldintroduceanunpredictabl eerrorinthemeasurement.Calculationof theporositythroughmassmeasurementsis possible,howeverthismethodrequiresalso precisevolumemeasurements.Therewereanum berofattemptstoutilizethistechnique, buttheseeffortsdidnotyieldusefulresults .Themainobstaclewastheporoussurfaceof sp-Si,whichcontainsfeaturesvaryingind imensionsfromthemicrometerscaletothe nanoscale.Thevolumecouldnotbemeasured withsufficientprecisionsincetheupper surfacecouldnotbemappedcorrectly(illustra tedonFigure8-3).Additionaldifficulties arisefromthefactthatthesp-SimaterialisnotsimplydepositedonaSisubstratebut


86 FigureA-1.Spark-processingofSi.Plasmad ischargesaredirectedfromatungstentipto aSisubstrate.Yisanaxisofsymmetry,whileistheplaneofcrosssectionalcutinFigure8-2.


87 O Y X FigureA-2.Cross-sectionalSEMmicrographofsp-Siatamagnificationofx120.Yis theaxisofsymmetry,Xisaradialaxis. FigureA-3.SEMmaofthesp-Sisurface.


88 extendsintoit,therebyoccupyingacertainvolumeinthesubstrate,whichisnoteasyto estimate.Inotherwords,theunderlyingsurfacebetweenthesp-SiandtheSisubstrate cannotbemappedcorrectlyeither. Solutiontotheseproblemswasachievedbytheapplicationofstereological measurements.The expectedvaluetheorems ofstereologyallowthecalculationof volumefractionofphases,surfaceareaperuni tvolume,averagefeaturesizeandfeature perimeter,tonameafew.Detaileddescriptionofthevariousstereologicaltechniquescan befoundintheliterature[108]. IntheMeasureTheory,thevolume Vofasetofpoints(in3-dimensional space)isdefinedasameasureoftheset.Themeasureofcanalsobeexpressedasa function f, whichassociatesanumber Vwiththeset:) ( =f V(8-1) UsingthePeano-JordanMeasurein3-dimensionalspace,wecanstatethatthevolume Vofthesetisproportionaltothenumberofpointsin,andthefunctional dependence f (equation8-1)hasanintegralform: = dxdydz dp V,(8-2) where dp isthedensityofpointsin3-dimensionalspace, dp=dxdydz .TheMeasure Theorywillthenallowthecalculationofther atiooftwovolumesof3-dimensionalsets1and2asaratiooftheircorrespondingmeasures: ) ( ) (2 1 2 1 = f f V V.(8-3)


89 Appliedtothecaseofsp-Si,thisratiowillbe = = = ) ( ) ( ) ( ) ( sample entire f voids f sample entire V voids V Pporosity p p sample entire voids sample entire voidsV dxdydz dxdydz dp dp = = = ,(8-4) where Vpisthevolumefractionofporosity.Th eaboveequationcanbeapplieddirectly forcalculationofporosityofsp-Sianditsformwillbe: p porosity pV sample entire the in s po of set the of measure phase porous the in s po of set the of measure P = = int int(8-5) where Ppistheso-calledpointfraction.Thisequationallowsustostudytheproperties ofapopulationofpointsin2-dimensionalspaceandapplytheresulttothe3-dimensional structureofthesample. Itisveryimportanttonote,thattheexpr ession(8-5)isvalidonlyforsamples, whichareIUR, i.e. isotropic,uniformandrandom.The applicationof(8-5)toasample, whichisnotIURwillleadtoabiasedresult. Sp-Sipresentsachallenge,sincethe sp-SisampleisnotIUR,butexhibits anisotropyofporosityalongtheX(radialanisotropy)andYaxes(axialanisotropy, Figure8-2).Toavoidbias,weneedtocalculateanaverageporosityofthesample,which removestheanisotropyeffect.Therefore,wehaveproceededasfollows: Asampleofsp-Siwascutinacross-sectionalmanner(Figure8-1); Thesamplewasembeddedinaresinandfine-polishedwithdiamondpowderto produceasmoothcross-sectionalsurface; Theimageofthecross-sectionalsurfacewascapturedusingscanningelectron microscope(SEM)atamagnificationofx120(Figure8-2);


90 Alinegridwasplacedovertheimage.Thespark-processedarea(definedbythe surfaceandtheinterfacelinesinFigure8-2)wasdividedinto154numberedtiles. Eachtileisasquarehavingasideof44.4m; Thesetof154tileswassubdividedinto32groupsofconsecutivetiles.Eachgroup contains4or5tiles; Fromeachgroup,weselectedrandomlyonetileasfollows: otilenumber4; otilenumber(4+5); otilenumber(9+4); otilenumber(13+5),andsoon. Thisprocessofrandomselectionprovi deduswith32tileswithnumbers4,9,13, 18,23,andsoon; SEMmicrographsatmagnificationsx650weretakenforeachofthe32random tiles.Atthismagnification, nanoporescouldnotbestudied; Lineargridswereplacedovertheimagesofeachtileandtheporositywas calculatedfromequation(8-5).Thenumer atoristhenumberofgridintersections overvoids(markedwithbrightcircles,Fig ure8-4),whilethedenominatorin(8-5) isthetotalnumberofgridintersections. Sincesp-Sialsocontainsporeswithnano meter-scaledimensions,theyhavetobe takenintoconsiderationwhenporosityiscal culated.Sinceamagnificationofx650is insufficientforcountingofnanopores,wep reparedasecondsetofSEMmicrographsof theabove32tiles,capturedatamagnificationofx3000andappliedequation(8-5)to calculatethenanoporosity(Figure8-5).The magnificationsofx3000showedsufficient detailandwerenotimprovedwithincreaseo fmagnification.Toavoidduplicatepore counting,allhigh-resolutionmicrographs werecapturedfromrandomareas(withinthe giventile)thatdonotcontainmacropores. Thus,thetotalporosity Pi totalmeasuredonatile i ,isdeterminedtobenano i micro i total iP P P + =.(8-6)


91 Onealsoneedstotakeintoaccountthefact ,thatthesp-Sisamplehascylindrical symmetry(Figure8-1)withanaxisofsymmetryY.Thecylindricalsymmetryis contingentuponthecharacteristicsofspar kprocessing.Normally,theSisubstrateis uniformlydopedandthereforeitsresistivit yisthesamethroughoutitsbulk.Onceaspark eventoccursatagivenpointofthesubstrates urface,theresistivityofthisparticular localityincreases,sincesparkprocessingcreatesclustersofhighlyresistivesurface compounds[3].Thenextsparkeventwillmos tprobablyoccuratanothersurfacepoint withlowerresistivity.Eachsparkoccursatasurfacespotsuch,thattheresistance betweenthesparkingtipandthespotisminimal.Thisfactguaranteesthecircularsurface pattern,observedaftersparkprocessingofSi(Figure8-1). SinceeachtileispositionedatsomedistancefromtheYaxis(Figure8-2),it representsavolumenViR R h Vi in = n2,(8-7) where RiisthedistancebetweentheYaxisandthegeometricalcenterofthetile i and h=R isthetileside.Then,toeachtileweassociateastatisticalweight wi =n n =32 32 1 tiles all k k i iV V w.(8-8)


92 (A) (B) (C)FigureA-4.Selectedtileimagesofthesp-Sisampleatamagnificationofx650.Theright columndisplaysrectangulargridspositionedovertheimagesofthematerial. Thebrightcircularmarksdenotethatthegridintersectionresidesovera void.A)Near-surfaceimage;B)Imageofthesp-Sibulk;C)Nearthe interfacesp-Si/Si.

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93 (a) (b) (c)FigureA-5.Selectedtileimagesofthesp-Sisampleatamagnificationofx3000. Therightcolumndisplaysrectangulargridspositionedovertheimages ofthematerial.Thebrightcircularmarksdenotethatthegridintersection residesoveravoid.A)Near-surface image;B)Imageofthesp-Sibulk;C) Neartheinterfacesp-Si/Si.

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94 Thetotalporosityofthesp-Sisamplewillbe= + =32 32 1) (tiles all i i nano i micro i Si spw P P P,(8-9) whichtakesintoaccountthefactthatthevolumeisanadditivequantity.ResultsandDiscussionThepointcountmeasurementcontainsacertainerror.Itisduemainlyto microscopyedgeeffectsneartheporebounda ries,whichappearbright(Figure8-4).In allcaseswhenagridintersectionwaspos itionedoverabrightpore-edgearea,we proceededasfollows: Thecorrespondingmarkwascountedintotheporosityiftheintersectionwas positionedwithintheinner(towardsthepore)lyinghalfofthebrightarea; Thecorrespondingmarkwascountedintotheporosityandalsocountedaserrorif theintersectionwaspositionedwithi ntheouterlyinghalfofthebrightarea. Thus,thecalculatedtotalporosityisanupperlimittothetrueporosity,andthe errorcorrespondstoanintervalofpossiblelowervalues.Thelineargridsusedinthe stereologicalmeasurementsconsistoflineswithfinitethickness.Thepointsof intersectionoftwolineswerethereforeconsideredtobelocatedonthepixelattheupper rightcorneroftheintersection. Theedgeeffectsandtheerrorassociatedwiththemwerelargelyabsentinthe high-resolutionimagesfornano-porositycal culation.Still,someerrorwasgeneratedin thesecasesduetothefact,thatcertainlocalizedareaswerenotflat.Themarkswithin themwerecountedintotheerrorofthemeasurementandintothenano-porosityaswell. Asaresult,theerrorofthenano-porositycountislargercomparedtoitscounterpartin themacro-porositymeasurement.

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95 Applyingtheequation(8-9),wecalcula tedthemicro-porosityofsp-Sitobe 26.0%withanaccuracyof2.0%.Thenano-porosityis16.9%withanaccuracyof4.0%. Therefore,thetotalporosityofsp-Siiscalculatedtobe42.9%withanaccuracyof6.0%. Thisshouldbeinterpretedtomeanthattr ueporositylieswithinanintervalwith numericallengthof6%,definedbytheupperlimitof42.9%andthelowerlimitof 36.9%:% 9 42 % 9 36 Si spP.(8-10) Figure8-6depictstheradialdistributionofporosity.Thetermradialrefersto thecylindricalsymmetryofthesp-Sisample,whereYistheaxisofthecylinder,andone ofitsradiiliesalongtheXaxis(Figures8-1and8-2).Theporosityislowestatthe sampleedgesandexhibitspeakssymmetricallypositionedwithrespecttotheYaxis.It canalsobenoticedthattheporositycanoccupyvalueshigherthan80%incertainsmall localities.AnotherdistributionisshownonFigure8-7.Thisistheradialporosity distributionofasurfacelayerwiththicknessofapproximately100m. P occupieshigh valuesevenattheedgesandispeakedinthemiddleofthesample.Undersuch circumstances,metalcontactdepositiononthesp-Sisurfacewillcreateabettercoverage intheperipheryofthesampleandwill belargelydiscontinuedinitscenter. Figure8-8displaysadepthprofileofporosity,achievedbyaveragingover horizontalslabswiththicknessofaround50m.Figure8-9depictsaporositydepth profile,whichhasbeenachievedbyaveragingoverlayerswiththesamethicknessas above.Inthiscase,allpointsofthelayersar eequallydistantfromthesurface.Bothpro-

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96 Figure8-6.Radialdistributionofporosityinsp-Si.Thelinesareaguidetotheeye.

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97 Figure8-7.Radialdistributionofporosityinalayerwiththicknessof100matthesurfaceofsp-Si.Thelinesareaguidetotheeye. filesshownon-lineardecreaseofporosity,havinglowestvalueofaroundafewpercent nearthesp-Si/Siinterface.DensityofSpark-processedSiTheestimateofthedensityofsp-Siisbasedonasmall-spotX-rayelectron spectroscopy(XPS)depthprofileofthemat erial,publishedbyLudwig[3](Figure1-2). Sincesp-Siisinhomogeneous,itsaveragedensitywillbe = = k Si sp k k Si sp Si sp Si sp phase solidV V V m ,(8-11)

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98 wherethesumistakenoverallvolumesofthevariousphasesinsp-Si.Thefactorinthe bracketsrepresentsthestatisticalweightofthedensitykofthecorrespondingphase k .It shouldbenotedthat(8-11)iscalculateden tirelybasedoninformationfromtheXPS measurementandassuchitrepresentsthedensityofthesolidphaseonly.Then,thetrue densityofsp-Siwillbe()Si sp phase solid Si sp Si spP = 1 ,(8-12) where Psp-Siistheporosityofthematerial,calculatedinequation(8-9). Toestimate(8-12),certainapproximat ionsareadopted.Basedonpreviously publisheddataforplasma-grownSioxynitri dematerialswithsimilardepthprofilesof SiO2,SiandSi3N4[44,82,83,91,109-113],weassumetheconnectinglinesintheXPS diagramofsp-Si(Figure1-2)torepresentdatapoints. Indetail,thisassumptionisbasedonthefollowing: Intheabovereferences,thedepthprofileofNistypicallypeakedneartheoxide/Si interfaceforallas-grownsamples,whichhavenotbeensubjectedtoadditional treatment;

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99 Figure8-8.Depthprofileofporosityinsp-Si .Theaveragingwithdepthhasbeenperformedoverhorizontalslabs,asshownininset. Figure8-9.Depthprofileofporosityinsp-Si.Theaveragingwithdepthhasbeenperformedoverlayers,equidistantfromsp-Sisurface(inset).

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100 ThequotedreferencesshowtheconcentrationofSiO2todecreaseinanon-linear fashion,similarlytotheprofileshowni nFigure1-2,andtheconcentrationofSi increasesinasimilarpattern. Unlesstheplasma-grownSioxynitridefilmshavebeensubjectedtoasecondary treatment(annealinginN,implantation,sec ondaryplasmatreatments),thedepthprofiles ofSiO2,NandSiexhibitbehaviorsimilartot heapproximationshownonFigure1-2. ThisapproximationallowsustogeneratedatapointsfortheconcentrationofSiO2, crystallineSi(c-Si),amorphousSi(a-Si)andSixNyfor250horizontalslabsofsp-Si havingthicknessof1meach(asinFigure8-8,inset).Asasecondapproximation,we assumeforSixNyx=3,y=4.ThisallowsustousethedensityofSi3N4inthecalculation. Thedensitiesoftheparticipatingchemicalcompoundsare:(a-SiO2)=2.4g/cm3[114],(c-Si)=2.3g/cm3[115],(a-Si)=2.2g/cm3[116,117]and(a-Si3N4)=3.0 g/cm3[118].Usingthesedensitiesandequation(8-11),wedeterminetheaveragesolid phasedensityofsp-Siineachofthe250slabs.TheresultsarepresentedinFigure8-10. Thepointsofdiscontinuityareduetoth efirstapproximationinthecalculation.decreasesfromthevalueof2.4g/cm3,correspondingtothedensityofSiO2,tothevalue of2.3g/cm3,correspondingtothedensityofc-Si. Theaveragedensityfortheentiresolidphaseisdeterminedbyequation(8-11), wheretheaveragingisconductedoverthe250sl abs.However,sincethesurfaceofsp-Si andtheinterfacesp-Si/Sisubstratecannot bemappedcorrectly,theprecisevolumeof eachslabcannotbeestimated.Inordertoavoi dthisobstacle,weassumedallslabsto haveequalvolumes.Mathematically,thismea nsthattheirdensitiesenterthesum(8-11)

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101 Figure8-10.Depthprofileofsp-Sidensity.T heaveragingwithdepthhasbeenperformed over250horizontalslabs,asshownintheinsetofFigure8-7. withequalweightsandartificiallyinc reasethevolumecontributionsfromthe surfaceandinterfaceareas,whichareotherwisesmall.Therefore,thecalculatedvalueof thesp-Sidensityisanestimate,whichoverstatestheparticipatingamountsofa-SiO2and c-Si. Ourcalculationdeterminessolidphase sp-Sitobe2.38g/cm3.Sincemostofthevolume ofthematerialisoccupiedbySiO2((a-SiO2)=2.4g/cm3),thevalueof2.38g/cm3showsthatSidioxideisthemaincontributor tothedensityofsp-Si.Thetruedensityof sp-Si,aftertakingintoaccountthecontributionsfromboththesolidphaseandthevoids inthematerial,iscalculatedbyequation(8-12):

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1023/ 36 1 cm gSi sp=.(8-13)ConclusionsThetotalvolumefractionofporosityins p-Siiscalculatedtobeapproximately 43%.Thesurfaceporosityofthematerialishigh,reachingupto69%inthecentralarea ofthesample.Thisstudywasconductedfors p-Sispecimen,grownwithinafixedsetof processingparameters.Despitethatthevariationofthegrowthparametersmayinfluence themicrostructureofthematerial,ourresultshavegeneralapplicabilityanddescribea non-traditionalmethodforsuccessfulporos itymeasurements.Thedensityofsp-Siis estimatedtobe1.36g/cm3.Themaincontributiontothedensityofthismaterialcomes froma-SiO2,whichoccupiesmostofitsvolume.

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110 BIOGRAPHICALSKETCH TheauthorwasbornApril26,1969,inthecityofVelingrad,Bulgaria.Mostofhis childhoodyearswerespentinthecityofVelikoTarnovo.Hereceivedhishigh-school diplomawithamedalandhonorsfromIvaGimnaziaatthecityofVelikoTarnovo.His studiescontinuedattheFacultyofPhysicsattheUniversityofSofiainSofia,thecapital cityofBulgaria.Hegraduatedwithamasters degreeinsolid-statephysicsandmethods ofteachingphysics.Duringhisuniversityeducation,hewasawardedagovernmental scholarshipforundergraduatestudiesinph ysics.Aftergraduation,hewasacceptedina doctoralprograminthelaboratoryofProf.KrassimiraGermanovaattheFacultyof Physics.HisgraduatestudiescontinuedattheUniversityofFlorida,Gainesville,inthe DepartmentofMaterialsScienceandEngin eering.Hisworkwasmainlyconductedinthe groupofProf.RolfHummelwithextensive collaborationwiththegroupofProf.HaiPingChengattheQuantumTheoryProjectattheUniversityofFlorida.Intheyear2002, hewasawardedamastersdegreeinMaterialsScienceandEngineering. JeliazkoPolihronovhasauthoredsevera lscientificpublicationsinrefereed journals.HeisamemberoftheAmericanPhysicalSociety.Currently,hehasaccepteda postdoctoralpositionwiththeDepartmentof PhysicsandAstronomy,UniversityCollege London,UnitedKingdom.

Permanent Link: http://ufdc.ufl.edu/UFE0000590/00001

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Title: Physical nature of light-emitting centers in spark-processed silicon
Physical Description: Mixed Material
Creator: Polihronov, Jeliazko G. ( Author, Primary )
Publication Date: 2002
Copyright Date: 2002

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Permanent Link: http://ufdc.ufl.edu/UFE0000590/00001

Material Information

Title: Physical nature of light-emitting centers in spark-processed silicon
Physical Description: Mixed Material
Creator: Polihronov, Jeliazko G. ( Author, Primary )
Publication Date: 2002
Copyright Date: 2002

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
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Dedicated to my wife, Angelina Polihronova


I would like to express my special gratitude to Dr. Rolf Hummel for being my

advisor and chairman of the committee that supervised my work. I am very grateful for

his support, encouragement and guidance through the years of my graduate studies. I

would like to thank him for providing me the opportunity to study in a world-class

university, which has enriched my scientific and research experience. I highly appreciate

the knowledge I have received about the art of modern engineering and experimental

physics. I am grateful to Dr. Hai-Ping Cheng, Dr. Paul Holloway, Dr. Susan Sinnott, Dr.

Robert DeHoff and Dr. Adrian Roitberg for the helpful discussions and for serving on my

supervisory committee. Many special thanks are extended to Dr. Magnus Hedstrom for

his invaluable contributions to the present work. I appreciate highly the encouragement

he has provided and the practical advice for the parameterization and applications of the

INDO computer code.

I would like to direct thanks to Dr. Nigel Shepherd, who has been a very good

colleague and friend. Many thanks also to Thierry Dubroca, Michele Manuel, Dr.

Michael Stora, Dr. Matthias Ludwig and Dr. Fabio Fajardo for their friendship and

collaboration. I would like to thank David Burton, Kwanghoon Kim, Anthony Stewart,

Grif Wise and Shidong Yu for their help and cooperation.

My sincere gratefulness is dedicated to my spouse Angelina Polihronova and to my

daughter Virginia Polihronova for their immeasurable love, encouragement and support.


A C K N O W L E D G M E N T S ...................... .. ..................................................................... iii

ABSTRACT ............... .......................................... vi


1 INTRODUCTION .............. .....................................................1..

2 THE MOLECULAR ORBITAL THEORY ....................... ............................6

The H artree-Fock A pproxim ation................. .. ......... ........................................... 6
Computational Implementation of the Hartree-Fock Approximation ........................ 11
Further Approximations within Hartree-Fock ................... ...... ... ... ........... 12
Intermediate Neglect of Differential Overlap (INDO).................. ........... 12
Neglect of Diatomic Differential Overlap (NDDO) ....................................... 13
C onfigu ration Interaction .................................................................... .................... 14

3 COM PUTATIONAL M ETHODS.......................................... ........................... 17

B a c k g ro u n d ...................................................................................................... 1 7
Z IN D O .................................................. ....................... .............. 18
M O P A C : A M 1 and P M 3 .............................................................................................. 20

4 CALCULATIONS AND RESULTS............................. ...... .................25

K now n Facts About Spark-processed Silicon.......................................... ... ................. 25
R research Procedure.... .. .............. .. .. .................... ............. ............ 27
Optical Properties of a-SiO2 based Clusters .............. ............................ ....... ....... 29
O ptical Properties of Silicon R ings..................................................... .............. 37
O ptical Properties of Other Silicon Clusters............................................ ... ................. 44
Com pound ........ ............................................ ....... ... .. .............. 46
Optical Properties of Silicon Particles in an Amorphous SiOxNy matrix................... 49
The Role ofN in the Optical Properties of Spark-processed Silicon ....................... 51
Silicon Spark-processed in Pure O xygen................................................ ... ................. 65
Si6 Clusters in Spark-processed Silicon.................................................................... 67

5 SUM M ARY OF RESULTS ................................................ .............................. 72

6 FUTURE WORK............. ..... ....................................75




A b stra c t ......... .. ....... ............................................................................................. 8 3
Introduction................................ .......... .......... 84
M eth o d ................................ ........... ......... ................... .............. 8 5
Results and Discussion .. ................. ............................ ............ 94
Density of Spark-processed Si ............ ............ ......................... 97
C onclu sions ............... ................................... ........................... 102

LIST OF REFEREN CES ......... .. ............... ............... .................................... 103

B IO G R A PH ICA L SK ETCH ......... ...........................................................................110

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Jeliazko G. Polihronov

December 2002
Chair: RolfE. Hummel

Spark-processed silicon (sp-Si) is an amorphous, luminescent material that

exhibits emission spectra, peaked around 385, 525 and 650 nm. In order to understand the

photoluminescence (PL) behavior of sp-Si, UV/visible optical absorption spectra of a

large variety of silicon-based molecular clusters were calculated and compared with

experimentally measured absorption spectra of sp-Si. All structures in this study were

optimized with the AM1 or the PM3 method. The optical absorption spectra were

calculated using the quantum-mechanical INDO method together with configuration

interaction, which was parameterized for Si.

The experimentally measured absorption spectrum of sp-Si exhibits peaks at 245,

277, 325 and 389 nm. In an attempt to reproduce this spectrum computationally, the

present work includes a detailed study of the optical properties of silica clusters, Si rings,

Si clusters and cages, Si oxides and oxynitrides.

While the spectra of silica, Si rings and OH-terminated Si clusters resemble certain

features of the experimental absorption spectrum of sp-Si, remarkable agreement is

achieved in the case of a Si cluster, surrounded by an amorphous matrix. The agreement

improves when the size of the model Si cluster increases from Si3 to Si14. X2 statistical

analysis of the calculated spectra shows that the presence or absence of N influences the

optical properties of such complexes.

Silicon spark-processed in pure O does not photoluminesce when excited by laser

light having a wavelength of 325 nm. The absorption spectrum of this material differs

from the one obtained on Si spark-processed in air. The statistical analysis comparing

various cluster models to the two spectra shows that certain Si cluster sizes are favored in

the case of Si processed in air, while this is not true for Si processed in O.


Silicon is a material of substantial importance for the electronic industry. It has

been studied in a course of decades and is extensively used in the production of electronic

elements and integrated circuits. Si is non-toxic, it is readily available and has stable

oxides, which are easily deposited and patterned on a Si substrate. Technologically, Si is

extracted from common sand (Si02) and purified to electronic, high-purity grade material

by various crystal growth techniques.

Advanced technology has the goal to create miniaturized, high-speed electronic

devices. Utilizing Si for the fabrication of such devices would be highly beneficial due to

the advantages of this material. Due to the high speed of light, very high speeds of

communication are achieved when optical and electronic devices are integrated on the

same chip. However, crystalline Si has an indirect band gap and cannot be used for the

production of light-emitting devices.

Recent research efforts have resulted in the development of novel Si-based

materials, containing miniature Si particles with nanometer sizes. The physical properties

of systems with small dimensions are governed by the laws of quantum mechanics. The

band gap of nanometer-sized Si particles is no longer narrow and indirect, thereby

allowing emission of light. Therefore, the materials, containing Si nano-particles are of

special interest due to the optical properties of the small Si clusters embedded in them.

Research efforts have been directed towards the understanding of the physical properties

of such materials with the goal of achieving detailed knowledge of the observed physical

phenomena, as well as preparing these materials for technological use.

In 1992, Hummel and Chang [1] developed a new method for preparation of a Si-

based luminescent material. The so-called spark-processed Si (sp-Si) photoluminesces in

the visible region, having characteristic peaks [2] near 385, 525 and 650 nm, as

established by Ludwig [3] (Fig. 1-1, the peak at 650 nm is seen as a shoulder of the

dominant blue/green peak). The photoluminescent properties of the material exhibit high

stability against etching in buffered hydrofluoric acid, thermal annealing up to 1100 C

and UV irradiation. During the past few years, a number of papers describing and

characterizing various properties of sp-Si have been published. The main focus of

previous research has been on the optical properties with the goal to provide a description

of the photoluminescence (PL) mechanism. Generally, two approaches have been

applied-the first approach represents an effort to narrow down the number of possible PL

mechanisms utilizing various experimental techniques; the second approach involves

experiments to identify the luminescent centers and the physical process of emission.

The first approach has resulted in the elimination of a number of proposed

mechanisms [4]. Nevertheless, the PL phenomenon has not been identified with certainty

and detail. The second approach is inherently limited since sp-Si, being an

inhomogeneous material, is very difficult to characterize at an atomic level. The

traditional X-ray diffraction, X-ray absorption and other related methods are not able to

provide definitive data in the case of inhomogeneous, multi-phase materials since their

results are averaged over the bulk of the material. The average chemical composition of

the sp-Si has been studied at various depths with small-spot X-ray Photoelectron



600 400

01 1 t I & 1
1.5 2.0 2.5 3.0 3.5


Figure 1-1. Room-temperature PL of (a) blue- (b) green-light emitting sp-Si.

Spectro-meter (XPS, Fig. 1-2). The material predominantly consists of four Si-based

phases amorphous Si02, amorphous and crystalline Si and Si nitrides [3, 5].

Amorphous SiO2 occupies most of the volume of the material. Crystalline Si and

amorphous Si clusters predominate in the areas, close to the Si substrate.

Earlier studies have shown that the presence of N in the ambient during spark

processing is essential for the optical properties of sp-Si [3, 6]. Since the origin of the

optical properties of sp-Si is unknown, it is appropriate that all four phases are studied by

examining the optical properties of molecular clusters that represent each phase.

To achieve this goal, quantum mechanical calculations have been used in the

present work to provide the geometry and optical spectra of the studied molecules.

Compared with first-principles calculations, these methods are faster, which allows a

large number of molecular clusters to be studied and the average trend of the change of

their physical properties to be identified. The calculated spectra of oxygenated Si

molecules in the present work are not applicable to sp-Si only; the optical characteristics

of any Si- or silica-based light-emitting material can be compared to the present results.

The clusters in this work can be related to OH-terminated, Si particles on the surface of

materials, or in the bulk when Si particles are buried in amorphous silica; likewise they

can describe Si particles, nucleating in the gas phase in the presence of oxygen during

laser ablation of Si or related growth processes of Si-based materials from the gas phase.

Our results are also applicable to the investigation and characterization of nebulae and

interstellar silicate dust clouds. Similar studies have been published in the literature [7 -


S60- -j SiO2

O -o-- crystalline Si
:--- amorphous Si
o ---- Si.N


0 50 100 150 200 250
Depth (micrometers)

Figure 1-2. Small-spot XPS data for sp-Si. (Adapted from Ludwig [3], Hummel and
Ludwig [4], and Ludwig et al. [5]).


The Hartree-Fock Approximation

Our understanding of the nature of the electronic wave functions in a molecule is

based on the understanding of the electronic wave functions in an atom. The theory of the

methods used in the present work, treats such systems by considering the valence

electrons only; the core electrons and the nucleus of the atom are considered to form an

ion, which interacts with the valence electrons. Thus, in all our studies the term

"electronic wave function" will be used to describe a wave function of a valence electron.

The problem for the electronic structure of a H-similar atom is commonly treated in

the general courses of Quantum Mechanics. It provides knowledge about the appropriate

mathematical form of an electronic wave function in an atom:

01,. = B pB+' e-"a Ln+1 (P) Y.)W(O, p) (2-1)

where B and ao are constants; n, 1 and m are the quantum numbers, L is a Laguerre

polynomial and Y is a spherical function. The general result is that the radial part of the

wave function of an electron in an atom can be approximated as an exponential function:

0(r) Ce-A (2-2)

where C and A are constants. Sometimes, 0(r) is approximated as a sum of Gaussians. In

chemistry, the electronic wave functions (2-2) for the atom are called Atomic Orbitals

(AO). The Molecular Orbital (MO) Theory has the goal to explain the properties of the

electronic wave functions in a molecule. Such wave function in a molecule with n

valence electrons is accepted to be approximately equal to a linear combination of AO's

of the type (2-2):

= '- j 0 (2-3)

with coefficients C,. In chemistry, the above wave function is called a Molecular Orbital


Since the electrons are Fermions (from the Pauli principle for a system of n

undistinguishable particles), the total wave function Ny of the electronic system in the

molecule must be anti-symmetric. Then, it can be represented as a Slater determinant:

V (rl) 1 (r2) (/i)
Trr, 1 (rl ) V2 (r2) V2 ) ( 2-4
1 (,() r (r2) ... n ) (2-4)

The Schrodinger equation for the molecule becomes:

H T(r,r2,....r,) = E Y(r,r2,....r,) (2-5)

where the Hamiltonian operator H is non-relativistic and time-independent. It assumes

fixed-ions and has the following form in atomic units (h = e = m = 1) [12]:

1 1 Z 1 Z
H = Ak -ZZ +Z + (2-6)
2 A RAz Izj A
A, B, 1, 2, ... designate ions; i, j, ... designate electrons and ZK is the corresponding

atomic number.

The equation (2-5) can be solved using the variational principle. A detailed solution

has been published by C. C. J. Roothaan [13]. However, if the variational principle is

applied over the MO's, this leads to a system of intractable differential equations. This is

the reason why the MO's are approximated as linear combinations of AO's (equation

2-3). Then the variational principle is applied over the AO's and the coefficients C,.

Substituting eq. (2-6) into (2-5) and multiplying both sides of the resulting equation by W

leads to

E= JH, + (Jj -K,) (2-7)

where J and K are the two-electron Coulomb and exchange operator accordingly:

1 1
iJ, = (1)0 (2) z (1), (2), K, = 0, (51) (2) (1)(, (2) (2-8)
r12 / 12

In the expression (2-7), the ion-related terms are missing, since the variational principle is

imposed over a trial wave function y, which contains the ion coordinates Rk as


Now we introduce another matrix, the so-called overlap matrix S as

S, = (2-9)

Varying (2-7) and the condition for orthonormality of the MO's Vk

SE= ZSH, +Z( J,-SK,,) (2-10)
2 ,,j

( u, t)hj=h (C, SCi =(SCui )SC,+CzS( SC,)=0

and using the method of the Lagrangian multipliers, we get

H + ( K) C' = SC- e,)
H + (J -Kj ) Y S Cj* ci

where (-ij) are the Lagrangian multipliers, Jj, Kj are the one-electron Coulomb and

exchange operator accordingly:

J, = (1) (1), (2)j, K, = (1) (1) / (2) (2-12)

and the matrices Ci are the coefficients for the MO Vi from eq. (2-3). It can be shown,

that the equations in (2-11) are equivalent, since the participating operators are


Then, if we define the total electron interaction operator G as

G= (J, K), (2-13)

the one-electron operator H as

H = A ZB(, B ) (2-14)
z, 2 B =B

and the Fock operator as

F =H+G, (2-15)

the equations (2-11) become

FC=SCe (2-16)

in matrix notation. This system of equations is known as Roothaan equations. Here one

needs to determine the MO energies, which are in the matrix e; the matrix C also needs to

be calculated as it contains the coefficients of the MO's from eq. (2-3).

We shall then proceed as follows first, the S matrix will be diagonalized via the


s, 0 ... 0

W+SW = Sd g s2 (2-17)

0 0 ... s

where Wis the transformation matrix. Second, we define the matrix S 1/2 as

S(-1/2) =WS-/2) W+ (2-18)

in which the matrix

S 0 ... 0

Sag '" (2-19)

0 0 ... C

Now we return to the Roothaan equations (2-16) and proceed to calculating e and C:

S(-1/2)FC= S(-1/2)C
S(-1/2)FS (-1/2) S(1/2) C = S (-1/2) C (2-20)
F'C' = C'
(C') F'C'=

In the last equation, F is in diagonal form and the MO energies ei can be determined. The

coefficients matrix C is calculated as

C= S(-1/2) C' (2-21)

As a criterion for achievement of self-consistent field (SCF), we shall use the so-called

first-order Fock-Dirac density matrix P:

Pl = Ck Cjk k, (2-22)

where n = diag{ni, n2, ...nn}; nk are electron occupation numbers which are 0 or 2 in the

case of a closed-shell (zero magnetic moment) molecule. After a number of the described

above consecutive approximations, the matrix elements P, will reach convergence. Then

we can say that a self-consistent field (SCF) has been obtained and the Hartree-Fock

approximation is complete.

Computational Implementation of the Hartree-Fock Approximation

The SCF-based computer routines normally follow the following procedure [12]:

* Calculate the integrals necessary to form the Fock matrix F (equation 2-15).
* Calculate the overlap operator's matrix S (2-9).
* Perform diagonalization of S (equation 2-17).
* Calculate Sdag (-1/2) and form S (-12) (equation 2-18).
* Form the Fock matrix F as:
_Aj)jZ :( k,l
-,= 2 j ki (1) (2) (1)k (2)) -

( (1) (2) -1 (1)j(2))


* Calculate F' (equation 2-20).

* Diagonalize F' (the last equation in 2-20) and obtain the energy eigenvalues k.

* Calculate the coefficients C, (equation 2-21).

* Calculate the density matrix P (equation 2-22).

* Check P for convergence. If the desired convergence tolerance has been reached,
then stop.

* If convergence has not been reached, extrapolate a new density matrix and repeat
steps 5 10 until SCF is reached.

* Output the results it a text format.

* Plot the calculated absorption spectra

* Optional: calculate the electron transition amplitudes for all excitations

Further Approximations within Hartree-Fock

Intermediate Neglect of Differential Overlap (INDO)

The INDO approximation represents further simplification of the Hartree-Fock

method. Certain approximations are being accepted with the goal to increase calculation

efficiency. Detailed treatment of the INDO method has been published [12, 14 17].

Generally, S,j is the overlap matrix (equation 2-9). It is approximated so that

products (1l) 4(1) are retained only in one-center integrals. However, the computational

efficiency of INDO is achieved mainly due to the approximations of the total electron

interaction operator G (equation 2-13). G, is a sum of two-, three-, and four-center

integrals of the type

(1) (1) k (2) A (2) dv dv2, (2-24)

which are set to zero unless i = 1 and j = k. Those that remain are set as parameters and

their values determined from atomic spectroscopy.

H is approximated as follows:

HAA = ZA ) (, B I ) (2-25)

HAA 0,- A (2-26)
2 RA

H AB = ( + ), (2-27)

where A is the Laplacian operator, ZA is the core charge of atom A, RA is the distance

between the i-th electron and ion A. #, is referred to as a "resonance integral" and is

approximated via the parameters flAB, fl and f3.

Neglect of Diatomic Differential Overlap (NDDO)

NDDO is defined by the substitution
(r) 0, (r) d3r -- 0 (r(r) 0 (r) dr, (2-28)

where A and B denote two different atoms (sometimes referred to as centers) and 6 is the

Kronecker symbol. In this situation, the Fock matrix will have the following elements

[12]: One-atom diagonal elements

A I- 2
2 R )+V+

kjl 2

where VAA is the so-called effective ion potential, being determined from experimental

measurements. VAA prevents the valence electrons of atom A from penetration into its

inner orbitals. One-atom off-diagonal elements

pyp I B BB. 01B/_
BA k,l k,l 2
A (2-30)

-ZZB 0\ B 1" B

Two-atom off-diagonal elements

F = H AB -Z P 'B (2-31)
ki 2
k 1 2

where Hy is given by equation (2-14). It is also important to note that NDDO includes

orbital anisotropies.

Configuration Interaction

The Hartree-Fock approximation enables us to solve the Schrodinger equation for a

molecule and provides us with the molecular wave function V(ri, r, ... r) (equation 2-5)

of the ground state and its energy so. This energy is an upper bound to the true ground

state energy Eo. The difference between these two values is called correlation energy


1co, = =Eo -c. (2-32)

The correlation energy accounts for interactions between valence electrons in the

molecule and amounts up to 1% of Eo. Despite that the percentage is small, it is

equivalent to a few eV. Therefore, the Hartree-Fock approximation can be further

improved. The improvement will provide the value of rcorr (or at least part of it) as well

as improved ground-state wave function of the molecule D. In addition, it will allow us

to calculate the energies and wave functions of the excited states and thus enable us to

predict the optical absorption spectrum of the molecule.

The correction of the Hartree-Fock approximation can be achieved via the so-called

configuration interaction (CI), also known as configuration mixing. It has been shown in

perturbation theory [18] that the molecular wave function contains contributions from

various electronic configurations. We shall express this dependence as a linear

combination [19]
(=T + Cr Y" +f C'" Y + I Ctt Yt + Cahbcd stu .. (2-33)
a a ab ab abc T abc rstu ab)
a,r a r
where V is the Hartree-Fock wave function of the ground state, D is the improved

ground state function, Car are coefficients and V,' are called "excited determinants". The

excited determinants are built from the function Y, as its a-th and the r-th row have

exchanged places (which is, electron from a-th MO has been excited into the r-th virtual

MO). Each of these Slater determinants represents a different configuration. The first sum

in equation (2-33) represents single excitations; the second, double excitations; the third,

triple excitations, and so on. Usually, the above equation is truncated and only single

excitations are calculated:

D= u + Car T, (2-34)
a, r

known as CI-S (CI-singles). For a Si-based molecule with 10 15 atoms, the number of

the excited determinants in the above sum (also known as CI size) is set to be around 65,

in order to provide good approximation. If the CI size is increased above this number, the

calculated energies do not improve.

The application of the variational principle to the coefficients Ca' leads to the

secular equation

det (H ES) = 0, (2-35)

where H is the CI matrix, written in a block form

[ K (2-36)

His the hamiltonian of the system, E is a column of the energies of the CI excited states,

and S is the overlap matrix for the CI wavefunctions. The energies E are the eigenvalues

of H, while its eigenfunctions

crI =3C a 'Y (2-37)

are also called CI vectors. The zero parts in the CI matrix are due to integrals of the type

K H 'I ', which are equal to zero according to the Brillouin's theorem [19].

If Y is the wave function of the ground state, YEXC is the wave function of the

excited state (one of the CI vectors) and r is the operator of distance, then the probability

of transition (also known as oscillator strength) is proportional to the square of

K('Exc er T)KY V V,,), (2-38)

where Yv,, are the vibrational wave functions and their overlap is called a Frank-Condon

factor. The first term (or rather, its square) determines the transition intensity, while the

second term gives the overlap of the two vibrational functions and determines the shape

of the line.

In order to justify the use of the calculated excited state energies from equation

(2-35), one needs to apply the Frank-Condon principle, which states that the excitation

(absorption) transitions are vertical, that is, the electrons move faster than the nuclei in

the molecule.

The calculated absorption spectrum f(E) containing a total of N transitions, has

the form

/ E-Eok
2.355 e -2.773 A
f(E)= pk e (2-39)
AV2Jr k=1

In this work, each individual spectral line is assumed to have a Gaussian shape with

adopted full width at half maximum A equal to 0.4 eV and a height pk, called an oscillator

strength (calculated as the square of equation 2-38).



There are several different methods available for studying chemical and physical

properties of materials at the atomic level. The most accurate is based entirely on

quantum mechanics without inclusion of adjustable parameters other than the quality of

the basis set expansion of the wave functions. The other extreme is classical molecular

dynamics, based on empirically determined interaction potentials between the atoms that

constitute the material or molecule under investigation. There are also various tight-

binding schemes (TB) that are quantum mechanical but rely heavily on empirical fitting

and therefore lack transferability to other systems, and bonding situations and so on, for

which they have not been parameterized.

Since the goal of the present work is to describe the optical properties of a real

material, one needs a fast and efficient method that allows a large variety of molecular

structures to be investigated. The most accurate methods are quite insufficient in that

respect, while the semi-empirical quantum-mechanical methods provide the efficiency of

calculation and acceptable accuracy. As it has already been described in Chapter 2, the

various semi-empirical methods use the approximation of Hartree-Fock for calculation of

the ground state energy of the molecule and the energy levels of its electrons. The

difference between the various methods is in the Hamiltonian they use, namely:

* The Hamiltonian operator is approximated in various ways within the different

* The Hamiltonian operator is parameterized with semi-empirical parameters, which
are specific for the given Zero Differential Overlap (ZDO) method.


This method is known also as INDO/S or INDO/CI [16, 17] and has been

developed by Prof. Michael C. Zerner at the Quantum Theory Project at the University of

Florida. The method is based on the Hartree-Fock approximation and uses CI for

calculation of optical spectra. The accuracy of prediction of the optical transition energies

is 2000 cm1, or 0.25 eV [12, 20].

The method has been successfully used in numerous studies of organic and organo-

metallic compounds and the parameters for H, C, N and O in particular have been

previously optimized to reproduce optical absorption spectra. Theoretical parameters for

Si, as well as those taken from atomic spectroscopy, have been implemented in the

program code.

In ZINDO, 31 theoretical/empirical parameters are used [21]. The following is a

list of the ZINDO parameters and their applicability for calculations of Si molecular


* 1, 2: Cs, ,p: Slater orbital exponents-according to Zerner [12, 22, 23], these are
taken from Santry and Segal [24] for Si atoms;

* 3-6: dl, its coefficient C1, -d2 and its coefficient C2. It is important to note that d-
orbitals are not used in the calculation for Si atoms;

* 7-9: Is, Ip, and Id-ionization potentials for Si published by Santry and Segal [24]
(atomic data for Si);

* 10-12: ps, pp and 3d (resonance integrals). In the case of Si, pd is neglected, psp=
-9 eV [25];

* 13-20: F2(p,p), Gl(s,p), F2(p,d), F2(d,d), F4(d,d), Gl(p,d), G2(s,d), G3(p,d)
-Slater-Condon factors, published by Bacon and Zerner [23] for Si. These seven
parameters are used in the module INDO/1 for geometry optimizations;

* 21, 22: Eatom-electronic energy of an isolated atom; Hatom heat of formation
of an isolated atom-these two parameters are known from experimental atomic

* 23-25: Is,a, Ip,a, Id,a-second set of ionization potentials, involving transitions to
d orbitals and are thus neglected in the case of Si;

* 25-28: Cl, C2 and C3,a-fractional contributions of d-configurations to the core
integral-neglected in the case of Si;

* 29-31: yss, yo7, ydd-two-electron one-center Coulomb integrals-calculated from
the Slater orbitals for Si, taken from Santry and Segal [24].

* Other parameters are set to be constants, such as f,=0.585, f,=1.267, for singlets
excitations. The two-center, one-electron integrals are used to calculate some of
the overlap matrix elements S, and are treated as parameters.

Before INDO/S was used in this study, there was a need to re-optimize the P

parameter for Si (Eq. (2-27)). In the literature, there are a number of papers that provide

experimentally measured IR spectra as well a UV/visible absorption spectra for

molecules containing Si [26 33]. Only molecules that contain Si and atoms, for which

the INDO/S has been previously parameterized, were selected. In the chosen structures,

Si participated with both 7n- (for instance, in the cases of silabenzene and H2SiCH2) and

o-bonding (for instance, in the cases of Me6Si2, (Me2Si)5 and (Me2Si)6). The geometry

of these molecules was optimized with the Austin Method 1 (AM1), predicting bond

length within a few percent of the corresponding experimental values. The absorption

spectra were calculated with the INDO/S for each molecule for various values of P.

Let us consider a total of N Si-containing compounds. The experimentally

measured absorption spectrum of each compound will exhibit electronic transitions with

energies El, E2, .... EMk where Mk is the total number of transitions for a given compound.

If the calculated prediction of a transition energy is denoted as ek(P), then

N Mk
(e, / )E, )2
Err(f) = k=1 = (3-1)

is the average error, associated with a given value of p.

The smallest average deviation was found to be 0.24 eV, which is achieved at P(Si)

= -9 eV. Table 3-1 shows a comparison between theoretical and experimental values for a

variety of transitions of ten different Si-containing compounds. It has to be emphasized,

that the error of 0.24 eV in the calculated transition energies, comes as a result of both

MOPAC geometry optimization and INDO/S spectroscopic calculation.

In conclusion, ZINDO is an INDO-based FORTRAN code, which allows one to

calculate optical absorption spectra (electronic structure) of molecules, containing the

elements H, Li, B, C, N, O, F, Si, P, S, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn with a

precision of 0.25 eV. Other elements have also been parameterized by research groups.

MOPAC: AM1 and PM3

In the 1970s, the MINDO/3 and MNDO codes (Zerner [12] and the references

therein) have been introduced. They represent a "Modified version of INDO",

specifically para- meterized for prediction of geometries and heats of formation of

molecules. A brief explanation of the Fock matrix elements within MINDO/3 and

MNDO as well as a discussion on their parameterization can be found in the literature


Both MINDO/3 and MNDO are NDDO-based. The first practical program that

contained both approximations was the code MOPAC [34, 35]. It has been parameterized

for geometry optimization of molecules, vibrational frequency spectra, heats of

formations and other properties [12]. However, the inability of MNDO to successfully

model hydrogen bonding has led to the development of the Austin Model 1 (AM1) and

the Parametric Method 3 (PM3), the last being the third parameterization of MNDO.

Table 3-1. Comparison between experimentally measured and theoretically calculated
transition energies and wavelengths for various Si-containing molecules
Compound Experiment [eV] INDO/S [eV]
3.88 4.28
(CH)5SiH [26] 4.56 4.59
5.85 5.56
H2SiCH2 [28] 4.68 4.68
4.00 4.20
MeSi(CH)5 [29] 3.85 4.20
3.85 4.20
(CH)6(CH2)2MeSi [29] 4.72 4.96
4.53 4.46
Me2Si(CH)2 [30] 5. 5.6
5.12 5.06
Me(H)SiCH2 [31] 4.77 5.15
6.43 6.60
Me6Si2 [32] 7.2 7.90
7.52 7.90
Me2Si [33] 2.76 2.95
Me2Si5 [33] 4.68 4.83
Me2Si6 [33] 5.17 5.10

It is important to note that since AM1 and PM3 are both NDDO-based, they are

therefore founded on the Hartree-Fock approximation. In AM1 and PM3, the variational

principle is applied to the AOs and the molecular wave function, as described in Chapter

2. However, the coordinates {Rk} of the atoms in the molecule are also varied until the


a Rk

=grad U = -Fk = 0


is satisfied, that is, until the forces acting on the different atoms are reduced to zero. U

represents the potential of interaction between the atoms in the molecule.

The Hartree-Fock method and the variational principle are applied multiple times,

while the coordinates {rk} are being varied at each step, searching for a minimum of the

norm of the gradient in equation (3-2). The common mathematical procedures for

searching of the potential energy minimum are the method of the steepest descent, the

method of the conjugate gradient, Newton-Raphson and eigenvector following [21].

Detailed description of these methods can be found in any textbook of numerical


During the Hartree-Fock NDDO calculation, various empirical parameters are used,

many of which have been listed in Section 2.2. Other parameters, specifically introduced

in MNDO, and their influence on the geometry calculations are described in the literature

[12, 34].

MOPAC can calculate 32 different molecular properties [34]. The study of sp-Si

did not require the use of all 32 and therefore attention will be given only to the

quantities, applicable to the present research work.

The heat of formation AHf of a molecule is calculated as follows: the Hartree-Fock

approximation applied to a system of n valence electrons in a molecule results in a

density, P, and Fock matrix, F. The one-electron matrix H, together with the matrices P

and F, participate in the expression for the total electronic energy

Electron =, H, + Fv ). (3-3)
2 ,=l vi =l

If the energy of repulsion between two nuclei is E, a"r, then the total energy of

repulsion between nuclei in the molecule will be given by

EueLear Z Eal (A, B). (3-4)

The energy necessary to strip all the valence electrons off atom A will be denoted

as E,,o,,(A) and the total energy necessary to take all atoms from the whole molecule to

infinity will be Eatomi,. Then the heat of formation of a molecule, calculated by the semi-

empirical methods AM1 and PM3 at a temperature of 298 K in the gas phase is given by

the expression [35]

AH/f = Eelectron + Enuclear + Y EIonz (A) + Eatomi (3-5)
all atoms

E,on,,(A) is calculated using empirical parameters. A detailed procedure and

description of these parameters has already been published. [34, 35]. The atomization

energy for the atoms in the molecule is

Eatomi, = E -C ZE(O)SCF(A), (3-6)
all atoms

E(O)SCF(A) being the lowest total energy for an isolated atom A in the self-consistent

field (SCF) approximation. For a cluster, containing a total of n, atoms, one can define

average atomization energy per atom as

(Eatomiz ) ESCF Ek) (3-7)
na k=1

It determines how strongly an atom is bound to the other atoms and therefore could

be used as a measure of the stability of the molecule.

In conclusion, MOPAC allows one to calculate 32 different molecular properties,

between which are the optimal atomic coordinates of a molecule (optimized geometry),

its heat of formation and ground state energy. AHf, being a result of the above semi-

empirical methods, is useful when two molecules are compared. The relative difference


of the heats shows the energy expenditure necessary for the transformation of one

molecule to another.


Known Facts About Spark-processed Silicon

Spark-processed Si (sp-Si) has been thoroughly studied since 1992, when found to

have visible PL at room temperature [1]. However, a large set of its properties have

technological importance only and as such will not be considered here. Some of the

characteristics of the material yield important information about the light-emitting centers

as follows:

* Sp-Si grown in air has PL spectra, which exhibit consistently three peaks: blue,
green and red (peaking around 385, 525 and 650 nm respectively). This fact
suggests that similar light-emitting centers are being formed always, when
crystalline Si (c-Si) is spark-processed in air.

* Temperature behavior of the PL suggests that quantum confinement is not the
mechanism of emission [3]. Therefore, c-Si or c-Si particles are not required in the
modeling of the light-emitting centers. However, the present study includes a
limited number of c-Si clusters for the sake of completeness.

* The PL of sp-Si is highly resistant against etching in hydrofluoric acid, aging, UV
irradiation and thermal annealing up to 11000C. This fact suggests that the emitting
centers occupy stable molecular geometries up to 1100C.

* X-ray diffraction studies [3, 36] show that sp-Si contains amorphous phases. This
fact suggests that the emitting centers, although similar throughout the bulk, are
posi tioned in different atomic surroundings. In other words, the emitting centers
belong to the same family of molecular clusters and have similar characteristics,
but do not have identical molecular geometries.

* Small-spot X-ray electronic spectroscopy (XPS) studies of sp-Si show that the
material consists of four phases: amorphous SiO2 (a-SiO2), a-Si, c-Si and SiNx or Si
oxynitrides [3, 5]. This fact suggests that the luminescent centers are located in one
of these phases or at an interface between them.

* Earlier studies [4] on sp-Si show that its PL does not originate from SiO2.
Therefore, the emitting centers do not originate from the Si02.

* An earlier study [3, 37] states that the PL decay time of sp-Si is in the order of
nanoseconds. A more recent study suggests decay times in the order of picoseconds
[6]. In either case, the decay times are fast and it seems therefore that charge or
energy transfer mechanisms in PL are not likely. The absorption and emission of a
photon occur on the same center. This fact is also confirmed by preliminary PLE
(photoluminescence excitation, Figure 4-1) and absorption spectra of sp-Si, both
showing identical peaks [38]. The absorption spectrum of sp-Si was measured by a
differential technique, called differential reflectometry. Line-shape analysis of the
differential reflectogram (DR) is presented in Appendix A.

* Sp-Si is a diluted magnetic semiconductor and exhibits ferromagnetic properties.
They are annealed out at around 6000C. The PL properties are observed after
thermal annealing until at least 11000C. This fact suggests that the two phenomena
are not related and the light emitting centers are probably non-magnetic, having
singlet ground states (zero spin).





-i. ... .,
1 \, *i, -

200 400 600

Wavelength [nm]

Figure 4-1. PLE, PL and DR (e.g., absorptivity, see Appendix A) characteristics of
Sispark-processed in air.

SDR Signal
- PLE at 380 nm

The surface area of sp-Si constitutes mainly of a-Si02. However, there is a

population of Si particles in the matrix of a-Si02 [3, 36]. The emitting centers could be

related to Si particles in a matrix of a-SiO2.

The optical absorption spectra of sp-Si processed in air and sp-Si processed in pure

oxygen show similar bands between 200 and 300 nm. However in one of the cases (in

pure 0) the bands are resolved (Figure 4-2), while they are convoluted in the other case

(in air). This fact suggests that the light-absorbing centers in both materials might be

related, but will have important differences.

Research Procedure

Since sp-Si consists of a-Si02, a-Si, c-Si and Si nitrides/oxynitrides, the light-

emitting centers will be modeled as

* Amorphous Si02 based clusters with and without participation of N atoms;
* Amorphous Si based clusters with and without participation of N atoms;
* Si nitride and oxynitride clusters;
* Clusters of the type a-Si02/a-SiNxOy or a-Si02/a-SiN,;
* Clusters of the type a-SiNxOy/a-Si or a-SiNx/a-Si;
* C-Si clusters will be included for completeness: a-SiNxOy/c-Si, a-SiNx/c-Si;
* Clusters of the type a-Si02/a-Si and a-Si02/c-Si.

For all 7 families of molecular clusters the following procedure was applied:

* Without exception, the cluster geometries were based on previously published
studies, showing sufficient experimental and/or theoretical support for their

* Modification of the above geometries was done strictly following the rules of
bonding for 0, N, Si and H;

* All dangling bonds were terminated with H atoms;

* The structures of all clusters were optimized with AM1/PM3;

* ZINDO/S spectroscopic calculation was performed for all clusters, resulting in a
calculated optical absorption spectrum;

* The calculated spectrum was compared with the spectrum of sp-Si.


2 0.5

0 .0 I = I I I = I I I
200 300 400 500 600 700
Wavelength [nm]

Figure 4-2. Differential reflectogram (e.g., absorption spectrum, see appendix A) of
Silicon spark-processed in O atmosphere. The material does not show
PL,when excited with a He-Cd laser (325 nm) [39].

Many of the studied complexes were tested for spin state contamination by

projecting the molecular Slater-type wave function T over wave functions, representing

the pure multiplicities (the eigenfunctions of the spin operator S2). In the case of

Unrestricted Hartree-Fock (UHF) type of field, all molecules studied in this work satisfy

the condition

S2 UHF = oUHF, (4-1)

where COis a scalar quantity. Therefore, the clusters studied in the present work have been

considered to have singlet ground states (closed shell configurations) and the Restricted

Hartree-Fock (RHF) implementation of the INDO code was used.

The high temperature stability of the PL in sp-Si suggests the emitting centers

occupy equilibrium molecular geometries, which excludes defects from consideration.

Certain defects in the sp-Si bulk are responsible for its magnetic properties, which are

annealed out at 600 OC [40], while the PL properties remain at this temperature. To add

more weight to this argument, one can also point to the fact that N atoms in Si-rich silica

are proven to improve the properties of the dielectric by reducing the density of charged

and neutral defects [41 50] and at the same time it has been established that N is of key

importance for the PL in sp-Si. Still, some high-strain structures and clusters with

hypercoordinated atoms were included systematically in the calculations, but did not

provide acceptable predictions of the properties of sp-Si.

The calculations with clusters from the various cluster families led to consecutive

approximations to the spectrum of sp-Si with increasing accuracy. They are presented

below in the order the original research was conducted.

Optical Properties of a-SiO2 based Clusters

Nearly 100 silica ring clusters (Fig. 4-3) were optimized with the AM1 and

modified by substitution of O atoms with N atoms [25]. Various schemes of attachment

of clusters were also applied with the goal to invoke a change in the optical properties of

the resulting structure. After the geometry optimization, INDO/S spectroscopic

calculations were performed for each individual cluster. The optical transitions of the

majority of the studied clusters occur at energies, higher than 6.2 eV (lower than 200

nm). Some of the structures though, allow optical transitions that are in close

resemblance of those in sp-Si. The two-member ring is a planar structure having two

double bonds Si=O [15, 51 55]. The ring was modified by

* Substitution of an 0 atom with a N atom;

* Substitution of Si=O with Si-(NH2);

* Replacing of all double bonds with single bonds, concomitant with the addition of a
H atom.

If an N atom takes the place of an O atom and if a double bond Si=O is present then

the resulting absorption spectra exhibit a single peak near 245 nm (5.05 eV, Fig. 4-4). If

all of the O atoms in the cluster are substituted with N atoms, or no N atoms are present,

the peak vanishes.

Figure 4-3. Silica ring-shaped clusters. (a) Two-member ring; (b) three-member ring;
(c) four-member ring; (d) five-member ring and (e) six-member ring.

The three-, four-, five- and six-member silica rings are non-planar structures [56]

that do not contain double bonds. Substitution of O atoms with N atoms does not result in

absorption peaks that are close to those of sp-Si. However, attachment of a modified two-

member ring may result in alteration of the optical properties. For instance, if a two-

member ring is attached to a six-member ring, an electron transition near 245 nm (Fig. 4-

5) emerges in its absorption spectrum. A similar trend can be observed for some clusters

that are structured as a combination of an extended two-member ring and a six-member

ring (Figs. 4-6 and 4-7).

Further understanding about the process of absorption can be obtained by

considering some specific features of the molecular orbitals in a given cluster. In CI, the

absorption spectrum is calculated from the transitions between CI vectors, which are

mathematically represented by linear combinations of Slater-type determinantal wave

functions. If a transition is possible for a pair of CI vectors, then the energy of the

transition can be identified. The Tabulator program within the CAChe code [57] builds a

three-dimensional coordinate grid and calculates at each point, the value of the electron

probability amplitude for the HOMO and the LUMO. Electron isosurfaces are

constructed, using all points, at which the above calculated amplitude is equal to 0.07

atomic units (a. u.). The occupied and unoccupied orbital surfaces are displayed in

different colors.

Fig. 4-8 is a three-dimensional image of silicon oxynitride molecules and the

orbital isosurfaces for the transition at 245 nm and its vicinity. Similar plots were done

for structures with different sizes. If these exhibit an absorption peak near 245 nm, then

always the HOMO and the LUMO at this excited configuration (which is, the electron

transition amplitude) are located over the small ring structures with participation of the

oxygen atom in the Si=O bond.

(a) (b)

220 240 260 280
Wavelength [nm]

Figure 4-4. Equilibrium geometries and spectra of modified two-member silica ring


12000- (a)



0 -
200 240 280 320 360 400
Wavelength [nm]

Figure 4-5. Equilibrium geometries and spectra of modified three- and six-member rings
via attachment of two-member silica ring.

If the desired peaks were preserved in the spectra of the two-member rings only and

nowhere else, then such structures cannot be used to model the properties of a real solid-

state material. The above facts show, however, that it is possible to incorporate the

strained two-member rings into larger structures and to impart their optical properties to

the whole molecule. Thus, the size of the cluster can be increased without alteration of

the desired properties.

However, the process of attachment does not always retain the transition of the

small rings. As can be seen from the above results, modified two-member ring clusters

turn out to be always inactive when attached to a four or five-member ring. This is also

true in many cases where three- and six-member silica rings are attached. Mere

substitution of O with N in the case of three-, four- and five-member silica ring-chains

does not result in the alteration of optical properties either.

These observations demonstrate that there are many possibilities for incorporation

of N atoms into amorphous SiO2, but only a limited number of them will result in an

optical excitation near 245 nm. The active centers are always dependent on the

availability of a modified two-member silica ring and a double Si=O bond.

The process of sp-Si growth randomly incorporates N and O atoms into an

inhomogeneous, disordered solid phase. It is virtually impossible to control the

microstructure of the material during the spark processing. In this situation, the cluster

structures that contain N atoms, will have dissimilar geometries accordingly. Thus, a

large number of N atoms will participate in the composition of various clusters, not being

able to contribute to the optical properties. A finite number of them are possible to take

part in the formation of modified two-member silica rings. In certain cases, such

structures will invoke alteration of the optical properties of the material, lowering the

optical absorption threshold energy to 5.05 eV, which corresponds to a wavelength of

245 nm.



.D r-

Figure 4-6. Attachment of two-member ring to six-member rings.




I (b)

0.5- ()

230 250 270 290
Wavelength [nm]
Figure 4-7. Calculated absorption spectra of modified six-member rings via attachment of
two-member silica ring. (a), (b) and (c) correspond to the clusters on Figure
4-6 respectively.


Figure 4-8. Three-dimensional molecular orbital surfaces,corresponding to the electron
transition at 245 nm.

In summary, silica rings alone cannot account for the optical properties of sp-Si,

since they reproduce only one peak of the sp-Si spectrum the peak at 245 nm. However,

by replacing O atoms by N, a remarkable alteration of the optical properties of certain

two-, three- and six-member silica rings is observed. These results suggest that silica

clusters are potential participants in the process of light emission of sp-Si.

Optical Properties of Silicon Rings

Si and Si02 clusters of different sizes and geometries participate in the plasma-

assisted vaporization process during spark processing and in the luminescent material as

well [3]. The ring-shaped clusters are an important subset of the large family of these

clusters (Figure 4-9). There is a substantial number of computational studies on Si ring

networks, publications on which can be traced back to 1974 [58 70]. These publications

show that theoretical modeling of a-Si with network of three to eight-membered Si rings

successfully predicts experimentally measured properties of material (e. g. radial

distribution function in X-ray diffraction, density of states, infrared spectra etc.).

Therefore, there is theoretical support for the existence of Si rings, which are the

building blocks of the random network of a-Si. Si rings have also been observed

experimentally in a-Si and oxygenated Si rings have been observed at Si/Si02 interfaces

[71 73]. It is therefore relevant to study the optical properties of Si ring-shaped clusters

and how they compare with the measured optical spectra of sp-Si and similar Si-

containing materials.


Si 0 H

Figure 4-9. Optimized geometries of the OH-terminated Si rings.

Previously published quantum mechanical calculations indicate stable geometries

of isolated three-, four-, five- and six-member Si ring-shaped clusters. At room

temperature, they will normally react with oxygen, hydrogen or nitrogen. Our

calculations indicate that this is energetically favorable. Table 4-1 contains data for the

isolated three-member Si ring and shows the trend in energetic when the ring reacts with

oxygen and nitrogen. The same trend has been observed in the cases of four-, five- and

six-member Si rings.

The AM1 semi-empirical calculations also reveal a definitive trend in the

energetic of all studied Si rings, when a silica ring is attached to them. In all cases, an

increase of the average atomization energy is observed when this type of attachment

takes place. The results are shown in Table 4-2.

Another common trend in the behavior of all studied hydrogenated Si rings is

observed when an O atom is substituted by an N atom. The average atomization energy

of such clusters decreases as the number of the substitute N atoms increase.

However, if the heat of formation of the molecule is denoted as AHf, then the difference

SAHf (k) AHf (isolated k member ring cluster) | (4-2)

diminishes in all cases for k = 3, 4, 5 and 6 when a substitute N is present. In other words,

it takes less energy to add the NH2 group to an isolated Si ring, compared to adding an

OH group. This fact is illustrated in Table 4-3, as well as in Table 4-1.

The optical absorption spectra of the Si ring-shaped clusters consistently show a

number of distinctive features. All spectra exhibit three characteristic peaks, positioned

Table 4-1. The energetic of the three-member Si ring as calculated by the semi-empirical
method AM1.
Compound Calculated , eV Calculated AHf, kcal/mol

Isolated Si3 ring 2.30 243.6
Hydrogenated Si3 ring, 3.20 49.1
Si3H5(OH) -3.66 -17.8
Si3H4(OH)2 4.06 90.2
Si3(OH)6 -5.07 -365.2
Si3H5(NH2) -3.63 22.7
Si3H4(NH2)2 3.94 7.0

Table 4-2. The energetic of the studied Si rings with attached four-member silica ring as
calculated by the semi-empirical method AM1.
Compound Calculated , eV Calculated AHf, kcal/mol

Oxygenated Si3 ring, 5.07 365.2
Four member silica ring 5.40 508.4
attached to Si3 ring
Oxygenated Si4 ring, 5.10 474.0
Four member silica ring 5.40 640.1
attached to Si4 ring
Oxygenated Sis ring, 5.10 -603.9
Four member silica ring 5.33 769.1
attached to Sis ring
Oxygenated Si6 ring, 5.10 -731.8
Four member silica ring 5.30 897.3
attached to Si6 ring

Table 4-3. The calculated energetic of the addition of NH2 and OH groups to an isolated
Sis ring cluster.
Compound Calculated , eV IAHf AHf(isolated Sis ring)|,
Oxygenated Si5 ring, 5.10 924.4
Sis(NH2)(OH)9 4.99 880.4
Sis(NH2)2(OH)8 4.93 837.4
Si5(NH2)3(OH)7 -4.86 794.8
Si5(NH2)4(OH)6 -4.81 751.2

between 200 nm and 350 nm. On average, the peak located in the neighborhood of 200

nm has the highest intensity, while the other two peaks at 260 nm and 320 nm have

comparable magnitude and usually overlap. However, the peak at 260 nm could dominate

in intensity mostly in the cases when larger clusters are studied. In many spectra, a low-

intensity peak appears, positioned in the interval between 400 nm and 500 nm (Figures 4-

10 and 4-11).

The substitution of an O atom by an N atom in a Si ring cluster does not

substantially influence its optical properties. This has been the conclusion from a

comparison of more than two hundred spectra of such clusters. Generally, the addition of

an N atom causes a separation of the peaks at 260 nm and 320 nm, which may otherwise


The results in Table 4-2 indicate that the atomization energy is further

increased in magnitude when a silica ring is attached to the Si cluster. This increased

stability suggests that Si ring-shaped clusters could be incorporated in an amorphous

silica matrix without compromising the stability of the molecule. It should be noted

however that this is a qualitative statement only, while the quantitative influence of

A on the structural properties has not been studied.

The optical absorption spectra of the OH-terminated Si ring-shaped clusters

consistently show three peaks in the neighborhood of 200, 260 and 320 nm (Figures 4-10

and 4-11). The attachment of small silica clusters does not change the optical properties.

Unlike the case of a four-member strained silica clusters with double Si=O bond [25],

substitution of an O atom with an N atom does not lead to alteration of the absorption

spectra of oxygenated Si rings. Additionally, the oxygenated Si ring-shaped clusters

exhibit a small peak in their absorption spectra, located between 400 and 500 nm. The

presence or absence of N atoms in the cluster does not influence the peak position or its

intensity. The positions of the peaks coincide with the positions of small peaks or

shoulders in the spectrum of sp-Si. This fact suggests that Si rings could be contributing

to the PL of sp-Si.



S-- Theoretical Spectrum
0.8 of Si4(NH)(OH),



200 400 600 800
Wavelength [nm]

Figure 4-10. Comparison between an experimentally measured absorption spectrum of
sp-Si (DR, see appendix A) and a calculated absorption spectrum of the
oxygenated Si4 ring Si4(NH2)(OH)7. The dark atoms represent 0, the gray
atoms represent Si, the small atoms represent H.



200 400 600
Wavelength [nm]

Figure 4-11. Comparison between an experimentally measured absorption spectrum of
sp-Si (DR, see appendix A) and a calculated absorption spectrum of the
oxygenated Sis and Si6 ring-shaped clusters.

Optical Properties of Other Silicon Clusters

The Si ring-shaped clusters reproduce a number of features of the optical

absorption spectrum of sp-Si. Compared to the spectra of silica clusters, they come much

closer to the spectrum of sp-Si. Since this is a point of interest, the study of Si clusters

was continued beyond the family of Si rings. The subject of the present section is focused

on amorphous oxygenated Si clusters with 2 to 14 Si atoms.

The calculated spectra of oxygenated Si molecules are not applicable to sp-Si only;

the optical characteristics of any Si- or silica-based light-emitting material can be

compared to the results in this dissertation. The clusters in this work can be related to

oxygenated, amorphous Si particles on the surface of materials, or in the bulk when

amorphous Si particles are buried in amorphous silica, or can represent Si particles,

nucleating in the gas phase in the presence of oxygen during laser ablation of Si or related

growth processes of Si-based materials from the gas phase.

All molecular structures in this section are based on previously published

geometries of isolated Si clusters, optimized with ab initio and DFT calculations and

widely accepted as stable [12, 74 79]. In the sp-Si material, Si clusters do not exist as

isolated molecules, but are rather bonded to oxygen and nitrogen atoms or to crystalline

Si particles. We have studied the energetic of addition of the NH2 and OH groups to the

Si clusters. Figures 4-12 and 4-13 display the geometries of certain representative

molecules Si3, Sis, Silo, Sill and Si14. Table 4-4 contains data for the energetic of Si3.

The modulus of the average atomization energy in the general case increases with

the hydrogenation and always increases with OH-termination of an isolated Si cluster. It

reaches its highest values when N atoms are absent. All of the studied structures in this

work conform to this rule. Identical results have been achieved for a large variety of Si

ring-shaped clusters [80]. Therefore, the conclusion is imposed that in Si-based

molecules the attachment of (OH) groups leads to structural stabilization which is most

pronounced in the absence of (NH2) groups. It should be noted however that this is a

qualitative statement only, while the quantitative influence of A on the structural

properties has not been studied.

Figure 4-14 displays calculated spectra of representative oxygenated Si molecules.

The spectra always exhibit a triple-peak feature at or around 205 nm, 250 nm and 320

nm. The variation of the peak positions is within 5 nm for the first peak, within 20 nm

for the middle peak and within 30 nm for the peak at 320 nm. Almost without

exception, a weaker peak between 400 nm and 500 nm is also observed. In the general

case the three peaks between 200 and 320 nm are resolved and still cannot reproduce a

dominant peak at 250 nm, as it is in the spectrum of sp-Si.

The behavior of the triple peak is explained by the following:

Presence of N atoms in the molecule: If an OH group in an oxygenated Si cluster

is replaced with a NH2 group, this invokes small changes in the optical spectrum, which

do not seem to follow a specific trend. In the majority of cases, upon such changes the

agreement between the calculated spectrum of the cluster and the observed spectrum of

sp-Si does not improve. The spectra of oxygenated Si molecules are far closer to the

spectrum of sp-Si, when compared to spectra of SiO2-based molecules and spectra of Si

nitrides. This conclusion is based on comparison between more than one hundred silica

and more than three hundred Si-based structures. Thus, the absorption of light in sp-Si is

highly dependent on Si molecules rather than atomic impurities in the amorphous SiO2

network. The study of the electronic transition amplitudes for the calculated high-

intensity transitions points towards Si particles within the amorphous SiO2 as responsible

for the light absorption of sp-Si.

Table 4-4. Energetics of the addition of the (OH) and (NH)2 groups to Si3. The left
column shows the values of the average atomization energy in eV.

Compound Calculated , eV
Isolated Si3 molecule 2.62
Hydrogenated Si3 molecule, Si3H8 3.10
Oxygenated Si3 molecule, Si3(OH)8 5.18
Si3(NH2)(OH)7 -5.10
Si3(NH2)2(OH)6 4.96
Si3(NH2)3(OH)5 4.90
Si3(NH2)4(OH)4 4.81


o 0

Figure 4-12. Geometries of OH-terminated Si3, Sis and Siio molecules.


j Si


,J H

Figure 4-13. Geometries of the cage-shaped oxygenated Sill and Si14 molecules.


Si (OH)s
S............... Si4(OH)
S 0.6

0.4 .


200 300 400 500 600
Wavelength (nm)

Figure 4-14. Calculated spectra of oxygenated Si4 and Si6 molecules. The dark atoms
represent 0, the gray atoms represent Si, the small atoms represent H.

* The role of the Si atoms: We have calculated the spectra of hydrogenated Si2 -
Si14. Interestingly, the triple-peak feature of the spectrum is preserved in most of
these cases. The peak at 205 nm is very strong, while the other two peaks overlap.
The low-energy peak at 400 nm is absent in the spectra of small, hydrogenated Si
molecules and reappears in the spectra of the larger ones (Silo and up), together
with neighboring smaller peaks. Despite that hydrogenated Si clusters are most
probably not present in sp-Si, the specific features of their spectra suggest that the
absorption of light in hydrogenated and oxygenated Si molecules occurs mainly
over the Si atoms, while the H, O and participating N atoms have minor role, which
could be related to a possible light emission in such molecules.

Within the set of calculated spectra of oxygenated Si clusters studied in this work,

we have obtained a limited number of optical absorption curves, which show close

agreement with the observed spectrum of sp-Si. Representative cage-shaped cluster

structures associated with these spectra are shown on Figure 4-13, while Figure 4-15

displays a comparison between the calculated and observed absorption. These clusters

have optical properties, which differ from the general trend of behavior of the studied

oxygenated Si molecules, by exhibiting a large peak centered near 250 nm and

reproducing the low-energy peaks of sp-Si between 500 and 700 nm.

Since sp-Si is inhomogeneous and amorphous, a small number of molecular

structures, however close they may match the spectrum of sp-Si, cannot be expected to

account for the properties of the material. This would be a deterministic approach, which

disagrees with the random nature of sp-Si. Rather, a family of stable clusters with

matching optical properties must be responsible for the PL of this material. Nevertheless,

the achieved higher level of agreement with the observed spectra of sp-Si at this stage

indicates that the present study has poceeded in the correct direction.

Optical Properties of Silicon Particles in an Amorphous SiOxNy matrix

As a next step, Si particles in an a-SiOxNy matrix were studied. In this case the

calculated absorption spectra remarkably well reproduced the spectrum of sp-Si. Si cages


and clusters were modeled as bonded to silica rings. The agreement between theoretical

prediction and experiment was achieved for any Si cluster, bonded to silica rings. The

degree of similarity between calculated and measured spectra varies for the different Si

particles, but the spectral features are similar (Figures 4-16 to Figure 4 25).

Our calculations suggest, that the Si particles in a-SiOxNy play a key role in the

process of light absorption in sp-Si. Time-resolved PL measurements with sp-Si have

shown PL decay times in the order of nanoseconds or even picoseconds [6]. This fact

indicates that charge- or energy transfer mechanisms are unlikely prior to light emission

in sp-Si, since such processes result in increased decay PL times. Photoluminescence

Excitation (PLE) and optical absorption spectra of the material show identical peaks

(Figure 4-1). This can be interpreted to mean that absorption is followed by emission on

the same center.

r < ^<


1. i L

SFigu ----o Spelrum oasp-Si (experoient)
Z, '*'... On 'll- ],

l. 0.6 4 ,1
s 0.4 i- ; ,

.o J
200 300 400 5OO 600 700
Wavelentgh (nm)
Figure 4-15. Calculated spectra of oxygenated Sin1 and Sil4 molecules.

The PLE spectrum shows that absorption around 320 nm most effectively results in

emission of photons with a wavelength of 380 nm. The absorption at 245 nm is very high,

but less efficient in producing blue emission. Still, laser excitation at 230 nm and lower

energies results in emission of blue light [81]. At these wavelengths, the PLE exhibits a

non-zero tail (Figure 4-1), consistent with the absorption measurements. It is therefore

proposed, that both the absorption and emission of light in sp-Si occur over the Si

particles, embedded in the amorphous insulator matrix of sp-Si.

The Role of N in the Optical Properties of Spark-processed Silicon

In the conducted experiments, the PL of sp-Si was excited by a He-Cd laser (325

nm). It is important to note that PL was observed only for sp-Si, processed in mixtures of

O and N gases (e. g. air). Firstly, the He-Cd laser was not able to excite sp-Si, processed

in pure O atmosphere, which suggests that such material either does not have an

absorption band at the excitation wavelength, or the excited electrons lose energy along

non-radiative pathways. Secondly, the absorption spectrum of sp-Si processed in air is

different compared to the spectrum of sp-Si, processed in pure O atmospheres. For these

reasons it has been inferred, that N plays a role in the optical properties of light-emitting

sp-Si. A large number of studies consistently shows that in a-SiOxNy systems the N atoms

pile up at the dielectric/Si interface [42, 44, 45, 47, 48, 82 91]. It has been suggested

that in such situations, Si2 N O bonding occurs at the interface [89, 90]. The

application of these facts to our calculations has resulted in structures of the type, shown

in Figures 4-19 to 4-24. Figures 4-16 to 4-18 and Figure 4-25 show good agreement as



1.0 -

0.8- Experiment
0.6 ii
0.4 -' .

L- 0.2 --

-0.2 -

200 400 600 800 1000
Wavelength [nm]
Figure 4-16. Si particle in amorphous silica matrix. The graph displays a comparison
between the measured DR spectrum of sp- Si (appendix A) and the
calculated spectrum of the cluster. The dark atoms represent O, the gray
atoms represent Si, the small atoms represent H.



200 400
200 400


Wavelength [nm]
Figure 4-17. Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.

--- Experiment



400 600 800
Wavelength [nm]

Figure 4-18.

Si particle in amorphous silica matrix. The graph displays a comparison
between the measured DR spectrum of sp- Si (appendix A) and the
calculated spectrum of the cluster. The dark atoms represent 0, the gray
atoms represent Si, the small atoms represent H.



---- Calculated

200 400 600 800
Wavelength [nm]


Figure 4-19. Si particle in amorphous silica matrix. The graph displays a comparison
between the measured DR spectrum of sp- Si (appendix A) and the
calculated spectrum of the cluster. The dark atoms represent 0, the gray
atoms represent Si, the small atoms represent H.


--- Experiment
---- Calculated

200 400 600 800


Wavelength [nm]
Figure 4-20. Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.





r jr






200 400 600 800


Wavelength [nm]
Figure 4-21. Si particle in amorphous silica matrix. The graph displays a comparison
between the measured DR spectrum of sp- Si (appendix A) and the
calculated spectrum of the cluster. The dark atoms represent 0, the gray
atoms represent Si, the small atoms represent H.


! s
VL U L __ _

---- Calculated

k 4 I.

200 400
200 400

Figure 4-22.

Wavelength [nm]
Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.

--- Experiment

200 400 600 800


Wavelength [nm]
Figure 4-23. Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.

1.0 -

0.8 -

0.6 -

0.4 -

0.2 -

0.0 -

-0.2 -



200 400 600 800
Wavelength [nm]


Figure 4-24. Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.

--- Experiment
---- Calculated



l i

/ 1I
\\ \ \

;ll/ \ V "'

)\A _\.

--- Calculated


Figure 4-25.

Wavelength [nm]
Si particle in amorphous silica matrix. The graph displays a
comparisonbetween the measured DR spectrum of sp- Si (appendix A)
and the calculated spectrum of the cluster. The dark atoms represent 0, the
gray atoms represent Si, the small atoms represent H.

Since the calculated spectra of clusters with and without N atoms look similar

(Figure 4-26), a X2 statistical analysis was performed in order to verify whether

2.0 -

c3 1.0

" 0.5




calculated absorption spectra of structures with N would show improved agreement with

the experimental spectrum of sp-Si. 2 was calculated as

Z" = 1 ( )-))2 (4-3)

for a family of n clusters, each of them having a calculated absorption spectrum E(X).

T(X) represents the absorption spectrum of sp-Si, processed in air. In this analysis, 5

different cluster families were studied:

* Si particles with 3, 4, 5, 6, 7, 8, 10 and 14 atoms, terminated with OH groups,
without N atoms;

* Si rings with 3, 4, 5 and 6 atoms, terminated with OH groups, without N atoms;

* Si particles with 3, 4, 5, 6, 7, 8, 10 and 14 atoms, embedded in a-SiO2 matrix
without N atoms;

* Si particles with 3, 4, 5, 6, 7, 8, 10 and 14 atoms, embedded in a-SiO2 matrix with
high concentration of N atoms around the Si particle with bonding configuration
Si2 N H;

* Si particles with 3, 4, 5, 6, 7, 8, 10 and 14 atoms, embedded in a-SiO2 matrix with
high concentration of N atoms around the Si particle with bonding configuration
Si2 N O H.

Each cluster group contained 17 different structures. The cluster families show different

average 2 within 10-2. (This is largely due to the fact, that all spectra were normalized to

unity prior to the implementation of the statistical analysis). If 2 is plotted vs. Si cluster

size (Figure 4-27), one can see that the agreement between theoretical prediction and

experiment improves for larger Si clusters.

--without N

.8 -- with N


< 0.2

0.0 -

200 400 600 800
Wavelength [nm]

Figure 4-26. Calculated absorption spectra of a Si particle in an amorphous matrix
withand without the participation of N atoms.

At a first glance, the obtained X2 values are nearly indistinguishable, because they

are all very close to zero. It seems also, that there is no criterion, based on which some of

the cluster families should be excluded as providing unsatisfactory x2. To resolve this

problem, we studied the differences between

* The experimental absorption spectrum of luminescent Si spark-processed in air;

* The experimental absorption spectrum of non-luminescent Si spark-processed in O
atmospheres. (A detailed analysis of these two spectra is provided in Appendix A).

The optical properties of the two materials are substantially different. Their

experimental absorption spectra are also qualitatively different. To quantify this

difference, we evaluated the 2 when the second spectrum is fitted to the first one. We

achieved a X2 value of a = 0.1. Therefore, any normalized calculated spectrum fitted to

the experimental spectrum is considered to be unacceptable, if the 2 of the fit is in the

order of 0.1 (this includes all 2 values between 0.05 and infinity). If the 2 of the fit lies

below 0.05, there is no reason to treat the fit as unacceptable.

The plot of 2 vs. Si cluster size shows, that best agreement between theory and

experiment is achieved for Sil4 (Fig. 4-27). Let us consider for a moment a cluster size of

14 Si atoms only. In this case, a substantial difference is observed between clusters with

and without N atoms. The clusters, where N is present, lie below the dividing line of 0.5.

In general, for Si cluster sizes between 6 and 14, the complexes that contain N lie within

the limit of acceptability. If the values of 2 for Si14 are extrapolated to infinity (the case

of a large Si cluster), one can conclude that acceptable precision of the prediction is

achieved in the cases when N atoms are present in the cluster.

Another issue that will be addressed here is the precision of the X2 estimate. The

noise-to-signal ratio of the DR is 10-5 (Appendix A). Therefore, no appreciable error in

the 2 will result from noise in the DR signal. The error of the calculation is 0.24 eV,

coming from both the MOPAC geometry optimization and the INDO/S spectroscopic

calculation. The error in the 2 values at Sil4 were estimated by the following procedure:

* The DR and the calculated spectrum were plotted with respect to energy;
* The calculated spectrum was translated with 0.24 eV;
* The resulting X2 values were calculated.

The deviation in the X2 values at Sil4 is estimated to be:

* (OH)-terminated Si clusters, no N: y2 = 0.08; X2 e [0.05, 0.1]
* Si/Si02 clusters, no N: x2 = 0.07; 2 e [0.07, 0.1]
* Si/Si02 clusters, with Si2-N-O-H bonding: y2 = 0.03; X2 e [0.03, 0.09]
* Si/Si02 clusters, with Si2-N-H bonding: y2 = 0.01; x2 e [0.01, 0.04]

The clusters that do not contain N have unacceptable x2 values (larger than 0.05). Si/SiO2

clusters, with Si2-N-O-H bonding provide an acceptable fit, but the x2 confidence interval

is large and assumes values, beyond the acceptability limit of 0.05. Si/SiO2 clusters with

Si2-N-H bonding have acceptable x2 values. Once again, the conclusion is that acceptable

precision of the prediction is achieved in the cases when N atoms are present in the

cluster. This trend will be further verified when more calculations are performed. It is

expected that the clusters, containing N will have x2 that converges to zero when the size

of the clusters increase to infinity. On the opposite, clusters that do not contain N atoms

will have x2 that diverges from zero when the size of the clusters increases.

Silicon Spark-processed in Pure Oxygen

The experimental absorption spectrum of this material is shown in Figure 4-2. It

shows three resolved peaks between 200 and 300 nm. Unlike sp-Si prepared in air, there

is no absorption band at 320 nm in this case. Due to this reason, PL cannot be excited

with a He-Cd laser (325 nm excitation wavelength). A X statistical analysis was

performed for the same cluster families as above with the only difference that x2 was

calculated with respect to the absorption spectrum of sp-Si, processed in pure O. Again,

all cluster families show x2 within 10-2 and only those having X2 < 0.05 can be preferred

as a group that describes best the properties of sp-Si processed in O. The structures,

containing N were included, since some N atoms may still exist in the processing

atmosphere or can be attached after the sample preparation.

Some trends were observed when 2 was plotted vs. Si cluster size (Figure 4-28).

Again, agreement between theoretical prediction and experiment improves for

larger Si clusters. When the values of x2 for Si14 are extrapolated to infinity, one can

conclude that acceptable precision of the prediction is achieved in the cases when N

atoms are absent (Figures 4-29 to 4-31). Si rings, terminated with OH groups, show poor

(higher) x2 values.

Once again, the precision of the x2 estimate needs to be addressed. Since the noise-

to-signal ratio of the DR is 10-5 (Appendix A), the x2 will not be influenced by the noise

in the DR signal. The error of the calculation is 0.24 eV, coming from both the

MOPAC geometry optimization and the INDO/S spectroscopic calculation. Once again,

the error in the X2 values at Si14 were estimated by the following procedure:

* The DR and the calculated spectrum were plotted with respect to energy;
* The calculated spectrum was translated with 0.24 eV;
* The resulting x2 values were calculated.

The deviation in the x2 values at Sil4 is estimated to be:

* (OH)-terminated Si clusters, no N: x2 = 0.05; x2 e [0.03, 0.05]
* Si/SiO2 clusters, no N: x2 = 0.03; x2 e [0.03, 0.07]
* Si/SiO2 clusters, with Si2-N-O-H bonding: 2 = 0.11; X2 e [0.07, 0.14]
* Si/SiO2 clusters, with Si2-N-H bonding: 2 = 0.13; 2 e [0.07, 0.18]

The clusters that contain N atoms have unacceptable x2 values (larger than 0.05). (OH)-

terminated Si clusters provide an acceptable fit, while the x2 confidence interval assumes

the value of 0.05, being the only one unacceptable value. Si/SiO2 clusters without N have

x2 that occupies both acceptable and unacceptable values.

In conclusion one can say that better precision of the prediction can be achieved in

the cases when N atoms are absent. Again, this trend can be further verified when more

calculations are performed. It is expected that the clusters, containing N will have x2 that

diverges from zero when the size of the clusters increase to infinity. On the opposite,

clusters that do not contain N atoms will have x2 that converges to zero when the size of

the clusters increases.

Silicon, Spark-processed in Air







2 4 6 8 10 12 14
Si Cluster Size

Figure 4-27. Silicon spark-processed in air. Statistical analysis for five different cluster

Si6 Clusters in Spark-processed Silicon

The plot of x2 vs. Si cluster size (Figure 4-27) gives further insights about the

difference between sp-Si processed in air and pure O at the molecular level:

* When the number of Si atoms is extrapolated to infinity, the agreement is expected
to improve depending on the presence or absence of N atoms;

* x2 exhibits minima over certain Si cluster sizes. This can be interpreted to mean that
the probability of the existence of such clusters is higher.

The cases of air and pure O are distinctly different with respect to these two features. For

sp-Si, processed in air, Si6 is a favored structure irrespective of bonding situation. This is

no longer true for sp-Si, processed in O. Similar is the case of Sis. This structure is again,

favored in sp-Si processed in air. Such conclusion is not true for sp-Si, processed in O.

One of the Si6 geometries is a cage structure [74 79]. It could be inferred that

other cage structures might be preferentially created in the air atmosphere during spark

processing. As seen above, processing in pure O seems to no longer favor the Si6 clusters.

It has to be noted also that further and extensive computational results are needed to

obtain a much larger variety of Si cluster sizes. After such a study is accomplished, a

possible trend in the minima of 2 may be more clearly visible.

Silicon, Spark-processed in Pure Oxygen

0.18- Si/SiO noN
-o-Si/SiO with Si2-N-O-H bonding
0.16- ----- Si/SiO with Si -N-H bonding
V (OH)-terminated Si Clusters no N
0.14 / (OH)-terminated Si Rings no N

0.12 -


0.08 -

0.06 .



2 4 6 8 10 12 14
Si Cluster Size

Figure 4-28. Silicon spark-processed in pure O. Statistical analysis for five different
cluster families.


Silicon, Spark-processed in Pure 0


-- Experiment

200 300 400 500
200 300 400 500

Wavelength [nm]

Figure 4-29. Si spark-processed in pure O atmospheres. The graph displays a comparison
between the measured spectrum and the calculated spectrum of the cluster,
shown in inset. Dark atoms represent O, small atoms represent H.



| ~-


Silicon, Spark-processed in Pure 0


0.5- Experiment
S. Calculated

200 300 400 500

Wavelength [nm]

Figure 4-30. Si spark-processed in pure O atmospheres. The graph displays a comparison
between the measured spectrum and the calculated spectrum of the cluster,
shown in inset. Dark atoms represent O, small atoms represent H.


Silicon, Spark-processed in Pure 0

200 250 300 350 400 450 500 5

Wavelength [nm]

Figure 4-31. Si spark-processed in pure O atmospheres. The graph displays a
comparisonbetween the measured spectrum and the calculated spectrum of
the cluster, shown in inset. Dark atoms represent O, small atoms represent


The results of the present work can be summarized as follows:

* The calculated absorption spectra of Si particles in a-SiOxNy matrix reproduce
remarkably well the experimental absorption spectrum of sp-Si. Further, the
similarities between the PLE and the absorption spectra of light-emitting sp-Si, as
well as the pico-second PL lifetimes, are interpreted to suggest that both the
absorption and emission of light in sp-Si involve the same centers. The calculated
absorption spectra strongly suggest that Si particles embedded in the amorphous
insulating matrix of sp-Si play a key role in the process of light absorption and
emission in this material.

* Si spark-processed in air: x2 statistical analysis with a large number of Si-based
clusters shows that agreement between theoretical prediction and experiment
improves for larger Si clusters. If the values of x2 for the largest Si cluster in this
study are extrapolated to infinity, one can conclude that acceptable precision (x2 <
0.05) of the prediction is achieved in the cases when N atoms are present.

* Si spark-processed in pure O atmospheres: Again, x2 statistical analysis with a large
number of Si-based clusters shows that agreement between theoretical prediction
and experiment improves for larger Si clusters. If the values of X2 for the largest Si
cluster in this study are extrapolated to infinity, one can conclude that acceptable
precision of the prediction (x < 0.05) is achieved in the cases when N atoms are

* The role of N in the optical properties of sp-Si: The computer models of the optical
properties of sp-Si show best agreement between theory and experiment for
molecular clusters with participation of N atoms. The N atoms pile up at the
dielectric/Si interface with bonding configurations Si2 N O.

* Si6 clusters in sp-Si: the plot of x2 vs. Si cluster size (Si spark-processed in air)
consistently exhibits minima at Si6, irrespective of bonding configurations. Similar
behavior is observed in the case of Sis. It can be concluded, therefore, that Si
clusters with sizes 6 and 8 are preferentially created during sp-Si growth. The
distinctive minima in the plot of X are no longer observed for Si spark-processed in
O. It has to be noted, though, that further extensive computational results are
needed for a much larger variety of Si cluster sizes. After such a study is
accomplished, the trend in the minima of 2 may be more clearly visible.

* Amorphous SiO2 was modeled with 2-, 3-, 4-, 5- and 6-member silica rings. In
general, silica clusters do not exhibit absorption bands below 6.2 eV (200 nm).
Upon substitution of O atoms with N in the structure, electronic excitations with
lower energies are possible. Such substitutions in the small 2-member silica ring
with double Si=O bond result in absorption peak at 5.05 eV (245 nm). This
property can be retained with attachment of the small ring to a larger one. The
electronic transition amplitude at 245 nm is located over the N atoms in the 2-
member silica ring.

* Amorphous Si was modeled with 3-, 4-, 5-, 6-member rings and with small Si
clusters having between 2 and 14 Si atoms, terminated with OH groups. All spectra
of Si rings exhibit three characteristic peaks, positioned between 200 nm and 350
nm. On average, the peak located in the neighborhood of 200 nm has the highest
intensity, while the other two peaks at 260 nm and 320 nm have comparable
magnitude and usually overlap. In many spectra, a low-intensity peak appears in
the interval between 400 nm and 500 nm.

The substitution of an O atom by an N atom in a Si ring cluster does not

substantially influence its optical properties. However, it has a certain influence on its

structure. The average atomization energy of such clusters decreases as the number

of the substitute N atoms increase. The atomization energy increases when a silica

ring is attached to the Si ring cluster. The degree of importance of the variations of

has not been studied.

OH-terminated Si2 Sil4 have properties very similar to those of OH-terminated Si

rings. The spectra always exhibit a triple-peak feature at or around 205 nm, 250 nm and

320 nm. The variation of the peak positions is within 5 nm for the first peak, within 20

nm for the middle peak and within 30 nm for the peak at 320 nm. Almost without

exception, a weaker peak between 400 nm and 500 nm is also observed. In the studied Si-

based molecules, the attachment of (OH) groups leads to structural stabilization, which is

most pronounced in the absence of (NH2) groups. The degree of importance of the

variations of has not been studied. The presence or absence of N atoms does not

influence substantially the optical properties of this cluster group.

The properties of sp-Si strongly depend on the chemical content of the processing

atmosphere. When N is present in the gas, certain Si geometries are created and

embedded in an amorphous solid phase material. The N atoms pile up around the Si

particles and exert influence on their structural and optical properties. Spark-processing

of Si in air is a technique that creates stable, light-emitting Si particles embedded in an

amorphous SiOxNy matrix.

The calculated spectra of silica ring-, Si ring-, Si cage-shaped clusters and their

combinations can be compared with the measured spectra of Si- or silica-based light-

emitting materials. The results of the present work can be used to provide further insights

about the role of Si particles in the optical properties of such materials.


The graph X2 VS. Si cluster size (Figure 4-26, Section 4) has a defined minimum at

Si6 in the case of Si spark-processed in air. Further calculations with clusters Si15 Si60

are necessary, since they can reveal similar minima, positioned over the magic numbers

Si20, Si33, Si45 and Si60. Also, the general trend of

%2 (Si) O 0 when n (6-1)

will be further verified.

The optical properties of the sp-Si material depend on the geometry of the light-

emitting clusters in its bulk. Further work on the structural properties can reveal whether

this dependence is valid on higher dimensional scales. Part of this study has already been

accomplished with the stereological study of the porosity and density of sp-Si (Appendix

B). It is currently being continued with fractal analysis of sp-Si and other spark-processed

materials. The accomplished stereological analysis (Appendix B) may prove helpful in

the calculation of the fractal dimension of spark-processed surfaces. So far, it has been

visually established that such surfaces exhibit fractal behavior in the case of sp-Si, since

they show repetitive structural features at various scales (Figure 6-1).

It has been shown by experiment [6], that N atoms play an important role in the

optical properties of various spark-processed materials. Further calculations can provide

models for the light-emitting centers in these substances and give clues about the

importance of N in the process of light emission.

Figure 6-1. The fractal nature of the sp-Si surface.


Differential reflectometry is an analytical technique, which uses UV/visible/IR

monochromatic light for the measurement of the optical absorption spectra of metals and

semiconductors. The incoming beam scans the surface of two adjacent samples with

reflectivities R1 and R2 (50 100 monolayers) and having a small difference in

composition X. A schematic representation of the experimental setup is shown on Figure

7-1. The output signal from a differential reflectometer is called a differential

reflectogram (DR) and has the form [92]

=A + 1 F OT (7-1)
(R dX dX


F(s, 9) = sin .(s) cos[o(s) 9]
b(s) = Arc sin

R, + R,
(R) =

F is used to denote the lifetime broadening frequency, coT is the electronic transition

frequency, A, s and 0 are parameters and X denotes the chemical composition of the

studied material. Detailed treatment on the DR experimental procedure and description of

the DR line-shape analysis has been published [93-95]. The signal-to-noise ratio of the

DR is 10-5. The line shape of the DR spectrum is determined by the function F.


Light Source

Tube Signal


Oscillating Low Pass
Mirror .Filter Lockin

------ ----- -- Samples


Figure A-1. A schematic representation of a differential reflectometer's instrumentation

2100 F(s)

-4 -3 -2 -1 1 2 3 4

-4 -3 -2-1 0 1 2 3 4


) J1L2 *N S
1 2 3 4



Figure A-2. F(s,O) for selected values of 0 [94].


-4 -3 -2 -1 (

Depending on the values of the 0 parameter, the different peaks in the DR spectrum

will have shapes, as shown on Figure 7-2.

Since in the crystalline material the electronic transitions occur between well-

defined energy bands, the DR spectrum in this case can be thoroughly analyzed, by fitting

a limited number of F functions to it. Each of the functions is analyzed, the value of 0 is

determined and finally, the precise transition energy is calculated.

In the case of amorphous materials, a variety of electronic transitions take place.

Only in one of the calculated spectra in this work, tens of electronic transitions are

observed. The experimental DR of sp-Si is a result of all the excitations from the variety

of clusters in the material and will therefore contain a very large number of transitions. In

such situations, a precise line-shape analysis of the DR spectrum is impossible.

Therefore, the analysis of the DR characteristic of sp-Si (Figure 7-3) will be based

on certain assumptions. First, the DR bands positioned between 200 and 450 nm will be

considered to have a 0 parameter = 900. Therefore, the electronic transition energies

within these bands do not need to be corrected. The bands between 450 and 800 nm

obviously have components with 90 900. They were not corrected, but it was rather

assumed that energy bands do exist in this region in the vicinity of the observed peaks

(the correction factors are usually around 10-2 eV).

The DR signal can be expressed in terms of the real and imaginary components of

the dielectric constant E [92]:

AR dek
-R k, (7-2)
(R) dX


1.0 -A
Figure 7-2= 90
I \


absorption spectra of various Si-based clusters. The comparison was done visually and a

good fit was considered to be one, which reproduced closely the DR envelope. The x2
200analysis, described in Section 4 was performed always between 200 70and 450 800nm, since

the rest of the DR spectrum was not corrected. The peaks between 450 and 800 nm do not

show negative absorption, but correspond to DR absorption peaks with 0 90, see

Figure 7-2.


The DR spectrum of Si spark-processed in pure O is plotted in Figure 7-4. As

shown above, it represents the absorption spectrum of the material. Again, similarly to

the above case, this spectrum was analyzed based on the assumption that the energy

bands between 200 and 450 nm have 0 = 900, while the bands between 450 and 800 nm

have components with 0 900. The latter were not corrected, but it was assumed that

energy bands do exist in this region in the vicinity of the observed peaks. The x2 analysis

to this spectrum (Section 4) was performed always between 200 and 450 nm, where 0




M 0.5-


200 250 300 350 400 450 500
Wavelength [nm]

Figure A-4. Differential Reflectogram of Si spark-processed in pure O atmospheres.

S- 900

zero line




Spark-processed Si (sp-Si) is a porous solid-state material. Due to the nature of its

structure and morphology, the traditional methods for porosity measurements are not

applicable. Using the Measure Theory and the expected value theorems of stereology, we

have calculated the porosity of sp-Si to be 43%. Stereological analysis was applied to sp-

Si specimen, prepared within a fixed set of growth parameters. Over 60 cross-sectional

scanning electron micrographs of the specimen were utilized in this work. The sp-Si

sample has a characteristic cylindrical symmetry due to the uniform surface resistance of

the Si substrate and to the random nature of spark processing. However sp-Si is not

isotropic, uniform and random (IUR), but rather exhibits radial and axial anisotropy of

porosity. To avoid bias in the calculation, we chose random areas of the cross-sectional

surface of sp-Si and calculated their porosities. The calculated values entered into a

weighted statistical distribution, in which the statistical weights were determined from the

symmetry properties of the sample. The statistical approach and the fact that volume is an

additive quantity, allowed us to use a 2-dimensional population of points in the

calculation of the 3-dimensional pore volume fraction and to satisfy the requirement for

IUR sample. Small-spot X-ray photoelectron spectroscopy studies of sp-Si were used in

the calculation of its density. In the case of inhomogeneous materials, the density is a

weighted (with respect to volume) average of the densities of all participating phases.

Taking into account the already calculated porosity, we have estimated the density

of sp-Si to be 1.36 g/cm3. The main contribution to this value comes from amorphous

SiO2, which occupies most of the volume of sp-Si.


There are a variety of Si-based materials, which offer a variety of physical

properties ranging from insulating to highly conductive. A subclass of these materials has

light-emitting properties and has been an object of increasing interest in the past decade.

However, the physical nature of the light emitting Si-based materials has presented some

challenges in the attempts to study their local atomic structure and other physical

properties closely related to it. The reason for that is the inhomogeneous structure of such

materials. Light-emitting Si achieved by laser ablation [97], porous Si [98] and a variety

of porous silica [99 104] have light-emitting properties and are inhomogeneous in most

cases. The bulk of these materials usually contains mixtures of phases crystalline,

amorphous, surface oxide layers and the frequently present voids (pores).

Technological application of the above materials requires deposition of metal

contacts or other thin films on their surface. In such procedures, surface and volume

porosity of the underlying material is quite important, since it can allow or disallow

smooth and continuous surface coverage. Thus, structural characterization and

understanding of morphology are vital if one is to develop a successful contact deposition


The present work represents a study of light-emitting, spark-processed Si (sp-Si,

Figure 8-1) and its topological and structural properties. Sp-Si has stable

photoluminescence (PL) [1], which is highly resistant against aging, UV irradiation and

thermal annealing up to 11000C [3]. In addition, sp-Si based electroluminescent devices

have successfully been built [105 107] and are currently undergoing a process of

optimization. Electroluminescent sp-Si devices are usually prepared in air, utilizing short

spark processing times (10 20 seconds). The material used in the present work was

prepared under identical conditions.

The bulk of sp-Si is highly inhomogeneous and porous. Its morphology and

structure have not been studied so far. Understanding of these properties has value from a

physical point of view; it can be also used to provide further insights for improved metal

contact deposition techniques.


The study of sp-Si porosity presents a serious challenge. The traditional methods

for porosity measurements cannot be applied due to the nature of sp-Si growth and

morphology. Surface atom adsorption techniques are not applicable, since sp-Si contains

a large portion of internally embedded, closed pores (Figure 8-2). The techniques that

involve pore filling are excluded for the same reason. In addition, the bulk contains pores

with dimensions in the order of nanometers. Filling of such pores with liquid may not be

complete and would introduce an unpredictable error in the measurement. Calculation of

the porosity through mass measurements is possible, however this method requires also

precise volume measurements. There were a number of attempts to utilize this technique,

but these efforts did not yield useful results. The main obstacle was the porous surface of

sp-Si, which contains features varying in dimensions from the micrometer scale to the

nanoscale. The volume could not be measured with sufficient precision since the upper

surface could not be mapped correctly (illustrated on Figure 8-3). Additional difficulties

arise from the fact that the sp-Si material is not simply deposited on a Si substrate but

Figure A-1.

Spark-processing of Si. Plasma discharges are directed from a tungsten tip to
a Si substrate. Y is an axis of symmetry, while a is the plane of cross-
sectional cut in Figure 8-2.

Figure A-2. Cross-sectional SEM micrograph of sp-Si at a magnification ofxl20. Y is
the axis of symmetry, X is a radial axis.

Figure A-3. SEM ma of the sp-Si surface.

extends into it, thereby occupying a certain volume in the substrate, which is not easy to

estimate. In other words, the underlying surface between the sp-Si and the Si substrate

cannot be mapped correctly either.

Solution to these problems was achieved by the application of stereological

measurements. The expected value theorems of stereology allow the calculation of

volume fraction of phases, surface area per unit volume, average feature size and feature

perimeter, to name a few. Detailed description of the various stereological techniques can

be found in the literature [108].

In the Measure Theory, the volume VQ of a set of points Q (in 3-dimensional

space) is defined as a measure of the set Q. The measure of Q can also be expressed as a

function which associates a number Vn with the set 2:

V = f(Q) (8-1)

Using the Peano-Jordan Measure in 3-dimensional space, we can state that the volume V

D of the set Q is proportional to the number of points in 2, and the functional

dependencef(equation 8-1) has an integral form:

VQ dp = dxdydz, (8-2)

where dp is the density of points in 3-dimensional space, dp=dxdydz. The Measure

Theory will then allow the calculation of the ratio of two volumes of 3-dimensional sets

Q2 and 02 as a ratio of their corresponding measures:

V f() (8-3)
VQn f(Q,)

Applied to the case of sp-Si, this ratio will be

porosity V(voids) f (voids)
SP V(entire sample) f (entire sample)

f dp f dxdydz
voids voids (8-4)
dp dxdydz
entire sample entire sample

where Vp is the volume fraction of porosity. The above equation can be applied directly

for calculation of porosity of sp-Si and its form will be:

Sporosiy measure of the set of points in the porous phase
Pr / =--------------- V (8-5)
measure of the set of points in the entire sample

where Pp is the so-called "point fraction". This equation allows us to study the properties

of a population of points in 2-dimensional space and apply the result to the 3-dimensional

structure of the sample.

It is very important to note, that the expression (8-5) is valid only for samples,

which are IUR, i. e. isotropic, uniform and random. The application of (8-5) to a sample,

which is not IUR will lead to a biased result.

Sp-Si presents a challenge, since the sp-Si sample is not IUR, but exhibits

anisotropy of porosity along the X (radial anisotropy) and Y axes (axial anisotropy,

Figure 8-2). To avoid bias, we need to calculate an average porosity of the sample, which

removes the anisotropy effect. Therefore, we have proceeded as follows:

* A sample of sp-Si was cut in a cross-sectional manner (Figure 8-1);

* The sample was embedded in a resin and fine-polished with diamond powder to
produce a smooth cross-sectional surface;

* The image of the cross-sectional surface was captured using scanning electron
microscope (SEM) at a magnification ofxl20 (Figure 8-2);

* A line grid was placed over the image. The spark-processed area (defined by the
surface and the interface lines in Figure 8-2) was divided into 154 numbered tiles.
Each tile is a square having a side of 44.4 am;

* The set of 154 tiles was subdivided into 32 groups of consecutive tiles. Each group
contains 4 or 5 tiles;

* From each group, we selected randomly one tile as follows:

o tile number 4;
o tile number (4+5);
o tile number (9+4);
o tile number (13+5), and so on.

This process of random selection provided us with 32 tiles with numbers 4, 9, 13,

18, 23, and so on;

* SEM micrographs at magnifications x650 were taken for each of the 32 random
tiles. At this magnification, nanopores could not be studied;

* Linear grids were placed over the images of each tile and the porosity was
calculated from equation (8-5). The numerator is the number of grid intersections
over voids (marked with bright circles, Figure 8-4), while the denominator in (8-5)
is the total number of grid intersections.

Since sp-Si also contains pores with nanometer-scale dimensions, they have to be

taken into consideration when porosity is calculated. Since a magnification of x650 is

insufficient for counting of nanopores, we prepared a second set of SEM micrographs of

the above 32 tiles, captured at a magnification of x3000 and applied equation (8-5) to

calculate the nanoporosity (Figure 8-5). The magnifications of x3000 showed sufficient

detail and were not improved with increase of magnification. To avoid duplicate pore

counting, all high-resolution micrographs were captured from random areas (within the

given tile) that do not contain macropores.

Thus, the total porosity P,1"or measured on a tile i, is determined to be

total = micro + nano. (8-6)
-1 .1 (81-6)

One also needs to take into account the fact, that the sp-Si sample has cylindrical

symmetry (Figure 8-1) with an axis of symmetry Y. The cylindrical symmetry is

contingent upon the characteristics of spark processing. Normally, the Si substrate is

uniformly doped and therefore its resistivity is the same throughout its bulk. Once a spark

event occurs at a given point of the substrate surface, the resistivity of this particular

locality increases, since spark processing creates clusters of highly resistive surface

compounds [3]. The next spark event will most probably occur at another surface point

with lower resistivity. Each spark occurs at a surface spot such, that the resistance

between the sparking tip and the spot is minimal. This fact guarantees the circular surface

pattern, observed after spark processing of Si (Figure 8-1).

Since each tile is positioned at some distance from the Y axis (Figure 8-2), it

represents a volume AVz

AV, = 2rhR, AR, (8-7)

where R, is the distance between the Y axis and the geometrical center of the tile i and

h=AR is the tile side. Then, to each tile we associate a statistical weight w,

all 32 tiles




Figure A-4. Selected tile images of the sp-Si sample at a magnification of x650. The right
column displays rectangular grids positioned over the images of the material.
The bright circular marks denote that the grid intersection resides over a
void. A) Near-surface image; B) Image of the sp-Si bulk; C) Near the
interface sp-Si/Si.



Figure A-5. Selected tile images of the sp-Si sample at a magnification of 000.
'... t I <. '..

Theright column displays rectangular grids positioned over the images

resides over a void. A) Near-surface image; B) Image of the sp-Si "bulk;
iNea the .iter fae 'Si/Si
"i/ "; *

"" F ,. -"i

Near" t i nt rf p- / --
(b )
." --- ^-- -- ------

S.. .


Figure A-5. Selected tile images of the sp-Si sample at a magnification ofx3000.
Theright column displays rectangular grids positioned over the images
of the material. The bright circular marks denote that the grid intersection
resides over a void. A) Near-surface image; B) Image of the sp-Si bulk; C)
Near the interface sp-Si/Si.