功能材料2：基礎(1)2013

無機功能材料

InorganicFunctionalMaterials

（AdvancedElectronicMaterials）

材料科學與工程學院郭露村

參考書：SuggestedReadings

沈能玨主編，《現(xiàn)在電子材料技術》，第一版，國防工業(yè)出版社，2000.1干福熹主編，《信息材料》，第一版，天津大學出版社，200.12楊大智主編，《智能材料與智能系統(tǒng)》，第一版，天津大學出版社，200.12雷永泉主編《新能源材料》，第一版，天津大學出版社，200.12余金中編，《半導體光電子技術》，第一版，化學工業(yè)出版社，2003.4吳德馨等編，《現(xiàn)代微電子技術》第一版，化學工業(yè)出版社，2002.1唐潔影等編，《電子工程物理基礎》，第一版，電子工業(yè)出版社，2002.6第二章半導體及光電子材料基礎

ChapterII

FundamentalsofSemicondutors&Optoelectronics§2.1半導體基礎知識§2.2光電子材料基礎§2.3功能材料界面現(xiàn)象

2.1.1自由電子氣模型

Freeelectrongasmodel化學鍵§2.1半導體材料基礎金屬金屬特性:自由電子在離子實(ioncore)之間幾乎不受約束自由電子氣模型:(1900年)

電子完全自由,猶如理想氣體分子,被表面勢場約束在金屬內(nèi)部.電子的能量是純動能的.

“Electrongasinbox”離子實EFEFT=0okT>0ok2.1.2費米能級FermienergylevelEEEFEFEFf(E)EFf(E)1/2費米能級與費-狄分布的關系Fermi-DiracDistribution：T=0okT>0ok結論：1.費米能級處電子存在的幾率為1/2。

2.費米能級不隨溫度改變。EE溫度對電子F-D分布的影響：高溫時還原成玻耳茲曼經(jīng)典分布TheEnergyDistributionFunction

Thedistributionfunctionf(E)istheprobabilitythataparticleisinenergystateE.Thedistributionisageneralizationoftheideasofdiscreteprobabilitydiscretetothecasewhereenergycanbetreatedasacontinuousvariable.Threedistinctlydifferentdistributionfunctionsarefoundinnature.ThetermAinthedenominatorofeachdistributionisanormalizationtermwhichmaychangewithtemperature.MoreInformationTheMaxwell-BoltzmannDistribution

TheBose-EinsteinDistribution

TheFermi-DiracDistributionTheMaxwell-Boltzmanndistribution

istheclassicaldistributionfunctionfordistributionofanamountofenergybetweenidenticalbutdistinguishableparticles.

Besidesthepresumptionofdistinguishability,classicalstatisticalphysicspostulatesfurtherthat:Thereisnorestrictiononthenumberofparticleswhichcanoccupyagivenstate.Atthermalequilibrium,thedistributionofparticlesamongtheavailableenergystateswilltakethemostprobabledistributionconsistentwiththetotalavailableenergyandtotalnumberofparticles.Everyspecificstateofthesystemhasequalprobability.Oneofthegeneralideascontainedinthesepostulatesisthatitisunlikelythatanyoneparticlewillgetanenergyfarabovetheaverage(i.e.,farmorethanitsshare).Energieslowerthantheaveragearefavoredbecausetherearemorewaystogetthem.Ifoneparticlegetsanenergyof10timestheaverage,forexample,thenitreducesthenumberofpossibilitiesforthedistributionoftheremainderoftheenergy.Thereforeitisunlikelybecausetheprobabilityofoccupyingagivenstateisproportionaltothenumberofwaysitcanbeobtained.FermionsFermionsareparticleswhichhavehalf-integerspinandthereforeareconstrainedbythePauliexclusionprinciple.Particleswithintegerspinarecalledbosons.Fermionsincudeelectrons,protons,neutrons.Thewavefunctionwhichdescribesacollectionoffermionsmustbeantisymmetricwithrespecttotheexchangeofidenticalparticles,whilethewavefunctionforacollectionofbosonsissymmetric.Thefactthatelectronsarefermionsisfoundationaltothebuildupoftheperiodictableoftheelementssincetherecanbeonlyoneelectronforeachstateinanatom(onlyoneelectronforeachpossiblesetofquantumnumbers).ThefermionnatureofelectronsalsogovernsthebehaviorofelelctroninametalwhereatlowtemperaturesallthelowenergystatesarefilleduptoalevelcalledtheFermienergy.ThisfillingofstatesisdescribedbyFermi-Diracstatics.MoreInformation§2.1.3

晶體能帶

Energybandincrystals能帶形成的解釋（一）

—原子、分子的電子能級與晶體中能帶的關系內(nèi)層電子的能級保持不變價電子的能級變?yōu)槟軒軒纬傻慕忉專ǘ悸搴詹ㄅc能帶一維周期性勢場周期性勢場內(nèi)形成的住波PotentialEnergyaIoncoreProbabilitydensityStandingwave1Standingwave2π/aπ/akkEgEnergyEnergy無勢場時自由電子一維周期性勢場下形成能隙Eg解表明:晶格內(nèi)會產(chǎn)生能隙.aThebanddiagramofSi,e.g.,thenassumesitsstandardform:GaAs三維能帶構造§2.1.4半導體及其能帶結構

semiconductorsandtheirbandstructures【電導與載流子】carries載流子濃度決定物質(zhì)的電導特性能帶結構決定載流子濃度!【價帶】Valenceband

由價電子形成的能帶【導帶】Conductionband

可參與導電的能帶【滿帶空帶】Filled&unfilledband

完全被電子占滿的能帶稱滿帶，完全未被電子占有的能帶稱空帶。滿帶空帶均不導電。【禁帶】Forbiddenband

電子無法進入的能帶。禁帶的寬度，又稱能隙bandgap能帶基本術語【金屬、絕緣體、半導體能帶結構比較】金屬價帶未滿，電子無須躍過禁帶可直接參與電導。價帶導帶Eg導帶Eg導帶價帶價帶絕緣體價帶滿,禁帶很寬,電子很難進入導帶。半導體價帶雖滿,但禁帶較窄,一部分電子可以跳入導帶半導體能帶寬度0.1-2eV【能帶中的費米能級的意義】FermilevelinbandFermienergy,orFermilevel,EFanditsmeaningEF費米能級(EF)是晶體中電子能量高低的基本指示標尺,晶體的能帶結構與EF密不可分。研究的重點是EF附近的能帶結構。遠離費米能級的能帶或能級無實際意義。費米能級的物理意義(2)EFEFT=0oKT>0oK本征半導體能帶結構價帶導帶Eg禁帶【本征半導體】Intrinsicsemiconductor本征缺陷濃度=電子濃度=空穴濃度

ni

=

ne=nh本征半導體載流子數(shù)（numberofcarries）或濃度服從Fermi-Dirac分布。載流子數(shù)隨溫度而定。EF純鍺是本征半導體,其載流子濃度隨溫度指數(shù)變化典型的半導體材料禁帶寬度非本征半導體extrinsicsemiconductors

（雜質(zhì)半導體

impuritysemiconductors）【施主與施主能級】Donoranddonorlevel【受主與受主能級】Acceptorandacceptorlevel

n-typeextrinsicsemiconductorsandthebandmodelP5價磷摻雜于4價硅中形成施主能級,產(chǎn)成n半導體EFEFp-typeextrinsicsemiconductorsandthebandmodelAlAl3價鋁摻雜于4價硅中形成受主能級,產(chǎn)成P半導體ImpurityLevelsin

Si:EG=1,124meVPhosphorous,P: EC-ED=44meVArsenic,As: EC-ED=49meVBoron,B: EA-EV=45meVAluminum,Al: EA-EV=57meVGallium,Ga: EA-EV=65meV§2.1.5p-n結

p-nJunction耗盡層p-n結固定的受主位（帶負電）固定的施主位（帶正電）EFpn結的內(nèi)電場（勢壘)的形成及其對自由電子和空穴的作用內(nèi)電場p-n結能帶形成示意圖耗盡層PNEF無外電場（偏壓）時pn結的能帶結構內(nèi)電場PN+V-ForwardBias外電場對外電場對pn結的能帶結構的影響內(nèi)電場外電場VReversebias+PN-外電場對pn結的能帶結構的影響內(nèi)電場外電場二極管（pn結）的電流電壓特性Wecreateap-njunctionbyjoiningtogethertwopiecesofsemiconductor,onedopedn-type,theotherp-type.Thiscausesadepletionzonetoformaroundthejunction(thejoin)betweenthetwomaterials.Thiszonecontrolsthebehaviourofthediode.Theanimationshowsthegeneralbehaviourofap-njunction.§2.2

光電子基礎

FundamentalsofOptoelectronics光與電磁波固體的光吸收與發(fā)射激光2.2.1

光與電磁波

Light&electromagneticwaves頻率（能量）波長電磁波光頻部分：紫外、可見、紅外5~0.2eV能量eV波長與光子能量對應關系UV100-400nm12.4-3.10eVViolet400-425nm3.10-2.92eVBlue425-492nm2.92-2.52eVGreen492-575nm2.52-2.15eVYellow575-585nm2.15-2.12eVOrange585-647nm2.12-1.92eVRed647-700nm1.92-1.77eVNearIR10000-700nm1.77-0.12eV【光與光子】Light&photonsI=I0e-αx2.2.2

固體的光吸收

Light&electromagneticwaves選擇吸收：呈色均勻吸收：灰黑光吸收基本公式(TheBeer-LambertLaw)xScattering(Mie,Rayleigh)AbsorptionEmission(Fluorescence)IncidentBeamsParticles光吸收機理：與物質(zhì)內(nèi)電子相互作用【金屬、絕緣體、半導體的光吸收譜比較】金屬：對可見光的吸收強烈，電子處于未滿帶，吸收后即可在帶內(nèi)到激發(fā)態(tài)。無機電介質(zhì)：吸收小，大多透明，是因為價電子處在滿帶，不能吸收光子而自由運動。半導體：與金屬類似。本征吸收(帶間吸收)fundamentalabsorptionν≥Eg/hν=Eg/h稱為吸收邊緣（absorptionedge）EgEg激子吸收(Excitonabsorption)

【自由載流子吸收】freecarrierabsorption又稱：帶內(nèi)吸

intrabandabsorption【雜質(zhì)吸收】Impurityabsorption【直接躍遷】directtransition【間接躍遷】indirecttransition

直接吸收與間接吸收GaAs和Si能帶結構的比較【光電導】photoconductivity【光生伏打效應】（光電效應）

photovoltaiceffectEF太陽能與太陽能電池DifferentPVmaterialshavedifferentenergybandgaps.Photonswithenergyequaltothebandgapenergyareabsorbedtocreatefreeelectrons.Photonswithlessenergythanthebandgapenergypassthroughthematerial.NewWayofHarnessingPhotonsforElectricityProposed

ScienceDaily(Nov.26,2012)“SolarEnergyFunnel"The"funnel"isametaphor:Electronsandholes--whicharesplitofffromatomsbytheenergyofphotons--aredriventothecenterofthestructurebyelectronicforces,notbygravityasinahouseholdfunnel.Thequesttoharnessabroaderspectrumofsunlight'senergytoproduceelectricityhastakenaradicallynewturn,withtheproposalofa"solarenergyfunnel"thattakesadvantageofmaterialsunderelasticstrain."We'retryingtouseelasticstrainstoproduceunprecedentedproperties,"saysJuLi,anMITprofessorandcorrespondingauthorofapaperdescribingthenewsolar-funnelconceptthatwaspublishedthisweekinthejournalNaturePhotonics.Whenthisdiodeisirradiated,thephotonsareabsorbedbythematerial,andeachphotongivesbirthtoanelectronandahole(thisiscalledanelectron-holepair).Thejunctionofthediodeseparatestheelectronsfromtheholes,creatingavoltagebetweenthenandpcontacts,andacurrentcirculatesifaresistorisplacedbetweenthediodecontacts(figure).太陽能電池供電系統(tǒng)2.2.3

固體的光發(fā)射

Lightemittingofsolids【發(fā)光】Luminescence

Luminescenceisthewordforlightemissionaftersomeenergywasdepositedinthematerial.物質(zhì)所發(fā)光的特性由能級差（能隙）決定【光致發(fā)光】

Photoluminescencedescribeslightemissionstimulatedbyexposingthematerialtolight-bynecessitywithahigherenergythantheenergyoftheluminescencelight.【熒光】

fluorescence

ifittakesshorttimes-within1second.

【磷光】

phosphorescence

ifittakeslongtimes-uptohoursanddays-fortheemission.【電激發(fā)光】

EL

electroluminescence

又稱：電致發(fā)光pn結發(fā)光原理無外電源正偏壓電源半導體量子阱發(fā)光結構激光二極管2.2.4

激光

Laser

Lightamplificationbystimulated

emissionofradiation【激光簡史】1917Einste,StimulatedEmission1960Maiman

thefirstlaser（ruby）1961Javan，firstgaslaser.1962FourgroupsstimuatedemissionfromGaAssemiconductordiodes1972Madeythefirstfreeelectronlaser

1985Matthewsx-raylaser(20nm)1993Kimura,GaN

blueLaser

Conventionalsource

Laser方向性

相干性

非相干光相干光【普通光源與激光的比較】

【受激輻射】

StimulatedEmission【自發(fā)輻射】

SpontaneousEmission

受激輻射過程Increasingtheintensityofalightbeamthatpassesthroughanamplifyingmediumamountstoputtingadditionalenergyintothebeam.Thisenergycomesfromtheamplifyingmediumwhichmustinturnhaveenergyfedintoitinsomeway.Inlaserterminology,theprocessofenergizingtheamplifyingmediumisknownas"pumping".【激光的3大基本條件】3BasicConditionsforLaser1.粒子數(shù)反轉(zhuǎn)

Inversion

2.受激輻射StimulatedemissionOnephotonhnimpingingonamaterialthatisinastateofinversion(withtherightenergydifferencehnbetweentheexcitedstateandthegroundstate)may,bystimulatedemission,causealotofphotonstocomeoutofthematerial.Moreover,thesephotonsareallinphase,i.e.wehavenowastrongandcoherentbeamoflight-amplificationoflightoccurred!3.共振腔Osillationchamber(oscillator)Standingwavesproducedonavibrating共振：產(chǎn)生注波共振：光放大（雪崩）

【氣體激光】【固體激光器】Thefirstmaterialusedwassyntheticruby.Rubyiscrystallinealumina(Al2O3)inwhichasmallfractionoftheAl3+ionshavebeenreplacedbychromiumions,Cr3+.

Anon-radiativetransitiondoesnotresultintheemissionoflight;theenergyreleasedinthetransitionisdissipatedasheatintherubycrystal.Thisisthesametaskastoproduceanoscillatorfromanamplifierinelectronics,andthesolutionofthistaskisachievedalongidenticallines.Feedbackonefrequencyfromtheoutputoftheamplifiertotheinputandmakesureitisinphase(oraswesayforlight,"coherent".Thisfrequencywillbeamplified,thefeedbackincreases,itwillbecomemoreamplified,...,prettysoonyoursystemisnowanoscillatorforthefrequencychosen.Thatis,ifyoufeedbackalargeenoughpartoftheoutputtoaccountforlossesthatmaybeoccurringinthefeedbackloopsothatstillsufficientamplitudeislefttodrivetheamplifier.TheessentialpartsareshowninthedrawingThepurposeofthemirrorsistoprovidewhatisdescribedas'positivefeedback'.Thismeanssimplythatsomeofthelightthatemergesfromtheamplifyingmediumisreflectedbackintoitforfurtheramplification.Lasermirrorsusuallydonotreflectallwavelengthsorcolorsoflightequallywell-theirreflectivityismatchedtothewavelengthorcoloratwhichthelaseroperates.Inappearance,theydonotlooklikeordinarymirrorsandaretransparentatsomewavelengths.Anamplifierwithpositivefeedbackisknownasanoscillator.MoreInformation

【半導體激光器】Thecurrentthroughthejunctionmustexceedaminimumthresholdvalue.Itmustprovideenoughholesandelectronssothattheradiationgeneratedbytheirrecombinationexceedsthelosses.Lossesarisefromseveralcauses,includingspreadingoflightoutoftheactiveregion,transmissionoflightthroughthemirrors,andabsorptionoflightbyfreecarriersinthejunction.半導體（pn結）發(fā)光原理：通過正偏壓使pn結處達到例子數(shù)反轉(zhuǎn)半導體激光器結構：共振Osillationchamberforasemiconductorlaser

Schematicsketchoftheoutputofalaserdiodeasafunctionofdrivecurrent.Thethresholdsforlaseroperationandforcatastrophicopticaldamageareindicated.半導體激光器LD與發(fā)光二極管（LED)LDLED半導體激光器的量子阱結構半導體激光器的量子阱結構Structureandindexofrefractionforvarioustypesofjunctioninthealuminumgalliumarsenidesystem.Top:Homojunction.

Middle:Singleheterojunction.Bottom:DoubleheterojunctionTheuseofasingleheterojunction(alsocalledasingleheterostructure)asshowninthemiddleportionofthefigureprovidedbetterconfinement.Inthisstructure,thereisonechangeincompositionofthematerialasonegoesthroughthejunction,sothedeviceiscalledasingleheterojunction.Thestructureprovidesalargechangeinindexofrefraction,accordingtothedatashowninFigure7.Theheterostructurereducesthelightthatleaksintothep+regionbecauseofwaveguidingeffects.Thisinturnleadstolowerlosses,lowercurrentrequirements,reduceddamage,andlon