功能材料2：基础(1)2013

无机功能材料

InorganicFunctionalMaterials

（AdvancedElectronicMaterials）

材料科学与工程学院郭露村

参考书：SuggestedReadings

沈能珏主编，《现在电子材料技术》，第一版，国防工业出版社，2000.1干福熹主编，《信息材料》，第一版，天津大学出版社，200.12杨大智主编，《智能材料与智能系统》，第一版，天津大学出版社，200.12雷永泉主编《新能源材料》，第一版，天津大学出版社，200.12余金中编，《半导体光电子技术》，第一版，化学工业出版社，2003.4吴德馨等编，《现代微电子技术》第一版，化学工业出版社，2002.1唐洁影等编，《电子工程物理基础》，第一版，电子工业出版社，2002.6第二章半导体及光电子材料基础

ChapterII

FundamentalsofSemicondutors&Optoelectronics§2.1半导体基础知识§2.2光电子材料基础§2.3功能材料界面现象

2.1.1自由电子气模型

Freeelectrongasmodel化学键§2.1半导体材料基础金属金属特性:自由电子在离子实(ioncore)之间几乎不受约束自由电子气模型:(1900年)

电子完全自由,犹如理想气体分子,被表面势场约束在金属内部.电子的能量是纯动能的.

“Electrongasinbox”离子实EFEFT=0ºkT>0ºk2.1.2费米能级FermienergylevelEEEFEFEFf(E)EFf(E)1/2费米能级与费-狄分布的关系Fermi-DiracDistribution：T=0ºkT>0ºk结论：1.费米能级处电子存在的几率为1/2。

2.费米能级不随温度改变。EE温度对电子F-D分布的影响：高温时还原成玻耳兹曼经典分布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

晶体能带

Energybandincrystals能带形成的解释（一）

—原子、分子的电子能级与晶体中能带的关系内层电子的能级保持不变价电子的能级变为能带能带形成的解释（二）—布洛赫波与能带一维周期性势场周期性势场内形成的住波PotentialEnergyaIoncoreProbabilitydensityStandingwave1Standingwave2π/aπ/akkEgEnergyEnergy无势场时自由电子一维周期性势场下形成能隙Eg解表明:晶格内会产生能隙.aThebanddiagramofSi,e.g.,thenassumesitsstandardform:GaAs三维能带构造§2.1.4半导体及其能带结构

semiconductorsandtheirbandstructures【电导与载流子】carries载流子浓度决定物质的电导特性能带结构决定载流子浓度!【价带】Valenceband

由价电子形成的能带【导带】Conductionband

可参与导电的能带【满带空带】Filled&unfilledband

完全被电子占满的能带称满带，完全未被电子占有的能带称空带。满带空带均不导电。【禁带】Forbiddenband

电子无法进入的能带。禁带的宽度，又称能隙bandgap能带基本术语【金属、绝缘体、半导体能带结构比较】金属价带未满，电子无须跃过禁带可直接参与电导。价带导带Eg导带Eg导带价带价带绝缘体价带满,禁带很宽,电子很难进入导带。半导体价带虽满,但禁带较窄,一部分电子可以跳入导带半导体能带宽度0.1-2eV【能带中的费米能级的意义】FermilevelinbandFermienergy,orFermilevel,EFanditsmeaningEF费米能级(EF)是晶体中电子能量高低的基本指示标尺,晶体的能带结构与EF密不可分。研究的重点是EF附近的能带结构。远离费米能级的能带或能级无实际意义。费米能级的物理意义(2)EFEFT=0ºKT>0ºK本征半导体能带结构价带导带Eg禁带【本征半导体】Intrinsicsemiconductor本征缺陷浓度=电子浓度=空穴浓度

ni

=

ne=nh本征半导体载流子数（numberofcarries）或浓度服从Fermi-Dirac分布。载流子数随温度而定。EF纯锗是本征半导体,其载流子浓度随温度指数变化典型的半导体材料禁带宽度非本征半导体extrinsicsemiconductors

（杂质半导体

impuritysemiconductors）【施主与施主能级】Donoranddonorlevel【受主与受主能级】Acceptorandacceptorlevel

n-typeextrinsicsemiconductorsandthebandmodelP5价磷掺杂于4价硅中形成施主能级,产成n半导体EFEFp-typeextrinsicsemiconductorsandthebandmodelAlAl3价铝掺杂于4价硅中形成受主能级,产成P半导体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结

p-nJunction耗尽层p-n结固定的受主位（带负电）固定的施主位（带正电）EFpn结的内电场（势垒)的形成及其对自由电子和空穴的作用内电场p-n结能带形成示意图耗尽层PNEF无外电场（偏压）时pn结的能带结构内电场PN+V-ForwardBias外电场对外电场对pn结的能带结构的影响内电场外电场VReversebias+PN-外电场对pn结的能带结构的影响内电场外电场二极管（pn结）的电流电压特性Wecreateap-njunctionbyjoiningtogethertwopiecesofsemiconductor,onedopedn-type,theotherp-type.Thiscausesadepletionzonetoformaroundthejunction(thejoin)betweenthetwomaterials.Thiszonecontrolsthebehaviourofthediode.Theanimationshowsthegeneralbehaviourofap-njunction.§2.2

光电子基础

FundamentalsofOptoelectronics光与电磁波固体的光吸收与发射激光2.2.1

光与电磁波

Light&electromagneticwaves频率（能量）波长电磁波光频部分：紫外、可见、红外5~0.2eV能量eV波长与光子能量对应关系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【光与光子】Light&photonsI=I0e-αx2.2.2

固体的光吸收

Light&electromagneticwaves选择吸收：呈色均匀吸收：灰黑光吸收基本公式(TheBeer-LambertLaw)xScattering(Mie,Rayleigh)AbsorptionEmission(Fluorescence)IncidentBeamsParticles光吸收机理：与物质内电子相互作用【金属、绝缘体、半导体的光吸收谱比较】金属：对可见光的吸收强烈，电子处于未满带，吸收后即可在带内到激发态。无机电介质：吸收小，大多透明，是因为价电子处在满带，不能吸收光子而自由运动。半导体：与金属类似。本征吸收(带间吸收)fundamentalabsorptionν≥Eg/hν=Eg/h称为吸收边缘（absorptionedge）EgEg激子吸收(Excitonabsorption)

【自由载流子吸收】freecarrierabsorption又称：带内吸

intrabandabsorption【杂质吸收】Impurityabsorption【直接跃迁】directtransition【间接跃迁】indirecttransition

直接吸收与间接吸收GaAs和Si能带结构的比较【光电导】photoconductivity【光生伏打效应】（光电效应）

photovoltaiceffectEF太阳能与太阳能电池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).太阳能电池供电系统2.2.3

固体的光发射

Lightemittingofsolids【发光】Luminescence

Luminescenceisthewordforlightemissionaftersomeenergywasdepositedinthematerial.物质所发光的特性由能级差（能隙）决定【光致发光】

Photoluminescencedescribeslightemissionstimulatedbyexposingthematerialtolight-bynecessitywithahigherenergythantheenergyoftheluminescencelight.【荧光】

fluorescence

ifittakesshorttimes-within1second.

【磷光】

phosphorescence

ifittakeslongtimes-uptohoursanddays-fortheemission.【电激发光】

EL

electroluminescence

又称：电致发光pn结发光原理无外电源正偏压电源半导体量子阱发光结构激光二极管2.2.4

激光

Laser

Lightamplificationbystimulated

emissionofradiation【激光简史】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【普通光源与激光的比较】

【受激辐射】

StimulatedEmission【自发辐射】

SpontaneousEmission

受激辐射过程Increasingtheintensityofalightbeamthatpassesthroughanamplifyingmediumamountstoputtingadditionalenergyintothebeam.Thisenergycomesfromtheamplifyingmediumwhichmustinturnhaveenergyfedintoitinsomeway.Inlaserterminology,theprocessofenergizingtheamplifyingmediumisknownas"pumping".【激光的3大基本条件】3BasicConditionsforLaser1.粒子数反转

Inversion

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

【气体激光】【固体激光器】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

【半导体激光器】Thecurrentthroughthejunctionmustexceedaminimumthresholdvalue.Itmustprovideenoughholesandelectronssothattheradiationgeneratedbytheirrecombinationexceedsthelosses.Lossesarisefromseveralcauses,includingspreadingoflightoutoftheactiveregion,transmissionoflightthroughthemirrors,andabsorptionoflightbyfreecarriersinthejunction.半导体（pn结）发光原理：通过正偏压使pn结处达到例子数反转半导体激光器结构：共振Osillationchamberforasemiconductorlaser

Schematicsketchoftheoutputofalaserdiodeasafunctionofdrivecurrent.Thethresholdsforlaseroperationandforcatastrophicopticaldamageareindicated.半导体激光器LD与发光二极管（LED)LDLED半导体激光器的量子阱结构半导体激光器的量子阱结构Structureandindexofrefractionforvarioustypesofjunctioninthealuminumgalliumarsenidesystem.Top:Homojunction.

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