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acceptor受主donor施主recombination复合majority多子minority少子transitionregion过渡区depletionregion耗尽区contactbarrier接触势垒p-njunctionpn结heterojunction/异质结EHP电子空穴对homojunction/同质结,Schottkybarrier/肖特基势垒barrierheight/势垒高度ideal/理想的workfunction/功函数practical/实际的electronaffinity/电子亲和能Fermilevel/费米能级rectifier/整流器electrostaticpotential/静电势breakdown/击穿rectifyingcontacts/整流接触Ohmiccontacts/欧姆接触surfacestate/表面态lattice-matched/晶格匹配的tunnelingeffect/隧道效应,半导体器件工作的基本方程,泊松方程,电流密度方程,电流连续性方程,Manyoftheusefulpropertiesofap-njunctioncanbeachievedbysimplyforminganappropriatemetal-semiconductor(MS)contact.,5.7Metal-Semiconductorjunctionsorcontacts(金属-半导体结、金-半接触）,5.7.1SchottkyBarriers,http:/en.wikipedia.org/wiki/Walter_H._Schottky,Possibly,inretrospect,Schottkysmostimportantscientificachievementwastodevelop(in1914)thewell-knownclassicalformula,nowwritten-q2/40 x,fortheinteractionenergybetweenapointchargeqandaflatmetalsurface,whenthechargeisatadistancexfromthesurface.Owingtothemethodofitsderivation,thisinteractioniscalledtheimagepotentialenergy(imagePE).Schottkybasedhisworkonearlierworkby(Lord)KelvinrelatingtotheimagePEforasphere.SchottkysimagePEhasbecomeastandardcomponentinsimplemodelsofthebarriertomotion,M(x),experiencedbyanelectrononapproachingametalsurfaceorametal-semiconductorinterfacefromtheinside.,1.Schottkyeffect,(TheimagePEisusuallycombinedwithtermsrelatingtoanappliedelectricfieldFandtotheheighth(intheabsenceofanyfield)ofthebarrier.Thisleadstothefollowingexpressionforthedependenceofthebarrierenergyondistancex,measuredfromtheelectricalsurfaceofthemetal,intothevacuumorintothesemiconductor:Here,eistheelementarypositivecharge,0istheelectricconstantandristherelativepermittivityofthesecondmedium(=1forvacuum).Inthecaseofametal-semiconductorjunction,thisiscalledaSchottkybarrier;inthecaseofthemetal-vacuuminterface,thisissometimescalledaSchottky-Nordheimbarrier.Inmanycontexts,hhastobetakenequaltothelocalworkfunction.ThisSchottky-Nordheimbarrier(SNbarrier)hasplayedinimportantroleinthetheoriesofthermionicemissionandoffieldelectronemission.Applyingthefieldcausesloweringofthebarrier,andthusenhancestheemissioncurrentinthermionicemission.ThisiscalledtheSchottkyeffect,andtheresultingemissionregimeiscalledSchottkyemission.,Theworkfunction(功函数):TheenergywiththeworkfunctionisrequiredtoremoveanelectronattheFermileveltothevacuumoutsidethemetal.(Al=4.3eV)theelectronaffinity(电子亲和能):Theenergywiththeelectronaffinityisrequiredtoremoveanelectronatthebottomoftheconductionbandtothevacuumoutsidethesemiconductors.(Si=4.1eV),Foursetsofcombination:(1)metal-ntypesemiconductor,qmqs(2)metal-ntypesemiconductor,qmqs(4)metal-ptypesemiconductor,qmqsMetal/n-typesemiconductor,2.Schottkybarriers（肖特基势垒）,chargetransferoccursuntiltheFermilevelsalignatequilibrium,theelectrostaticpotentialofthesemiconductormustberaisedV0theelectronenergymustbelowered.qV0thedepletionregionisformednearthejunction.Contactpotentialbarrier:qV0=qm-qspotentialbarrierheightqB=qm-q,BiscalledSchottkybarrier,（2）Metal/ptypesemiconductor,qmqs,ElectronsflowfrommetaltosemiconductortilltheFermilevelsalignatequilibrium,theelectrostaticpotentialofthesemiconductormustbeloweredV0theelectronenergymustberaisedqV0thedepletionregionisformednearthejunction.Contactpotentialbarrier:qV0=qs-qm,V0retardsholediffusionfromthesemiconductortothemetal,5.7.2Rectifyingcontacts(diode),YoucantreattheSchottkybarrierforM/n-typeS(orM/p-typeS)astheP+N(orN+P)junctionexceptthatnoholeinjectionoccursfromthemetalintothesemiconductor.,(a)Forwardbias,ElectronsflowfromsemiconductortoMetalunderforwardbias.,Case1:Metal-ntypecontact,(b)Reversebias,OneimportantfeatureisthatthesaturationcurrentI0dependsuponBandisunaffectedbythebiasvoltage.I0Exp(-qB/kT),Howaboutp-njunction?,Forpnjunction:ForM-Sjunction,10-11A/cm2,Case2:metal-ptypeSchottkycontact?,(a)Forwardbias,(b)Reversebias,Holesflowfromsemiconductortometalunderforwardbias.,Areversevoltageincreasesthebarrierforholeflowandthecurrentbecomesnegligible.,5.7.3Ohmiccontacts(ideal,resistor),Inmanycaseswewishtohaveanohmicmetal-semiconductorcontact,havingalinearI-Vcharacteristicinbothbiasingdirections.Forexample,theinterconnectedlines(互连线)arerequiredinIC.So,itisimportantthatsuchcontactsbeohmic,withminimalresistanceandnotendencytorectifysignals.,R,Thebarriertoelectronflowbetweenthemetalandsemiconductorissmallandeasilyovercomebyasmallvoltage.,Case1M/ntype,qmqs,Unliketherectifyingcontacts,nodepletionregionoccursinthesemiconductorinthesetwocasessincetheelectrostaticpotentialdifferencerequiredtoaligntheFermilevelatequilibriumcallsforaccumulationofmajoritycarriersinthesemiconductor.,5.7.3Ohmiccontacts(practical),Inpractice,itisalwaysimpossibleforustoformtheohmiccontactsofmetal-semiconductorbychoosingtheappropriateworkfunctionofthemetal.Thereasonisthatthesemiconductorsurfacecontainssurfacestatesduetoincompletecovalentbonds.Themetal/semiconductorcontactsformalwaysabarrierwhatevermetalsareused.So,toobtaintheohmiccontactsformetal/semiconductor,apracticalmethodisbydopingthesemiconductorheavilyinthecontactregions.Therefore,ifabarrierexistsattheinterface,thedepletionwidthissmallenoughtoallowcarrierstotunnelthroughthebarrier.,Tunnelingprobabilitycanbereferredto(P236-238).,5.7.4TypicalSchottkyBarriers,Pinningeffect(钉扎效应）:becauseofsurfacestatesandinterfaciallayer,P168ItiseasiertoobtainthewidthofthedepletionregionatM-SSchottkyjunction.,Forp-njunction,ForM-ntypeSchottkybarrier,ForM-ptypeSchottkybarrier,PROBLEM1,Whatisthedifferencebetweenp-ndiodeandSchottkybarrierdiode?,Problem2,ASchottkybarrierisformedbetweenametalhavingaworkfunctionof4.3evandptypeSi(electronaffinityis4ev).TheacceptordopingintheSiliconis1017cm-3.(a)CalculateqV0anddrawtheequilibriumbanddiagram.(b)Drawthebanddiagramwith0.3Vforwardbiasand2Vreversebias.,3.一块Ge材料(),其中掺有51013cm-3的施主杂质和2.51013cm-3的受主杂质（均匀掺杂），Dn=100cm2/s，Dp=50cm2/s.试计算该样品的电导率。设该样品的电子亲和势为4.0ev，则它与功函数为4.5eV的金属接触时，功函数之差为多大？所形成的接触是整流接触还是欧姆接触？,
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