Electron-emission-in-intense-electric-fields--经典FN

ElectronEmissioninIntenseElectricFieldsAuthor(s):R.H.FowlerandL.NordheimSource:ProceedingsoftheRoyalSocietyofLondon.SeriesA,ContainingPapersofaMathematicalandPhysicalCharacter,Vol.119,No.781(May1,1928),pp.173-181Publishedby:TheRoyalSocietyStableURL::24/08/201322:19YouruseoftheJSTORarchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,[e-mail]..TheRoyalSocietyiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoProceedingsoftheRoyalSocietyofLondon.SeriesA,ContainingPapersofaMathematicalandPhysicalCharacter.:19:13PMAllusesubjecttoJSTORTermsandConditions173ElectronEmissioninIntenseElectricFields.ByR.H.FOWLER,F.R.S.,andDr.L.NORDHEIM.(ReceivedMarch31,1928.)?1.Introduction.-Themainfeaturesofthephenomenonoftheextractionofelectronsfromcoldmetalsbyintenseelectricfieldsarewellknown,andanapproximatetheoryoftheeffectwasfirstdevelopedbySchottky.*Morerecentlytheexperimentaldatahavebeenmuchimproved,notablybyMillikanandEyring,tandMillikanandLauritsen:.Thetheoryhasbeenconsideredafreshby0.W.Richardson?andbyHoustonliworkingwithSommerfeld.Itseemstous,however,thatthereisstillroomforimprovementinthetheo-reticalexpositionanditscorrelationwiththeexperiments.Neither0.W.RichardsonnorHoustonreallytreatthetheoryinthesimplestraight-forwardwaywhichisnowpossibleinthenewmechanics,usingtherevivedelectrontheoryofmetalswhichweowetoSommerfeld.Again,whileMillikanandLauritsenseemtohaveestablishedquitedefinitelythelawsofdependenceoftheemissiononthefieldstrengthF,theyspeakoftheimplicationsoftheirresultinawaywhichishardtojustifyandmightincertaincircumstancesprovetobedefinitelymisleading.MillikanandLauritsenshowthataplotoflogI,whereIisthecurrent,against1/Fyieldsagoodstraightlinewhenevertheexperimentalconditionsaresufficientlystable.Atordinarytemperaturesthesecurrentsarecompletelyindependentofthetemperature.TheformulaforthesecurrentsisI=Ce-a/,(1)whichis,ofcourse,indistinguishablefromI=CF2e-a(2)Millikanandhisassociateshavealsoshownthatasthehighertemperatures,atwhichordinarythermionicemissionbegins,areapproached,thestrongfieldemissiondoesbecomesensitivetotemperatureandfinallyblendsintothethermionic.*Schottky,'Z.f.Physik,'vol.14,p.80(1923).tMillikanandEyring,'Phys.Rev.,'vol.27,p.51(1926)..MillikanandLauritsen,'Proc.Nat.Ac.Sci.,'vol.14,p.45(1928).?O.W.Richardson,'Roy.Soc.Proc.,'A,vol.117,p.719(1928).|1Houston,'Z.f.Physik,'vol.47,p.33(1928).Thiscontentdownloadedfrom146.232.129.75onSat,24Aug201322:19:13PMAllusesubjecttoJSTORTermsandConditionsR.H.FowlerandL.Nordheinm.OnthestrengthofthesefactstheysuggestthatperhapstheremayexistageneralformulaforthecurrentI=A(T+cF)2e-b(T+c),(3)validoverwiderangesoftemperature(T)andfieldstrength.Thisformulais,ofcourse,correctforlargeTandsmallFandalsoforlargeFandsmallT.Atintermediatestrengthsitdoesnotappeartohavebeentestedquantitativelyandthereforeyetawaitsexperimentalandtheoreticalinvestigation.Ononeotherdeduction,however,theylaygreatemphasis,andthiswefindliabletomislead.Theyassertthatadistinctionshouldbedrawnbetweentheelectronswhichcanfunctionasthermionsandtheordinaryconductionelectronswhichyieldtheemissionatgreatfieldstrengthsandareabsolutelyindependentofthetemperature.Inthispaper,therefore,weextendtheresultsofNordheim*toincludetheeffectofanexternalfieldusingthesamemethodsandthesameunderlyingpictureofthemetal(Sommerfeld's).Weestablishtheformula(2)independentofTatlowtemperaturesinagreementwithexperiment.Wefailtofindanytheoreticaljustificationfor(3),though,ofcourse,somejustificationmayexist.CombiningourresultswiththoseofNordheimweshowthatSommerfeld'spictureofametalyieldstheformulabothforstrongfieldsandforthermionicemission.AsinglesetoffreeorconductionelectronsdistributedaccordingtotheFermi-Diracstatisticssufficesforbothpurposes.ItisforthisreasonthatwetakeexceptiontothestatementsofMillikanandLauritsenrecordedabove.Wegladlyadmitthateverythingtheysaycanbereconciledwithourtheory,butonlybyaforcedinterpretationoftheirstatementswhichweconsiderlaytheemphasiswrongly.OurcalculationsarecloselyalliedtosomerecentworkbyOppenheimertonthehydrogenatominanexternalelectricfield.Oppenheimernoticesthathisworkhasabearingontheemissionofelectronsinstrongfields,buthedoesnotpursuethematterfurther.Forourpurposesthecalculationscanbeshornofirrelevanciesandmadesomuchsimplerthatitisworthwhileattackingtheproblemdenovo.?2.TheReflectionofElectronsataPotentialJumpwhenanElectricFieldactsononeSide.-InthepaperquotedNordheimhascalculatedexactlythereflectionoremissioncoefficientsforelectronsofgivenenergyWincidentfromtheleftonasurfaceatwhichtheirpotentialenergyissuddenlyincreasedby*Nordheim,'Z.f.Ph