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355Vol.35No.5200610JournalofUniversityofElectronicScienceandTechnologyofChinaOct.20061122(1.618307;2.610054)NottinghamNottinghamNottingham;Nottingham;;O462.4AAnalysisoftheTipTemperatureofConeFieldEmittersJIANGTian-fu1TIANShi-kai1ZENGBao-qing2YANGZhong-hai2(1.CollegeofComputerScience,CivilAviationFlightUniversityofChinaGuanghanSichuan618307;2.SchoolofPhysicalElectronics,Univ.ofElectron.Sci.&Tech.ofChinaChengdu610054)AbstractBasedontheheatingflowequation,thetiptemperatureoftheconefieldemitterswerecomputedself-consistentlyinNottinghameffectandinJouelheating.Thetemperatureasafunctionofstructureparameterandphysicalparameteroftheconeemitterwascalculated.TheresultsshowthatNottinghameffect,thermalconductivityandcrosssectiondeterminethetiptemperatureobviously,thetemperaturefromthisheatingcannotpossiblybeacauseforfailureinmosttipsundernormaloperatingconditions.Keywordsconefieldemitters;Nottinghameffect;ouelheating;self-consistentcalculation[1]SpindtSpindt[2-4]NottinghamTEφkρT11.1Nottingham[5]dw[6]712243/244()8.7010exp[6.8310(/)(3.7910(/))]ln[1exp(1.1610(/))]PwTwEvEwwTφ−−=×−××+−×+(1)TEϕ41/2()(3.7910(/)vyvEw−=×NordheimT2005-05-13(2002061400)(2002061400)(1969-).5:7851()e()()daWHTPφφ−−=+∫(2)02()e()()dvHTPφφ−−=+∫(3)3/2124120e3.7410/eVvEE−==×ESchottky30()()(2)thHTJTvkTφ=−−25400120exp[()/8.610][1.7210]TvTvTφφ−−=−−×−+×(4)thJEφ123()()()()HTHTHTHT=++(5)1.2Nottingham1[7]4223224(d/d)2(d/d)(/πtg)yTyyTyIkbρθ+=−=(6)0yhTT==(7)[]0/()()yykTyHTHT=∂∂==(8)T0H(T)T(2)(5)(7)(8)rθ2424222220222233/2tg/tg/tg(())/2tg/tg/tg(())TTJrhJrkrkhHTJrkJrkhrkHTρθρθθθρθθ=+++−−−(9)220/πtgJIyθ=(10)(2)(5)(9)(10)TMATLAB2k=1.38W·cm−2ρ=5.7×10−6W·cmϕ=4.35eVh=1µmθ=10°r=20nm2.12Fowler-Nordheim(F-N)Nottingham5×1081×1091.5×1092×1092.4×1090500100015002000250030003500T/KA/cm2050010001500200025003000T/K3.84.34.8/eV23yhθy01357862.2108V·cm−145.3eV3F-NNottingham2.3107V·cm−110−61.1−5W·cm(9)H(T)=0Nottingham[4]()2.4107V·cm−10.62.9W/cm2·K2.59.6×107V·cm−15°10°20°θ45°1.65×109A/cm210°2.60×109A/cm220°5.67×109A/cm25°158µA10°992µA20°1060µASpindt102A/cm2NottinghamSpindtNottingham5001000150020002500300000T/K51015202530/(°)5001000150020000T/K0.20.40.60.81.01.20/µm51020452.69.5×107V·cm−1r=20nm55°10°20°5°0.08µm0.3µm0.3µm()5:7873Nottingham()[1]SpindtCA,BrodieI,HumphreyL,etal.Physicalpropertiesofthin-filmfieldfield-emissioncathodeswithmolybdenumcones[J].J.Appl.Phys.,1976,47:5248.[2]BrodieI.Temperatureofasrtonglyfieldemittingsurface[J]Int.J.Electron,1965,18:223.[3]RobertBMarcusK,ChinK,etal.Simulationanddesignoffieldemitters[J].IEEETransactonsonElectronDevices,1990,37(6):1545.[4]AnconaMGThermomechanicalanalysisoffailureofmetalfieldemitters[J].J.Vac.Sci.Technol.,1995,B13(6):2206.[5]NottinghamWB.Onthethermodynamicinterpretationofcertainthermionicandthermoelectricphenomena[J].Phys.Rev.,1941,(59):889-896[6]MurphyEL,GoodRH.Thermionicemission,fieldemission,andthetransitionregion[J].Phys.Rev.,1956,102(6):1464.[7]BrodieI.Temperatureofastronglyfieidemittingsurface[J].J.Electron,1965,(18):223.[8]YuZX,WuSS,XuNS.Theoreticalstudyofthermalinstabilityofmotipswithanwithoutdiamondcoatings[J].J.Vac.Sci.Technol.,1999,B17(2):562.-------------------------------------------------------------------------------------------------------------------------------------------(769)1McCallumlg(Q)E{lg(Q)}lg(Q)/(%)/sMcCallum10−3.710−2.310−1.710480.992010−410−310−2.550248.39703McCallumMcCallumCauchyCauchy[1][1]McCallumBC.Blinddeconvolutionbysimulatedannealing[J].OpticsCommunications,1990,75(3):101-105.[2]KundurD,HatzinakosD.Blindimagedeconvolution[J].IEEESignalProcessingMagazine,1996,13(3):43-64.[3],.CauchyGaussian[J].(),2000,40(9):109-112.[4]YanLei-po,WangLi-po.Imagerestorationusingchaoticsimulatedannealing[C]//ProceedingsoftheInternationalJointConferenceonNeuralNetworks,2003,4:3060-3064.[5].[M].:,2001.