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Experimental Study of Thermionic Emission Energy Distributions From ElectronElectron EmissionEmission fromfrom NanoscaleNanoscale CarbonCarbon MaterialsMaterials Timothy S. Fisher Purdue University Birck Nanotechnology Center Birck Nanotechnology Center Seminar 26 April 2007 Nanoscale Thermo-Fluids Lab OutlineOutline • Introduction and Basic Theory • Thermionic Energy Distribution Measurements • Nanotip-Enhanced Schottky Effect •Conclusions Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 2 ElectronElectron EmissionEmission ProcessesProcesses thermionic • Electrons can emit over potential barriers electrons (thermionic emission), OR • They can tunnel through them (field φ tunneling emission) δ electrons • First studied in detail by Fowler and EFc Nordheim (1928) for metal-vacuum-metal structures • Emission is a strong function of field EFa strength • Tunneling probability −δ vacuum anode Te∝ cathode δ=local barrier thickness voltage Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 3 IntroductionIntroduction toto ThermionicsThermionics • Brief historical background – Frederick Guthrie (1873) • Electrons escape a red-hot iron sphere. – Thomas Edison (1881) • Edison effect: Electrons travel from heated electrode to positively charged collector, in vacuum. – Owen Richardson (1928) • Quantified theory of thermionic emission (Nobel Prize) • Richardson Equation: saturation current density for thermionic emission Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 4 ApplicationsApplications •Electron source – Flourescent bulbs – TV, X-ray tubes – Mass spectrometers Howstuffworks.com – Vacuum gauges – Scanning electron microscopes • Thermionic converter –Solar Howstuffworks.com – Nuclear –Combustion – Refrigeration Schematic of a thermionic converter. Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 5 ThermionicThermionic CurrentCurrent • Observed first by Edison (1880s) • Current density derived by Richardson (1912) 2 dk mkB q 2 ⎧ −φ ⎫ Jq=− vfk() = Texp⎨ ⎬ ∫ x 323 kT W >μ+φ 42ππh ⎩⎭B ⎛⎞amp ⎧⎫−Φ = 120 T 2 exp ⎜⎟22 ⎨⎬ ⎝⎠cm K ⎩⎭kTB – W is the energy associated with motion in the direction of emission Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 6 ThermionicThermionic EnergyEnergy DistributionDistribution • Thermionic Emission Energy Distribution – High energy tail –Approximation of work function φ Ef Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 7 ThermionicThermionic DeviceDevice OperationOperation • Electrons become thermally effect of space charge excited above the chemical potential μ according to the Fermi-Dirac distribution Φ1 E φ Φ2 function. vac 2 • At a material surface, these φ1 μ2 excited electrons may μ vacuum escape the material if their 1 energy exceeds a surface or vapor anode, T2 potential barrier, known as εν(1,1) the work function, φ. E=0 • Additional potential barriers cathode, T exist due to space charge 1 and/or generated voltage, Electron motive diagram for a qV0 = μ2 - μ1. For these cases, the sum of all such thermionic power generation diode, with T > T . barriers and the work 1 2 function is denoted by Φ. Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 8 NetNet CurrentCurrent inin aa ThermionicThermionic DiodeDiode • Current flows in both directions – Higher cathode-anode current (1Æ2) due to higher cathode temperature – Reverse current from anode to cathode also exists mk2 q ⎡⎤⎧⎫−Φ ⎧−Φ ⎫ JT=−B 22exp 12 Texp net 23⎢⎥12⎨⎬ ⎨ ⎬ 2π h ⎣⎦⎩⎭kTBB12 ⎩ kT ⎭ mk2 q ⎡ ⎧⎫−φ() +qV ⎧ −φ ⎫⎤ =−B TT22exp 20 exp 2 23⎢ 12⎨ ⎬⎨⎬⎥ 2π h ⎣⎢ ⎩⎭kTBB12⎩⎭kT ⎦⎥ Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 9 EnergyEnergy ExchangeExchange ProcessesProcesses • Take energy moment of integral over f to find average energies of emitting electrons – Emitting electrons from the cathode are replaced by electrons near the chemical potential mk2 ⎧−φ( +qV ) ⎫ qq"2e=φ+Vk + TTB 2 xp20 HB,1− 2() 2 0 123 1 ⎨ ⎬ 2π h ⎩⎭kTB 1 – Electrons arriving at the cathode from the anode deposit thermal energy mk2 ⎧−φ( ) ⎫ qq"2e=φ+Vk + TTB 2 xp2 HB,2− 1() 2 0 223 2 ⎨ ⎬ 2π h ⎩⎭kTB 2 Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 10 EnergyEnergy ConversionConversion CapacityCapacity andand EfficiencyEfficiency • Energy conversion capacity is the product of generated voltage and net current PVJ" = 0 net • Thermal efficiency is defined as the ratio net heat input at the cathode (hot side) to the conversion capacity P" η= q"H mk2 ⎧−φ( +qV ) ⎫ qqVkTT"2e=φ+ + B 2 xp20 HB()20 123 1⎨ ⎬ –where 2π h ⎩⎭kTB 1 mk2 ⎧⎫−φ() −φ+qV +2 k TB T 2 exp 2 ()20B 223 2⎨⎬ 2π h ⎩⎭kTB 2 Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 11 HistoricHistoric LimitationsLimitations •High work functions • Adverse surface phenomena – Shorting between electrodes (Luke et al., 2000) – Deformities and contaminants (Wandelt, 1997) • Instability at elevated temperatures – Surface termination instability at 725 C (Köck et al. 2002; Robinson et al., 2006) Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 12 ExampleExample ResultsResults 2.5 1 ) • Capacity begins at zero 2 0.9 (no voltage) and Program Target Power Capacity (2 W/cm2) 2.0 0.8 increases until V0 is so large that the net 0.7 current becomes very 1.5 0.6 small 0.5 • Ideal efficiency 1.0 0.4 (neglecting all thermal 0.3 Thermal Efficiency losses) increases, but 0.5 0.2 becomes significant Program Target Efficiency (20%) only at impractically 0.1 Power Generation Capacity, P'' (W/cm P'' Capacity, Generation Power low capacities 0.0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 • Solution: operate at Generated Voltage, V0 (V) higher temperatures to find a practical Thermionic power generation capacity and thermal efficiency of a bulk, cesiated emitter system (φ2=1.68 eV) as condition of high a function of generated voltage under idealized conditions efficiency and capacity with maximum cathode temperature (T1=1000°C) and minimum anode temperature (T2=27°C). Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 13 FieldField EmissionEmission • Field Emission – Potential Barrier modified by applied electric field – Electrons tunnel through barrier – Low-energy-tail Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Gröning et al., 1999 Slide 14 GeometricGeometric EnhancementEnhancement • Spindt (1968) created micron- sized metallic tips to enhance r field emission Flocal = βFave ~ Fave / r β = Field enhancement factor • Field enhancement is caused by band bending predicted by E electrostatic theory Fc EFa Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 15 BasicBasic FieldField EmissionEmission TheoryTheory • Fowler-Nordheim theory linearizes the highly nonlinear potential profile – Uses field enhancement factor β – Allows analytic form for current density 1 . 5×6− 10 β 2F 2 10⎛ .⎞ 46−⎛ . 44 ×7 10 3 φ /⎞ 2 J = exp⎜ ⎟ exp⎜ ⎟ ⎜ ⎟ ⎜ ⎟ φ ⎝ φ ⎠ ⎝ βF ⎠ • Neglects temperature dependence of emission – Ignores high-energy tail of Fermi-Dirac distribution – Not useful for thermodynamic modeling Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 16 FowlerFowler--NordheimNordheim LinearizationLinearization Tip Emitter Electron potential profile Vacuum near a tip emitter. Solid line represents actual potential field. Dashed Zero Energy Datum, W=0 line represents approximate, linearized Work Function, φ field. Both fields produce the same emission Fermi Level, ζ Field Emission current. Actual Potential Profile Electron Energy Linearized with Field Enhancement Factor -Wa Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 17 ImprovedImproved EmissionEmission ModelingModeling • Current density integral over electron energies∞ W 0 = )()( dWWNWDqJ -1 ∫ -1 −Wa (e V) ζ V • D (W) is the quantum -2 transmission coefficient -2 – From Schrodinger equation -3 -1012345 solution -4 R=5 nm – Wentzel-Kramers-Brillouin (WKB) R=50 nm approximation Electron Potential, R=100 nm -5 • Expansion about the Fermi level R=10 nm R=20 nm • Strictly valid for relatively low R=∞ -6 fields 246810 • N(W) dW is the electron supply Axial Position, x (nm) function Effect of emitter radius on potential profile – Integral over Fermi-Dirac function as a function of position from emitter and for metallic emitters emitter radius. All profiles produce the same current density, J = 10 A/cm2. φ = 1.7 eV. T = 300 K. Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 18 AnodeAnode HeatingHeating StudiesStudies ¾ Field emitted electrons accelerate 35 under an electric potential ¾ High energy electrons impact anode 33 surface causing heating 31 ¾ Electron beam is localized on the anode surface creating a high energy 29 deposition flux ¾ Prior theoretical work T.S. Fisher et al., IEEE CPT 26 317 (2003). 27 D.G. Walker et al., J. Vac. Sci. Tech.-B 22 1101 (2004). 25 Infrared image of anode. The applied voltage is 446 V and the emission current is ~36 μA Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 19 ExperimentalExperimental SetupSetup Tips etched from tungsten wire ¾ Wire diameter: 0.25 mm ¾ Solution: NaOH ¾ Voltage:10 VDC ~ 6 min. 25 μm Etched tungsten tip with multi-walled CNT Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 20 TemperatureTemperature DistributionsDistributions ¾ Applied voltage: 446 V data line 1a 35 ¾ Measured current: 36.7 μA ¾ Electrode gap: 2.6 mm 33 data line 2a 31 data line 2b 37 29 35 27 33 data line 1b 31 data line 1a 25 29 data line1b Temperature (ºC) 27 data line 2a data line 2b 25 02468 r (mm)r (m) Westover and Fisher, Int. J. Heat Mass Trans., 2007. Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 21 ThermionicThermionic EnergyEnergy MeasurementsMeasurements • Hemispherical energy analyzer – Counts the number of electrons in a certain energy range emitted from a material – Several adjustable analyzer parameters can affect resolution Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 22 AnalyzerAnalyzer ParametersParameters • Kinetic energy, Ekin • Retarding ratio, R • Entrance slit width, Concentric S Hemispherical 1 Electrodes • Exit slit width, S2 • Iris diameter, Entrance Slit Exit Slit Bias Voltage Diris Electron Electron Multiplier Vbias Optics Detector Voltage Vdet Iris Aperture Analyzer Aperture Sample Emitter Nanoscale Thermo-Fluids Lab T.S.
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