Experimental Study of Thermionic Emission Energy Distributions From

Home , Thermionic emission

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

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

105.1 − β× F 226 ⎛ 4.10 ⎞ ⎛ 1044.6 φ×− 2/37 ⎞ 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. Fisher, 3/4/2006 Slide 23 AnalyzerAnalyzer ResolutionResolution

• Distortion of the energy distribution by the analyzer – σ : standard deviation of instrument function (“resolution”)

– fwhmGIS: full width at half maximum of the Gaussian instrument function

• Depends on slit widths (S1 and S2) and pass energy (Epass) – a: constant prefactor

– R0: nominal radius of hemispherical electrodes (100mm)

2 11'⎡ ⎛⎞EE− ⎤ GInst. =−exp ⎢ ⎜⎟⎥ σπ2 ⎣⎢ 2 ⎝⎠σ ⎦⎥

fwhmGIS ()SS12+ σ ==aEpass 2.356 (2.356)4R0

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 24 CalibrationCalibration

• Calibration of the analyzer work function – Work function of (100) tungsten (SCW): 4.56±0.04eV

Reference Herring Brown Nichol Smith, and et al., s, 1940 1954 Nichols, 1950 1949

Richardson 117 N/A 156 105 Constant (Amp/cm2K2) Work Function 4.56 4.59 4.56 4.52 (eV)

TEED from SCW (100) at 1273K. The form of the distribution is representative of free-electron thermionic emission theory.

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 25 Results:Results: MWCNTMWCNT ArrayArray

• Ni catalyst on Si substrate • Work function MWCNT array at 812K 4.39±0.05eV • Gronig et al. (2000) 1 4.85±0.02eV 0.8 • Average work function of Ni (Fomenko, 1966) 0.6 4.50eV 0.4

Intensity (a. u.) 0.2

33.544.555.566.5 Energy (eV)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 26 SWCNTSWCNT ArrayArray

• SWNTs: MgO catalyst support – Wide band gap insulator – Average work function of SWCNT array at 974K MgO (Fomenko, 1966): 3.1eV-4.4eV 1

• Peaks: 3.96eV and 4.65eV 0.8 • Gronig et al. (2000): 3.7±0.3eV 0.6 0.4

Intensity (a. u.) 0.2

33.544.555.566.5 Energy (eV)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 27 GraphiticGraphitic CarbonCarbon NanofibersNanofibers with Lukehart group (Robinson et al., Appl. Phys. Lett., 2005)

• Mat of graphitic carbon nanofibers TEED: GCNF at approximately 1053K (GCNF) – Heating cycle: 970K – 1053K – 970K – FWHM at 970K: 0.30eV • Expected: 0.21eV – Peaks: 4.73eV, 4.71eV and 4.66/4.74eV

TEED: GCNF at approximately 970K TEED: GCNF at approximately 970K

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 28 PotassiumPotassium IntercalatedIntercalated GCNFsGCNFs

600C w/ K 1 700C w/ K 0.8 750 C w/o K

0.6

0.4 intercalation

0.2 Intensity (a. u.)

0 1.5 2.5 3.5 4.5 5.5

Energy (eV)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 29 HydrogenHydrogen--TerminatedTerminated NanoDiamondNanoDiamond (HND)(HND) with Swain and Reifenberger groups (Robinson et al., Diam Rel Mater, 2006)

1 750C before max temp 1085C max temp 750C after max temp 0.8

0.6

0.4 4 μm Intensity (a. u.) 0.2

0 33.544.555.566.5 Energy (eV)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 30 ResidualResidual GasGas AnalysisAnalysis (HND)(HND)

3.00 0.12 750C before max temp 0.10 1085C max temp 2.50 0.08 torr)

750C after max temp -6 0.06 2.00 0.04

0.02 torr)

-6 1.50 Equivalent (x10 0.00 Partial Pressure, Nitrogen 1216 (x10 (m/z) Charge-to-Mass Ratio 1.00

0.50 Partial Pressure, Nitrogen Equivalent Nitrogen Equivalent Pressure, Partial 0.00 1 3 5 7 9 1113151719212325272931333537394143454749 Mass-to-Charge Ratio Mass spectra from hydrogen-terminated nanocrystalline diamond at 750°C, 1085°C and again at 750°C. The inset displays the partial pressure of three particular mass-to-charge ratios (1 and 2, and 16) corresponding to H, H2, and CH4, respectively. These species may form during the desorption of the hydrogen termination layer.

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 31 NitrophenylNitrophenyl--terminatedterminated NanocrystallineNanocrystalline DiamondDiamond (NND)(NND)

750C before max temp 1 1089C max temp 750C after max temp 0.8

0.6

0.4

0.2 Intensity (arb. units)

0 3.5 4 4.5 5 5.5 6 Energy (eV) Sequential TEEDs from nanocrystalline diamond film with nitrophenyl termination measured at 750°C, 1089°C and 750°C. The shift in the energy at maximum intensity before and after the maximum temperature indicates that the relative area of higher work function has increased in size.

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 32 RegeneratedRegenerated HydrogenHydrogen TerminationTermination

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 33 NanotipNanotip--EnhancedEnhanced SchottkySchottky EffectEffect

• Schottky effect reduces the q qFβ apparent work function due to Δφ = 0 2 πε image charge 0 • Effect is enhanced by tip geometries that produce high local electric fields, or embedded grain boundaries φ Evac

μ2 Tip radius, r μ1 vacuum Pitch, p or vapor anode, T2 Height, h E=0

cathode, T1

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 34 NanotipNanotip ExampleExample

• Assumptions – Entire surface has an inherent work Plan View function of φ = 3eV – Constant tip height, h = 1μm – Local field enhancement factor, β≈h / r – Macroscopic field due to difference between cathode and anode work functions, F0 = 0.5 V/μm – Negligible space charge – Temperature, T = 2000 K – Negligible electrostatic interactions among Pitch, p tips • Vary tip radius (r) and pitch (p) to assess benefit Tip radius, r

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 35 ExampleExample ResultsResults

• Results show little ) 40 benefit unless 2 p ≈ r Pitch, p = 25 nm • Suggests that dense 30 fiber or tube arrays

are clearly superior 20 to cones and Pitch = 100 nm pyramids Pitch = 1000 nm 10

0 Average Cathode Current Density (A/cm 0246810 Tip Radius r (nm)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 36 ConclusionsConclusions • Energy exchange associated with electron emission can potentially be useful in energy conversion, but significant challenges remain • Electron energy spectroscopy is a powerful tool in evaluating thermionic emission from nanomaterials • Carbon nanotubes exhibit work functions similar to graphite’s at elevated temperatures • Potassium intercalation can stably and signficantly reduce nanofiber work functions at least up to 750C • Common means of reducing diamond work functions by surface termination exhibit thermal instability near 750C • Schottky effect appears to be a practical means of work function reduction only for dense emitters with high aspect ratios (i.e., fiber/tube arrays instead of cones or pyramids)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 37 AcknowledgmentsAcknowledgments • Graduate students: Vance Robinson, Tyler Westover • Faculty: Greg Swain (Michigan State Chemistry), Ron Reifenberger (Purdue Physics), Chuck Lukehart (Vanderbilt Chemistry) • Sponsors: NSF Nanoscale Interdisciplinary Research Team program (CTS and DMII), NSF CAREER (CTS), Cooling Technologies Research Center

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 38 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 39 ThermionicThermionic DeviceDevice OperationOperation

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 40 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 41 ApplicationsApplications

Schematic of a thermionic converter.

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 42 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 43 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. Fisher, 3/4/2006 Slide 44 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 45 HydrogenHydrogen--TerminatedTerminated NanoDiamondNanoDiamond (HND)(HND) with Swain and Reifenberger groups (Robinson et al., Diam Rel Mater, 2006)

1 750C before max temp 1085C max temp 750C after max temp 0.8

0.6

0.4 4 μm Intensity (a. u.) 0.2

0 33.544.555.566.5 Energy (eV)

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 46 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 47 RegeneratedRegenerated HydrogenHydrogen TerminationTermination

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 48 Questions

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 49 NanotipNanotip ExampleExample

Nanoscale Thermo-Fluids Lab T.S. Fisher, 3/4/2006 Slide 50