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THERMAL-FIELD ELECTRON EMISSION FROM NANOSTRUCTURED CVDDIAMOND FILMS

C. Thomas HarrisPaul W. MajsztrikTimothy S. Fisher

Department of Mechanical EngineeringVanderbilt UniversityNashville, TN 37235

email: [email protected]: [email protected]

email: [email protected]

Jimmy L. DavidsonWeng P. Kang

Department of Electrical EngineeringVanderbilt UniversityNashville, TN 37235

email: [email protected]: [email protected]

ABSTRACT

This work reports the behavior of electron field emission fromnanostructured CVD diamond films at elevated temperatures.The study is motivated by the possibility of using thesestructures in high-temperature electronics or direct energyconversion processes. Four nanostructured CVD diamondfilms were tested: nanocrystalline diamond, nitrogen-dopednanocrystalline diamond, peaked diamond microtips, andtruncated diamond microtips. All samples displayed reason-ably efficient field emission characteristics. For each, theonset of field emission decreased as the sample temperatureincreased. Truncated diamond microtips were found toprovide the largest current-carrying capacity and effectiveemission current density. These values were 90µA and12 1 1010A/cm2 respectively. At a temperature of 700 K,peaked diamond microtips showed the lowest turn-on fieldrecorded at 38V µm. The highest turn-on field, at this sametemperature, was found from the undoped nanocrystallinediamond and recorded at 90V µm.

Address all correspondence to this author.

NOMENCLATURE

A effective emission areaD tunneling transmission coefficient, see Eq. 2E electron energyEa conduction band energyEF Fermi levelEx axial electron energyF applied electric fieldh Planck constanth̄ reduced Planck constantJ current densitykB Boltzmann constantm electron rest massN electron supply function, see Eq. 5p electron momentumq electron chargeT temperatureV voltagex axial coordinateβ field enhancement factorφ work functionµ chemical potential

1American Institute of Aeronautics and Astronautics

8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-3024

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

INTRODUCTIONMuch attention has been paid to diamond thin films

because of their potential applications in optics, high-speedelectronics and thermal management devices. Diamond ischemically inert and has superior mechanical stability overtypical materials used as electron field emission devices.Diamond’s sp3 tetragonal configuration consists of a centralcarbon atom with linear covalent bonds to neighboring carbonatoms 10. This particular arrangement facilitates phonontransport through the lattice of the structure, giving diamonda thermal conductivity four times that of pure copper 6.Furthermore, diamond is a wide band gap semiconductor.This material property results in diamond being an excellentelectrical insulator. Diamond’s unique characteristic of beingan excellent thermal conductor and electrical insulator makeit ideal for nanoeletromechanical devices and electronicpackaging.

Nanocrystalline diamond films show strongly enhancedfield emission properties that can be demonstrated repro-ducibly 9. The success of doping these films coupled with theabsence of microscale features (i.e., using as-deposited films)make fabrication and implementation of nanocrystallinediamond relatively straightforward 13. Diamond tip arraysappear to be promising candidates for electron field emissiondevices (FEDs) because of the field enhancement producedby their geometry 1;8. This geometric enhancement effectoccurs due to a deformation of the potential field. The alteredpotential field enhances the local electric field, enablingemission of electrons into vacuum at lower applied voltages.However, unlike nanocrystalline diamond, manufacturingdiamond tips and gated tip arrays often requires manylaborious post-fabrication etching processes.

The present work reports the thermal effects of fieldemission for both nanocrystalline diamond and diamond tiparrays. High-temperature field emission experiments wereperformed on each sample. Current-voltage and Fowler-Nordheim plots are analyzed and discussed with corre-sponding theoretical formulations. Results show substantialdifferences between the electron field emission characteristicsof the four samples.

THEORETICAL FORMULATIONA detailed discussion on the physics of field emission can

be found from 5, and 4. The following provides an outline ofthe major physical concepts.

The emission current density is defined as

J q∞

Ea

D E N E dE (1)

where D E N E is defined as the number of electrons

Figure 1. DEFORMATION OF THE POTENTIAL FIELD OF A

METAL-VACUUM-METAL INTERFACE. V x REPRESENTS PO-

TENTIAL FIELDS FOR VARIOUS GEOMETRIC ENHANCEMENTS.

emerging from the surface of the metal per second per unitarea per unit energy. Here, q is the electron charge and Ea

is the bottom of the conduction band. D E is defined asthe quantum tunneling transmission coefficient. This quantityrepresents the probability that an electron impinging on asurface barrier will transmit through it. This value has beencalculated analytically by Fowler and Nordheim 3 for a metalsubjected to a linear potential field at 0K . The Fowler-Nordheim analytical solution is

D Ex4 Ex φ µ Ex

φ µ

exp43

2m

h̄2

1 2 φ µ Ex3 2

Fq(2)

where h̄ is the reduced Planck’s constant, φ is the material’swork function, F is the applied field, µ is the chemicalpotential, and m is the electron rest mass.

More complex potential fields can occur due to surfacefeatures on the device 2. As previously mentioned, theimpact of device features on the potential field is referredto as geometric enhancement. Image charge coupled withgeometric enhancement results in an altered potential nearthe tip (Fig. 2). The lowering of the potential field in Fig.2 is a consequence of applied field and surface features.The observed higher-order curve shift in the x-directionis a result of the image charge from an emitted electron.When seeking solutions to such potential fields, calculationof the transmission coefficient can become an arduous task.To facilitate this process, Wentzel, Kramers, and Brillouindeveloped a method for approximating the transmission


Figure 2. POTENTIAL FIELD PROFILE FOR THE WKB APPROXI-

MATION, INCLUDING IMAGE CHARGE EFFECTS. THE HATCHED

PORTION IS THE REPRESENTATIVE AREA UNDER THE CURVE

FOR THE WKB INTEGRAL.

coefficient for a one-dimensional potential barrier 11. Thisapproximation is

D E exp 22m

h̄2

1 2 x2

x1

V x E 1 2 dx (3)

where x1 and x2 are the roots of the effective potential V xfor a given electron energy E . This result is known as theWKB approximation and can be implemented easily.

The supply function N E dE is the product of the Fermi-Dirac distribution,

f E1

1 exp E EFkBT

(4)

and the number of cells in the corresponding volume ofphase space. The supply function expanded using theaforementioned definition is shown as

N Ex dEx

∞

py ∞

∞

pz ∞

px

m2h3

d pxd pyd pz

1 exp Ex EFkBT

(5)

If only the x-direction is considered, then the supply functionis the number of electrons with x-part of their energy withindEx incident on a surface per second per unit area. Makingthe substitution of px d px for mdEx and introducing polarcoordinates for y and z momenta, the double integral can be

Figure 3. FERMI-DIRAC DISTRIBUTION UNDER THERMAL IN-

FLUENCE.

reduced to

N Ex4πmkT

h3 ln 1 expEx EF

kBT(6)

The Fermi-Dirac distribution (Eq. 4) provides the proba-bility of an electron being at a particular energy in a metal. Agraphical representation of this distribution is shown in Fig.3. For a metal at 0K, the highest electron energy level isthe Fermi level, EF . The probability of an electron belowEF is 1, and the probability is zero for any level above theFermi energy. For temperatures near 300 K, this distributionchanges only slightly. Thus, researchers have often assumedthe null temperature Fermi-Dirac distribution when analyzingfield emission at room temperature. However, high temper-ature effects cause a shift in the Fermi distribution. Thisshift increases the probability of an electron population abovethe Fermi level. N E dE is a product of the Fermi leveland momentum constituents; thus, a significant increase intemperature increases the supply function. The higher-energyelectrons also experience smaller potential barriers, as shownby Fig. 2, and consequently the transmission coefficientincreases. The net result is a greater emission current withincreasing temperature.

The current work uses a tradition Fowler-Nordheimapproach 12 to analyze field emission. The emission currentdensity can be expressed as

I aV 2 exp b V (7)


where

a 1 4 10 6 Aβ2

φexp

9 89φ1 2

(8)

b 6 53 107 φ3 2

β(9)

In the foregoing equations, the unit of current I is amperes (A)and the unit of V is volts (V). φ is the emitter’s work function(in eV); A is the effective area of the emitter (in cm2); and βis the field enhancement factor (in cm 1). Dividing Eqn. 8 byV2 and taking the natural log of both sides results in a linearform of the Fowler-Nordheim equation.

lnI

V 2 C1 A β φ1V

C2 β φ (10)

Here C1 is the slope of the line and C2 is the y -intercept. Thislinear-fit method is used to confirm field emission. The slopeof the resulting line determines β, and the y -intercept is usedto calculate an effective field emission area. We note that theFowler-Nordheim approach neglects temperature effects.

EXPERIMENTAL PROCEDUREFour samples were prepared at the Vanderbilt University

Diamond Technologies Laboratory using chemical vapordeposition and post-fabrication techniques described by 7.The truncated and peaked diamond microtip samples areshown in Fig. 4. The samples, backed with a molybdenumelectrode, were mounted on a heated stage with temperaturemeasurement via K-type thermocouples. A floating stainlesssteel probe was introduced as the biasing anode. Vacuum gappositioning was controlled in the vertical direction using aBurliegh 1700-25 inchworm motor and 6000 ULN controller.A voltage bias ranging from 0 - 1000 V was placed acrosseach of the samples under a vacuum of approximately 10 7

torr. This procedure was repeated for various temperatures inthe range 300 K to 900 K.

RESULTSThe results of field emission current as a function

of applied voltage for undoped and doped nanocrystallinediamond thin films are shown in Fig. 5. The results indicateroom temperature field emission occurring at 60V µm forthe n-type sample and no emission for the undoped sample.As the sample temperature increased, the turn-on voltagefor the n-type sample dramatically decreased with only aslight change in emission for the undoped sample. Figure

(a) TRUNCATED DIAMOND MICROTIPS

(b) PEAKED DIAMOND MICROTIPS

Figure 4. SEM IMAGE OF DIAMOND MICROTIPS

5 illustrates the effect of field emission enhancement dueto the nitrogen doping of the n-type sample. The donorelectrons increase the supply function, placing a greaternumber of electrons above EF . Based on these experiments,the nitrogen-doped nanocrystalline thin film is a superior fieldemitter. However, typical studies show turn-on voltages forn-type nanocrystalline diamond in the range of 3 - 5V µm9. This result suggests the n-type sample was not heavilydoped. Therefore, a higher doping concentration of nitrogenin the nanocrystalline thin film could substantially change itsperformance characteristics.

The inset of Fig. 5(b) shows the Fowler-Nordheim plotfor the nitrogen-doped sample. The plot indicates thateach curve has approximately the same slope. The similarslopes suggest a relatively unchanging field enhancementfactor. For the nitrogen doped sample, β was calculated tobe 1 56 105 cm 1, and 1 25 105 cm 1 for the respective


0

10

20

30

40

50

0 200 400 600 800 1000

Cur

rent

(µA

)

Applied Voltage (V)

300K500K700K

-17-16-15-14-13-12-11

0.001 0.0012 0.0014

ln(I

/V2 )

1/V

(a) UNOPED FILM

0

10

20

30

40

50

0 100 200 300 400 500 600 700 800 900 1000

Cur

rent

(µA

)

Applied Voltage (V)

300K500K

-19-18-17-16-15-14-13-12-11-10

-9

0.001 0.0014 0.0018

ln(I

/V2 )

1/V

(b) NITROGEN-DOPED FILM

Figure 5. CURRENT-VOLTAGE BEHAVIOR OF NANOCRYS-

TALLINE DIAMOND THIN FILM

temperatures of 300 K and 500 K. These values are shownin Table 1. The corresponding field enhancement factor forthe undoped sample was 9 81 104 cm 1 at a temperatureof 700 K, and is shown as the inset of Fig. 5(a). AFowler-Nordheim plot was made only for the 700 K sampledue to the fact that 300 K and 500 K data produced noisyplots. These calculated values of β are similar to thosefound in other experiments 9. As previously mentioned,both undoped and doped nanocrystalline diamond thin filmsproduced higher currents for a given voltage as the sampletemperature increased. This result can be attributed to thesupply function’s temperature dependence.

A shift resulting from thermal excitation was also seen inthe Fowler-Nordheim plots. The horizontal shift to the rightis due to the fact that the units of the abscissa are 1/V. The

Table 1. FIELD ENHANCEMENT FACTOR AND

CORRESPONDING TEMPERATURE FOR NITROGEN-DOPED

NANOCRYSTALLINE DIAMOND

Temperature β

300 K 1 56 105 cm 1

500 K 1 25 105 cm 1

curve must shift in order for the device to accommodate alower turn-on voltage while maintaining a relatively constantβ.

Referring to Fig. 5, values of β were higher for the dopedthin film versus the undoped sample. In view of the factthat both samples are nanocrystalline diamond, one wouldexpect the same field enhancement factor due to their similargeometries. This evidence further supports the claim thatadded nitrogen donors in the doped sample have increasedthe field enhancement of the device.

Figure 6 displays the current-voltage characteristics ofthe peaked and truncated diamond microtip samples. Thesesamples vary only slightly in their emission trends. Themajor difference between these samples is their behaviorat room temperature. Both samples appear to have nearlythe same turn-on voltage at 300 K, but the peaked tipsproduce a lower current for a given voltage compared tothe truncated sample. However, when thermally excited,the peaked-tip device carries a higher current for a givenvoltage, as demonstrated by the 500 K and 700 K data. Froma geometric standpoint, it is typically assumed that sharper-peaked tips will provide more enhancement when comparedto a truncated tip. However, further inspection of Fig. 4shows that the silicon mold was not completely removed fromthe device. Incomplete removal of the growth mold fromthe microtips causes a reduction in available emission sites.The top of the truncated sample also could have behavedas a crown of four tips, giving the truncated sample bettergeometric enhancement. This feature may also explain theability of the truncated tips to accommodate greater current-carrying loads versus the peaked-tips.

A Fowler-Nordheim plot for the two diamond tip devicesis shown as the inset of Fig. 6. These plots confirm that bothdevices exhibit field emission behavior. Values of β for thetruncated sample are estimated to be 3 29 105 cm 1, 5 02105 cm 1, 2 91 105 cm 1, and 7 63 104 cm 1 for thetemperatures of 300 K, 500 K, 700 K, and 900 K, respectively.Calculated values of β for the peaked-tip samples were3 42 105 cm 1, 2 78 105 cm 1, and 2 50 105 cm 1 forthe temperatures of 300 K, 500 K, and 700 K, respectively.These values are displayed in Table 2 and Table 3. Truncated


0

10

20

30

40

50

60

70

80

90

0 200 400 600 800

Cur

rent

(µA

)

Applied Voltage (V)

300K500K700K900K

-15-14-13-12-11-10

-9-8-7

0.001 0.002 0.003

ln(I

/V2 )

1/V

(a) TRUNCATED DEVICE

0

10

20

30

40

50

60

0 200 400 600 800 1000

Cur

rent

(µA

)

Applied Voltage (V)

300K500K700K

-16

-14

-12

-10

-8

0.001 0.002 0.003

ln(I

/V2 )

1/V

(b) PEAKED DEVICE

Figure 6. CURRENT-VOLTAGE BEHAVIOR OF DIAMOND MI-

CROTIPS

tips and peaked tips follow the same thermal trend as the thinfilms. That is to say, each of the plots shows a shift to theright when the temperature is increased, while at the sametime maintaining a relatively constant β. Similar to the dopednanocrystalline thin film, the diamond tip samples have thesame order of magnitude values of β for 300 K, 500 K, and700 K. However, the 900 K plot for the truncated-tips displaysa β quite similar to the undoped sample. This phenomenonsuggests that at higher temperatures the flat portion of thetruncated tip may behave as a nanocrystalline emitter.

Effective field emission area was calculated and com-pared between the nitrogen-doped thin film, truncated mi-crotips, and peaked microtips. This analysis was performedfor a voltage of 720 V and a temperature of 500 K. Theeffective emission area of the doped sample was found to

Table 2. FIELD ENHANCEMENT FACTOR AND CORRESPOND-

ING TEMPERATURE FOR PEAKED DIAMOND MICROTIPS

Temperature β

300 K 3 42 105 cm 1

500 K 2 78 105 cm 1

700 K 2 50 105 cm 1

Table 3. FIELD ENHANCEMENT FACTOR AND CORRESPOND-

ING TEMPERATURE FOR TRUNCATED DIAMOND MICROTIPS

Temperature β

300 K 3 29 105 cm 1

500 K 5 02 105 cm 1

700 K 2 91 105 cm 1

900 K 7 63 104 cm 1

Table 4. EFFECTIVE FIELD EMISSION AREA AND EFFECTIVE

CURRENT DENSITY AT 500 K AND 720 V

Sample Emission Area Current Density

n-type film 3 81 10 12 cm2 2 6 106 A/cm2

Peaked-tips 1 01 10 14 cm2 4 4 109 A/cm2

Truncated-tips 4 34 10 16 cm2 12 1 1010 A/cm2

be 3 81 10 12 cm2 at a current of 9 8µA. The areas forthe truncated and peaked microtips were 4 34 10 16 cm2 at53µA, and 1 01 10 14 cm2 at 45µA respectively. Effectivecurrent density was calculated by dividing the effectiveemission area by the corresponding current for each device.The largest current density, 12 1 1010 A/cm2, was foundfrom the truncated sample. An effective current density of4 4 109 A/cm2 was calculated for the peaked-tips, and 2 6106 A/cm2 for the nitrogen doped sample. This calculationshows the truncated tips are the most robust emitter. Valuesfor effective field emission area and effective current densityare given in Table 4 for the nanocrystalline nitrogen-dopedsample, the peaked diamond microtips, and the truncateddiamond microtips.


CONCLUSIONSAmong the four devices, the peaked diamond microtip

sample displayed the greatest change in field emissioncharacteristics under thermal influence. At a temperatureof 700 K, it produced a current of 55µA for a voltage inputof 470 V. Nevertheless, the truncated microtip device ac-commodates the largest current carrying capacity, displayingcurrent outputs near 90µA at a voltage of 410 V and atemperature of 900 K. The truncated sample showed thelargest effective current density of 12 1 1010 A/cm2. Thenitrogen-doped nanocrystalline thin film showed a significantchange in current-voltage behavior and superior performanceas compared to the undoped nanocrystalline film. However,as a field emitter it is outperformed by the peaked andtruncated nanotip devices.

ACKNOWLEDGEMENTThe authors would like to gratefully acknowledge fund-

ing support through an NSF CAREER grant (CTS-9983961),NRO (000-01-C-0230), and DARPA/ARO (DAAD19-01-1-0639).

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8 V. I. Merkulov and D. H. Lowndes. Field-emission studiesof smooth and nanostructured carbon films. AppliedPhysics Letters, 75:1228–1230, 1999.

9 K. Okano. Metal-insulator-vacuum type electron emissionfrom N-containing chemical vapor deposited diamond.Applied Physics Letters, 79:275–277, 2001.

10 Oxtoby, Freeman, and Block. Chemistry, Science ofChange. Saunders College Publishing, 1998.

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