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TRANSCRIPT
-
Diamond Field Emitter Arrayson Micromachined Silicon
Nano Science & Engineering Lab
ECE
Old Dominion University
Norfolk, Virginia 23529
Dr. Wehai Fu
Dr. Sacharia Albin
-
Outline
Summary
Introduction
Field emission
Experiments
I
II
III
IV
Field emission and applications
Advantages of diamond field emitters
Project goal
Fowler-Nordheim field emission
Field emission enhancement
Silicon tip array fabrication
Diamond emitter fabrication
Results and discussion
V
Silicon tip array wet etching
Diamond film characterization
Diamond emitter I-V characteristics
-
I. Introduction
Thermal excitation
Photo excitation
Tunneling
Electron emission mechanisms
Surface barrier
Surface barrier bending
due to applied field
Advantages of field emission
Low energy consumption
High current density
Small device size (sharp tips)
-
Cold cathode
Flat panel display
Vacuum microelectronic device
Microsensor
Scanning probe microscope
for surface imaging
Anode
Gate
Emitter
Probe
Gate
Emitter array
Phosphor
Conductive
coating
5 mm
d
E-beam
Emitter array
Extracting
gate
Focusing
electrode
Field Emission Applications
Pressure
I. Introduction
-
Requirements for applications:
Drawbacks of metal and silicon emitters:
Low turn-on voltage
Large emission current
Uniform over the array
Stable emission
High extracting field
Sputtering damage
Surface adsorption
Emitter overheating
Anode
Emitter
I. Introduction
-
Diamond Field Emitter
Hardest known material
10,400 kg/cm2
Highest thermal conductivity
20 W/cm-oC
5 times larger than copper
Chemically inert
Small effective work function
Properties of diamond
Advantages for field emission
Low threshold voltage for electron emission
Resistance to sputtering damage by residual gas
Efficient and fast thermal dissipation
Robust performance in harsh environment
I. Introduction
-
Research Developments
1928 Field emission theory proposed (Fowler and Nordheim)
1968 First metal field emitter with self-aligned gate demonstrated (Spindt)
1990 Silicon field emitter array with self-aligned gate developed (Betsui)
1979 Negative electron affinity (NEA) of diamond discovered (Himpsel)
1976 Enhanced chemical vapor deposition (CVD) diamond developed (Deryagin)
1994 Mold-filled CVD diamond tip array fabricated (Okano)
1997 Diamond film coated silicon sharp tips demonstrated (Zhirnov)
1997 Diamond tips for tunneling microscopy developed (Albin)
Year
Highlights
I. Introduction
1999 Diamond field emitter arrays with self-aligned gate succeeded (Albin)
-
Project Goal
Scanning electron microscopy
Optical emission spectroscopy
Raman spectroscopy
I-V measurement
Design, fabricate, and characterize diamond
field emitter arrays using:
Silicon surface micro-machining
Plasma enhanced CVD diamond
I. Introduction
-
Surface Energy Barrier#
Image Charge
Applied Field
Combined effect
# S. O. Kasap, Principles of Electrical Engineering Materials and Devices (McGraw-Hill, 1997).
II. Field Emission
f
Ef
Ef
Ef
x
x
x
f
Feff
f
- exF
Pe(x)
Pext(x)
P(x)
Schottky barrier
reduction
d
Surface barrier
thinning
Vacuum
Level
Vacuum
Level
Vacuum
Level
-
Fowler-Nordheim Equation#
m mass of electron work function of the cathode y function of F and t(y), v(y) approximated as constants
# R. H. Fowler and L. W. Nordheim, Proc. R. Soc. London A119, 173 (1928).
J emission current density e electron charge h Plancks constant F electric field at cathode
II. Field Emission
Field Emission Current Density
N(T,S): electron density
D(F,s,): tunneling probability
s: kinetic energy
T: temperature
F: applied field
: work function
-
F-N Plot
Where:
Simplified F-N Equation#
a emitting area
f emitter work function
field enhancement factor
# C. A. Spindt, I. Brodie, L. Humphrey, and E. R.Westerberg, J. Appl. Phys. 47, 5248 (1976).
5.5 eV
3 eV
2 eV
5 eV
4 eV
I-V Plot
F-N Plot
II. Field Emission
or
(400 tip array with a tip radius of 20 nm and a field enhancement factor of 105 cm-1)
Chart2
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179.22319291246.74555650220.37197868690.02216635310.0053667978
Voltage (v)
Emission current (A)
Sheet1
23455.523455.5
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43145.21249029350.02260919660.00000000223.95571603786175E-172.86389753360995E-21
162762.0978763110.22667572610.000000070606.90277330114284E-19
513542.9236669911.65304607460.000001388607.68372420688193E-17
1403470.92216159.33800075770.000018534300
3410935.9277909242.83990894290.00018043480.00000000020
7522568.82874859165.50226222830.00135388860.00000000370
15294423.0390804553.83733520140.00817399590.00000004320.0000000001
29027019.5021241641.65841642650.04108015130.00000039510.0000000009
51943555.47072774388.13647582880.17660244470.0000029120.0000000084
88360951.309050110731.98294948520.66391101440.00001782740.0000000672
143844920.06427124302.53172101962.22239266710.00009296760.0000004451
225342379.99083751460.39827211696.72390936960.00042162090.0000025121
341286850.625046102734.66102054618.61787794610.00169188520.000012318
501674663.178503194710.51300523447.67623018350.00609525450.0000533652
718111687.988366352402.548905532113.91923878310.01995870970.0002071739
1003831752.05693612126.433216778255.92221623550.06002775830.0007294813
1373688978.83721024858.00074753544.07675208910.16732561510.0023539319
1844126966.374231660046.057028451100.7595533520.43565077880.0070235275
2433128087.782152609825.032139152129.71348366341.06661592710.0195283023
3160146316.377313993557.40691263957.23518664532.47015049970.0509396112
4046026910.878565962624.126828667087.96185437985.4390092920.1254001517
5112916100.666848705374.2031820412278.133754520911.43834811780.2928542265
6384163634.1637312452142.140503820629.165979977823.06695594960.6517954787
7884220731.9231117480243.218121933704.189561014444.76514739941.3881818263
9638535647.7929424118861.324390453669.925161680583.86524000982.8394222522
11673448706.356932753751.258031783465.8467256035152.10333736115.5958578193
14016088366.220543831686.4389761127002.098326891267.734964213910.6564859144
16694269564.939557864593.1312177189387.069577122458.420944883119.6608143172
19736395337.070775433322.9771657277184.939268992765.072680262335.2246318251
23171362463.768397191026.3811598398702.8891721311246.866546580161.4140436346
27028471710.4347123866099.66712564307.0938008561987.6544533895104.3991906832
31337343036.7788156264688.678579786766.0282872883104.0107277826173.3364565186
36127836019.0463195272740.3848391081619.122237634755.1636819824281.5354321007
41429975604.5806241857601.978041467568.335610987155.0629312886447.9742047763
47273883221.4556297069173.8296521966889.8521847510586.8304502793699.233399727
53689713187.9414362040628.5092142605862.78219715419.83441393441071.9255720002
60707594305.3542437988712.8796383415211.5400113922129.61021772881615.7017832736
68357576470.9524526213654.126724430558.4139516331320.83305905412396.9212862746
76669582112.7276628098693.5294755692882.7702428943753.52161465483503.0730046641
85673362223.203745109273.9178427248983.3259016660372.62332332655048.0388037732
95398456752.9435878791908.1862789151939.9797460182341.09933543067178.2883113392
105874159114.8631030772757.0281811461571.7989324111076.59213611510080.0932288826
117129484546.2841202755944.3168914244887.9126073148291.72202741313987.8456821199
129193142075.9151396521638.3700817576528.2563438196038.0208986219193.5602452887
142093509846.5711613923926.774321539191.3331512256753.4738236826057.6329312662
155858613550.6851856888511.5891126224046.4015163333313.60174241735020.9227924066
170516107743.9112127410250.6581931731127.7612392429085.98248065946618.2129789122
186093259811.7092427550569.4875938169709.0774629547988.07323022261493.0983257575
202616936374.4372759434766.756845658655.956687694548.16584011780414.3359731711
220113591927.6513125249235.0499454326755.2608556873969.277268244104293.684364508
238609259525.8743527238616.8689464313019.91266971092195.75161796134205.244405877
258129543329.6723967702914.4465475766968.20368641355982.32755639171406.30480745
278699612847.4414448994570.3409888848876.86375091672965.40571645217359.681842448
300344198714.5814973515534.28518103730007.3837042051736.23498124273757.532130035
323087589863.7085543714330.29697120592805.3015212501915.7243267342546.605732129
346953631950.1046162083136.64649139631072.3639313034230.57808599425954.895993819
371965726906.736831154889.92986161050111.6605093660590.44697536526519.632277266
398146833512.6857553500423.22289185066845.9948044394165.78482224647116.552145137
425519468868.118331725647.08711211909909.9074375249466.10146549790990.380728326
454105710677.0949168468781.07667241819715.8993376242418.30553174961786.437031692
483927200248.15210066397642.3489275048495.5200437390444.836491551163583.27984044
515005146129.40511028206997.0126311860316.0867878712541.293311631400926.29972118
547360328302.56712056615978.9555352531073.88574110229353.2768891678862.15838227
581013102866.41913154365580.0753397348464.77820511963252.1750222002973.97237048
615983407146.48614324216215.0889446611933.19254613938409.63168822379417.13472404
652290765173.27215568945363.4182500632600.5283816180870.45661822814955.66575502
689954293476.61416891345290.0334559733174.03376718718623.7463353316998.98256416
728992707148.51418294220846.583624247837.24008621581672.00376143893638.97615995
769424326131.23419780387353.6413694522123.05371224802098.05996394553687.28511411
811267081691.55321352668564.4621770912770.60963328414129.61841245306712.65548666
854538523045.78123013894710.2332853787566.9905632454201.25912576163078.27823965
899255824103.6524766900626.4776943525174.90683336961013.75706357133978.99747236
945435790302.27726614523959.94381040514947.418341975590.58600098231478.28549111
993094865504.38328559603455.05921145156730.7600947541331.49572969468544.88391539
1042249138937.5330604977318.79121257860656.3107353704063.066684210859089.0136581
1092914352153.6532753481662.56181379046922.7134660512086.161883112417998.0606413
1145105905990.2135007949019.69331509145569.1316168016220.211325714161171.6484649
1198838867516.6237371206936.72081648596240.5856376269844.278639616105556.0138769
1254127976951.139846076636.7911797847946.2844885328934.87376218269177.6057474
1310987654535.0342435371753.26951957358811.8277695252100.488734220671175.8332769
1369432007353.3445141897131.6062127595826.11709106100612.84624423331834.8943227
1429474836090.8647968447697.44592309034583.77687117938434.86236526272614.6199623
1491129641715.7650917807388.93732502159023.84586130832245.33598329516180.276692
1554409632082.653992748151.15242707461165.4617144851460.3876633086431.2729435
1619327728448.0957196028990.52762925440841.22192160068251.68020937008528.7218529
1685896571894.2560530395087.22143156605428.86626176557561.4619741308921.8174181
1754128529653.7863998576963.29423401469581.88698194397114.48177746015372.9862884
Electric Field (107 V/cm)
Current Density (A/cm2)
Sheet2
1/F (10-7 cm/V)
ln (J/F2) (ln(A/V2)
10
10
10
10
10
5
5
5
5
5
3.3333333333
3.3333333333
3.3333333333
3.3333333333
3.3333333333
2.5
2.5
2.5
2.5
2.5
2
2
2
2
2
1.6666666667
1.6666666667
1.6666666667
1.6666666667
1.6666666667
1.4285714286
1.4285714286
1.4285714286
1.4285714286
1.4285714286
1.25
1.25
1.25
1.25
1.25
1.1111111111
1.1111111111
1.1111111111
1.1111111111
1.1111111111
1
1
1
1
1
0.9090909091
0.9090909091
0.9090909091
0.9090909091
0.9090909091
0.8333333333
0.8333333333
0.8333333333
0.8333333333
0.8333333333
0.7692307692
0.7692307692
0.7692307692
0.7692307692
0.7692307692
0.7142857143
0.7142857143
0.7142857143
0.7142857143
0.7142857143
0.6666666667
0.6666666667
0.6666666667
0.6666666667
0.6666666667
0.625
0.625
0.625
0.625
0.625
0.5882352941
0.5882352941
0.5882352941
0.5882352941
0.5882352941
0.5555555556
0.5555555556
0.5555555556
0.5555555556
0.5555555556
0.5263157895
0.5263157895
0.5263157895
0.5263157895
0.5263157895
0.5
0.5
0.5
0.5
0.5
0.4761904762
0.4761904762
0.4761904762
0.4761904762
0.4761904762
0.4545454545
0.4545454545
0.4545454545
0.4545454545
0.4545454545
0.4347826087
0.4347826087
0.4347826087
0.4347826087
0.4347826087
0.4166666667
0.4166666667
0.4166666667
0.4166666667
0.4166666667
0.4
0.4
0.4
0.4
0.4
0.3846153846
0.3846153846
0.3846153846
0.3846153846
0.3846153846
0.3703703704
0.3703703704
0.3703703704
0.3703703704
0.3703703704
0.3571428571
0.3571428571
0.3571428571
0.3571428571
0.3571428571
0.3448275862
0.3448275862
0.3448275862
0.3448275862
0.3448275862
0.3333333333
0.3333333333
0.3333333333
0.3333333333
0.3333333333
0.3225806452
0.3225806452
0.3225806452
0.3225806452
0.3225806452
0.3125
0.3125
0.3125
0.3125
0.3125
0.303030303
0.303030303
0.303030303
0.303030303
0.303030303
0.2941176471
0.2941176471
0.2941176471
0.2941176471
0.2941176471
0.2857142857
0.2857142857
0.2857142857
0.2857142857
0.2857142857
0.2777777778
0.2777777778
0.2777777778
0.2777777778
0.2777777778
0.2702702703
0.2702702703
0.2702702703
0.2702702703
0.2702702703
0.2631578947
0.2631578947
0.2631578947
0.2631578947
0.2631578947
0.2564102564
0.2564102564
0.2564102564
0.2564102564
0.2564102564
0.25
0.25
0.25
0.25
0.25
0.243902439
0.243902439
0.243902439
0.243902439
0.243902439
0.2380952381
0.2380952381
0.2380952381
0.2380952381
0.2380952381
0.2325581395
0.2325581395
0.2325581395
0.2325581395
0.2325581395
0.2272727273
0.2272727273
0.2272727273
0.2272727273
0.2272727273
0.2222222222
0.2222222222
0.2222222222
0.2222222222
0.2222222222
0.2173913043
0.2173913043
0.2173913043
0.2173913043
0.2173913043
0.2127659574
0.2127659574
0.2127659574
0.2127659574
0.2127659574
0.2083333333
0.2083333333
0.2083333333
0.2083333333
0.2083333333
0.2040816327
0.2040816327
0.2040816327
0.2040816327
0.2040816327
0.2
0.2
0.2
0.2
0.2
0.1960784314
0.1960784314
0.1960784314
0.1960784314
0.1960784314
0.1923076923
0.1923076923
0.1923076923
0.1923076923
0.1923076923
0.1886792453
0.1886792453
0.1886792453
0.1886792453
0.1886792453
0.1851851852
0.1851851852
0.1851851852
0.1851851852
0.1851851852
0.1818181818
0.1818181818
0.1818181818
0.1818181818
0.1818181818
0.1785714286
0.1785714286
0.1785714286
0.1785714286
0.1785714286
0.1754385965
0.1754385965
0.1754385965
0.1754385965
0.1754385965
0.1724137931
0.1724137931
0.1724137931
0.1724137931
0.1724137931
0.1694915254
0.1694915254
0.1694915254
0.1694915254
0.1694915254
0.1666666667
0.1666666667
0.1666666667
0.1666666667
0.1666666667
0.1639344262
0.1639344262
0.1639344262
0.1639344262
0.1639344262
0.1612903226
0.1612903226
0.1612903226
0.1612903226
0.1612903226
0.1587301587
0.1587301587
0.1587301587
0.1587301587
0.1587301587
0.15625
0.15625
0.15625
0.15625
0.15625
0.1538461538
0.1538461538
0.1538461538
0.1538461538
0.1538461538
0.1515151515
0.1515151515
0.1515151515
0.1515151515
0.1515151515
0.1492537313
0.1492537313
0.1492537313
0.1492537313
0.1492537313
0.1470588235
0.1470588235
0.1470588235
0.1470588235
0.1470588235
0.1449275362
0.1449275362
0.1449275362
0.1449275362
0.1449275362
0.1428571429
0.1428571429
0.1428571429
0.1428571429
0.1428571429
0.1408450704
0.1408450704
0.1408450704
0.1408450704
0.1408450704
0.1388888889
0.1388888889
0.1388888889
0.1388888889
0.1388888889
0.1369863014
0.1369863014
0.1369863014
0.1369863014
0.1369863014
0.1351351351
0.1351351351
0.1351351351
0.1351351351
0.1351351351
0.1333333333
0.1333333333
0.1333333333
0.1333333333
0.1333333333
0.1315789474
0.1315789474
0.1315789474
0.1315789474
0.1315789474
0.1298701299
0.1298701299
0.1298701299
0.1298701299
0.1298701299
0.1282051282
0.1282051282
0.1282051282
0.1282051282
0.1282051282
0.1265822785
0.1265822785
0.1265822785
0.1265822785
0.1265822785
0.125
0.125
0.125
0.125
0.125
0.1234567901
0.1234567901
0.1234567901
0.1234567901
0.1234567901
0.1219512195
0.1219512195
0.1219512195
0.1219512195
0.1219512195
0.1204819277
0.1204819277
0.1204819277
0.1204819277
0.1204819277
0.119047619
0.119047619
0.119047619
0.119047619
0.119047619
0.1176470588
0.1176470588
0.1176470588
0.1176470588
0.1176470588
0.1162790698
0.1162790698
0.1162790698
0.1162790698
0.1162790698
0.1149425287
0.1149425287
0.1149425287
0.1149425287
0.1149425287
0.1136363636
0.1136363636
0.1136363636
0.1136363636
0.1136363636
0.1123595506
0.1123595506
0.1123595506
0.1123595506
0.1123595506
0.1111111111
0.1111111111
0.1111111111
0.1111111111
0.1111111111
0.1098901099
0.1098901099
0.1098901099
0.1098901099
0.1098901099
0.1086956522
0.1086956522
0.1086956522
0.1086956522
0.1086956522
0.1075268817
0.1075268817
0.1075268817
0.1075268817
0.1075268817
0.1063829787
0.1063829787
0.1063829787
0.1063829787
0.1063829787
0.1052631579
0.1052631579
0.1052631579
0.1052631579
0.1052631579
0.1041666667
0.1041666667
0.1041666667
0.1041666667
0.1041666667
-188.8999889397
-343.1364309613
-524.796339811
0
0
-97.8246355229
-175.8203229501
-267.196339811
-370.3754063466
-426.0165341743
-67.466184384
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-52.2869588145
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-190.3719341578
-218.3483764081
-43.1794234728
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-8.9706321894
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-8.9177429017
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-8.8673135809
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-8.8191765019
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-8.7959192615
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-8.707891857
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-8.687055583
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-8.6666579675
-12.0266593181
-15.0194977057
-17.9475555349
-19.4241410742
-8.6466853023
-11.9899671892
-14.9630064776
-17.8686066436
-19.3330585488
Work Function (eV)
Current Density (A/cm2)
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5.5
5.5
5.5
5.5
5.5
1439.194
51943555
2430000000
19700000000
76700000000
0.0000594
4388.136
2609825
75433323
628000000
0
0.176602
2129.713
277184.9
5692883
1.69E-22
0.00000291
1.066616
765.0727
43753.52
1.93E-27
0.0000000084
0.019528
35.22463
3503.073
Voltage (v)
Emission current (A)
Sheet3
Chart1
-108.6356217965-186.6305525085-278.0077254364-381.1797926873-436.8265461303
-63.0981217965-102.9730525085-149.2077254364-201.1797926873-229.1590461303
-47.9189551299-75.0872191751-106.274392103-141.1797926873-159.9365461303
-40.3293717965-61.1443025085-84.8077254364-111.1797926873-125.3252961303
-35.7756217965-52.7785525085-71.9277254364-93.1797926873-104.5585461303
-32.7397884632-47.2013858418-63.3410587697-81.1797926873-90.7140461303
-30.5713360823-43.2176953656-57.2077254364-72.6083641159-80.8251175589
-28.9449967965-40.2299275085-52.6077254364-66.1797926873-73.4084211303
-27.680066241-37.906108064-49.0299476586-61.1797926873-67.6398794637
-26.6681217965-36.0470525085-46.1677254364-57.1797926873-63.0250461303
-25.8401672511-34.5260070539-43.8259072545-53.9070654146-59.249273403
-25.1502051299-33.2584691751-41.874392103-51.1797926873-56.1027961303
-24.5663910273-32.1859371238-40.2231100518-48.8721003796-53.4403922842
-24.0659789394-31.266623937-38.8077254364-46.8940784016-51.1583318446
-23.6322884632-30.4698858418-37.5810587697-45.1797926873-49.1805461303
-23.2528092965-29.7727400085-36.5077254364-43.6797926873-47.4499836303
-22.9179747377-29.157611332-35.5606666128-42.3562632755-45.9230167186
-22.6203440188-28.6108302862-34.7188365475-41.1797926873-44.565712797
-22.3540428492-28.12160514-33.9656201732-40.1271611084-43.3512829724
-22.1143717965-27.6813025085-33.2877254364-39.1797926873-42.2582961303
-21.8975265585-27.2829334608-32.674392103-38.3226498302-41.2694032732
-21.7003945238-26.9207797812-32.1168163455-37.5434290509-40.3704097667
-21.5204044052-26.5901177258-31.6077254364-36.8319666003-39.5495896086
-21.3554134632-26.2870108418-31.1410587697-36.1797926873-38.7971711303
-21.2036217965-26.0081525085-30.7117254364-35.5797926873-38.1049461303
-21.0635064119-25.7507448161-30.3154177441-35.0259465335-37.4659692072
-20.9337699447-25.5124043603-29.9484661771-34.5131260206-36.8743239081
-20.813300368-25.2910882227-29.6077254364-34.0369355444-36.3249389875
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-20.4985250224-24.712810573-28.7174028557-32.7926959131-34.8894493561
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-20.1627646537-24.0959810799-27.7677254364-31.465506973-33.358260416
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-20.022108283-23.8375795355-27.3698875985-30.909522417-32.7168164006
-19.9573323229-23.7185788242-27.1866728048-30.6534768978-32.4214145514
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-19.78196326-23.396406167-26.6906522656-29.9602804922-31.6216680815
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-19.5845106854-23.0336636196-26.1321698808-29.1797926873-30.721212797
-19.5405131009-22.9528351171-26.0077254364-29.0058796438-30.5205678695
-19.498387754-22.8754461255-25.8885765002-28.8393671554-30.3284610239
-19.4580176299-22.8012816751-25.774392103-28.6797926873-30.1443586303
-19.4192952659-22.7301443452-25.6648682935-28.5267314628-29.9677706201
-19.3821217965-22.6618525085-25.5597254364-28.3797926873-29.7982461303
-19.3464061103-22.596238783-25.4587058285-28.2386162167-29.6353696597
-19.3120641042-22.5331486623-25.3615715902-28.1028696104-29.4787576688
-19.279018023-22.4724393009-25.2681027949-27.9722455175-29.3280555643
-19.2471958706-22.4139784344-25.1780958067-27.846459354-29.1829350192
-19.2165308875-22.3576434175-25.0913618-27.7252472328-29.0430915849
-19.1869610823-22.3033203656-25.0077254364-27.6083641159-28.9082425589
-19.1584288141-22.2509033856-24.927023682-27.495582161-28.7781250777
-19.1308804172-22.2002938878-24.8491047467-27.386689239-28.6524944062
-19.1042658643-22.1513999661-24.7738271313-27.2814876026-28.5311224015
-19.0785384632-22.1041358418-24.7010587697-27.1797926873-28.4137961303
-19.0536545834-22.0584213609-24.630676256-27.0814320316-28.3003166221
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-19.0062567172-21.9713461592-24.4966143253-26.8940784016-28.0841651779
-18.9836686715-21.9298493835-24.4327254364-26.8047926873-27.9811555053
-18.9617756427-21.8896294315-24.3708023594-26.7182542258-27.8813153611
-18.940546039-21.850628266-24.3107557394-26.6343381419-27.7845006758
-18.9199501548-21.8127913144-24.2525015558-26.5529270157-27.6905759811
-18.8999600318-21.7760672143-24.1959607305-26.4739103344-27.5994137774
-18.8805493328-21.7404075809-24.1410587697-26.3971839917-27.5108939564
-18.8616932251-21.7057667942-24.0877254364-26.3226498302-27.4249032732
-18.8433682754-21.6721018042-24.0358944505-26.2502152225-27.3413348627
-18.8255523521-21.6393719529-23.9855032141-26.1797926873-27.260087797
-18.8082245363-21.6075388098-23.9364925597-26.1112995366-27.1810666783
-18.7913650398-21.576566022-23.8888065174-26.0446575522-27.1041812655
-18.7749551299-21.5464191751-23.842392103-25.9797926873-27.0293461303
-18.7589770597-21.5170656663-23.7971991206-25.9166347926-26.9564803408
-18.7434140043-21.4884745864-23.7531799818-25.8551173626-26.8855071693
-18.7282500017-21.460616611-23.7102895389-25.7951773027-26.8163538226
-18.7134698978-21.4334639009-23.66848493-25.7367547126-26.7489511936
-18.6990592965-21.4069900085-23.6277254364-25.6797926873-26.6832336303
-18.6850045126-21.3811697924-23.5879723499-25.6242371317-26.6191387229
-18.6712925283-21.3559793377-23.549188851-25.5700365897-26.5566071059
-18.6579109532-21.3313958819-23.5113398942-25.5171420849-26.4955822749
-18.644847987-21.3073977465-23.474392103-25.465506973-26.436010416
-18.6320923848-21.2839642732-23.4383136717-25.415086805-26.377840248
-18.6196334245-21.2610757643-23.4030742736-25.3658391989-26.3210228745
-18.607460877-21.238713428-23.3686449766-25.3177237218-26.2655116476
-18.5955649784-21.2168593266-23.3349981636-25.2707017782-26.2112620394
-18.5839364033-21.1954963287-23.3021074588-25.2247365075-26.1582315236
-18.572566241-21.174608064-23.2699476586-25.1797926873-26.1063794637
-18.5614459724-21.1541788821-23.2384946671-25.1358366433-26.0556670094
-18.5505674487-21.1341938128-23.2077254364-25.0928361656-26.0060569999
-18.5399228718-21.11463853-23.1776179095-25.0507604292-25.9575138723
-18.5295047753-21.095499317-23.1481509683-25.0095799213-25.9100035771
-18.5193060071-21.0767630348-23.1193043837-24.9692663715-25.8634934987
-18.5093197132-21.0584170918-23.0910587697-24.9297926873-25.8179523803
-18.4995393223-21.0404494157-23.0633955395-24.8911328935-25.773350254
-18.4899585312-21.0228484268-23.0362968649-24.8532620751-25.7296583752
-18.4805712915-21.0056030135-23.0097456384-24.8161563237-25.6868491606
-18.4713717965-20.9887025085-22.9837254364-24.7797926873-25.6448961303
1/V (1/V)
ln(I/V2) (A/V2)
Sheet1
202.64368013052173E-453.54356890727403E-797.325527581101E-1191.14229799420822E-1637.77501898347378E-188400 tips with radius of 20 nm
406.32344678286746E-253.04432836036757E-422.53529306407785E-626.80528234063405E-854.80408596407681E-97b= 10e5 cm-1
605.56371287381822E-188.83766533281595E-302.52301854537045E-431.74862861262691E-581.24951956786857E-66
8001.78462426942883E-239.43306428716453E-343.32207559490913E-452.38833598225963E-51
10001.19830089237853E-195.78343351147276E-283.40824032865019E-373.89762793930845E-42
1200.00000000014.56101061321648E-174.46365058355251E-247.98778719065231E-325.77767124683741E-36
1400.00000000102.80063551684011E-215.73910533485507E-281.55007787118086E-31
1600.000000006903.63910932578391E-194.64217157224046E-253.3679663457615E-28
1800.000000030801.64857721847342E-178.71964174980045E-231.36432740413664E-25
2000.000000104803.5618169170757E-165.87748529001078E-211.70070988215188E-23
2200.0000002901001.87630880456338E-198.97868769772678E-22
2400.00000068840.000000000203.4144513910213E-182.48477863784563E-20
2600.00000144840.000000000704.02775626689451E-174.1790658669254E-19
2800.00000277070.000000002103.37657638613955E-164.7482638008729E-18
3000.00000490760.0000000053003.93915171705394E-17
3200.00000816080.000000012002.5294954327909E-16
3400.00001287680.0000000251000
3600.00001944080.00000004860.000000000100
3800.00002827030.00000008840.000000000300
4000.0000398080.00000015220.000000000600
4200.0000545160.00000024980.000000001100
4400.00007286920.00000039390.000000002200
4600.00009535050.00000059920.00000000400
4800.00012244590.00000088340.000000006900
5000.00015464080.00000126690.00000001150.00000000010
5200.00019241640.00000177260.00000001850.00000000020
5400.00023624720.0000024260.00000002870.00000000030
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0.0005-18.4713717965-20.9887025085-22.9837254364-24.7797926873-25.6448961303
Sheet1
1/V (1/V)
ln(I/V2) (A/V2)
Sheet2
Sheet3
-
Field Enhancement Factor
Anode
Cathode
= F / V
Field enhancement factor for typical emitters#
# H. G. Kosmahl, IEEE Trans. Electron Devices 38 (6), 1534 (1991)
h
d
r
F: electric field at emitter tip
V: voltage between anode and cathode
II. Field Emission
r
Spacer
-
Emitter Structure Effect Simulation
Tip height (top to bottom)
4 mm
3 mm
2 mm
1 mm
0.5 mm
Tip radius (top to bottom)
10 nm
20 nm
40 nm
60 nm
80 nm
100 nm
Effect of tip radius
Effect of emitter height
II. Field Emission
Chart1
30.31848936550.106921316685.3859451441117.8764131384148.7608525507
19.192604102830.31848936550.106921316668.229429061785.3859451441
15.153546567923.045306400337.181638090450.106921316662.3177213531
13.075156485619.192604102830.31848936540.49913865850.1069213166
11.84217141816.792423484226.014789669334.476428794542.4592279104
11.062745544915.153546567923.045306400330.31848936537.1816380904
10.563175130213.967572115720.864944756727.261368195433.3015008252
10.255351484513.075156485619.192604102824.911685632330.318489365
10.090985264812.385312219417.867923953323.045306400327.947784756
10.0428601811.84217141816.792423484221.524727438326.0147896693
10.096275018111.409493440215.90211864120.260689433324.406241904
10.244926900611.062745544915.153546567919.192604102823.0453064003
10.489014515210.784753990914.516099923118.277828169221.8779339404
10.834658166310.563175130213.967572115717.485435244220.8649447567
11.294320702410.388954568613.491442744516.792423484219.9772106938
0.5mm
1mm
2mm
3mm
4mm
Emitter radius (nm)
Field enhancement factor
Sheet1
tip radius
1030.31848936550.106921316685.3859451441117.8764131384148.7608525507
2019.192604102830.31848936550.106921316668.229429061785.3859451441
3015.153546567923.045306400337.181638090450.106921316662.3177213531
4013.075156485619.192604102830.31848936540.49913865850.1069213166
5011.84217141816.792423484226.014789669334.476428794542.4592279104
6011.062745544915.153546567923.045306400330.31848936537.1816380904
7010.563175130213.967572115720.864944756727.261368195433.3015008252
8010.255351484513.075156485619.192604102824.911685632330.318489365
9010.090985264812.385312219417.867923953323.045306400327.947784756
10010.0428601811.84217141816.792423484221.524727438326.0147896693
11010.096275018111.409493440215.90211864120.260689433324.406241904
12010.244926900611.062745544915.153546567919.192604102823.0453064003