stephen guerrera research qualifying exam

8/13/2019 Stephen Guerrera Research Qualifying Exam

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Scaling of High Aspect Ratio Current

Limiters for the Individual Ballasting of

Large Arrays of Field Emitters

Stephen A. Guerrera

Luis F. Velasquez-GarciaAkintunde I. Akinwande

[email protected]

RQE Presentation11/01/2011
mailto:[email protected]:[email protected]:[email protected]


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RQE - 11/1/2011

Overview

Introduction and Motivation

Modeling and Simulation Device Fabrication

Device Characterization and Analysis Conclusions

2


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RQE - 11/1/2011

Overview



Device Characterization and Analysis Conclusions

3


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RQE - 11/1/2011

Motivation Many applications require compact, efficient electron sources

4

!"#$ %& ()*+ ,-.+ /0001,2,+ 1345 63+ 7889

5* :;()%+ ?* #@ A)(=B#C

D$%)> 3E$==$#F !#;G#;(&$#FCCC*%H%(E>%I$J%=*J#E

Multi e-beam lithography Portable Vacuum Sources X-rays

Displays Terahertz Devices Ionizers/Neutralizers


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RQE - 11/1/2011

Physics of Electron

Sources

5

EF

e-

metal vacuum

EF

e-

metal vacuum

Ex

x V(x>0) = -qFx

(a) (b)

W

00

Ex

Ex

x= 0 x

Thermionic or Photoemisssion Field Emisssion


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RQE - 11/1/2011

Physics of Electron

Sources

6

EF

e-

metal vacuum

EF

e-

metal vacuum

Ex

x V(x>0) = -qFx

(a) (b)

W

00

Ex

Ex

x= 0 x

Thermionic or Photoemisssion Field Emisssion


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RQE - 11/1/2011

Field Emission Physics:

A two step process

Spindt Approximations to the Fowler-Nordheim Model:

7

2D Fermi sea of electrons

J=qnv F

Ef e-Ec

Flux of electrons

to the surface

Transmission ofelectrons through

the barrier

!

J = q N(Ex )D(F,Ex )EC

!

" dEx

J =AF

2

1.1!exp

B !1.14"107

!1/2

#

$%

&

'(exp )

0.95 !B !!3/2

F

#

$%

&

'(


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RQE - 11/1/2011

Schematic Cross-section of a

Microfabricated Field Emitter

8

Sharp emitter tips arerequired for emission becauseof the large electric fields

required for field emission

Field enhancement results atthe tip from solutions toLaplaces equation

In general, a self-alignedstructure is preferred formaximum transmission

EmitterCone

Si

Substrate

Poly-Siextraction

gate

Anode

Emitted

Electrons


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RQE - 11/1/2011

Ball-In-Sphere

Electrostatics Model

9

Simple analytical model to describe the

electrostatics of a field emitter with a

proximal gate

Boundary value problem readily evaluated

in spherical coordinates to obtain the

magnitude of the electric field:

From this, an expression for the fieldfactor, !, is obtained:

Emitter

Cone

D

R

Poly-Si

extraction

gate

F(r) =V0D !R

D"R

1

r2

! =D

D! R

1

R


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RQE - 11/1/2011

Scaling

10

All dimensions reduced by

scaling factor s

Assume current density

constant

Cross-sectional area

decreases

Packing density increases bysame amount

To first order, no net change

in current density for the

array


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RQE - 11/1/2011

Benefits of Scaling

FEA Dimensions Denser packing of field emitters

More redundancy for a given array size

Higher current density and overall emissioncurrent possible by increasing doping

More uniform emission current

Smaller aperture, allowing for higher fieldfactor, lower turn on voltage

Smaller energy distribution

11


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RQE - 11/1/2011RQE - 11/1/2011

Tip Radii Statistical

Distribution

12

0 100 200 300 400 500

1014

1012

1010

108

GatetoEmitter Voltage, VGE

[Volts]

EmissionCurrent,IE[A]

Burn out limit

ro=40 nm

M. Ding et al, TED 2002

Tip radii follow a log-normal or Gaussian

distribution (long tails)

Array sub-utilization anddamage due to Jouleheating and burnout


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RQE - 11/1/2011

Tip Radii Statistical

Distribution

13

M. Ding et al, TED 2002

0 100 200 300 400 500

1014

1012

1010

108

GatetoEmitter Voltage, VGE

[Volts]

EmissionCurrent,IE[A]

Burn out limit

ro=10 nm

Tip radii follow a log-normal or Gaussian

distribution (long tails)

Array sub-utilization anddamage due to Jouleheating and burnout


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Individual Current Limiters

Allow Higher Overall Current

14


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Load-Line Analysis of

Supply Control

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tip radius: r1< r

2< r

3

V

I

I

V

I

V

I

Passive Resistance Dynamic Resistance

tip radius: r1< r

2< r

3

V

I

V

Slope = 1 / R

Slope = 1 / Ro

Pure resistors!Simultaneous high current and low currentdispersion not possible (or at least very hard)

Current sources!Simultaneous high current and low current

dispersion possible


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RQE - 11/1/2011

V

I

V

I

I

Passive Resistance Dynamic Resistance

V

I

V V

I

Scaling

Load-Line Analysis of

Supply Control

16

Pure resistors!Simultaneous high current and low currentdispersion not possible (or at least very hard)

Current sources!Simultaneous high current and low current

dispersion possible


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Individually Ballasted

FEA-FET Structure

17

VCT

n-Silicon Substrate VG= VGE+ VDS

Si Pillar

UngatedFET

Si FieldEmitter

D

S

VGE

VDS

E

G

A

Gate

Anode

VGS

VAS

Oxide DielectricFill / Void


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In the linear regime, the potential varies linearly along thelength of the channel

A linear conductance can be defined

Above a critical field, the velocity of electrons saturates, anda depletion region forms at the drain end of the channel

Additional voltage applied is dropped across the depletionregion

Output conductance arises from channel length modulation

RQE - 11/1/2011

Vertical Ungated FET

Operation

18

ID =qAnedV(x)

dx

qAneVDS

L

GLIN =qAne

L

Anode

Gate

n-type Silicon Substrate

x = 0

x = L

Sil

iconPillar

Oxide/DielectricFill

Emitter

ID = IDSS[1 + VDS] = IDSS+ GOUTVDS

ID= qA(x)ne

1 +

evsat

2 dV(x)dx

2dV(x)

dx


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RQE - 11/1/2011

Prior Work

19

GeometryParameters:

Pillar dimensions:

1!m x 1!m x 100

!m

Pitch: 10!m

Tip radius:


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RQE - 11/1/2011

Overview



Device Characterization and Analysis

Conclusions

20


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Scaled Vertical Ungated

FET Simulation Results

Geometry: 100 nm x 100 nm x 10 !m ND= 5x1014cm-3

L!"IDSS#, rlin!, ro!

Simulations performed using SILVACOtoolset Full Si Process Simulator (ATHENA) Poisson equation and continuity

equation solver in Silicon (ATLAS)

21


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Geometry: 100 nm x 100 nm x 10 !m 100:1 Aspect Ratio

ND!"IDSS!, rlin#, ro#22


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Doping density: 2x1014cm-3

Aspect ratio: 100:1 (100 nm x 100 nm x 10 !m) Chosen to yield 1 nA/tip Thus 0.1-1.0 A/cm2for 1 um pitch

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Overview




Conclusions

24


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Fabrication of Si

FEA-FETs

25

Photolithographyto define dots

a)

b)

c)

SiO2 Si PR

e)

PR Removal,oxidation sharpening

and oxide removal

d)

Rough tip formation and

pillar formation

Grow oxidehardmask

RIEto pattern hardmask


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Completed FEA-FET

Structure

26

100 nm

Pillar Height: 10!m

Pillar Diameter: 0.11!m

Tip Radius: < 10nm

Pitch: 5!m


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Overview




Conclusions

27


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Current-Voltage Characterizationof Ungated FETs Without Emitters

28

Single FET 4M FET Array


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Field Emission

Characterization Setup

29


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Field Emission I-V

Characterization

30


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Field Emission I-V

Characterization

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Analysis of Field

Emission Data Array size: 1.36 M emitters !(from 2-D electrostatic simulations of the structure in COMSOL):

1.34x104 cm-1.

Sensitivity analysis: !(spacing reduced to 12.5 !m): 5.84x104cm-1

!(tip radius reduced to 2.5 nm): 1.81x104cm-1

Saturation current (expected), Isat: ~1.3 mA (current of ~1 nA/emitter)

Current saturation voltage, VGSS, extrapolated from F-N curve: ~1.5kV

Upper bound on array burnout current (from failure analysis ofindividual vertical ungated FETs and heating analysis): ~10 A

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Overview




Conclusions

33


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RQE - 11/1/2011

Conclusions

Successfully demonstrated the fabrication ofvertical ungated FETs with dimensions of100nm x 100nm x 10um with 1 micron pitch

This is the smallest, most dense array ofvertical ungated FETs ever reported

Demonstrated field emission and ballastingfrom Si emitters on top of scaled verticalungated FETs with five micron pitch, withcurrent density greater than 100 !A/cm2.

34


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RQE - 11/1/201135


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RQE - 11/1/2011

Backup Slides

36


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Future Work

Devices with higher doping density should be built toensure higher currents can be obtained.

Better planarization / trench-filling techniques needto be explored

A process for integrated, self-aligned gates needs tobe adapted and developed for the FET-FEA structure

More complete analysis of the tip radius distribution

Lifetime analysis Adapting the FEA-FET structure to real applications

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Field Emission Requires

Large Electric Fields

38

107

108

109

1010

108

106

104

102

100

F [V/cm]

T

ransmissionProbability


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Preliminary Tip Radius

Distribution

39


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Additional Hi Res Tip

SEMs

40


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RQE - 11/1/201141

!"#"$%&%# '"()%

!" #$%&%' )*+,

- %& .*

/ !01& 2*3#

4"55 &6#7% 2/

8"55 &6&,9 8

:-4! ;67, 25

: #61? @5

Axisymetric Simulation

of Vertical Ungated FETs


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RQE - 11/1/2011

Thermal Failure

Analysis

42


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Field Emission

Characterization Setup

43


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Field Emission

44


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Electrostatics Simulations:

!for devices with 1"m Pitch

45

0

500

1000

1500

2000

2500

3000

3500

0

20004000

6000

8000

10000

1200014000

16000

18000

20000

0 2 4 6 8 10

Distance Above Substrate [microns]

[cm-1

]

Turn on voltage [V]


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RQE - 11/1/2011

COMSOL Field

Enhancement Simulation

46

Zero charge / symmetry boundary

+VG

GND

Example Simulation Result

Solving the Laplaceequation

Field emitter: 30 coneangle with 5 nm or

2.5 nm radius Pillar width: 100 nm Pillar height: 10 !m Pitch: 5 !m # of Emitters: 5 Anode separation: 25 nm,

12.5 nm

Maximum field measuredat right-most field

emitter

CO SO


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RQE - 11/1/2011

COMSOL Field

Enhancement Simulation

47

Solving the Laplaceequation

Field emitter: 30 coneangle with 5 nm or

2.5 nm radius Pillar width: 100 nm Pillar height: 10 !m Pitch: 5 !m # of Emitters: 5 Anode separation: 25 nm,

12.5 nm

Maximum field measuredat right-most field

emitterTip Meshing Detail


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RQE - 11/1/2011

Energy Distribution of

Emitted Electrons

48

!=12.5x105 /r 0.7

ro=30x10-7

dr=3x10-7


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Energy Distribution of

Emitted Electrons

!=62.5x105 /r 0.7

ro=30x10-7

dr=3x10-7

stephen guerrera research qualifying exam

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