small scale transport Field Emission-Driven research

small scaletransport

research laboratoryresearch laboratory

Field Emission-Driven

Microdischarges

Prof. David B. Go [email protected]

http://www.nd.edu/~dgo

Aerospace and Mechanical Engineering

03/16/2012

slide 2 �D B. Go 03/16/2012�

Effects of Confinement*

•� decreased electrode spacing ��

affects charge density distribution & Debye length

•� increased surface-to-volume ratio � affects energy balance and distribution

Microplasmas and Microdischarges

Microplasmas/discharges •� gas discharges with a characteristic

dimension less than 1 mm •� advantageous pd scaling enables stable

operation at high p (1 atm) •� high pressure leads to new chemical

pathways � new applications

Lighting

http://www.edenpark.com/ http://www.plasmainstitute.org/

Medical and Dental Environmental and

Chemical Analysis Nanomaterial

Synthesis

Harper et al., Anal. Chem., 2009 *Mariotti & Sankaran, J. Phys D: Appl. Phys., 2010

As surfaces begin to play a dominant role, it is necessary to establish

a better understanding of plasma/surface interactions

slide 3 �D B. Go 03/16/2012�

Plasma/Surface Interactions •� Plasma/surface interactions important for applications

–� liquid/flesh/sputtering/cells/etc.

–� electrochemistry/biological/environmental

•� Plasma/electrode damage � important for device

development –� device lifetime/robustness/design …

•� Plasma/electrode coupling � important for fundamental

understanding –� emission processes (secondary/photo/thermionic/field)

–� charging processes (dielectric barriers)

slide 4 �D B. Go 03/16/2012�

Outline

Experimental Evidence

of Field Emission-Driven

Microdischarges

Field Emission and

Microscale Breakdown

Fluid Models for


Microdischarges

0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2

Applied Potential, V

Eio

n, V m

�1

1 μm

20μm

Theory for Modified

Paschen’s Curve

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)

electrode spacing (μm)

slide 5 �D B. Go 03/16/2012�

Outline



Microdischarges

Field Emission and


Theory for Modified

Paschen’s Curve

Fluid Models for


Microdischarges

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)


0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2


Eio

n, V m

�1

1 μm

20μm

slide 6 �D B. Go 03/16/2012�

History on Microscale Breakdown •� Microscale breakdown was originally studied in the 1950s in a series of

papers out of IBM

•� Rejuvenated in 1990s by surge of interest in MEMS devices � preventing

sparks and device failure

•� Near universal deviation from the classic Paschen’s breakdown curve �

modified Paschen’s curve

Go and Pohlman, J. Appl. Phys. (2010)

slide 7 �D B. Go 03/16/2012�

Deviation from Paschen’s Curve

anode

cath

ode

electron impact ionization

(�-process)

ion-induced secondary

emission (�i-process)

~1-10 μm

e�

e�

e�

e�

Deviation from Paschen’s curve occurs because either •� secondary emission is a function of the electric field

•� alternative charge creation processes are at play

field emitted electrons

(�’-process) e�

At the microscale, the electric field can be

very high (~10-100 V/μm) such that electrons tunnel from the cathode

•� electron field emission acts as an additional charge source and it is

also a function of the electric field

At pressure, ions in the electrode gap

affect the electric field •� ion-enhanced field emission

Boyle & Kisliuk

Phys. Rev. Lett. 1955

slide 8 �D B. Go 03/16/2012�

PIC/MCC Simulations of Breakdown Radmilovi�-Radjenovi�, Lee, Iza, Park,

J. Phys. D. Appl. Phys., 2005 Zhang, Fisher, Garimella

J. Appl. Phys., 2004

Radmilovi�-Radjenovi�, Radjenovi�,

IEEE Trans. Plasma Sci., 2007

PIC/MCC simulations

confirmed the role of

field emission

slide 9 �D B. Go 03/16/2012�

Remaining Questions

•� Is there a basis for a theory to describe the

deviation from Paschen’s curve?

•� What is the nature of the interaction between field

emission and the discharge?

•� Can field emission play any other role in the

discharge? � Implications?

slide 10 �D B. Go 03/16/2012�

Outline



Microdischarges

Field Emission and


Theory for Modified

Paschen’s Curve

Fluid Models for


Microdischarges

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)


0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2


Eio

n, V m

�1

1 μm

20μm

slide 11 �D B. Go 03/16/2012�

Classic Breakdown Theory Volumetric breakdown characterized by Paschen’s curve

Pre-Breakdown Current

jpre�breakdown =joe

�d

1� � i e�d �1( )e�d � 1+1 � i( )

Breakdown Condition –

Townsend Criterion

Traditional exponential form for

ionization coefficient, �

� = Ape�

BpdV

Vb =Bpd

ln pd( ) + lnA

ln 1 � i +1( )

�

� � �

�

�

= f pd( )

Breakdown Voltage: pd scaling

A & B – coefficients

p – pressure d – electrode gap

V - voltage

balance of multiplication and secondary emission

slide 12 �D B. Go 03/16/2012�

Ion-Enhanced Field Emission

Fermi energy

solid vacuum

�F

�

f(�)

work function

e–

Fowler-Nordheim Equation (1928)

j =AFN �E[ ]

2

�� 2 y( )exp

�BFN�3 2v y( )

�E

�

� �

�

�

*theoretically require fields ~1000 V/μm

but practically as low as 10-100 V/μm

Can use 0th-order approximation to derive theory for

field emission’s role in breakdown

Fermi energy

solid

�F

�

f(�)

work function

e–

0th-order ion enhanced field emission

j =AFN �E + Eion[ ]

2

�� 2 y( )exp

�BFN�3 2v y( )

�E + Eion

�

� �

�

�

*the ion’s potential thins the potential barrier

making it easier for an electron to tunnel from

the cathode

slide 13 �D B. Go 03/16/2012�

Field Emission Breakdown

j field + = CFN EA + Eion( )2exp �

DFN

EA + Eion( )

�

� �

�

� � jfield = CFN E2 exp �

DFN

E

�

� �

�

� �

•� From a 0th order perspective, superposition can be used to account for

the ion-enhanced effect

jfield+ = jfield eMj field+

n( )� � =

jfield+

jion

= Ke�

DFNdV

•� Can derive relationship for ion-enhanced field emission

effective secondary emission coefficient

Boyle & Kisluik,

J. Appl. Phys, 1955

•� Recall the Townsend criterion

� i e�d �1( ) =1

replace �i by �’

Ke�

DFN dVb e�d �1( ) =1

Radmilovi�-Radjenovi� & Radjenovi�,

Plasma Sources Sci. Technol., 2008

This formulation reproduces linear

deviation from Paschen’s curve

slide 14 �D B. Go 03/16/2012�

Semi-Empirical Modified Paschen’s •� Generally, secondary emission coefficients can be added

linearly

–� ion-induced, metastable-induced, photoemission

•� Semi-empirical analytical formulation for modified Paschen’s

curve

K is an ill-defined parameter that is a combination of a number of other

parameters – essentially a fitting factor

� net = � i + � � � i + Ke�Dd

V� � � �

e�d �1( ) =1

e�d � 1+1 ��( )Townsend Criterion:


slide 15 �D B. Go 03/16/2012�

Semi-Empirical Modified Paschen’s

field emission only

Paschen’s curve

combined equation:

modified Paschen’s curve

� i + Ke�Dd

V� � � �

e�d �1( ) =1


slide 16 �D B. Go 03/16/2012�

Semi-Empirical Modified Paschen’s

•� K~107-109 � physical

interpretation?

•� some arguably questionable

assumptions in derivation of

Can a more complete ab initio

formulation be derived?


� �

slide 17 �D B. Go 03/16/2012�

Ion-Enhanced Field Emission

Revisit 0th order perspective,

j =AFN �EA + Eion( )

2

�� 2 y( )exp

�BFN�3 2v y( )

�EA + Eion

�

� �

�

�

The number of electrons field emitted because of the presence of a single

ion is the integration of the current density over area and ion’s time of flight

Nemit =1

qj E( )dAsdt

As

�T

� � � '=Nemit

Nion

cathode surface area influenced by single ion

time of flight of ion

� i + � � ( ) e�d �1( ) =1Substitute into breakdown condition

Tirumala and Go, Appl. Phys. Lett. (2010)

explicit form for Eion using a

single ion and method of images

slide 18 �D B. Go 03/16/2012�

Since EA = V/d � Numerically solve for breakdown potential Vb

Analytical Modified Paschen’s Curve

� i +1

q(2�rdr)

0

R

� dtE r,t( )�t 2 y( )

exp�BFN�

3 / 2v( f )

E r, t( )

�

� �

�

�

�

� � �

�

� � 0

T

�

�

� �

�

�

� �

eApd exp �Bpd V( ) �1( ) =1

E(r,t) = (�EA ) +q

2��0

L0 � bEA t

L0 � bEA t( )2

+ r2( )3 / 2

where

T = lifetime of ion

R = radius of interaction b = ion mobility

Fully Analytical Model

Effective emission coefficients �’ < 1 � effect

of ion on the field averaged over “time of

flight” is fairly small but not insignificant

slide 19 �D B. Go 03/16/2012�

50

100

150

200

250

300

350

400

450

500

��

ap

plied

dc v

olt

ag

e (

V)


Analytical Modified Paschen’s Curve


Experimental Breakdown Curve: Slade and Taylor (2002)

Simulated Breakdown Curve: Zhang et al. (2004)

Semi-empirical breakdown model: Go and Pohlman, (2010)

Analytical breakdown model: Tirumala and Go, (2010)

Paschen’s curve

S

AAAA

modified Paschen’s

curve

slide 20 �D B. Go 03/16/2012�

Implications: pd vs. d Scaling


slide 21 �D B. Go 03/16/2012�

Implications: pd vs. d Scaling

At the microscale, scaling no longer pressure�distance


slide 22 �D B. Go 03/16/2012�

Remaining Questions

•� Is there a basis for a theory to describe the deviation

from Paschen’s curve?

•� What is the nature of the interaction and/or

coupling between field emission and the

discharge?



slide 23 �D B. Go 03/16/2012�

PIC/MCC Simulations of Breakdown

Simulated Breakdown Curves of Argon for 3 Cases:

jFE = f VA d( )

jFE = f VA d + ESC( )

(b) Field emission as a function of applied field

only (native field emission)

(c) Field emission as a function of applied field and

space charge (ion-enhanced field emission)

jFE = 0(a) No field emission, secondary emission only

native field

emission

ion-enhanced

field emission

slide 24 �D B. Go 03/16/2012�

Cathode Coupling to Discharge

cathode emission vs. time at the breakdown voltage

d = 3 μm; p = 760 torr

(b) Field emission as a function of applied field

only (native field emission)

(c) Field emission as a function of applied field and

space charge (ion-enhanced field emission)

native field

emission

ion-enhanced

field emission

jFE = f VA d( )

jFE = f VA d + ESC( )

slide 25 �D B. Go 03/16/2012�

Positive Feedback Mechanism

�

E e-

e�

emitted

electron

ionization

ion enhances

electric field

Breakdown requires a positive feedback

mechanism � cathode emission must

respond to the discharge

Ion-enhanced field emission responds

to positive build up of space charge in

the discharge � mobility difference in

the pre-quasi neutral regime

slide 26 �D B. Go 03/16/2012�

Remaining Questions

•� Is there a basis for a theory to describe the deviation

from Paschen’s curve?

•� What is the nature of the interaction and/or coupling

between field emission and the discharge?



slide 27 �D B. Go 03/16/2012�

Outline



Microdischarges

Field Emission and


Theory for Modified

Paschen’s Curve

Fluid Models for


Microdischarges

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)


0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2


Eio

n, V m

�1

1 μm

20μm

slide 28 �D B. Go 03/16/2012�

Glow Discharge-Type Experiments

At what point does this canonical

i-V curve become invalid?

discharge

tube micropositioner

stage pre

-bre

akdow

n

breakdown

glow

tungsten cathode

nickel anode

slide 29 �D B. Go 03/16/2012�

Representative Glow Results

10�12 10�9 10�6 10�30

100

200

300

400

500

Current, i(A)

Pla

sma

Vol

tage

, Vp (

Vol

ts)

5 μ m

7 μ m

10 μ m

20 μ m50 μ m

100 μ m

500 μ m

1 mm

Rumbach and Go, 2011 Gaseous Electronics Conference

pre

-bre

akdow

n

breakdown

glow

From 1000 to 5 μm the typical transition to glow was observed

•� Townsend discharge current ~pA

Argon, 100 Torr

slide 30 �D B. Go 03/16/2012�

Field Emission Results

Rumbach and Go, 2011 Gaseous Electronics Conference

Below 5 μm, growth in current was anomalous (~nA

rather than ~pA) and consistent with field emission

2 4 6 8 10x 10�9

0

50

100

150

200

Current, i(A)

Pla

sma

Vol

tage

, Vp (

Vol

ts)

0.004 0.006 0.008 0.01 0.012 0.014 0.016�35

�34

�33

�32

�31

�30

�29

�28

1/Vln

(i / V

2 )

N2 d=4μ m, p=100torr

Ar d=4μ m, p=200torr

Argon, 200 Torr, 4 μm

N2, 100 Torr, 4 μm

Current-Voltage Response

N2, 100 Torr, 4 μm

Fowler-Nordheim Plot

ln i V 2( )��1 V

steady current increase without

‘breakdown’

slide 31 �D B. Go 03/16/2012�

Field Emission – Exotic Materials

active region 5-20 μm gap

Planar microscale devices operated in open, atmospheric air

Go, Fisher, Garimella & Bahadur, Plasma Sources Sci. Tech (2009)

Electrodes fabricated out of plasma-enhanced chemical vapor deposited diamond

10 �m 2 �m

diamond

electrode

diamond

electrode

diamond

electrode

etched gap

etched gap

slide 32 �D B. Go 03/16/2012�

Field Emission – Exotic Materials

Go, Fisher, Garimella, & Bahadur, Plasma Sources Sci. Tech (2009)

steady current increase (~μA)

without ‘breakdown’

ln i V 2( )��1 VFowler-Nordheim Plot

Using materials with favorable field emission properties

can obtain ‘Townsend discharge’ ~μA due to field

emission

slide 33 �D B. Go 03/16/2012�

Field Emission in the Literature Peterson, Zhang, Fisher, Garimella


diamond & CNTs;

open air; 10-20 μm

Venkattraman, Garg, Peroulis, Alexeenko

Appl. Phys. Lett., 2012

nickel; open air; ~3 μm Kim

J. Phys. D. Appl. Phys., 2006

CNTs; ~1-100 mTorr;

~500 μm Additional evidence in

literature of field emission-

driven discharges

slide 34 �D B. Go 03/16/2012�

Field-Emission Driven Discharges

Opportunity to develop field-emission driven discharges:

•� moderate current (~μA), high-pressure Townsend discharges

•� modulate cathode electron production

Operation Below Breakdown Plasma-based Photodiodes

Tchertchian, Wagner, Houlahan, Li, Sievers , Eden

Contrib. Plasma Phys., 2011 Peterson, Zhang, Fisher, Garimella


slide 35 �D B. Go 03/16/2012�

Outline



Microdischarges

Field Emission and


Theory for Modified

Paschen’s Curve

Fluid Models for


Microdischarges

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)


0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2


Eio

n, V m

�1

1 μm

20μm

slide 36 �D B. Go 03/16/2012�

Fluid Model

dJ e

dx=�J e

dJ +

dx= �

dJ e

dx

� ��

E =dE

dx=�+ � �e

�0

A self-consistent 1-D Townsend fluid model that includes ion-enhanced

field emission.

electron conservation ion conservation Poisson’s Equation

Solution Paths:

•� Analytical solution possible by using simplifications for the more

complex relationships � semi- self consistent

•� Numerical solution using standard integration procedures � fully

self consistent

Cathode boundary condition

J e (x = 0) = J FE (E0 ) + �J + (x = 0) + j0

Incorporate Fowler-Nordheim field emission in the BC

J+ (d) = 0

V = �E(x)dx0

d

�

Electric Field B.C.

slide 37 �D B. Go 03/16/2012�

Fluid Model – Breakdown Analytical assumptions lead to a transcendental equation that only has

a subset of voltages that are solutions …

Prediction of breakdown consistent with

both theory and PIC/MCC model.

0 2 4 6 8 10 12 140

50

100

150

200

250

300

350

400

450

500

Gap distance, d, μm

Bre

akdo

wn

Vol

tage

, VB, V

olts

g

PaschenNumeric FluidGo/TirumalaPIC/MCCFluid Solvability

solvability condition =

breakdown condition

Ar, 760 torr

slide 38 �D B. Go 03/16/2012�

0 100 200 300 40010�2

100

102

104

106

108


Eio

n, V m

�1

1μm

20μm

Scaling Relationships If we make the assumption that the field due to space charge is much smaller than

the applied field ESC < VA/d � obtain analytical relationships for critical properties

Jtot =e�d

1� � (e�d �1)JFE

�Vd( ) + j0[ ]

ESC =JFE

�VAd( ) + j0

1� �(e�d �1)A VA ,d, p( )

n+(x) =e�d � e�x( )

eb+VA

d( ) 1� �(e�d �1)[ ]JFE

�VAd( ) + j0[ ]

A(VA ,P,d) =1

VA�0b+

1� 2 (1� e�d ) + d 2

2 e�d + d�[ ]

where

electric field due to

ions can approach

107 V/μm as d � 1 μm

1 μm

20 μm

N2, 760 torr

Primary Insights:

•� Virtually all the relationships scale as � experimental confirmation?

•� Field due to space charge becomes very large (~107 V/μm!) � analytical

approximation incomplete

~ e�d JFEVA

d( )

slide 39 �D B. Go 03/16/2012�

40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5x 106 Field due to ions, N

2, d =3e�06 m, S = 0.01


Eio

ns, V

/ m

NumericApproximate

0 50 100 150 200 250 3001

2

3

4

5

6

7

8

9

Applied potential, V

J tot /

J FE

NumericApprox. (Avalanche)

Numeric vs. Analytical

Total current divided by

native field emission

Analytical solution accurate for most of Townsend discharge

� strong divergence within ~10 % of breakdown voltage as

feedback mechanism begins to dominate

Electric field due to

space charge

N2, 760 torr,

d = 3 μm

N2, 760 torr,

d = 3 μm

bre

akdow

n

bre

akdow

n

slide 40 �D B. Go 03/16/2012�

Impact of Ion-Enhancement

The ion enhancement (space charge) effect only becomes

prominent within ~30% of breakdown voltage

0 20 40 60 80 100 120 140 160 1800

0.5

1

1.5

2

2.5

3

3.5x 105 Total current, N

2, d =3e�06 m, S = 0.01

Applied potential, V

Cur

rent

den

sity

, A /

m2

NumericApproximateNative FE

bre

akdow

n

slide 41 �D B. Go 03/16/2012�

Comparison to PIC/MCC

Qualitatively, numerical model matches well with

PIC/MCC simulations

0 0.5 1 1.5 2 2.5 3x 10�6

108

109

1010

1011

1012

10132 AP

Position, x, mN

umbe

r de

nsity

, cm�

3

ElectronsIons

Ion and electron

concentrations

slide 42 �D B. Go 03/16/2012�

Outline



Microdischarges

Field Emission and


Theory for Modified

Paschen’s Curve

Fluid Models for


Microdischarges

Conclusions and

Future Work

50

100

150

200

250

300

350

400

450

500

��

ap

pli

ed

dc

vo

lta

ge

(V

)


0 50 100 150 200 250 300 350 400 45010

�2

100

102

104

106

108

2


Eio

n, V m

�1

1 μm

20μm

slide 43 �D B. Go 03/16/2012�

Conclusions •� Electron field emission can play a critical role in microscale

discharges

–� modified breakdown condition

–� field emission-driven Townsend discharges

•� Field emission inherently coupled to the ionization in the

electrode gap (discharge/cathode coupling)

–� ion-enhanced field emission

•� Opportunities for new types of devices that capitalize on field

emission phenomenon

–� tuning field emission properties

–� understanding/measuring discharge properties

slide 44 �D B. Go 03/16/2012�

Future Work •� Extending the theory

–� 0th order � more accurate (resolving quantum mechanics)

–� incorporation of enhanced theory into PIC and fluid models

–� AC fields

–� comprehensive emission theory � secondary + field + thermal

•� Experiments

–� controlling discharge properties with cathode materials (nanoparticles,

nanostructured surfaces, semi-conductors)

–� pushing the envelope on scalability below 1 μm

slide 45 �D B. Go 03/16/2012�

Acknowledgements Current Students •�Rakshit Tirumala – theoretical

•�Jay Li – PIC/MCC •�Paul Rumbach – experiments/fluid model

•�Danny Taller •�Ben Rollin (u)

•�Matt Goedke (u)

Former Visitors/Post-Docs/Students •�Dr. Jenny Ho (visiting scientist)

•�Dr. Ming Tan (post-doc) •�Dr. Nishant Chetwani (post-doc)

•�Dr. Alejandro Guajardo-Cuéllar (Ph.D.) •�Katie Isbell (M.S.)

•�Sajanish Balagopal (M.S.)

•�15+ undergrads

Collaborators •�Prof. Hsueh-Chia Chang

•�Prof. Mihir Sen •�Prof. Aimee Buccellato

•�Dr. Paul Brenner •�Prof. Norm Dovichi

•�Dr. Carlos Gartner

•�Prof. Mohan Sanakran (CWRU)

Funding •�Air Force Office of Scientific Research

Young Investigator Award (AFOSR Grant FA9550-11-1-0020)

•� Intel Corporation

•�Notre Dame Faculty Scholarship Award

slide 46 �D B. Go 03/16/2012�

Acknowledgements

Documents

small scale transport Field Emission-Driven research