small scale transport Field Emission-Driven research ...
Transcript of 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
Field Emission-Driven
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
Experimental Evidence
of Field Emission-Driven
Microdischarges
Field Emission and
Microscale Breakdown
Theory for Modified
Paschen’s Curve
Fluid Models for
Field Emission-Driven
Microdischarges
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)
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
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
Experimental Evidence
of Field Emission-Driven
Microdischarges
Field Emission and
Microscale Breakdown
Theory for Modified
Paschen’s Curve
Fluid Models for
Field Emission-Driven
Microdischarges
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)
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
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:
Go and Pohlman, J. Appl. Phys. (2010)
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
Go and Pohlman, J. Appl. Phys. (2010)
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?
Go and Pohlman, J. Appl. Phys. (2010)
� �
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
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250
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�� �� �� �� �� �� � � �� �� ��� ��� ��� ��� ��� ���
ap
plied
dc v
olt
ag
e (
V)
electrode spacing (μm)
Analytical Modified Paschen’s Curve
Tirumala and Go, Appl. Phys. Lett. (2010)
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
Tirumala and Go, Appl. Phys. Lett. (2010)
slide 21 �D B. Go 03/16/2012�
Implications: pd vs. d Scaling
At the microscale, scaling no longer pressure�distance
Tirumala and Go, Appl. Phys. Lett. (2010)
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?
•� Can field emission play any other role in the
discharge? � Implications?
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?
•� Can field emission play any other role in the
discharge? � Implications?
slide 27 �D B. Go 03/16/2012�
Outline
Experimental Evidence
of Field Emission-Driven
Microdischarges
Field Emission and
Microscale Breakdown
Theory for Modified
Paschen’s Curve
Fluid Models for
Field Emission-Driven
Microdischarges
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)
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
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
Plasma Sources Sci. Technol., 2005
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
Plasma Sources Sci. Technol., 2005
slide 35 �D B. Go 03/16/2012�
Outline
Experimental Evidence
of Field Emission-Driven
Microdischarges
Field Emission and
Microscale Breakdown
Theory for Modified
Paschen’s Curve
Fluid Models for
Field Emission-Driven
Microdischarges
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)
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
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
Applied Potential, V
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
Applied Potential, V
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
Experimental Evidence
of Field Emission-Driven
Microdischarges
Field Emission and
Microscale Breakdown
Theory for Modified
Paschen’s Curve
Fluid Models for
Field Emission-Driven
Microdischarges
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)
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
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