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Modeling quantum yield, emittance, and surfaceroughness effects
from metallic photocathodes
D. A. DimitrovTech-X Corporation, Boulder, CO
This work is funded by the US DoE office of Basic Energy
Sciences under the
SBIR grant # DE-SC0013190.
P3 Workshop, LANL, NM, October 2018
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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This work was done in collaboration with:
Howard Padmore and Jun Feng, Lawrence Berkeley National Lab.
John Smedley and Ilan Ben-Zvi, Brookhaven National Lab.
Siddharth Karkare, Arizona State University.
George Bell, Tech-X Corp.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Outline
1 Motivation
2 Modeling
3 Simulations
4 Summary & future developments
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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MotivationDevelopments in materials design and synthesis have
resulted inphotocathodes that can have a high quantum yield (QY),
operate atvisible wavelengths, and are robust enough to operate in
high electricfield gradient photoguns for application to free
electron lasers, indynamic electron microscopy and
diffraction.However, synthesis often results in roughness, both
chemical andphysical, ranging from the nano to the microscale. The
effect ofroughness in a high gradient accelerator is to produce a
smalltransverse accelerating gradient, which therefore results in
emittancegrowth.Although analytical formulations of the effects of
roughness havebeen developed, detailed theoretical modeling and
simulations thatare verified against experimental data are
lacking.We aim to develop realistic, verified and validated,
electron emissionmodeling and 3D simulations from photocathodes
with controlledsurface roughness to enable an efficient way to
explore parameterregimes of relevant experiments.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Momentatron experiments allow investigation of
emissionproperties and surface roughness effects.
Recent advances in material science methods have been
demonstrated(H. A. Padmore. Measurement of the transverse momentum
of electronsfrom a photocathode as a function of photon energy, in
P3 2014) tocontrol the growth of photoemissive materials (e.g. Sb)
on asubstrate to create different types of rough layers with a
variablethickness of the order of 10 nm.
Momentatron experiments have been developed (J. Feng et al.,
Rev.Sc. Instr., 86, 015103-1/5, 2015) to measure transverse
electronmomentum and emittance.
It was demonstrated (J. Feng et al., Appl. Phys. Lett., 107,
134101-1/42015) recently how data from momentatron experiments can
be usedto investigate the thermal limit of intrinsic emittance of
metalphotocathodes.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Overview of our modeling approach
The overall modeling capabilities implemented in the
VorpalParticle-in-Cell (PIC) code framework to simulate electron
emission fromphotocathodes with controlled rough surfaces consist
of
electron excitation in a photoemissive material in response
toabsorption of photons with a given wavelength
charge dynamics due to drift and various types of scattering
processes
representation of rough interfaces
calculation of electron emission probabilities that takes into
accountimage charge and local field enhancement effects (as a
function ofposition on rough surfaces).
particle reflection/emission updates and efficient 3D
electrostatic(ES) solver for a simulation domain that has
sub-domains withdifferent dielectric properties separated by rough
interfaces.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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We have developed simulations with different types ofsurface
roughness.
Figure 1: The surfaces are represented with stair step or
cut-cell grid boundaries.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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The simulations effectively implement the 3 step model
forelectron emission from metallic photocathodes.
Figure 2: A simplified diagram indicates the three main
processes to model, theimportance of electron-electron scattering
and temperature effects.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Electron energy sampling takes into account the density ofstates
of photocathode materials.
−8 −6 −4 −2 0E − µ (eV)
0.0
0.1
0.2
0.3
0.4
p(E)
Figure 3: Electron energies on occupied states are sampled from
a probabilitydistribution with density function p (E) ∼ g (E) f
(E), where g (E) is the densityof states (DoS), and f (E) = 1/
(e(E−µ)/kBT + 1
)is the Fermi function. The DoS
used is from published band structure calculations: Sb (left) is
from Bullet (1975)and Au (right) is from Christensen & Seraphin
(1971).D. A. Dimitrov Modeling Electron Emission from Controlled
Rough Surfaces 9/27
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We implemented two models for electron-electronscattering for
Monte Carlo particle simulations.
For transport in Sb, we used the unified model proposed by Ziaja
et al.J. Appl. Phys., 99 033514 (2006) giving mean free path (in
Å):
λee(E) =√E
a (E − Eth)b+E − E0 exp (−B/A)A ln (E/E0) + B
,
with Eth a threshold energy for the scattering (Eth = 0 for
metals andEth = EG for semiconductors), E0 = 1 eV, and a, b, A, and
B arefitting constants.
For transport in Au, we implemented a model proposed by K.
Jensenet al. J. Appl. Phys., 102 074902 (2007) with a
temperature-dependentscattering rate (with only one adjustable
parameter, Ks):
1/Γee [E(k)] =8~K 2s
α2fsπmc2
(E(k)kBT
)2((1 +
(E(k)− µπkBT
)2)γ
(2k
q0
))−1.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Electron-electron (el-el) scattering is the dominant
energyrelaxation mechanism in metallic photocathodes.
1 2 3 4 5 6 7 8
E − µ (eV)
1011
1012
1013
1014
1015
Γ(E
)(1/s
)
Au-KJCu-KJCuAgBeSb, b = 3.8Sb, b = 1.5
0 1 2 3 4 5
E − µ (eV)
1011
1012
1013
1014
1015
Γ(E
)(1/s
)
Au-VorpalAu-KJel-ac. ph Vorpalel-ac. ph.
Figure 4: The el-el scattering rates for Sb and Au used in the
simulations areshown in the left plot. The electron-acoustic phonon
rates for Au are about anorder of magnitude smaller than the el-el
rates for the range of photon energies ofinterest to electron
emission.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Electron emission probabilities are calculated using atransfer
matrix approach.
The surface potential energy is
V (x) = µ+ φ− Fx − Qx,
0.0
0.1
0.2
0.3
0.4
x(µ
m)
0.20.40.60.81.0
y (µm)
Ex (MV/m)
−0.01−0.63−1.26−1.88−2.50
where φ is the work function, Q = Q0 (Ks − 1) / (Ks + 1) , with
Ks thestatic dielectric constant of the emitter, and Q0 = q
2/ (16πε0) with q thefundamental charge and ε0 the permittivity
of vacuum. The Schottkyeffect is taken into account by using the
electrostatic potential in thesimulations to evaluate the electric
field F along local normal directions.This is included in the
calculation of emission probabilities at positionswhere electrons
attempt to cross the photocathode surface.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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We compare simulation results on electron emission fromflat and
3-ridge rough emission surfaces of Sb and Au.
For simulations with uniform work function on the surface, we
usedφSb = 4.5 eV and φAu = 4.9 eV for Sb and Au, respectively.
A constant potential difference is maintained across the x
length ofthe simulation domain leading to an applied field
magnitude in thevacuum region of the order of 1 MV/m (it varies on
the roughemission surface).
We use periodic boundary conditions in the transverse
directions.
Typical parameters for both 3-ridge and flat emission
surfacesimulations: 0.4268× 1.182× 0.394 (in µm) domain size,
with88× 264× 16 number of cells; time step: ∆t = 2.5× 10−16
s.Details of the models for photo-excitation, transport, and
emission,together with material parameters used, are given in:D. A.
Dimitrov et al. J. Appl. Phys., 122 165303 (2017).
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Electron dynamics inside and out of an antimonyphotocathode at
selected simulation times.
0.0
0.1
0.2
0.3
0.4
x(µ
m)
0.20.40.60.81.0y (µm)
t = 12.5 (fs) 0.0
0.1
0.2
0.3
0.4
x(µ
m)
0.20.40.60.81.0y (µm)
t = 37.5 (fs)
0.0
0.1
0.2
0.3
0.4
x(µ
m)
0.20.40.60.81.0y (µm)
t = 0.0 (fs) 0.0
0.1
0.2
0.3
0.4
x(µ
m)
0.20.40.60.81.0y (µm)
t = 25.0 (fs)
Figure 5: Photo-excited electrons (red spheres) have effectively
diffusive dynamicsin the photocathode. Vacuum electrons (green
spheres) move ballistically.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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The implemented models for Sb are validated againstexperiments
on quantum yield.
Figure 6: Simulations with the higher electron-electron
scattering rate showagreement with experimental data (J. Feng, D.
Voronov, and H. A. Padmore,unpublished) on quantum yield from
antimony with a flat emission surface.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Simulations with controlled surface roughness showincreased
quantum yield.
Figure 7: The increased QY is likely due to a geometric effect:
electrons excitedon the sides of the ridges are effectively closer
to the emission surface thanelectrons excited in Sb with a flat
vacuum interface.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Modeling intrinsic emittance: 3-step model with constantDoS, T =
0 K
If there is no correlation between transverse position and
momentumdistributions of emitted electrons, the intrinsic emittance
�y per mmof rms laser spot size σy is (Dowell & Schmerge,
PRSTAB, 12, 073401,2009):
�y/σy =√〈
p2y〉/mec,
where py is a transverse momentum component of an
emittedelectron.
A 3-step model with a constant DoS and T = 0 K leads to〈p2y〉/me
= (~ω − φ)/3, (1)
and predicts zero intrinsic emittance for ~ω = φ.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Modeling intrinsic emittance: 3-step model with generalDoS and T
> 0 K
When temperature effects and the DoS of the photocathode
materialare taken into account, the intrinsic emittance can be
obtained bynumerically calculating the mean transverse energy (J.
Feng et al.,Appl. Phys. Lett., 107, 134101-1/4 2015) from:
〈p2y〉
me=
∞∫µ+φ−~ω
g(E)f (E)(E + ~ω)h(E , φ, ~ω)dE
∞∫µ+φ−~ω
g(E)f (E)(
1−√
µ+φE+~ω
)dE
, (2)
where h(E , φ, ~ω) = 23 −√
µ+φE+~ω +
13
(µ+φE+~ω
) 32.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Intrinsic emittance from simulations is in agreement
withexperimental data on emission from flat Sb surfaces.
−0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00~ω − φ
(eV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
emit
tan
ce(µ
m/m
mrm
s)
Eq. (1)
Eq. (2) with constant DoS
Eq. (2) with DoS from D. W. Bullett (1975)
Figure 8: The antimony DoS and temperature effects had to be
included in theimplemented model to obtain agreement with
experimental data (J. Feng et al.,Appl. Phys. Lett., 107,
134101-1/4 2015). Simulations with the higherelectron-electron
scattering rate in Sb are in agreement with both the QY
andintrinsic emittance data.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Surface roughness effects on intrinsic emittance
fromantimony.
−0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00h̄ω − φ
(eV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
emit
tan
ce(µ
m/m
mrm
s)
3-Step, const DoS, T = 0 K
3-Step, const DoS, T = 300 K
3-Step, DoS theory, T = 300 K
at flat emission surface
near domain exit (flat)
at rough emission surface
near domain exit (rough)
experiment, J. Feng (2015)
Figure 9: Intrinsic emittance increases due to emission from the
sides of the ridgesand to presence of transverse electric field
components near the rough emissionsurface.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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3 step model for quantum yieldWe have started to compare
simulation results on QY from Au with the 3step model for metallic
photocathodes (Dowell et al., PRSTAB, 9, 063502,2006; Dowell &
Schmerge, PRSTAB, 12, 073401, 2009):
QY (ω) =
∫∞µ+φ−~ω dEp (E , ω)
∫ 1cos θmax
d (cos θ)Fe−e (E , ω, θ)2∫∞µ−~ω dEp (E , ω)
, (3)
with probability density to excite an electron from E to E +
~ω:
p (E , ω) ∝ g (E + ~ω) (1− f (E + ~ω)) g (E) f (E) ,
cosine of maximum incident angle allowing conservation of
transversemomentum: cos θmax =
√(µ+ φ)/(E + ~ω) and probability that an
excited electron reaches the emission surface without el-el
scattering:
Fe−e (E , ω, θ) =λee (E + ~ω) cos θ
λopt (ω) + λee (E + ~ω) cos θ.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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3 step model for quantum yield: constant DoS, T = 0 K
Analytical formula for the QY can be obtained under the
additionalapproximations that cos θ ≈ 1 when θmax is small and
theelectron-electron mean free path λee (E + ~ω) is slow varying
over therange of excited electron energies considered in some
experiments:
QY0 (ω) =Fee (ω)
2~ω
(1−
√µ+ φ
µ+ ~ω
)2(µ+ ~ω) , (4)
where Fee (ω) = 1/(1 + λopt (ω) /λee (ω)
),
λee (ω) =1
~ω − φ
∫ µ+~ωµ+φ
λee (E) dE ,
and ~ω > φ.Under these approximations, QY0 (ω) ≡ 0 for ~ω ≤
φ.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Quantum yield from Au is strongly affected by its DoS inthe
3-step model.
190 200 210 220 230 240 250 260λ (nm)
10−6
10−5
10−4
10−3
10−2
10−1
QY
(λ)
(%)
simulaitons, DoS theory, T = 300 K
simulations, DoS (m1), T = 300 K
3-step model, const DoS, T = 0 K
3-step model, DoS theory, T = 300 K
3-step model, DoS (m1), T = 300 K
−8 −6 −4 −2 0E − µ (eV)
0
1
2
3
4
5
(Ele
ctro
ns/
atom
)/eV
DoS theory, PRB (1971)
DoS (m1)
Figure 10: Simulations using the Au DoS from relativistic band
calculations leadsto markedly lower QY compared to the 3-step model
with constant DoS andT = 0 K. Including the DoS and temperature
effects in the 3-step model improvesthe agreement. However, a model
using only direct optical transitions for photonabsorption might be
sufficient to explain QY from gold (compare Christensen
&Seraphin, PRB, 4 3321 (1971) to Krolikowski & Spicer, PRB,
1 478 (1970)).
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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The DoS of Au indicates that a significant number ofphotoexcited
electrons will not contribute to emission.
−10 −8 −6 −4 −2 0 2 4 6 8E − µ (eV)
0
1
2
3
4
5
Den
sity
ofst
ates
(Ele
ctro
ns/
atom
/eV
)
µ−~ω
µ+φ−~ω
µ φ µ+~ω
φ = 4.9 (eV)
~ω = 6.2 (eV)
Au
−10 −8 −6 −4 −2 0 2 4 6 8E − µ (eV)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
f(E
)(1−f
(E+~ω
))g(E
)g(E
+~ω
)
µ−~ω
µ+φ−~ω
µ φ µ+~ω
φ = 4.9 (eV)
~ω = 6.2 (eV)
Figure 11: In the 3 step model, only electron energies in the
narrow region nearthe Fermi level contribute to emission. Small
changes in the DoS in this regionwill lead to large changes in
quantum yield.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Physical and chemical surface rougness effects on quantumyield
from Au
200 210 220 230 240 250 260λ (nm)
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
0.0200
0.0225Q
Y(λ
)(%
)
Au simulations: flat vs rough emission surfaces with φ(u, v)
flat, DoS th. (m1)
ridges, ∆φ = 0.00 eV
ridges, ∆φ = 2.30 eV, 95 % cov.
ridges, ∆φ = 0.30 eV, 95 % coverage
ridges, ∆φ = 0.25 eV, 95 % coverage
Figure 12: Surface roughness and variable work function effects
could lead to acrossover in the QY relative to emission from a flat
surface.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Summary
Simulation results on quantum yield and intrinsic emittance are
inagreement with experimental data on emission from Sbphotocathodes
with flat emission surfaces.
Agreement with experimental data was obtained only after
includingthe Sb DoS and temperature effects in the modeling.
Results on QY from gold also show strong dependence on its
DoS.
The relative MTE growth due to controlled surface roughness
islargest near emission threshold and at the emission surface
(around50 % in the Sb simulations).
Simulation results on QY vs wavelength from Sb and Au are
higherfrom the controlled rough surfaces vs flat ones when using
uniformwork functions and light absorption. This is due to
photo-exitedelectrons effectively closer to the rough emission
surface.
Future work will focus on using additional data from band
structurecalculations, modeling of nonuniform light absorption on
roughsurfaces, and electron heating.
D. A. Dimitrov Modeling Electron Emission from Controlled Rough
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Acknowledgements
We would like to acknowledge helpful discussions on the physics
ofphotocathodes with:
Triveni Rao, Erdong Wang, Erik Muller, and Mengjia Gaowei,
BNL.
Kevin Jensen, NRL.
Ivan Bazarov, Cornell University.
David Smithe, John R. Cary, and Sean Zhu, Tech-X Corp..
We are grateful to the DoE office of Basic Energy Sciences for
funding thiswork.
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MotivationModelingSimulationsSummary & future
developments