modeling quantum yield, emittance, and surface roughness e ... · recent advances in material...

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 Surfaces 1/27

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.


Outline

1 Motivation

2 Modeling

3 Simulations

4 Summary & future developments


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.


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.


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.


We have developed simulations with different types ofsurface roughness.

Figure 1: The surfaces are represented with stair step or cut-cell grid boundaries.


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.


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

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.


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.


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.


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).


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.


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.


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.


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.


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.


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.


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.


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.


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.


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)).


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.


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.


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.


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.


MotivationModelingSimulationsSummary & future developments

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