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Response time of Alkali Antimonides
John SmedleyBrookhaven National Laboratory
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Overview
• The Three-Step Model and Response Time– Metallic Photocathodes– Semiconductor Photocathodes
• Positive Electron Affinity (Alkali Antimonide)• Negative Electron Affinity (Cs: GaAs)
• Diamond Electron Amplifier
Modern Theory and Applications of PhotocathodesW.E. Spicer & A. Herrera-Gómez
SAC-PUB-6306 (1993)
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ΦEnergy
Medium Vacuum
Φ
Vacuum level
Three Step Model of Photoemission - Metals
Filled S
tatesE
mpty S
tates
h
1) Excitation of e- in metalReflection
Absorption of light Energy distribution of excited e-
2) Transit to the Surface e--e- scattering
mfp ~50 angstroms Direction of travel
3) Escape surface Overcome Workfunction Reduction of due to applied
field (Schottky Effect)
Integrate product of probabilities overall electron energies capable of escape to obtain Quantum Efficiency
Light
Φ’
M. Cardona and L. Ley: Photoemission in Solids 1, (Springer-Verlag, 1978)
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“Prompt”
Metals have very low quantum efficiency, but they are prompt emitters, with fs response times for near-threshold photons:
To escape, an electron must be excited with a momentum vector directed toward the surface, as it must have
The “escape” length verses electron-electron scattering is typically under 10 nm in the near threshold case. Assuming a typical hot electron velocity of 106 m/s, the escape time is 10 fs.
(this is why the LCLS has a Cu photocathode)
W.F. Krolikowski and W.E. Spicer, Phys. Rev. 185, 882 (1969)D. H. Dowell et al., Phys. Rev. ST Accel. Beams 9, 063502 (2006)T. Srinivasan-Rao et al., PAC97, 2790
m
k
2
22
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Energy
Medium Vacuum
Φ
Three Step Model - Semiconductors
Filled S
tatesE
mpty S
tates
h
1) Excitation of e-
Reflection, Transmission, Interference
Energy distribution of excited e-
2) Transit to the Surfacee--phonon scattering
mfp ~100 angstromsmany events possible
e--e- scattering (if hν>2Eg)Spicer’s Magic Window
Random WalkMonte CarloResponse Time (sub-ps)
3) Escape surface Overcome Electron Affinity
Light
No S
tates
Eg
Ea
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A.R.H.F. Ettema and R.A. de Groot, Phys. Rev. B 66, 115102 (2002)
-3 -1 1 3 5 7 9 110.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
K2CsSb DOS
eV
Sta
tes/
eV
Filled States
Empty States
Band Gap PHYSICAL REVIEW B 66, 115102 (2002)
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Unproductive absorption
In “magic window”
Onset of e-escattering
Spectral Response – Bi-alkali
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Cs3Sb (Alkali Antimonides)Work function 2.05 eV, Eg= 1.6 eV
Electron-phonon scattering length ~5 nm
Loss per collision ~0.1 eVPhoton absorption depth
~20-100 nmThus for 1 eV above threshold, total path
length can be ~500 nm (pessimistic, as many electrons will escape before 100 collisions)
This yields a response time of ~0.6 ps
Alkali Antimonide cathodes have been used in RF guns to produce electron bunches of 10’s of ps without difficulty
D. H. Dowell et al., Appl. Phys. Lett., 63, 2035 (1993)W.E. Spicer, Phys. Rev., 112, 114 (1958)
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Diamond Amplifier Concept(first strike solution?)
TransparentConductor
Diamond(NEA)
Photocathode
SecondaryElectrons
Photon
PrimaryElectron
3-10 kV
Thin MetalLayer
(10-30 nm)MCP
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Hydrogenated surface Diamond
0- to 10-keV Electron beam
A
CCD camera
Phosphor Screen Focusing
Channel Pt metal coating
Anode with holes
H.V. pulse generator
Diamond Amplifier Setup
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With focusing
Demonstrated emission and gain of >100 for 7 keV primaries
Would need large area polycrystalline diamonds, probably still too expensive
Maybe NEA GaAs amplifier?
Diamond Amplifier Results
X. Chang et al., Phys. Rev. Lett. 105, 164801 (2010).
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Closing Thoughts
Thanks!
D. Dowell (SLAC/LCLS), Henry & Klaus for the invitation; V. Radeka, I. Ben-Zvi, and my colleagues at BNL
While not strictly “prompt” in the manner of metals, the alkali atimonides have sub-ps response time
Could be improved to some extent (at the cost of QE) by making the cathode very thin
Electron stimulated desorption/Ion back-bombardment?
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Energy
Medium Vacuum
Filled S
tatesE
mpty S
tates
h
1) Excitation of e-
Reflection, Transmission, Interference
2) Transit to the Surfacee--lattice scattering
thermalization to CBMdiffusion length can be 1µmrecombination
Random WalkMonte CarloResponse Time (10-100 ps)
3) Escape surface Laser
No S
tates
Eg
Ea
Three Step Model – NEA Semiconductors
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hE
E
f
f
dEhENEN
hENENhEP
')'()'(
)()(),(
Probability of absorption and electron excitation:
Step 1 – Absorption and Excitation
•Medium thick enough to absorb all transmitted light
•Only energy conservation invoked, conservation of k vector is not an important selection rule
Iab/I = (1-R)
Fraction of light absorbed:
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Step 2 – Probability of reaching the surface w/o e--e- scattering
)()(1
)()(),(
phe
phe
E
EET
•Energy loss dominated by e-e scattering
•Only unscattered electrons can escape
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f
f
Eh
E
dEEDETEPRIY
)(),()())(1)(()(
Yield:
f
f
Eh
E
dEEDETEPRQE
)(),()())(1()(
Quantum efficiency:
EDC and QE
At this point, we have N(E,hn) - the Energy Distribution Curve of the emitted electrons
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Step 3 - Escape Probability
• Criteria for escape:
• Requires electron trajectory to fall within a cone defined by angle:
• Fraction of electrons of energy E falling with the cone is given by:
• For small values of E-ET, this is the dominant factor in determining the emission. For these cases:
• This gives:
fT EEm
k
2
22
21
min )(cosE
E
k
k T
T
T
f
f
Eh
E
Eh
E
dEEDdEEDQE)(
)()()(
2)()( hQE
))(1(2
1)cos1(
2
1''sin
4
1)( 2
1
0
2
0 E
EddED T
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D. H. Dowell et al., Appl. Phys. Lett., 63, 2035 (1993)
Cathode ParametersK2CsSb
5%-12% QE @ 527nmPeak Current 45-132A
Average Current 35 mA(140 mA @ 25% DC)
Lifetime 1-10 hrs
Gun Parameters433 MHz
26 MV/m peak field0.6 MW RF Power
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Laser Propagation and Interference
210-7 410-7 610-7 810-7 110-6
0.2
0.4
0.6
0.8
Vacuum K2CsSb200nm
Copper
543 nm
Laser energy in media
Not exponential decay
Calculate the amplitude of the Poynting vector in each media
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Thickness dependence @ 543 nm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 50 100 150 200 250
Thickness (nm)
Tra
nsm
issi
on
/Ref
lect
ion
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
QE
Ref
trans
Total QE
QE w/o R&T
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2 2.2 2.4 2.6 2.8 3 3.2 3.40
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
QE vs Cathode Thickness
50 nm
200 nm
20 nm
20 nm
10 nm
photon energy [eV]
QE
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Spatial Variation of QE for a Thin K2CsSb Cathode
QE in reflection mode
0
0.2
0.4
0.6
0.8
1
1.2
1.4
465 470 475 480 485 490 495
Position in mm
QE
%
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Ene
rgy
Filled States
Empty States
Primary e- penetrate < 1μm into diamondLose energy via e--e- scatteringExcite e- into conduction band
Some e- and holes will diffuse to metal (probability based on drift velocity)
Secondary e- lose energy via e--e- and e--phonon scatteringEventually, e- reaches the bottom of the conduction band
Holes drift toward metal layer, e- into diamond
Some e- are trappedMost drift to vacuum side (hopefully)Trapped e- modify field in diamond
Bulk Trap
Eg
Ea
Hydrogen termination lowers electron affinity (achieve NEA)Some e- trapped at surface
Most will be emitted (hopefully)
Surface Trap
Electron Transport in Diamond
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• Electrons must escape diamond– Diamond must <30 μm for 700 MHz RF– Negative Electron Affinity (NEA) surface for emission– Field in the diamond is a critical parameter
• Field should be high enough for ve to saturate
• Field should be low enough to minimize e- energy• Modeling suggests 3 MV/m – good for SRF injector
• Diamond must not accumulate charge– Material must have a minimum of bulk/surface traps– Stimulated detrapping– Metal layer required to neutralize holes
• Minimize energy loss in metal (low Z, low ρ)• Practical aspects
– Electron stimulated desorption– Heat load and thermal stresses (1100K to 77K)– Effect of ion/electron back-bombardment on H-terminated surface
ChallengesWatanabe et al, J. of Applied Physics, 95 4866 (2004)
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x-rays/e-
Diamond Measurements in Transmission Mode
Diamond is metallized on both sides
Contact is made by annular pressure
Electrodes are used to bias diamond and measure current
Outer electrodes biased to prevent photoemission
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Gain in Transmission Mode
0 0.5 1 1.5 2 2.50
50
100
150
200
250
300
4keV 330nA 5keV 340nA 6keV 250nA 7keV 270nA 8keV 260nA
Field in diamond [MV/m]
Gai
n
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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.0001
0.001
0.01
0.1
1 keV photon
Field (MV/m)
Res
po
nsi
vity
(A
/W)
Diamond X-ray Response
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0 1000 2000 3000 4000 5000 6000
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
measured
modeled
1/W (13.3 eV)
Photon energy (eV)
Res
po
nsi
vity
(A
/W)
C edge
Ti edge
Pt edge
Diamond X-ray ResponseNSLS U3C/X8A
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Diamond Timing – Hard X-rays
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Diamond Timing – Soft X-rays