ULTRA-LOW EMITTANCE III-V SEMICONDUCTOR PHOTOCATHODES Siddharth Karkare Advisor: Ivan Bazarov

Acknowledgements Prof. Ivan Bazarov Dr. Luca Cultrera, Dr. Dimitri Dimitrov, Dr. Bill Schaff and Tobey Moore Prof. Kyle Shen, Prof Tomas Arias, Prof. Richard Hennig, Prof. Jim Sethna Undergrads – Yoon-Woo Hwang, Ashwathi Iyer, Eric Swayer, Teresa Esposito, Nick Erickson, Andrew Kim, Laurent Boulet High brightness electron source group members CHESS and XSEDE for computational facilities NSF and DOE

Outline Overview of Photocathodes, Motivation Photoemission from III-V Semiconductor photocathodes Photocathode diagnostics- Measuring electron energy distributions Overview of Photocathodes, Motivation Photoemission from III-V Semiconductor photocathodes Photocathode diagnostics- Measuring electron energy distributions

Photocathodes and Applications Ez Big linear accelerators electrons LCLS electron beam Photocathode Small MTE has big impact on photocathode applications Cornell ERL Laser 𝐵∝ 𝐸 𝑧 MTE Beam brightness CEBAF 12 GeV Lab scale ultrafast electron diffraction 𝐿∝ 1 MTE Coherence length 𝜖 𝑥 = 𝜎 𝑥 MTE 𝑚 𝑐 2 Emittance

No cathode satisfies all What else do we need? QUANTUM EFFICIENCY ROBUSTNESS LOW MTE RESPONSE TIME Robust to vacuum and ion back-bombardment Ion damage Off center KCsSb film Silicon substrate Semiconductor cathodes (need 10-11 torr vacuum) GaAs (Cs/O) Alkali antimonides Metal cathodes (10-7 torr vacuum) Cu, Pb, Ag Response Time : <ps required Most photocathodes satisfy this. But III-V semiconductors need consideration High Current Applications (>1 mA) >1% QE in visible Semiconductor cathodes GaAs(Cs/O) Alkali antimonides QE : Defines laser requirements Low Current Applications (< mA) >10-3-10-5 QE in UV Metals Cu, Pb, Ag No cathode satisfies all

Best MTEs Today Practically used MTEs Metals 25-40 meV near threshold (1.4 μm/mm) 1 eV Practically used MTEs MTE= 1 2 𝑚 𝑣 ⊥ 2 Add emittance Add specfic materials Metals 25-40 meV near threshold Very low QE<10-7. Alkali-antimonides Low QE <10-4. GaAs/(Cs,O) Very long response time 100 meV (0.44 μm/mm) Why this limit?? 10 meV (0.14 μm/mm) MTE limited by disorder induced heating 1 meV

Why GaAs? Well studied material – best to study VBM CBM Vacuum level GaAs – Vacuum interface Fermi level Band Gap = 1.42 eV 0.5 eV 4-5 eV Best known photocathode Source of spin-polarized electrons VBM CBM Vacuum level GaAs – Vacuum interface Fermi level Band Gap = 1.42 eV 0.5 eV Surface barrier Easy to grow layered structures Well studied material – best to study low energy photoemission Ga As Cs

Outline Overview of Photocathodes, Motivation Photoemission from III-V Semiconductor photocathodes Photocathode diagnostics- Measuring electron energy distributions

3-Step Photoemission Model for GaAs VBM CBM Vacuum level GaAs – Vacuum interface Fermi level Band Gap = 1.42eV Excitation Transport Emission 0.5eV Surface barrier For GaAs 3-step model works!!

Monte Carlo Photoemission Simulation Code >10k lines of vectorized code Few days on a normal PC Few hours on a cluster Lots of bench-marking!!! Mention hours for simulation Matlab based – New Python version in development Karkare et al., J. App. Phys. 113 (10), 104904 (2013)

Photoemission Step 1 - Excitation K-space Real space Surface Heavy hole band Split-off band Light hole band Direct transitions Indirect transitions -15 -10 -5 x(μm) Direct transitions – two body process Indirect transitions – three body process (ignored) All transitions are direct and hence all electrons are excited into gamma valley Exponentially decaying distribution within surface

Photoemission Step 2 - Transport Scattering processes Charged Impurity Scattering Phonon Scattering Acoustic Optical intervalley scattering Polar Optical Piezoelectric Carrier Scattering Electron-Plasmon Electron-Hole Vacuum Level CBM VBM Calculate k-vectors Calculate velocity vectors Calculate positions Scatter (change k and v vectors) 𝑬 is derivative of the Conduction band profile

Photoemission Step 3- Emission Simulation V 𝐸 𝑣 𝐸 𝐸= ℏ 2 𝑘 𝑧 2 + 𝑘 𝑡 2 2 𝑚 Γ 𝐸 𝑣 = ℏ 2 𝑘 𝑣𝑧 2 + 𝑘 𝑣𝑡 2 2 𝑚 𝑒 𝑬 𝒗 =𝑬−𝑽 Conservation of energy CULPRIT Conservation of transverse momentum 𝐸 𝑡𝑣 𝐸 𝑡 = 𝑚 Γ 𝑚 𝑒 =0.067 𝒌 𝒕 = 𝒌 𝒗𝒕

Engineering Photocathodes Light Easy to grow using MBE e- Can we tune structure to improve photoemission? Surface Layers have different doping and different material (GaAs/AlGaAs…) Change in material causes change in band-gap Band profiles can be calculated using a Schrodinger-Poisson solver We can tune – light absorption X-valley min electric fields Γ-valley min scattering valley heights Valance Band Max Change in doping causes bands to bend

Low Emittance Layered Cathodes QE p-GaAs p-GaAs Simulation Experiment Layered structure MTE MTE is Layered structure p-GaAs Layered structure Simulation Experiment Karkare et al, PRL 112 (9), 097601 (2014)

What Can Cause Surface Scattering? Transverse Asymmetry – Work function variation and sub-nm scale roughness Scattering with phonons, plasmons at the surface KE=0−0.2 eV 𝜆=4−20 nm

What Does GaAs/Cs Surface Look Like 𝟏𝟕𝒏𝒎×𝟑𝟕𝒏𝒎 ~1 nm Surface Roughness GaAs(100) ~𝟏𝟐𝟎 𝒎𝒆𝑽 Random Cs adsorption Raised Ga Dimer Reconstruction ~𝟏𝟎𝟎 𝒎𝒆𝑽 ~𝟏𝟓𝟎 𝒎𝒆𝑽 ~𝟐𝟓𝟎 𝒎𝒆𝑽 ~100 meV Work-function Variation Ga 𝟏𝟓𝟎𝒏𝒎×𝟏𝟓𝟎𝒏𝒎 Top Views As Cs Amorphous Cs adsorption J. Kim, M.C. Gallagher and R.F. Willis, Appl. Surf. Sci., 67, 286 (1993) Karkare et al. PRB, 91, 035408 (2015)

Effects of Work Function Variations Electric field 𝐸 0 = ∅0 𝐿 0 𝑧= 𝐿 0 , ∅=∅0 ∅=𝑓 𝑥,𝑦 ≪∅0 x,y z anode 𝑓 𝑥,𝑦 =𝒉 𝑠𝑖𝑛 2𝜋 𝑎 𝑥 sin 2𝜋 𝑎 𝑦 ℎ~100 mV is potential variation 𝑎~100 nm is periodicity 𝛾=2𝜋 2 𝑎 2 cathode ∅ 𝑥,𝑦,𝑧 = ∅ 0 1− 𝑧 𝐿 0 + ℎ 1− 𝑒 −2 𝐿 0 𝛾 𝑒 −𝑧𝛾 − 𝑒 (𝑧−2 𝐿 0 )𝛾 sin 2𝜋 𝑎 𝑥 sin 2𝜋 𝑎 𝑦 Calculate fields – Poisson equation Track electron trajectories – numerical integration Calculate final MTE – Assume initial MTE is zero

Effects of Work Function Variations Variation with electric fields Variation with initial kinetic energy MTE reduces with initial KE…contrary to observations Should be measurable in RF guns

Effects of Sub-nm Scale Roughness Simplified surface – no Cs barrier, no work function variation 𝑉 ℎ 𝑥,𝑦 =𝑉𝑓(𝑥,𝑦) 𝑧 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 =𝑓 𝑥,𝑦 𝜓 2 𝑓 𝑥,𝑦 ≪𝜆 𝜓 1 𝑉 𝑉 zmin zmax GaAs Interface Vacuum 𝑚= 𝑚 𝑒 GaAs Vacuum 𝑧=0 H=− ℏ 2 2 𝛻 1 𝑚 𝛻 +𝑉∗𝑆 𝑧 + 𝑉 ℎ 𝑥,𝑦 𝛿(𝑧) S(z) is the heavy-side function

Effects of Sub-nm Scale Roughness Scattered electrons 1 nm e- MTE increasing with Kinetic energy of electrons Can explain experimental results Karkare et al. Phys. Rev Applied, submitted (2015)

Photoemission from III-V Semiconductor Photocathodes Monte Carlo simulations explain observed photoemission properties Engineering of layered structures Effects of surface non-uniformities Similar arguments hold for all cathodes Light

Outline Overview of Photocathodes, Motivation Photoemission from III-V Semiconductor photocathodes Photocathode diagnostics- Measuring electron energy distributions

Story of Narrow Cone Emission in GaAs Starts in 1974 when… However in 2005: Zhi Liu et.al, J. Vac. Sci. Technol. B 23(6) (2005) Pollard first observed ±15o deg electron emission from GaAs(Cs/O) Equivalent to <5 meV MTE Measurement error or special cathode surface? J.H. Pollard, Proceedings of the second European Electro-Optics Markets and Technology Conference (1974) Terekhov et.al, Appl. Phys. Lett. 71 (20),(1997) Bazarov et.al, J. Appl. Phys. 103, 054901 (2008) Needs a border 1974 onwards: Almost no MTE measurement of <25 meV D C Rodway Phys. D: Appl. Phys. 19, 1353 (1986)  Bradley, J. Phys. D: Appl. Phys., Vol. 10, 1977

Hemispherical Analyzer Ag Obtain energy and angular distributions Not good for low kinetic energy (< 1 eV) electrons Sensitive to stray E/B fields Accessible…don’t use feasible. Used for Angle Resolved Photoemission Spectroscopy (ARPES)

Solenoid Scan Technique Photocathode Anode Corrector coils Scintillator screen e beam MTE 37 meV Solenoid HV Electron gun in Wilson In photocathode research lab (Newman)

2-D Energy Analyzer 3x Resolution 50x Signal to noise ratio MARK1 MARK2 B field CATHODE 2-D distribution from K2CsSb 3x Resolution 50x Signal to noise ratio Compact size First Marking Electrode Varying Magnetic Field Second Marking Electrode Beam Current Detector Karkare et al. Rev. Sci. Instr. 86, 033301 (2015)

Achieving Low Energy Resolution 1 mm 2 mm Design by Hoppe* et al. 𝜎~15 mV Hoppe et al, 𝜎=16.3 mV Original design 𝜎=110 mV Our original design 𝜎 𝑑 <0.1 mV New design 𝜎=5.7 mV 𝜎<0.1 mV 3 mm 9 mm 1 mm 5 mm New design *Differential energy analysis of electron beams: A study of photoemission from NEA GaAs: Hoppe, Ph.D thesis, University of Heidelberg (2001)

Photocathode Growth and Diagnostics at Cornell dedicated MBE system over in Wilson Lab actual injector Phillips Newman Wilson over in Newman Lab Photocathode growth & analysis chamber over in Phillips Hall Cornell University campus Vacuum Suitcase

The Active Photocathode Group  L. Cultrera, S. Karkare, H. Lee, X. Liu, B. Dunham, I. Bazarov, Phys. Rev. Lett., (2015), submitted. S. Karkare, I. Bazarov, Phys. Rev. Applied, (2015), submitted. S. Karkare, Y. Hwang, R. Merluzzi, L. Cultrera, I. Bazarov, Rev. Sci. Instrum., 86, 033301 (2015) S. Karkare, L. Boulet, R. Hennig, A. Singh, I. Bazarov, Phys. Rev. B., 91, 035408 (2015) S. Karkare, L. Boulet, L. Cultrera, B. Dunham, X. Liu, W. Schaff and I. Bazarov, Phys. Rev. Lett., 112, 097601 (2014) L. Cultrera, M. Brown, S. Karkare, W. Schaff, I. Bazarov and B., J. Vac. Sci. Technol., B, 32, 031211 (2014) S. Karkare, D. Dimitrov, W. Schaff, L. Cultrera, A. Bartnik, X. Liu, E. Sawyer, T. Esposito and I. Bazarov, J. Appl. Phys., 113, 104904 (2013) L. Cultrera, S. Karkare, B. Lillard, A. Bartnik, I. Bazarov, B. Dunham, W. Schaff and K. Smolenski, Appl. Phys. Lett.,103, 103504 (2013) . Gulliford, A. Bartnik, I. Bazarov, L. Cultrera, J. Dobbins, B. Dunham, F. Gonzalez, S. Karkare, H. Lee, H. Li, et al., Phys. Rev. ST Accel. Beams, 16, 073401 (2013) B. Dunham, J. Barley, A. Bartnik, I. Bazarov, L. Cultrera, J. Dobbins, G. Hoffstaetter, B. Johnson, R. Kaplan, S. Karkare et al., Appl. Phys. Lett, 102, 034105 (2013) L. Cultrera, J. Maxson, I. Bazarov, S. Belomestnykh, J. Dobbins, B. Dunham, S. Karkare, R. Kaplan, V. Kostroun, Y. Li et al., Phys. Rev. ST Accel. Beams, 14, 120101 (2011) L. Cultrera, I. Bazarov, A. Bartnik, B. Dunham, S. Karkare, R. Merluzzi and M. Nichols, Appl. Phys. Lett., 99, 152110 (2011). I. Bazarov, L. Cultrera, A. Bartnik, B. Dunham, S. Karkare, Y. Li, X. Liu, J. Maxson and W. Roussel, Appl. Phys. Lett., 98, 224101 (2011) S Karkare and I Bazarov, Appl. Phys. Lett., 98, 094104 (2011) …

Conclusions Monte Carlo simulations explain observed photoemission properties Engineered better photocathodes: layered structures Highlighted effects of surface non-uniformities on photoemission Built an instrument to measure low energy electron distributions Photocathode facilities at Cornell

Delta function approach Fourier basis -> 𝑉 ℎ 𝑥,𝑦 = 𝐤 𝐫 𝑉 𝐤 𝐫 𝑒 𝑖 𝐤 𝐫 ⋅𝐫 𝑚= 𝑚 𝑒 𝑚=0.067 𝑚 𝑒 𝑧=0 𝜓 1 = 𝑒 𝑖 𝐤 𝐢𝐧𝐫 ⋅𝐫+ 𝑘 𝑖𝑛𝑧 𝑧 + 𝐤 𝐫 𝛽 𝐤 𝐫 𝑒 𝑖 𝐤 𝐫 ⋅𝐫− 𝑘 𝑖𝑛𝑧 𝑧 𝜓 2 𝜓 1 𝜓 2 = 𝐤 𝐫 𝛼 𝐤 𝐫 𝑒 𝑖 𝐤 𝐫 ⋅𝐫+ 𝑘 2𝑖𝑛𝑧 𝑧 Match wave function at boundary Match derivative at boundary Compare coefficients with same exponential

Delta function approach 𝐷 𝑘 𝑟0 − 𝑉 0 − 𝑉 𝑘 𝑟0 − 𝑘 𝑟1 − 𝑉 𝑘 𝑟1 − 𝑘 𝑟0 𝐷 𝑘 𝑟1 − 𝑉 0 −𝑉 𝑘 𝑟0 − 𝑘 𝑟2 … − 𝑉 𝑘 𝑟1 − 𝑘 𝑟2 … − 𝑉 𝑘 𝑟2 − 𝑘 𝑟0 −𝑉 𝑘 𝑟2 − 𝑘 𝑟1 ⋮ ⋮ 𝐷 𝑘 𝑟2 − 𝑉 0 … ⋮ ⋱ 𝛼 𝑘 𝑟0 𝛼 𝑘 𝑟1 ⋮ 𝛼 𝑘 𝑖𝑛𝑟 ⋮ ⋮ = 𝑉 𝑘 𝑟0 − 𝑘 𝑖𝑛𝑟 𝑉 𝑘 𝑟1 − 𝑘 𝑖𝑛𝑟 ⋮ 𝑉 0 +𝑅 𝑘 𝑖𝑛𝑟 ⋮ ⋮ For a sinusoidal 1D surface roughness 𝑉 ℎ =2 𝑉 1 𝑐𝑜𝑠 𝑘 𝑠 𝑥 it reduces to trigonal system 𝐷 𝑘 𝑖𝑛𝑟 −𝑚 𝑘 𝑠 − 𝑉 1 − 𝑉 1 𝐷 𝑘 𝑖𝑛𝑟 − 𝑚−1 𝑘 𝑠 0 … − 𝑉 1 … 0 −𝑉 1 ⋮ ⋮ ⋱ … ⋮ ⋱ 𝛼 𝑘 𝑖𝑛𝑟 − 𝑚𝑘 𝑠 𝛼 𝑘 𝑖𝑛𝑟 − (𝑚−1)𝑘 𝑠 ⋮ 𝛼 𝑘 𝑖𝑛𝑟 ⋮ ⋮ = ⋮ 0 𝑉 1 𝑅 𝑘 𝑖𝑛𝑟 𝑉 1 0 ⋮

2D Energy Analyzer Demonstrated resolution up to 5 meV CATHODE B field MARK1 MARK2 B field CATHODE MARK1 MARK2 2-D distribution from KCsSb Demonstrated resolution up to 5 meV

Measuring Resolution Set Bi = Bf Then (2) = (3) Mark with Gun, measure with RFA Voltage in RFA Signal Ideal Practical 𝜎=5.7 mV MARK1 MARK2 𝜎 2 = (3.5 mV)2 + (2 mV)2 + (~4 mV)2 Amplitude of am Noise in voltage Design of electrodes (𝜎d)