1. University of Illinois at Chicago
European Workshop on Photocathodes for Particle Accelerator Applications
June 6-8, 2016
UIC
Characterization of a
PbTe(111) photocathode
W. Andreas Schroeder
Physics Department
University of Illinois at Chicago
Tuo Li
Benjamin Rickman
National Science Foundation
PHYS

2. UIC Electron beam (pulse) quality
RMS transverse emittance:
… a conserved quantity in a ‘perfect’ system.
ESC
Ecath
Photocathode
Image charge
Laser pulse
Electron pulse
Surface charge density
x0 determined by laser spot size
and limited by Child’s Law:
pT0 is an intrinsic property of the
photocathode material:
… the standard expression.
D.H. Dowell & J.F. Schmerge, Phys. Rev. ST – Acc. & Beams 12 (2009)
K.L. Jensen et al., J. Appl. Phys. 107 (2010)

3. UIC Photoemission Theory I
− The semi-classical three-step ‘Spicer’ model  ħω EF 1 2 3 e-
Vacuum
Photocathode
1. Photoexcitation
2. Transport to surface
3. Emission from surface
Transport  Real electronic band
 Photoexcitation into upper state
near vacuum level
Emission from upper excited state
 High quantum efficiency (PE)
AND
Response time  Lifetime (ps-ns)
 NOT suitable for UED
Examples: NEA GaAs, KCsSb, GaSb,
diamond, Cu(111)?
C.N. Berglund & W.E. Spicer, Phys. Rev. 136, A1030-A1044 (1964)
P.J. Feibelman & D.E. Eastman, Phys. Rev. B 10, (1974)

4. UIC Photoemission Theory II  EF e- Vacuum Photocathode ħω
− The ‘quantum mechanical’ one-step model
Photoexcitation into a virtual state (excited copy of filled band)
emitting into the vacuum in one step
Low PE ~ 10-5 to 10-7
‘Instantaneous’ emission process
Suitable for UED
Examples: Most metals
G.D. Mahan, Phys. Rev. B 2, (1970)

5. UIC Band Structure Effects pT pF pT,max. E ħω EF E pT pF pT,max. E ħω
− Transverse momentum pT conserved in photoemission
‘Classical’ metal (m* = m0)
Metal with m* < m0
>
Photoemitting states in red:
E and pT conserved
Vacuum level
Virtual excited states in ‘one-step’ photoemission  
Band states for which E  0

6. UIC Band Structure Effects pT pF pT,max. E ħω EF E pT pF pT,max. E ħω
− Transverse momentum pT conserved in photoemission
‘Classical’ metal (m* = m0)
Metal with m* < m0
>
Vacuum level  

7. Low m* hole-like states preferred
Vacuum level pT E E ħω
EF+ħω
Electron-like (m* < m0)
Hole-like (m* < m0)
Electron-like vs. Hole-like States
UIC
− pT0 and its sensitivity to Te
Higher pT electrons at high E
More high pT states occupied
as Te increases
Lower pT electrons at high E
Less high pT states occupied
as Te increases
Low m* hole-like states preferred

8. UIC PbTe Band Structure Lightly p-type PbTe crystal
− Evaluation using QUANTUM ESPRESSO
Lightly p-type PbTe crystal
 EF at top of VBM at
L point of Brillouin zone
Very low hole mass
(m* = 0.022m0) transverse to
-L direction
 (111)-face emission
(111)
NOTE:
For emission from (111) face,
no CBM exist above 2eV at L point.

9. DFT-based thin-slab prediction:
UIC
pPbTe(111): ϕ(111)
− Evaluation using thin slab technique
(111)
Rock salt (simple cubic) crystal structure of PbTe
 Pb or Te terminated regions on (111) surface
 Different  due to surface dipole orientations Pb + _ Te
PbTe
-V
+V
DFT-based thin-slab prediction:
ϕ(111),Te  ϕ(111),Pb eV  4.53eV
… Photoemission possible for ħω = 4.75eV
C. J. Fall et al., Journal of Physics: Condensed Matter 11, 2689 (1999)

10. DFT-based photoemission prediction:
UIC
pPbTe(111): pT0
− ‘One-step’ photoemission from L-point VBM with m* = 0.022m0
Emitting states for E = 0.3eV
E, pT conservation
PLUS
Barrier transmission, T(pz,pz0)
DFT-based photoemission prediction:
pT0  0.1 (m0.eV)1/2 for ħω = 4.75eV
T. Li et al., J. Appl. Phys. 117, (2015)

11. UIC pT0 Measurement: Solenoid Scan 2W, 250fs, 63MHz , diode-
pumped Yb:KGW laser
 ~4ps at 261nm (ħω = 4.75eV)
YAG scintillator optically
coupled to CCD camera
 Beam size vs. magnetic coil
(lens) current measured
 Analytical Gaussian (AG) pulse
propagation model to extract ΔpT0
J.A. Berger & W.A. Schroeder, J. Appl. Phys. 108 (2010)

12. UIC PbTe(111): Solenoid Scan Results PbTe(111) ħω = 4.75eV
− Comparison with AG pulse propagation model
Current2 (A2)
HW1/eM Spot Size (mm)
PbTe(111)
ħω = 4.75eV 
pT0(AG model)
[(m0.eV)1/2]
0.1
0.2
0.3
0.4
0.5
pT0 = 0.29(0.02)
(m0.eV)1/2
n/Δx 
0.4 mm.mrad/mm

13. UIC PbTe(111): Experiment vs. Theory PbTe(111): DFT analysis Dowell
Padmore
Dowell
ħω < ϕ
Expt. result:
pT0 = 0.29 (m0.eV)1/2
Proc. FEL 2013, TUPSO83, pp
Expected range of pT0 from DFT

14. UIC Work Function Variation 1st Fourier component (h = 2ϕ/)
− pT0 increase due to Ecath perturbation by ϕ + _ ϕ x
PbTe(111) Pb Te
Ecath
Esurface
1st Fourier component (h = 2ϕ/)
dominates pT0 increase:
… ;
 pT0(ϕ)  0 as
 Effect insignificant
S. Karkare & I. Bazarov, Phys. Rev.. Appl. 4 (2015)

15. UIC Semiconductor Physics For lead chalcogenides,
− Depletion region of p-type PbTe (NA  1016cm-3)
Energy z VB CB Eg
PbTe Vacuum
-zd EF
For lead chalcogenides,
EF ‘pinned’ at mid-gap at surface
Length of depletion region
 1m
… Eg = 0.34eV; r  400
NOTE: -1  23nm at 261nm Ed
Depletion region; No free charges
Pure dielectric/vacuum interface

16. LARGE internal E// at dipole direction changes
UIC
Internal Fields: ϕ(x)
− 1-D extension of Phys. Rev.. Appl. 4 (2015) into depletion region L ϕ z x
Vacuum
PbTe
-zd
Ecath
Ed & Ecath
Esurface (internal)
Esurface
Analysis using
(i)
(ii) E// conserved
(iii) D conserved
Total internal field:
LARGE internal E// at dipole direction changes

17. UIC E//(internal) Estimate Near atomic-scale ‘flip’ of
− Realistic ϕ(x)
Near atomic-scale ‘flip’ of
PbTe dipoles; so expect
… for L/2 < x < L/2
and where lattice
constant a = 6.46Å
 Fourier series for ϕ(x)
terminates at n  L/a
Wafer polish  L  0.1  1m L ϕ z x
Vacuum
PbTe
-zd
Esurface (internal)
Esurface a
 ~ 1MV/m expected

18. UIC Lattice Distortion Zero-field DFT not valid PbTe properties:
− Due to E//(int)
PbTe properties:
- Relative permittivity, r  400
- Lattice constant, a = 6.46Å  Number density of bulk Pb-Te dipoles,
- Ionic charge, q  0.2e
Linear dielectric response:
… as r large
  0.1
… for E = 1MV/m
Zero-field DFT not valid
Significant band structure distortion expected

19. UIC PbTe(111): Photoemission Efficiency At 261nm: n = 0.76 +1.80i
− Faraday cup measurement
106 Photons/Pulse
Electrons/pulse
PE  5.110-6 e-/
PbTe(111)
ħω = 4.75eV
i  60
p-polarization
At 261nm: n = i
 TIR at i  60
BUT Rp = 0.12
 Photoemission from
absorbed evanescent wave
NOTE: At i  0, R  0.52
 PE(0)  0.55PE(60)
= 2.810-6 e-/ 
N. Suzuki & S. Adachi, Jpn. J. Appl. Phys. 33 (1994) 193

20. UIC
Summary
“Theory-driven experimental studies of planar photocathodes”
 Emission from low m* states: pF > pT,max  Lower pT0
 Oriented single crystal photocathodes (ħω > (ijk))
 ‘Hole-like’ emission states are preferred:
Even lower pT0 and less sensitive to Te (e.g., laser heating)
PbTe(111): Emission from VBM with m* = 0.022m0
 pT0 = 0.29(0.02) (m0.eV)1/2 … 2 value predicted by DFT analysis
 Perturbation of band structure by Einternal due to dipole ??
Future work
 GaSb(001) Bi(111) Mo(001) Nb(001) …
 Tunable UV laser source: Measurement of ϕ (in situ) and pT0(ħω)
 Search for ultra-low pT0 solid-state photocathodes:
pT0 approaching cold atom electron sources  TID issues? X

21. UIC
Thank You!