1. PbTe(111): DFT analysis and experimental results
Photocathode Physics for Photoinjectors (P3) 2016
Jefferson Laboratory, October 17-19, 2016
UIC
PbTe(111): DFT analysis and experimental results
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.
Initial electron beam size, x0, at photocathode is dependent upon;
(i) Laser spot size (e.g., focusing conditions),
(ii) Photocathode optical damage threshold,
(iii) Photoinjector’s operational phase-space (e.g., LCLS),
and (iv) limited by Child’s Law: in short-pulse regime.
Initial RMS transverse momentum, pT0, of emitted electrons is an
intrinsic property of photocathode material:
 Standard expression,
 Must be reduced to improve performance of UED/UEMs, X-FELs, etc.
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: ‘One-step’ Model  EF e- Vacuum Photocathode ħω
− The ‘quantum mechanical’ one-step model
Photoexcitation into a virtual state
(excited copy of filled band)
emitting by coupling to the vacuum states
Quantum efficiency, PE < 10-4 e-/
‘Instantaneous’ emission process
Suitable for UED/UEM,
X-FELs, ICS sources …
Examples: Most metals …
 any material for which no real
state can be excited in the
crystalline emission direction ~
G.D. Mahan, Phys. Rev. B 2, (1970)

4. 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

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
>
Vacuum level  

6. 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
High E electrons at higher pT
More high pT states occupied
as Te increases
High E electrons at lower pT
Less high pT states occupied
as Te increases
Low m* hole-like states preferred

7. 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.

8. 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),Pb  ϕ(111),Te  0.32eV  4.21eV
… Photoemission possible for ħω = 4.75eV
C. J. Fall et al., Journal of Physics: Condensed Matter 11, 2689 (1999)

9. 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)

10. 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 I
J.A. Berger & W.A. Schroeder, J. Appl. Phys. 108 (2010)

11. 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
pT = 0.29(0.02)
(m0.eV)1/2
Normalized emittance
n  0.4 m

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

13. UIC Work Function Variation 1st Fourier component dominates
− pT0 increase due to Ecath perturbation by ϕ + _ ϕ x
PbTe(111) Pb Te
Ecath
Esurface
1st Fourier component dominates
pT0 increase:
… ;
As , effect is significant !
pT()  0.2 (m0.eV)1/2
S. Karkare & I. Bazarov, Phys. Rev.. Appl. 4 (2015)

14. UIC Total Photocathode Emittance
− Quadrature addition of effects
 (0.1)2 + (0.2)2 + … = ( ) m0.eV
 pT,tot.  ( …) (m0.eV)1/2
… c.f. pT,expt. = 0.29(0.02) (m0.eV)1/2
Other effects:
(i) p-PbTe(111) is a semiconductor with ~1m surface depletion region
 Large internal fields due to (x); E//(int.)  1MV/m
 Band structure distortion expected
(ii) PbTe is piezoelectric …
(iii) (21) surface reconstruction on pristine PbTe(111)
(iv) Oxidation: Weak, but may pin EF near VBM at surface

15. 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

16. UIC
Summary
“Theory-driven experimental studies of planar photocathodes”
 Emission from low m* states:  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
 pT,expt. = 0.29(0.02) (m0.eV)1/2 … 2 value predicted by DFT analysis
 MTE increase likely due to dipole
 Perturbation of band structure by Einternal due to dipole ??
Future work
 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 …

17. UIC
Thank You!