1. Metal Photocathodes: Three-Step Model and Beyond W. Wan 1, H. A. Padmore 1, T. Vecchione 1 & T.-C. Chiang 2 1 ALS, Lawrence Berkeley National Laboratory 2 Deptartment of Physics, University of Illinois Photocathode Physics for Photoinjectors (P3) Workshop Cornell University Ithaca, New York October, 2012

2. Motivation  Understand conventional metal cathode in detail Extension of the simplified 3-step model  Find ways to reduce emittance using band structure One-step model to describe emission from surface state Sqrt(QE) vs Photon Energy Questions posted by experimental data Why is the QE curve NOT straight?Why is ε n NOT going to zero? As photon energy approaches work function,

3. Digression: Search for the Culprit Fowler function at 0 and 300 K 1.All conceivable errors from the instrument evaluated 2.All become negligible at V < 3 kV 3.Focused on temperature, found good agreement on QE 4.At 300 K, emittance reaches a non-zero minimum, but at roughly half the value of the experimental data T = 300 K;  E ph : 0-80 meV H. A. Padmore, unpublished technical note

4. Back to the Three-Step Model D. H. Dowell et al. PRST-AB 9, 063502 (2006) Original formulation: Simplified formulation: Transverse emittance: D. H. Dowell and J. F. Schmerge PRST-AB 12, 074201 (2009)

5. Three-Step Model with Finite Temperature Quantum efficiency: Transverse emittance:

6. Replacing the Integral with a Taylor Series Quantum efficiency: Transverse emittance: 1000 times faster! T. Vecchione, unpublished technical note μ = E F

7. QE &Transverse Emittance at 300 K  QE & emittance goes to 0 near threshold at T = 0K QE ~ (E ph -W) 2 and ε n ~ (E ph -W) 0.5  QE extend roughly 0.1 eV below threshold at T = 300 K roughly 4 times kT  Emittance reaches a limit below threshold at T = 300 K N ~ exp[-(E-E F )/kT],  E ~ 4kT

8. Distribution in p x E ph -W = 0.5 eV After integrating out p y, we obtain Sharp cutoff for T = 0 KMore Gaussian-like near threshold E ph -W = 0.5 eV

9. Beyond Normal Metal – Surface State  Distinct dispersion relationship  Strong QE dependence on polarization  Indicating non-isotropic emission  Can theory say anything about these features? Ag(111) surface state (T = 30 K)QE ratio of Ag(111) F. Reinert et al. PRB 63, 115415 (2001)

10. Emittance from the Surface State T = 0 K, P F 2 = 2m*E F, DOS uniform in p x – p y plane T > 0 K:

11. Emittance from the Surface State (cont)  Ag(111), based on data from F. Reinert et al. PRB 63, 115415 (2001)  Plots emittance reduction as Fermi level shifts downward  Assuming no change in the electron mass  At 300 K, reduction in emittance is small  At 75 K, reduction becomes significant  Reducing the electron maybe more promising

12. QE from the Surface State  Non-isotropic emission: one-step model  Modified two-band model: bulk and surface  Main contribution from the surface state  Main goal: explain the QE peak at grazing angle T.-C. Chiang Surf. Sci. Rep. 39, 181 (2000)

13. Wave Function of the Surface State  Surface state lies in the gap, k is complex  Adjust z 0 to set the energy level  1/q is on the order of 1 nm  Confined near the surface, p z is ill-defined  Final state is the upper s-p band, p z not conserved T.-C. Chiang Surf. Sci. Rep. 39, 181 (2000) Transition matrix: Surface state:

14. More on the Transition Matrix Bulk contributionSurface contribution For s-polarized light, A z = 0 For p-polarized light

15. The Light Wave in Metals Decay along z only, the decay length is The real tilt angle in the metal is

16. Plots of Decay Length and Angle  Ag: E ph = 4.66 eV, n = 1.38, k = 1.29  Decay length decreases ~10% from 0 to 90 deg  Decay length ~15 times larger than the width of the surface state  Real angle inside the metal goes up only to 40 deg

17. Plots of Transition Matrix (s & p)  Plot on the right looks very much like the data (insert, Gartlend, et al. PRL 30, 916 (1973))  Endriz (PRB 7, 3464 (1973)) worked along similar line though he didn’t plot explictly A z vs angle  Green plus red on the right can be used to fit data Fresnel equationsContribution of A z

18. Summary  Including temperature in the simplified 3-step model reveals the lower limit of the emittance of normal metals, which is 0.23 μm/mm  Surface state on the (111) plane of noble metals, esp., Ag, offers a way of reducing the emittance pass the limit for the normal metals, which is 0.16 μm/mm at LN2 temperature  One-step model has the potential of quantitatively describing the great enhancement of QE from (111) surface states at grazing angle and predicting the increase of interested metals  Work on this front is on going