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ARGONNE NATIONAL LABORATORY DECEMBER 6, 2005 Argonne, IL

ARGONNE NATIONAL LABORATORY DECEMBER 6, 2005 Argonne, IL. Numerical Modeling of Field-Enhanced Photoemission from Metals and Coated Materials. NRL: K. L. Jensen J. L. Shaw J. E. Yater. UMD: D. W. Feldman N. A. Moody P. G. O’Shea. We gratefully acknowledge:

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ARGONNE NATIONAL LABORATORY DECEMBER 6, 2005 Argonne, IL

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  1. ARGONNE NATIONAL LABORATORYDECEMBER 6, 2005 Argonne, IL Numerical Modeling of Field-Enhanced Photoemission from Metals and Coated Materials NRL: K. L. Jensen J. L. Shaw J. E. Yater UMD: D. W. Feldman N. A. Moody P. G. O’Shea We gratefully acknowledge: FUNDING by Joint Technology Office & Office of Naval Research INTERACTIONS with (alph). S. Biedron , C. Bohn, C. Cahay, D. Dimitrov, D. Dowell, J. Lewellen, J. Petillo, J. Smedley • ANL Beams and Applications SeminarHost: John Lewellen ASD • Bldg. 401, Room A1100 Tuesday, 1:30 pm

  2. OUTLINE • Electron Sources • Photocathodes and Photocathode Issues • The Dispenser Photocathode Concept • Electron Emission Fundamentals • 1st Generation Emission Model & Usage • Next Generation Components & Application • Bare Metals • Cesiated Surfaces & Gyftopoulos-Levine Model • Quantum Distribution Function • Quantum Effects on Barrier & Scattering • Conclusion

  3. ELECTRON EMISSION Metal Field Thermionic Courtesy of C. A. Spindt www.sri.com/psd/microsys/vacuum/ • The Manner in Which Electrons Are Extracted Dictates the Technological Gambits Invoked HeatWave Labs http://www.cathode.com/c_cathode.htm Photo ANL-BNL-JLAB Gun: Ilan Ben-Zvi www.agsrhichome.bnl.gov/eCool/MAC_Ilan.pdf

  4. PHOTOINJECTORS & PHOTOCATHODES rf Klystron Master Oscillator Drive laser Photo- cathode Linac High Power FEL Demands on Photocathode: CHARGE PER BUNCH: 0.1 - 1 nC in 10-50 ps pulse FIELD: 10 - 100 MV/m in pressure of 10-8 Torr (approx) OPERATION: Robust, Prompt, Operate At Longest l LIFETIME: Longevity & Reliability Paramount • Critical Components of Free Electron Lasers, Synchrotron Light & X-ray Sources

  5. PHOTOCATHODE RESPONSE TIME • Pulse Shaping • Optimal Shape for emittance: beer-can (disk-like) profile • Laser Fluctuations occur (esp. for higher harmonics of drive laser) • Fast response: laser hash reproduced • Slow response: beer-can profile degraded • Optimal: 1 ps response time • Mathematical Model (wn = 2pn/T) Formulation based on model of J. Lewellen

  6. CATHODE + LASER NONUNIFORMITY Laser Non-uniformity + work function non-uniformity(sim) Combined Nonuniformity • Cathode Emittance Is Important (esp. in Gun) • Pulse Shape Can Result in Reduction of Emittance • Prediction of Photocathode / Drive Laser Combos & Beam Crucial to Design of Larger Systems • Realistic Initial Distributions Needed: Advanced Codes (Michelle, Argus, Magic, Mafia, Vorpal, Etc.) Need Adequate Emission Models, Photoemission Studies Sparse, Emission Distributions Are Unknown Laser Laser Nonuniformity Work Function Nonuniformity

  7. PROGRAM OBJECTIVE Interpore ≈ 6 µm; Grain Size≈ 4.5 µm; Pore Diam. ≈ 3 µm Metal Conventional Dispenser Top View monolayer Side View W plug w/ Cs Cs O Al2O3 Potting Controlled Porosity Heater Maryland Dispenser Cathode A Cs-dispenser Photocathode Concept IDENTIFY factors that affect QE (e.g., laser, environment, photocathode material) DEVELOP a custom-engineered controlled porosity photo-dispenser cathode • Generic Parameter Range • Assumptions: • Charge = 1 nC • Wavelength = 266 nm • Pulse FWHM = 10 ps • Example Cases of Io(QE) • For Radius of 0.3 cm • Io(1%) = 0.165 MW/cm2 • Io(0.01%) = 16.5 MW/cm2 • For Radius of 0.1 cm • Io(1%) = 1.48 MW/cm2 • Io(0.01%) = 148 MW/cm2

  8. DISPENSER CATHODE POROSITY ANALYSIS Pore to Pore: Log-Normal Distribution • Central Questions: • Pore-to-Pore separation &Grain Size • Desorption & migration rates of low work function coating over surface Grain Size: Effective Diameter SEMS: Nathan Moody, UMD

  9. STATISTICAL MECHANICS OF ELECTRON GAS Semiconductor Metal Ec   o  Fvac Fvac o Ev Ec Electrons Incident On Barrier Are Distributed In Energy According To A 1-D “Thermalized” Fermi Dirac Distribution Characterized By The Chemical Potential and Called The “Supply Function” f(k) obtained by integrating over the transverse momentum components • Electron Number Density r • Zero Temperature (m(0 ˚K) = mo = EF) • N does not change with T so m must: BAND BENDING Metal vs. Semiconductor

  10. CURRENT - A CLASSICAL APPROACH dx’ dn’ dk’ dk dn dx • f(x,k,t) is the probability a particle is at position x with momentum hk at time t • Conservation of particle number: to order O(dt) Boltzmann Transport Equation velocity & acceleration “Moments” give number density r and current density J: Continuity Equation

  11. CURRENT IN SCHRöDINGER REPRESENTATION Simple Case: Gaussian Schrödinger’s Equation • Consider a pure state Time-dependence of Operators governed by commutators with Hamiltonian The form most often used in emission theory Basis for FN & RLD Equations

  12. THERMIONIC VS FIELD EMISSION Richardson Fowler Nordheim • The most widely used forms of: • Field Emission: Fowler Nordheim (FN) • Thermal Emission: Richardson-Laue-Dushman (RLD) High Temperature Low Field Low Temperature High Field Transmission Probability Electron Supply Emission Equation Constants for Work Function in eV, T in Kelvin, F in eV/nm

  13. A GENERAL THERMAL-FIELD EQUATION Field Thermal X(F[GV/m],T[K]) • Supply Function • General Transmission Coefficient • Define Slope Ratio: • n « 1: Richardson-Laue-Dushman Eqn » 1: Fowler Nordheim Equation Maxwell Boltzmann Regime T(7,300) T(0.01,2000) Fermi f(0.01,2000) 0 K-like Regime f(7,300)

  14. INTEGRATED SCATTERING & EMISSION MODEL ENERGY Clean W(001) Potential z(q) k  &  f& U(x) q Ba/O/W(001) W cores W cores Scattering & Electron Transport & Emission Relaxation Time & Thermal Model POSITION (x/ao) QDF  W Ba O Coverage-Dependent Work Function Hemstreet, et al. PRB40, 3592 (1989) • Quantum Distribution Function (QDF) Simulation Simultaneously Relates Scattering (), Barrier Emission (), Thermal () and Density Effects

  15. EXP. VALIDATED PHOTOEMISSION MODEL • COMPONENTS: • Work function variation with coating ) • Gyftopolous-Levine theory • Thermal & Material; laser , R(), f • Transient heating & heat diffusion • Simple Photoemission Model U-function • Revised Fowler-Dubridge Model • Quantum effects @ hi F & T U, f • barrier due to e- density; scattering • Transmission through barriers U • Relate barrier to emission probability • GOAL • Predict Quantum Efficiency From Laser & Material Parameters • Analyze Experimental Results from UMD, NRL, Colleagues in FEL Program • Emission Model For Beam Code for NRL, SAIC, Tech-X, NIU, Colleagues First Generation Beam Code Model • Photocurrent depends on • Scattering Factor: f • Absorbed laser power: (1-R) I • Escape Probability: U-terms Next Generation Beam Code Model

  16. DETERMINATION OF R[%] & d Consider W, Cu, Au… …other metals in database • Algorithm: • Spline-fit experimental optical data (e.g., CRC, AIP Handbook) for index of refraction (n), damping constant (k) • Designate incident angle = q • Use Equations to determine Reflectance R[%] and penetration depth of laser for given wavelength

  17. POST-ABSORPTION SCATTERING FACTOR k z(q) q Average probability of escape argument < 1 argument > 1 • Factor (fl) governing proportion of electrons emitted after absorbing a photon: • Photon absorbed by an electron at depth x • Electron Energy augmented by photon, but direction of propagation distributed over sphere • Probability of escape depends upon electron path length to surface and probability of collision (assume any collision prevents escape) • path to surface &scattering length • To leading order, k integral can be ignored • Ex: Copper: •  = 266 nm •  = 12.9 nm •  = 0.85 fs •  = 7.0 eV • F = 4.3 eV sec(y) = 7.7 fl = 0.038 ko: minimum k of e- that can escape after photo-absorption d: penetration of laser (wavelength dependent); t: relaxation time

  18. QM-EXTENSION OF FOWLER-DUBRIDGE EQ. “Fowler factor” • RLD-based Fowler Dubridge Model • U(x): depends on thermal distribution and barrier for emission probability • Reflectivity R and Scattering Factor fldepends on material & relaxation time coating = 2.0 eV • Copper * •  = 266 nm; F = 5 MV/m;  = 3 • R = 33.6%,  = 4.3 eV, EF = 7.0 eV • QE [%] (analytic) 1.31E-2 • QE [%] (time-sim) 1.36E-2 • QE [%] (exp) 1.40E-2 QM contributes for photon E near barrier height, large fields,and cold temperatures Exp data: T. Srinivasan-Rao, et al., JAP69, 3291 (1991).

  19. SCATTERING & Electrical / Thermal Conductivity Field Temp Electrical Conductivity Specific Heat Thermal Conductivity WIEDEMANN-FRANZ LAW • If an electric field F (or temperature gradient T) is removed, then distribution “relaxes” back to equilibrium after a “relaxation time”  Electric Field Temperature Distribution for Fermi-Dirac is approximately constant except near Fermi Energy 

  20. LASER HEATING OF ELECTRON GAS Electron & Lattice Specific Heat Laser Energy Absorbed Power transfer by electrons to lattice 285.1 GW / K cm3 (W @ RT) • Differential Eqs. Relating Electron to Lattice Temp Diffusion mimics the temporal spread of Dirac-Delta-like pulses with Do Do acts as Length2 / time Length ≈ O(laser penetration depth) Model captures physics… as long as there is an estimate for to

  21. PHOTOEMISSION MODULES IN BEAM CODE VORPAL Cu Photocathode Beam Emission and Evolution • Goal: modules for 3D RF gun / beam codes for the analysis of beam generation and transport. • Present model: high-T scattering operator with T evaluated using Delta-diffusion model as function of laser intensity for copper; probability of emission factor based on Fowler Dubridge but without QM • Next generation to include all-temperature scattering, QM, metal & coating library Hemisphere unit cell model • SIMULATION CODE: VORPAL (TECH-X) • 3D visualization of photo emitted electron particles (white dots) following the beam emission and its evolution at different times from simulations with steady-state photocathode model. • Cu photocathode at left boundary. Front of laser pulse has reached the photocathode and emission of the electron beam has started. • D. Dimitrov, et al., 8th DEPS, Lihue, HI (2005) • SIMULATION CODE: MICHELLE (SAIC) • Photoemission from laser-illuminated Cu hemisphere Using 1st generation photoemission model • J. Petillo, et al., 8th DEPS, Lihue, HI (2005)

  22. THEORETICAL EVALUATION OF SCATTERING Mathiessens Rule • Scattering in metals due to collisions with lattice (acoustic phonons & defects) and e-e collisions. If mechanisms independent, then: Phonons: • For T > TD (Debye Temp), then ac goes as T, but at low T, goes as T^5. Scattering cross section is also related to • deformation potential  (related to stress on lattice) • sound velocity vs Electron-Electron: e-e scattering in simple metals is not simple. Model of Lugovskoy & Bray [1] depends on electron energy above Fermi Level (E) and Thomas-Fermi Screening Wave Number qo (depends on electron density) & dielectric Ks Ag Cu Au W Pb [1] A. V. Lugovskoy, I. Bray, J Phys D: Appl. Phys. 31, L78 (1998)

  23. EXPERIMENT VS. THEORY (BULK METALS) • Field Enhancement 3.0 • Macroscopic field 1.0 MV/m • Work Function 3.97 eV • Temperature 300 K • Data & ImageCourtesy of J. SMEDLEY (BNL) BNL SLAC • Field Enhancement 1.0 • Macro field (MV/m) 0.01 • Work Function 4.31 eV • Temperature 300 K • Data Courtesy of D. DOWELL (SLAC)

  24. EXPERIMENT VS. THEORY (PART II) Experiment Theory M-type • How the comparison is made: • Time-Dependent Thermal Photoemission Model using ee(E=+h) ran for each incident laser intensity • Laser pulses were Gaussian in time • Total energy and charge emitted evaluated via integration over Gaussian pulse (Laser) and Emitted charge profile (electron) • Use of library values for Copper only (no adjustable constants) B-Type Scandate • Measured (UMD), calculated (NRL), & literature for various DISPENSER CATHODES • (1st Generation model used) • B-TYPE: B. Leblond, NIMA317, 365 (1992) UMD experimental data • M-TYPE UMD experimental data • SCANDATE UMD experimental data

  25. COVERAGE DEPENDENT WORK FUNCTION W C R b Hard Sphere Model of Surface Dipole • Gyftopolous-Levine Theory relates Work Function to coverage factor. Dependent upon Covalent Radii rx, Factors “f” and “w” (Act As “Atoms Per Cell”, Values of which Depend on Crystal Face). • General Surface = “Bumpy [B]” • alkali metal (n = 1) • alkaline-earth metal (n = 1.65) Modified Gyftopolous-Levine Theory

  26. GYFTOPOLOUS-LEVINE MODEL PERFORMANCE • LEAST SQUARES ANALYSIS:Minimize Difference between GL theory & Exp. Data With Regard to scale factor, monolayer work function value, and f coverage factor • Tightly constrained parameter variation • Unique determination of theory based on experimental values • Predictive ability from basic experiments C-S Wang, J. Appl. Phys. 44, 1477 (1977) J. B. Taylor, I. Langmuir, Phys. Rev. 44, 423 (1933). R. T. Longo, E. A. Adler, L. R. Falce, Tech. Dig. of Int'l. El. Dev. Meeting 1984, 12.2 (1984). G. A. Haas, A. Shih, C. R. K. Marrian, Applications of Surface Science 16, 139 (1983)

  27. EXPERIMENTAL MEASUREMENTS @ UMD • Test and evaluation chamber @ 2E-10 Torr • Surface preparation using H-ion beam • Surface deposition of various coatings • Deposition monitor (+/- 0.01nm thickness) • Femto-ampere current measurements (for QE) • Solid state CW lasers on single-axis robot • QE as function of time, temp, coverage, wavelength, and laser intensity (AUTOMATED)

  28. QE OF Cs ON W: EXP. VS. THEORY Experiment Theory 405 nm: x 1 (theory x 1.40) 532 nm: x 4 (theory x 1.40) • CONDITIONS: • Coverage Is Uniform • Field & Laser intensity low: Schottky barrier lowering & heating negligible • For 407 nm • Cs deposited rapidly: Exp measured mass by a “depth” factor. Therefore: Scale factor = (100%/Atomic diameter) • For 532 nm and 655 nm • Cesium deposited slowly: accumulation rate affected by desorption (scale a) • Peak value affected by residual cesium left on W (center xmax) • Presence of O (hard to remove) affects work function variation • To account for effects: 655 nm: x 35 (theory x 0.84)

  29. QE OF Cs ON W: EFFECT OF TEMPERATURE • Consider “typical” conditions of: • Laser Intensity10 MW/cm2 • Field at cathode 10 MV/m • Field enhancement 2 (generic) • Pulse length10 ps • Relaxation Time Is Temperature-dependent: Impact of Operating Photocathode at Lower Temperatures Is to Raise QE (all other things being equal) Under these conditions For r = 0.1 cm2:

  30. QE OF Cs ON Ag: EXP. VS. THEORY • Cs ON Ag Exp: • INITIAL COMPARISON METHODS for data taken week of Aug 8 2005 • Experimental conditions sameas for Cs-W for 532 and 655 nm exp. • Used same scale  as Cs on W • Shift factor aligns peaks for each experiment • Data taken by ANNE BALTER

  31. HYPOTHESES OF EXP-THEORY DIFFERENCES Solid Tungsten 500x q Shadows model: fraction of surface illuminated (f) q Solid Silver 500x Nathan Moody (UMD) • Actual surfaces differ from theory models because of • Surface geometry (altered by cleaning?) • Reflectivity changes with exposed face (inc. angle) • Crystal Faces can have different work functions (e.g., Cu(111) = 4.86, Cu(110) = 5.61, etc) • Contaminants (e.g., Carbon-based  ≈ 5.5 eV) & possibility of only sub-area contributing

  32. IMPACT OF COATINGS ON WORK FUNCTION Clean W(001) Potential Ba/O/W(001) - + W Friedel Oscillations Ba O tanh model • Conventional View: charged atoms at surface & image charge = dipole • QM View: Electron penetration of barrier determined by height and width • Exchange-Correlation & Poisson’s Eq: Changes in density = changes in V(x) L. A. Hemstreet, et al. PRB40, 3592 (1989) ENERGY ExCorr + Poisson W cores W cores POSITION (x/ao)

  33. EXCHANGE CORRELATION ENERGY OF e- Kinetic Exchange Correlation F Vxc m Metal Vacuum • Aspects of system of • interacting e- in ground state • determined by density • Exch.-Corr. Potential: change in r gives rise to change in V •  = Fermi Level • = electron density ao = Bohr radius Kinetic Energy e-e interaction e-lattice interaction self-interaction of background Typical Metals

  34. OTHER CONTRIBUTIONS TO SURF. BARRIER Lattice origin in relation to electron Dipole due to electron-lattice difference • Why bother looking at Friedel Oscillations? For two good reasons: • Friedel Density profile has analytic V(x) sol’n • Metal + Ba Density profile can be decomposed into Friedel component + Gaussian add-on: enables an analytic solution to Poisson Eq… or at least a very easily solved solution • How? • Approximations exist for location of background positive charge • Poisson’s Eq. easily solved with Friedel Density where  = 2kF(xi – xo) • Simple Theory: Wave function penetration creates dipole & gives Friedel Oscillations

  35. QUANTUM DISTRIBUTION FUNCTION Copper parameters Field = 1 eV/nm vacuum metal vacuum metal integrate both sides with respect to momentum (k) get density and current density • Heisenberg • Representation f(x,k,t): quantum phase space distribution acts like probability distribution function Wigner Distribution function (WDF) Contours mimic classical trajectories; when potentials are smooth and slowly varying, they are classical trajectories

  36. ANALYTICAL WDF MODEL: GAUSSIAN V(x) • How does V(x,k) behave? Consider a solvable case where V(x) is a Gaussian: large Dx samples f(x,k') near k small Dx samples f(x,k') far from k Broad Dx2 = 0.1 Sharp Dx2 = 5.0

  37. ANALYTICAL WDF MODEL (II): GAUSSIAN V(x) • The behavior of V(x,k) signals the transition from classical to quantum behavior: • Sharp: classical distribution • Broad: quantum effects • Can V(x,k) give a feel for when thermionic or field emission dominates? • Consider most energetic electron appreciably present(corresponds to E = m or k = kF) • If sin(kFx) does not “wiggle” muchover range Dx, QM important • Thermionic Emission:Dx is very large - expectclassical description to be good • Field EmissionkFDx = O(2p) implies Image Charge Potential

  38. ELECTRON DENSITY TO EMISSION BARRIER • Numerically solve QDF to Obtain Electron Density • Render Density in Terms of Friedel Components • Evaluate Potential From Exchange-Correlation Relation & Poisson’s Equation from the Friedel Representation • Change in Barrier seen to be due to shift in lF and xo terms

  39. EMISSION BARRIER TO TRANSMISSION PROB. • Modified Airy Function Approach: • V(x) = Vo + F(x-xn): • V(x) V(xn): N Linear Segments at xn • , ∂x Matched at xn, xn+1, etc. Zi = Linear combinations of Airy Functions Ai(z), Bi(z)

  40. CONCLUSION • Components of the Photocathode Program • Analysis of Coated & Bare Metals (extend to semiconductors) • Development Custom Engineered Controlled Porosity Photocathodes • Creation of Photoemission Models Validated By Exp. for Beam Codes • Theory Components included in photoemission code • Work function dependence on coverage & components; local variation • Spatial & Time Dependence of Temperature for laser & material parameters • Fundamental models of scattering, photoemission, QE & Barrier • Validation by bare and coated metal QE (macro) measurements • Status of Modeling Effort • Integrated Simulation Model Framework Without Recourse (Insofar As Possible) to “Fit” Parameters for “Library” Metals Using Quantum Distribution Function, Emission Theory, Coatings Theory • Photoemission Modules Appropriate for Beam Simulation Code (1st Generation Model distributed) From Integrated Simulation Model

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