1. LAPPD Collaborative Meeting, June 10-11, 2010 Muons, Inc. 1 Comparison & Discussion of Secondary Electron Emission (SEE) Materials - Theory Z.Insepov, V. Ivanov, S. Jokela

2. Muons, Inc. 2 Outline Simulation chart SEE Yields for various materials Future SEE tasks Charge relaxation time Future simulation plans Summary

3. Muons, Inc. 3 Simulation work chart MCP Experiments Macro-scopic Gain, Rt, saturation simulations Micro-scopic SEE, PE Saturation Heating & Aging simulations Macroscopic Fringe-field Comsol simulations SEE = f(E) SEE = g(  )  – relax. time T = f(z) Gain, Rt SEE, PE Escape length Mater. properties Map of electric fringe field Relaxation times Materials properties Materials properties Relaxation times

4. Muons, Inc. 4 Low-Energy Monte Carlo codes Algorithm of SEE calculations J  – the mean ionization potential  – energy for production of SE – mean free path, escape length  - screening factor Casino simulation   Al 2 O 3, D. Joy (1995) Inelastic, Bethe-Joy (1989) Elastic, Rutherford Berger-Seltzer (1970)  = 20 eV = 60 Å Insulators, Kanaya (1978)

5. Muons, Inc. 5 SEE yield calculation via MC Monte Carlo algorithm Initial electrons are created, E = 0.1 - 4 keV,  = 0-89  New electron, new trajectory, similar to previous – The process continued until the electron E < E 0 1-10K trajectories computed for each sample (error  1/N) h=10 2 -10 4 Å samples were simulated (100Å - 1  m) Experimental data from literature Experimental SEE yields were compared with our calculations

6. Muons, Inc. 6 SEE Yield calculations MgO MgO Al2O3 Al2O3 ZnO ZnO Copper Copper Gold Gold Molybdenum Molybdenum Target  SEE h E, ev Nel=10 3 -10 4

7. Muons, Inc. 7 Simulation Group paper Z. Insepov, V. Ivanov, H. Frisch, Comparison of Candidate Secondary Electron Emission Materials (accepted for publication in NIMB)

8. Muons, Inc. 8 Why Monte-Carlo ? Empirical, semi-empirical SEE Models are too bad Specific material, bulk, flat surface, one element, no angular dependence Monte Carlo simulation algorithm is simple Search for high SEE materials -- Gain/TTS critical to SEE at first strikeSearch for high SEE materials -- Gain/TTS critical to SEE at first strike Higher QE PC for thin films, ML, nanostructured coatingsHigher QE PC for thin films, ML, nanostructured coatings Mixture of materials (Alumina+ZnO)Mixture of materials (Alumina+ZnO) Surface roughness can be studiedSurface roughness can be studied Materials aware MCP simulation – against blind experimentationMaterials aware MCP simulation – against blind experimentation Experimental data from literature are not good SEE for E-dependence, no angular Experimental data at Argonne ANL characterization experiments are in progress ANL characterization experiments are in progress

9. Muons, Inc. 9 Empirical Models No space charge effect, no surface charging effectNo space charge effect, no surface charging effect Poisson distribution for the SEEPoisson distribution for the SEE Maxwellian energy and Cosine angular distributionsMaxwellian energy and Cosine angular distributions Bulk material, flat surface, no temperature effectsBulk material, flat surface, no temperature effects Guest (1971)  – adjustable parameter Ito (1984) Yakobson (1966) Agarwal (1958) 

10. Muons, Inc. 10 Comparison of SEE- models

11. Muons, Inc. 11 Alumina SEE Yield: MC vs Experiment

12. Muons, Inc. 12 ZnO SEE Yields: MC vs Experiment

13. Muons, Inc. 13 Metal SEE Yields: MC vs Experiment

14. Muons, Inc. 14 MgO SEE Yields: MC vs Experiment

15. Muons, Inc. 15 MgO SEE Yield vs  (E-different)

16. Muons, Inc. 16 Charge relaxation time

17. Muons, Inc. 17 Electric field Gain Shape function E 0z, M 0 – electric field and a gain for non-saturated mode I 0 – initial current of photo electrons, I R – resistance current τ – relaxation time for induced positive charges Analytical model of saturation effects [Berkin et al, Tech. Phys. Lett.(2007) 75]

18. Muons, Inc. 18 AZO Maxwell relaxation times Channel Resistive Layer Material 70% Zn/(Zn+Al) Maxwell relaxation time 1  10 -6 sec Channel Resistive Layer Material 60% Zn/(Zn+Al) Maxwell relaxation time 1  10 -3 sec

19. Muons, Inc. 19 DD-Model of charge relaxation [1] A.K. Jonscher, Principles of semiconductor device operations, Wiley (1960). [2] A.H. Marshak, Proc. IEEE 72, 148-164 (1984). [3] A.G. Chynoweth, J. Appl. Phys. 31, 1161-1165 (1960). [4] R. Van Overstraeten, Solid St. Electronics 13 (1970) 583-608. [5] L.M. Biberman, Proc. IEEE 59, 555-572 (1972). [6] Z. Insepov et al, Phys.Rev. A (2008) [7] I. Costina et al, Appl. Phys. Lett.78 (2001) r rr z r = 20  m  r = 10 nm Aspect ratio 40 A. Spherical symmetry B. Cylindrical symmetry D  – diffusion coefficient,   - mobility, n  - density of carriers (  = e, h) z r r = 10 nm Al 2 O 3 +ZnO Primary electron SEE

20. Muons, Inc. 20 Input parameters for DDM Diffusion coefficients of amorphous alumina are unknown Diffusion coefficients of amorphous alumina are unknown Carrier mobilities for alumina are known for limited mixture content Carrier mobilities for alumina are known for limited mixture content [1] Ruske, Electrical transport in Al-doped zinc oxide, J. Appl. Phys. (2010). ZnO with 1% of Al 2 O 3 was measured:  =40 cm 2 /Vs,  =1.4  10 −4 (  cm) [1] Conductivity of AZO with 20% Al:  = 10 7 (  cm), mobility unknown. Assuming linear dependence between conductivity and mobility, mobility of a mixture Al2O3+ZnO was extrapolated from low Al-content to high. Diffusion coefficients via Einstein relation: D =  k B T/e.

21. Muons, Inc. 21 Proposed material constants Mobility and diffusion constants of carriers were extrapolated from low Al-content to high [1] SiO2, Dapor [Dapor, Surf. Interface Anal. 26, 531È533 (1998)]

22. Muons, Inc. 22 Charge dissipation in Al2O3+ZnO Set of equations for the drift-diffusion model were numerically solved for several values of material constraints and the relaxation times were obtained.

23. Muons, Inc. 23 Internal Electric field

24. Muons, Inc. 24 Hole densities vs time, Al 2 O 3 +ZnO D h =1.2e-11 cm 2 /s D h =1.2e-10 cm 2 /s D h =1.2e-9 cm 2 /s D h =1.2e-8 cm 2 /s Variable – diffusion coefficients, D h

25. Muons, Inc. 25 Relaxation times via DDM Relaxation time vs diffusion coefficients D h =1.2x10 -11 cm 2 /s D h =1.2x10 -10 cm 2 /s D h =1.2x10 -8 cm 2 /s Maxwell relaxation time SiO2, Dapor (1998)

26. Muons, Inc. 26 Status of relaxation time Experimental verification of relaxation time model – under progress (APS/HEP) Experimental verification of relaxation time model – under progress (APS/HEP) Our calculations will be extended to electrons and two types of holes – to be compared to Auger Different local nano-structures of the mixture Different local nano-structures of the mixture Two types of geometries: plane and cylindrical Ambipolar drift-diffusion model is essential Relaxation time is obtained via numerical solution of the kinetics of charge carriers Impact ionization model will be added Impact ionization model will be added

27. Muons, Inc. 27 Relaxation time measurement Continuous delay within 5m (15 ns) Continuous delay within 5m (15 ns) Laser flashing (Ed May) – 1  s Laser flashing (Ed May) – 1  s B. Adams

28. Muons, Inc. 28 Future simulation work Photo-electron bunch formation Photo-electron bunch formation Microscopic model of the photo-electron emission (Zeke, Klaus, Bernard); Angular and energy distribution for the photo-emitted electrons (Zeke); Bunch formation for electron optical calculations (Valentin); Systematic study the charge relaxation time vs. the material properties (Zeke); Continue study how saturation phenomena affect on the gain & time resolution for real devices, comparison the simulations and experiment (Valentin). Saturation effects Heating effects Aging effects Roughness effects Mixing and multilayer effects