1 Comparison and discussion of candidate SEE materials Z. Insepov (ANL), V. Ivanov (Muons Inc.) Muons, Inc.

2Outline  Motivation  Semi-empirical theories  Monte Carlo simulations  Empirical models  Comparison with experiment  Summary

3Motivation  Gain and TTS can drastically be improved by increasing SEE at first strike  Higher QE PC can be obtained by using Al 2 O 3, MgO, and ZnO.  Multilayer structures can improve SEE  Surface roughness can affect the SEE  We need a tool to be able to predict SEE based on materials properties

4 Empirical Models  Space charge effect, charging effect of the emitting surface and reflection of incident electrons are not considered.  Number of emitted secondary electrons is determined by Poisson distribution having average value from equation below.  Secondary electrons have Maxwellian energy distribution and Cosine angular distribution.  Guest (1971)  – adjustable parameter  Ito (1984)  Yakobson (1966)  Agarwal (1958)

5 Comparison SEE models

6 SEE for models vs experiment

7 Comparison between theory and experiment

8 SEE of a rough surface Kawata at al, JNM (1995) The effect of surface roughness on the SEE from Be at E < 1 keV electron bombardment was studied by Monte Carlo simulation. With increasing aspect ratio H/W of the bowl structure, the SEE Yield increases, whereas for large H/W the yield is smaller. Krasnov, Vacuum (2004)

9 Semi-empirical theories  “Universal law of SE yield” Al 2 O 3 - Young (1956) e-e- Joy (1987) primary secondary

10 Low-Energy Monte Carlo codes  Algorithm of SEE calculations Screening factor  

11 Simulation results: 5 nm Al 2 O 3  Comparison of various models of SEE

12 Simulation results 5 nm Al 2 O 3  SEE vs primary electron angle and energy This parameterized set of SEE yield is used as an input to a macroscopic gain code for MCP simulation

13 Comparison with experiment  SE yields of an Al2O3 were measured by a pulsed technique where surface was replenished by electron shower between the two pulses [21]. Materials data used in MC simulations:  Z av = 10  A av = 20.4   = 3.9 g/cm 3   = 20 eV,  = 60 Å  J = 145 eV None of them are from experiment except for J which is unimportant at low energies

14Summary  None of the existing Monte Carlo codes can simulate low- energy SEE from new, engineering materials, and with charge effects.  We need to build a MC code that will be able to treat mixtures, rough, multilayer surfaces, low energy, with charge accumulation.  Our current approach combines simple MC simulation, empirical models, and comparison to experiment.  Al 2 O 3 SE yields were parameterized for two variables: E PE and incident angle and submitted as an input to macroscopic gain code.  We obtained a close agreement with experiment for Al 2 O 3.  We plan to extend this approach to MgO, ZnO, and Al2O3+ZnO mixtures where experiment is sparse.

15Acknowledgments David C Joy ORNL Pierre Hovington McGill University Raynald Gauvin McGill University