1. Comparison of Candidates Secondary Electron Emission Materials
Valentin Ivanov1, Zeke Insepov2, Henry Frisch3
1Muons, Inc, 2Argonne National Laboratory, 3University of Chicago
Muons, Inc.
Introduction
Theoretical method for calculating secondary electron emission (SEE) yields have been developed. The method uses Monte Carlo simulation, empirical theories, and close comparison to experiment, in order to parameterize the SEE yields of highly emissive materials for micro channel plates (MCP). We have successfully applied this method to bulk Al2O3, a highly emissive material as well as to thinly deposited films of Al2O3,ZnOand MgO. The simulation results will be used in the selection of emissive and resistive materials for the deposition and characterization experiments that will be conducted by a large-area fast detector project at Argonne National Laboratory.
Gain factor
SEE Yields of various materials: Simulation vs Experiment
SEE yield calculation
Monte Carlo algorithm
Initial electrons are created, E=0.1-4 keV, q =0-89
New electron, new trajectory, similar to previous
The process continued until the electron E < E0
104 trajectories computed for each sample
h=100Å- 1mm samples were simulated
Experimental data from literature
Experimental SEE yields were compared with our calculations
The set of universal curves [1] for the gain factor vs. aspect ratio a=L/D for different voltage V at MCP is shown at Figure 12. Here L is a length, and D is a diameter of channels.
Different models of secondary emission
SEE simulation model
1. Guest’s formula for true secondary electron emission
Figure 2. Schematic of MC simulation: Nel – the number of electrons bombarding the target, E – the energy of electron, q – the incoming angle.
θ – incident angle, ε – impact energy, α – surface absorption factor, β – smooth factor , εmax – impact energy corresponds to a maximum of SEE yield,
Figure 13. Gain factor vs. D for MCP thickness =0.5mm, V = 2kV, Maximal SEE = 3.
2. Ito’s Model
3. Lie-Dekker’s Model =
4. Agarwal’s Model
Z is atomic number and A the atomic weight =
Figure 12. Universal curves for gain factor
5. Rodney-Vaugham’s Model
These approximations were used in simulation of the INCOM MCP with parameters: D = 40um, L/D = 40, L = 1.6 mm, Voltage U=1kV. The results of numerical simulations for different SEE models are presented in Table 1
Figure 14.Secondary emission properties for different materials common used as the emitters in MCP
s=0.62 for v<1, and s=0.25 for v>1.
V0 is biggest value for SEE curve σ(V0)=1 =
Figure 3. Secondary EE yield of MgO calculated via MC method and compared to experiment.
Figure 4. 2d-plot of SEE yield of MgO calculated via MC method for different energies and incoming angles.
k=0 for textured carbon, 1.5 for polished surface, 2 for crystalline (1 – default);
zm - is an argument value corresponds to the maximum of gn(z),
n – is an adjustable parameter (default value is 0.35 for V≤ Vmax,
zm=1.84, gn(zm)=0.725, and 1 for V>3 Vmax);
Table 1
Comparative analysis of SEE models
Figure 15. The approximations of SEE curve for a composite material (30%Al2O3+70%ZnO) used in different semi-analytical models
Model
Guest
Ito
Composite
Gain
1179
1132
1016
T res., ps
28.3
32.9
26.7
Figure 5. Secondary EE yield of Molybdenum via MC method and compared to experiment.
Figure 6. Secondary EE yield of Copper via MC method and compared to experiment
Conclusions
MCP gain and transient time simulations are closely related to the SE yields calculated in this work. The SE yields are expressed as a parameterized function of two variables: primary electron energy and incident angle. We have presented an approach that combines
Monte Carlo simulation of the secondary electron emission with empirical SE theories and experiment. We showed that this approach gives a close agreement for Al2O3, for which extensive experimental data and theory exist for important simulation parameters such
as energy and escape length of secondary electrons.
Figure 1. Comparative analysis for different models of secondary emission
Parameterization of SEE yield energy and angular dependencies
Al2O3 high-energy SEE Yields
Al2O3 low-energy SEE Yields
Figure 7. Resistivity of ZnO/Al2O3 films measured
Using the four-point probe and the mercury probe
Figure 8. Resistivity of ZnO/Al2O3 films measured
Using the four-point probe and the mercury probe
Reference SEE for Gold: MC vs Experiment
References
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[2] S. Jokela, (2010) Private communication, ANL.
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[5] M. Ito, (1984) IEEE Trans. NS-31, pp
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[5] V. Ivanov, Z.Insepov, Micro Channel Plate Simulations: State of the Art, Pico-Second Workshop VII, February 26-28, 2009; Argonne National Lab.
Figure 9. Comparison of simulated SEE yield for Gold and experimentally measured at Argonne*).
Figure 10. SEE of ZnO/Al2O3 films parametrized at low energies.
Figure 11. SEE of ZnO/Al2O3 films parametized at high energies
*) Cortesy of S. Jokela