3/3/2009 Z. Insepov, V. Ivanov 1

Our plans for the MCP simulationsOur plans for the MCP simulations We are working in two directions: Mixed Analytical/Numerical approach for

macro models (Valentin Ivanov) Numerical model for micro simulations

(Zeke Insepov) Our numerical (Monte Carlo) tracking

model includes new important elements SEE simulation for materials TTS simulation Resistance simulation

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Monte Carlo calculation of SEE yieldMonte Carlo calculation of SEE yieldThe mean free path of primary electrons

∑ ⋅=Λ

⋅Λ−=∆

−

ii

i

Ai

ANcRs

σρ1

),ln(

Λ - mean free path of elastic scatteringR – uniformly distr. random numberρ – average densityNA – Avogadro numberAi – atomic weight of i-th elementci –the concentration σi – the total elastic cross section

Material composition: [A]x[B]y

[A]x[B]y

[K. Murata, Scann. Microscopy, 1996

∑ ⋅=Λ

⋅Λ−=∆

−

ii

i

Ai

ANcRs

σρ1

),ln(

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Electron scattering algorithmElectron scattering algorithmThe Mott cross-section [N. Mott 1929]:

Ji = 9.76Zi + 58.8Zi-0.19 [Berger, Seltzer, 1964].δ– The number of secondary emitted electronsε – adjustable parameter, can be obtained from experiment.

• The positions of the secondary electrons and the emission angles are generated uniformly distributed.

f (θ), g(θ) – the scattering amplitudes

Inelastic E loss at each step – byBethe law [Joy, Luo (1989)]Ji -- the ionization potential

Probability of SE emission – Gryzinski (1965), Vriens (1966)

Universal inelastic mean free path of SE - Seah, Dench (1979)

[M. Yasuda, Jpn. J. Appl. Phys, 2004]

,|)(||)(| 22 θθσ gfdd +=

Ω

∑ +⋅⋅=−i i

ii

Ai

JEZ

EANce

dsdE ),166.11ln(2 4 ρπ

.)(

)( 5.2bs

s EEkES

−=

,1 sdsdE ∆⋅⋅−=

εδ

.11.04912

1

2

+= s

s

EEρ

λ

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Cross-sectionsCross-sections

Cross-section are calculated by the Penelope code, Ep=200 eV

We use the Penelope Monte Carlo code to calculate the cross-sections of electron scattering, the energy and angle dependence of SEE for several materials.

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CASINO simulations of normal electron CASINO simulations of normal electron impactsimpacts

Monte Carlo Simulation of electron trajectories in solids, Tabulated electron Mott elastic cross sections Experimental stopping power E=0.1-30 kV Multi-layer: 10A of SiO2, 1A of Si, 200A of SiO2, 2000A of copper film

105 Electron trajectories passing through a SiO2 multi-layer MCP structure by a CASINO code

Absorbed energies of 250 eV electrons

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MC simulation of MCP coatingsMC simulation of MCP coatings

SiO2 – 1 nm, density 2.61 and 11.5 g/cc

Si, Al, Cu, Au, W for efficient reflection of electrons

TiO2 – 2 nm, density 2.42 g/cc

ITO – 2 nm, density 4.27 g/cc

Alumina

ITO

TiO2

SiO2

Reflective metal

Al2O3 – 20 nm, density 1.9 g/cc

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SEE trajectories in MCP coatings: SiO2 SEE trajectories in MCP coatings: SiO2 + High-Z Mirror @ 45+ High-Z Mirror @ 45°°, E=250 eV, E=250 eV

Al Cu Au W

Maximum penetration depths of PE @ 45°

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SEE trajectories @ 75SEE trajectories @ 75°° of PE, E=250 ev of PE, E=250 ev

Si

Maximum penetration depths of PE @ 75°

Si

Al

Al

Cu W

Cu W

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Penetration depths @ 45 and 75Penetration depths @ 45 and 75°°, 250v, 250v

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MCP Coating: TiO2+ITO+AluminaMCP Coating: TiO2+ITO+Alumina

We can calculate back-scattered electrons, absorbed energy, penetration depth of primary electron in various coating compositions.

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TTS simulationTTS simulation

g(τ,E)

•Secondary electrons cannot be emitted instantly. •They have time delay and angular and energy distribution g(τ,E).•All models that do not take this into account cannot predict correct TTS.

time delay

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Surface resistance calculationSurface resistance calculationResistance of SiO2 thin films depends strongly on temperature and the film thickness

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Future materials tasksFuture materials tasksThe physical and computational resistance models of a non-uniform, multi-layer are still missing.The low-energy SEE and PE models are under construction and will be included into the Penelope code.Stress, contamination, and temperature dependencies of SEE and PE of materials will be our main future tasks. These models should be benchmarked and verified by experiment.

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SEE of non-uniform MCP thin film coatingsSEE of non-uniform MCP thin film coatings

Density of state (DOS) of MCP electron emitting materials can be calculated by a Density-Functional quantum mechnaics method.

We use wien2k (and VASP) DFT packages to calculate density of states (DOS) of electrons, phonon spectra in SiO2, Al2O3.

This is an important task to calculate SEE of SiO2, Al2O3 etc. at various (high) densities typical for thin film coatings of MCP channels.

DOS of MCP materials will aslo be calculated for imperfect coatings, such as damaged, having defects (vacancies, interstitials, cavities, etc.) which directly affects reliability and aging of MCP.

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SummarySummary Existing MC codes cannot be applied for calculation

of SEE and PE of multi-layered MCP channel surfaces.

There is a lack of simulation of resistivity of multi-layered coating inside the MCP channels.

A large-scale benchmarking is required to validate the physical/material properties of photo- and secondary emitters, implemented in the computational models.