Transcript Poster - indico in2p3

Gain and Time Resolution Simulations in Saturated MCP Pores
Muons, Inc.
Valentin Ivanov, Zeke Insepov, Sergey Antipov
Charge
relaxation
times
Introduction
Author
author Institution
Materials
properties
Al
O
+
ZnO
coating
resistivity
2
3
We
have
simulated
the
electric
field
inside
the
pores
of
Micro channel plate (MCP) amplifiers are commonly used in detectors of fast
Pore structure
1First
time signals with a pico-second resolution. The main parameters of the MCP
amplifier, such as the gain factor and time resolution are strongly dependent on
the work regime of the device. The saturation effects take place for a high-level
input signal. In our paper these effects have been studied numerically for large
area fast photo detectors. It was shown that the saturation effect for short
pulses can be reduced by introducing a thin resistive layer between the bulk
material and the emissive coating. The results of our simulations were compared
with the simulations of other authors and with the available experimental data..
Monte Carlo simulations can be successfully used for large area photo detectors
with micron and Pico-second resolution range. The 3D computer code MCS
(Monte Carlo Simulator) have been developed. It can simulate all types of MCP
amplifiers (Single plate, Chevron pair, Z-stack and Funnel-type MCP) with taking
into account fringe fields, saturation effects, pillar-structure photo cathodes,
multi-layer coating of secondary emitters.
Fringe
fields
simulations
in
3D
2
Institution, Second Author Institution, 3Third
chevron-type MCP’s using a multi-physic COMSOL software
and verified this study by an analytical solution. The
simulations show that in a highly-conductive environment,
the electric field in the pore is directed axially inside the pore,
having a gradual turn from the value in the resistive layer
near the surface. In a simulation we assume that ε/σ
relaxation time is small for a thin resistive layer with
the properties of a mixture 30% Al2O3 and 70% ZnO.
Pore diameters – 20 mm
Al2O3+ZnO coatings – 1-5 mm
Aspect ratio -- 40
S
1.29 10 9 m 2
12
  R  (90 - 500) 10 
,
-3
l
1.6 10 m
  (0.725 - 4.03) 1010 (  cm).
  (1.38  0.25) 10 10 (  cm) 1
Materials parameters:
Glass:
s = 110-17 S/m, e=5.8
Al2O3+ZnO: s = 110-8 S/m, e=6.9
Air:
s = 110-17 S/m, e=1
Charge dissipation in
Al2O3+ZnO
One-pore modeling: E-field angle ~ 8°
MCP parameters
Relaxation time calculated via Drift-Diff.Model
Analytical model of saturation effects in MCP
There are different approaches to simulation of saturation effects [1]-[5]. All of
them use some constants to adjust the model to experimental data. Therefore
we use in our simulations the analytical model suggested by A.Berkin and
V.Vasilev [6] with no additional constants. The set of equations describes the
E ( z, t )  E h ( z, t ),
Electric field distribution
h ( z, t )
M ( z, t )  M
,
z
0z
Color: Angle=Atan(Ex/Ez). Streamlines in cross section represent the
electric field in the pore.
Edge Effects: E-field
at the pore edge
Electric field inside 7 pores
Hole densities vs. time
Relaxation time vs diffusion coefficients
E
E
tp T 

1  hE ( z , t p )  1 exp 



ln M 0 
hE ( z , t ) 
,
ln M 0   ln 1  C (t )  ln 1  C (t )M 0 1  C (t )ez
0
Gain factor



Shape function



I
c(t )  0 1  e t /  .
IR
Here Ezo, Mo – electric field and a gain for non saturated mode; T – pulse period;
Io – initial current of photo electrons, Ir – resistance current; ts - off-duty factor;
τ – relaxation time for induced positive charges, resistive material property.
4.00E+06
τ=6.e-6 s
R=5.e14Ω
3.50E+06
1.00E-10
2.00E+06
I=1.e-17
1.00E-11
I=1.e-16
1.00E-12
I=1.e-15
Iout, A
2.50E+06
Ez(z)
Electric field inside 19 pores
The normal way to reduce the saturation effects is to introduce the low- resistance layer
coating the channel surface. Another way is to vary inter-plate gap of chevron pair or Z-stack
in order to distribute the secondary electrons from one pore of 1-st plate to many channels
of 2-nd and 3-rd plates. By this way one can reduce the currents in each individual pore of
last cascades, and keep the total gain. We used the code MCS to provide those simulations.
1.00E-09
3.00E+06
1.00E-13
I=1.e-17
Input
current,
I=1.e-16
A
I=1.e-15
1.50E+06
I=1.e-14
1.00E-14
I=1.e-14
1.00E+06
I=1.e-13
1.00E-15
I=1.e-13
5.00E+05
I=1.e-12
1.00E-16
I=1.e-12
0.00E+00
0
0.0002
0.0004
0.0006
1.00E-17
0.00E+00
0.0008
2.00E-04
z, m
tau=
1.e-3
1.E-16
1.E-15
1.E-14
6.00E-04
8.00E-04
MCP-current profile vs. initial
current I, relaxation τ=6μs.
1.E-13
1.E-12
Io, A
Time resol., ps
1.00E+00
9.00E-01
8.00E-01
7.00E-01
6.00E-01
5.00E-01
4.00E-01
3.00E-01
2.00E-01
1.00E-01
0.00E+00
1.E-17
4.00E-04
Electric field inside 7 pores
z, mm
Electric field profile vs. initial
current I, relaxation τ=6μs.
M/Mo
The effect of inter-plate gap variation
500
450
400
350
300
250
200
150
100
50
0
1.00E-17
MCP amplifier sketch.
Edge effect for the electric field
Small gap. Electrons from 1-st plate come to one pore of 2nd plate. Gain M=1.2E6 for τ=1μs, and M=1.5E5 for τ=1ms.
Blue – photo electrons; red – secondary electrons.
τ=1.e-3
τ=1.e-6
1.00E-16
1.00E-15
1.00E-14
1.00E-13
1.00E-12
Initial current, A
Gain vs. initial current MCP parameters:
D=20μm, L/D=40, U=1kV, Gain Mo=1.E6
Time resolution variations
vs. the initial current I.
Computer code “Monte Carlo Simulator”, Windows Ver.2.0
The code MCS is full 3D simulator with friendly user’s interface and graphical
post-processor. Numerical models include the angular, energy and spatial
distributions for photo- and secondary emitters, fringe fields, saturation effects
and other features representing different multi-layer materials. It can evaluate
all parameters of realistic MCP devices: gain, transit time spread, angular,
energy and spatial distributions of photo- and secondary electrons in pre
defined cross-sections. Typical CPU-time for simulation of 1 million particles is
1 to 10 minutes at desktop or laptop computer with 1.8GHz CPU.
Large gap. Electrons distributed to 3 pores of 2-nd plate. Gain M=3.4E6 for
τ=1μs, and M=1.13E6 for τ=1ms.
References
User’s interface for the code MCP
[1] L.Giudicotti, NIM A 480(2002) 670-679.
[2] P-L.Liu et al., IEEE Trans. MWTT, V.47, N7, 1999.-P.1297-1303.
[3] G.W.Fraser et al., IEEE Trans. Nucl. Sci., V.NX-30, N1, 1983.-P.455-460.
[4] O.L.Landen et al., SPIE Vol. 2002
[5] P.M.Shikhalev, NIM A 420 (1999) 202-212.
[6] A.B.Berkin, V.V.Vasilev, Zhurnal Tekhnicheskoi Fiziki, V.76, N2.-P.127-129.
[6] V. Ivanov, Micro Channel Plate Simulator, User’s Guide, Muons, Inc., 2009.