1. Development of Large-Area Photo-detectors:
MCP development
S. Antipov, Z. Insepov, V. Ivanov m
Muons, Inc.
Abstract
Electric field inside high gain microchannel plate multipliers was studied. The COMSOL Multiphysics® simulation package was employed that facilitates all steps in the modeling process — defining geometry, meshing, specifying physics, solving Maxwell equations and finally, visualization of the results. An AC/DC Module was used that sets the stage for modeling the performance of a system containings dielectrics, resistors, and an AC/DC current passing through the resistive elements. The calculations were based on a highly conductive approach and were obtained by the solution of the Maxwell equations for various number of pores inside a dielectric matrix (glass) with one, and several (up to 19 in 3d and 21 in 2d) micron scale pores. The pore model includes a thin Al2O3+ZnO mixture coating that covers the internal pore surface. The preliminary results are important to study the gain and temporal characteristics and the performance of MCP's . The Comsol results were compared to an analytical solution. The future tasks were outlined.
Preliminary results
One pore: In a 3D simulation we assume
that ε/σ relaxation time is small for a thin
resistive layer with the poperties of
a mixture 30% Al2O3 and 70% ZnO.
Results show that electric field aligns
along the pore.
Analytical Solution for tilted
cylindrical pore in dielectrics
E-field in pore
E-field Angle ~ 8°, field aligns along the pore
Problem 1. Cylindrical channel of radius R with dielectric constant ε1 is in the medium ε2 in external electric field of strength E.
Electric field in the channels of chevron pairs can be represented as a sum of 1-D analytical field of middle part and fringe fields of entrance and exit of the channel.
Color: Angle=Atan(Ex/Ez)
Arrows: Electric field
E-field inside 7 pores
Simultaneous DC and Electrostatics
Modeling
Mesh restriction (Nel ~ 40,000)
The coating is too thin -- memory restriction
Artificial thickening of coating was used
Effective boundary approach with distributed
resistance was not successful
Relaxation time issue is being researched
Due to very low coating conductivity the
charge relaxation time is too large.
Potential and electric field distributions fir infinite-length channel are given by formulae
Color: Angle=Atan(Ex/Ez)
Streamlines in cross section
- electric field
cross talk of the pores is not significant
Problem 2. Cylindrical channel in tilted electric field E0 with angle a.
Problem3. Internal surface of the channel is coated with thin layer of the material with conductance σ.
Geometry of the pores and MCP parameters
Pore structure
Pore diameters – 20 mm
Alumina coatings – 1 mm and 5 mm
Aspect ratio 5
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
Al2O3+ZnO
Table 1: Dielectric constants [1] and resistivities [2] for Al2O3/ZnO ALD films
Al2O3 + ZnO coating resistivity
Edge Effects: E-field at the pore edge 8
The external field can be expanded onto parallel and perpendicular components
Parallel component does not make a perturbation, but perpendicular one excites the field of the Problem 1. Actual field in cylindrical channel is
Finally the angle between cylinder axis and the vector of internal electric field is
 Conductive material excites the surface currents which increase the electric field from external side of the layer and decreases the field from internal one – analogue of dipole charge layer. It creates the screening effect of lowering for the external field Eext in the pore.
r = 20 mm
d = 1 mm
h = 1.6 mm
Color: Ez
Arrows & streamlines: Electric field
% DEZ* exposures 10 25 33 50
Dielectric Constant
6.8 ± 0.5
6.5 ± 0.4
6.9 ± 0.3
7.2 ± 0.2
6.6 ± 0.3
  Resistivity (W cm)
~1016
5x1015
5x1014
1014
1013
Conclusion
R = N  R1
We have simulated the electric field inside the pores of shevron-type MCP’s using a Multiphysics Comsol software package and verified this study by an analytical solution. The main conclusion is that in a highly-conductive envireonment, 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.
N = 5106 pores
R1=R*N = ( MW)  5106 = (90-500)1012 W