Simulation of electric fields in silicon detectors

Report
Towards simulation of electric fields
in silicon detectors using the Robin
Hood method
Hrvoje Štefančić
Theoretical Physics Division
Ruđer Bošković Institute
(based on joint work with Hrvoje Abraham and
Predrag Lazić)
Electric field strength in a segment of a
Si microstrip detector
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Peculiar behavior of the Si
microstrip detector at the interstrip
region observed by the IRB group
(communicated by Soić and Grassi)
The configuration of the electric
field in the interstrip region might
be relevant for the explanation
Robin Hood as a method for the
precise calculation of the field
This workshop as a testing ground of
the idea (with some preliminary
results)
Discuss and asses the potential of
the method in Si detectors
Learn about possible unpercieved
opportunities or overlooked pitfalls
In which direction to proceed
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Outline of the presentation
• The description of the Robin Hood method – a novel tool
• Properties of the RH method (capacity of a unit cube,
corrugated surfaces) – a powerful tool
• Applications in particle detectors (micro-pattern) – a tool
relevant for the field of particle detectors
• Preliminary results for silicon detectors – a discussion
point
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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The Robin Hood method
• How do we calculate the electric field in some electrostatic
system with a complex geometry?
– Solve the Poisson equation by the discretization of the 3D space Finite Difference Methods (FDM), Finite Element Methods (FEM)
– Determine the sources at surfaces (surface charge distributions at
conductors, polarization of dielectrics) – Boundary Element Methods
(BEM)
– The Robin Hood method falls into the class of Boundary Element
Methods
• Predrag Lazić, Hrvoje Štefančić, Hrvoje Abraham, J. Comp.
Phys. 213 (2006) 117.
• Predrag Lazić, Hrvoje Štefančić, Hrvoje Abraham, Engineering
Analysis with Boundary Elements, 32 (2008) 76.
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The Robin Hood method – how does it
work?
• Imagine and example of a point charge close to an
insulated sphere
– Divide the surface of the sphere into triangles (discretization)
– Calculate the initial value of the electric potential at all triangles
– Find the triangles with the maximal and the minimal value of
the potential
– Transfer charge from the triangle with the maximal potential to
the triangle with the minimal potential so that after the transfer
their potentials are equal (that is why the Robin Hood name –
taking from the rich to give to the poor)
– Update the value of the potential at all triangles
– Iterate the procedure (find max and min, charge transfer,
update) until the requirement on the precision is achieved
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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The result – a point charge close to an
insulated sphere
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The Robin Hood method
• The Robin Hood method is also applicable to
– Conductors at a fixed potential
– Dielectrics (the condition of equipotentiality is
replaced by the condition on fields on both sides
of the interface between the dielectrics)
– Magnetostatics
– Electromagnetism
– Systems of linear equations
– ...
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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The metallic plate at a fixed potential
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Water in connected pits – the
redistribution problem
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Linear memory consumption
• The required memory scales linearly with N (number of
triangles) – other BEM have a memory requirement ~ N2
• The record (2008) in the precision of the capacity of the unit
cube: C=0.66067786 ±8 x 10-8 in units of 1/4 π ε0
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Complex geometries
• Corrugated plane (P.Lazić, B. N. J. Persson, Surface-roughness–
induced electric-field enhancement and triboluminescence,
Europhys. Lett. 91 (2010) 46003)
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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The same convergence at many scales
• Point charge close to the sphere kept at a fixed
potential
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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The Robin Hood method and the
particle detectors and accelerators
• Micro-pattern detectors (Micromegas)
• Katrin collaboration experimental setup
• IEC fusor
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Micro-pattern detectors
Predrag Lazić, Denis Dujmić, Joseph A. Formaggio, Hrvoje Abraham, Hrvoje
Štefančić, New approach to 3D electrostatic calculations for micro-pattern
detectors, JINST 6 (2011) P12003
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Types of micro-mesh
• Dependence of the electronic transparency on the type of
micro-mesh (rectangular, cylindrical, woven, calendered)
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Electric field at the micro-mesh
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Electric potential at the micro-mesh
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Ez at the micro-mesh
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Exy at the micro-mesh
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Transparency vs. field
• Calculations using the electric-field tracking (EFT)
method and micro-tracking (MT)
• The less symmetrical the electric field at the micromesh, the larger the electronic transparency
• Transparency in general higher for EFT than for MT
• Transparency the best for cylindrical and calendered,
intermediate for woven and the worst for rectangular
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Electronic transparency vs. optical
transparency
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Dielectric spacer
• Full cylinder or hollow (capillary), vertical or
horizontal
No spacer
Full spacer
Silicon Detector Workshop, Split, Croatia, 810 October 2012
Hollow spacer
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Detector system of the KATRIN
experimental setup
J. A. Formaggio, P. Lazić, T. J. Corona, H. Štefančić, H. Abraham, and F. Gluck,
Solving for Micro- and Macro-Scale Electrostatic Configurations Using the
Robin Hood Algorithm, Progress In Electromagnetics Research B, 39 (2012) 1.
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IEC fusor
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Si microstrip detectors – from the
viewpoint of electric field modeling
• Periodic structures with many details
• Various dielectric layers (SiO2, Si with various
dopants)
• The geometry of dielectric layers is not precisely
known (especially for SiO2)
• Particular elements have orders of magnitude
different dimensions (e.g. Al strips have length ~
cm, width ~ mm, thickness ~ mm) – potential
problems with sharp-angled triangles
• The separation of strips (~ 50 mm) is much
smaller than their width
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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Si microstrip detectors – modelling
assumptions
• Entire system could be analyzed in full (this lies within
the capabilities of the Robin Hood Solver), but it is
more instructive to focus on the interstrip region
– the most interesting configuration of the electric fields
– Observed reversed polarity signals for particles passing the
interstrip region (Soić, Grassi)
• Define an “elementary cell” – centered at the interstrip
region
• All layers of Si (differently doped) have the same
dielectric constant (Capan)
• Al strips can be well described as conducting plates
• Various geometries for the SiO2 layer
Silicon Detector Workshop, Split, Croatia, 810 October 2012
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No SiO2 – total field strength
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No SiO2 – field strength in the x
direction
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No SiO2 – field strength in the y
direction
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No SiO2 – field strength in the z
direction
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“Thick” SiO2 layer – start from the Si
block
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“Thick” SiO2 layer – add a Si cylinder
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“Thick” SiO2 layer – make a Boolean
difference of the Si plate and the cylinder
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“Thick” SiO2 layer – add a SiO2 cylinder
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“Thick” SiO2 layer – make a Boolean
difference of the SiO2 cylinder and a cube
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“Thick” SiO2 layer – add Al plates
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What next?
• Realistic geometry of the SiO2 layer
• Dependence on the thickness of the Si
(decoupling of top and bottom strips)
• Spatial charge accumulated at SiO2
• Full system analysis (interference of adjacent
strips)
• Simulation of charge transport (big step)
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THANK YOU FOR YOUR ATTENTION
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