Simulation of Optical Crosstalk in SiPM - NDIP 11

On the Efficiency of Photon Emission
during Avalanches in Silicon
A. Nepomuk Otte
University of California in Santa Cruz
Santa Cruz Institute for Particle Physics
paying the conference fee
was
Max-Planck-Institut für Physik, Munich
paying the hotel
supported by the American Astronomical Society
paying the flight ticket
work published in
2007 JINST TH 003
photon emission in avalanches
(Sciacca, 2003)
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Outline
• SiSi the SiPM Simulator
One example application of SiSi:
characterize photon emission,
which results in optical crosstalk
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SiSi*: The SiPM Simulator
* Elisabeth ”Sis(s)i” von Wittelsbach the
empress consort of Emperor Franz Joseph
of Austria. She was born 1837 in Munich,
Bavaria and murdered 1898 in Geneva,
Switzerland
a 3D Monte Carlo simulation package of SiPM
for the community
to make it most affordable:
It is free!
send me an e-mail:
nepomuk@scipp.ucsc.edu
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An application of SiSi:
Why?
Study Photon Emission in
The emission spectrum is uncertain:
and so is the underlying physics
• spectral measurements differ
Avalanches
• absolute intensity/efficiency uncertain
- direct measurement is difficult task
- unit: photons emitted per avalanche carrier
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SiPM-Simulator: 3D-Geometry
depleted and sensitive volume
cross section of one cell 390µm
42µm
21µm
geometrical description of a SiPM:
• any number of cells / array layout
• arbitrary
- depleted / undepleted volumes
- avalanche region
- insensitive regions
- …
depleted but non-sensitive volume
2.5µm
non-depleted bulk
avalanche region
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SiPM-Simulator: Treatment of Photons
photon emission in avalanches:
• emission spectrum (free parameter)
use Planck-spectrum
• intensity/efficiency (free parameter)
• isotropic emission
ray-tracing of photons in the SiPM:
• surface reflections
• wavelength dependent absorption
creation of charge carrier
• diffusion (in non-depleted volume)
• drift (in depleted volume)
possible
breakdown of
another cell
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Two Simulated Events
one cell triggered at random (blue)
SiPM with 24x24 cells
simulated device
correlated firing of other cells optical crosstalk
MEPhI / Pulsar from 2003
the excess noise of SiPM
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How to learn about Photon Emission?
1. take an
existing device
+
have a good
relationship to
the producer
3. Repeat
measurement
in the
simulation
MEPhI / Pulsar
4. change free parameters
temperature and intensity
until
measured crosstalk
distributions match
(minimizing χ²)
2. trigger on dark
counts and measure
how often N cells are
fired simultaneous
(crosstalk distribution)
same data but
different binning
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Find Parameters that match
Crosstalk Distribution
T = 4500 K
Total intensity = 1.45x10 -4
photons per avalanche
carrier
not a unique solution for Temperature and Intensity
Residuals
dark counts, which are
not simulated
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Optical Crosstalk Photons:
Photons that cause a breakdown of another SiPM cell
energy distribution of optical crosstalk photons
2000K and 4500K
emission spectra
after adjusting the intensity,
different spectral shapes result in
the same energy distribution of
optical crosstalk photons
Precise knowledge of
spectral shape not
required
reduces the free parameters to one:
the intensity of photon emission between
~1.1 and 1.4 eV
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note the
log-scale
~10µm – 1mm absorption length
= characteristic lengths of the SiPM
strong energy dependent absorption of photons in silicon
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Photon Emission during Avalanches
in Silicon
integrating the emission spectrum 1.1eV …1.4 eV:
photons with energies
between 1.1eV and 1.4eV are emitted with
an efficiency of
3*10 -5 photons per avalanche carrier
result does not depend on the shape of the emission spectrum
the result does depend on:
uncertainties in the geometry of the measured SiPM
homogeneity of avalanche region and SiPM
introduces a systematic uncertainty by a factor of 2
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Conclusions
• SiSi a free SiPM Simulator
– write me: nepomuk@scipp.ucsc.edu
• crosstalk measurements can be used to characterize photon
emission during avalanches
• only photons within a narrow energy interval (1.1eV-1.4eV) cause
optical crosstalk; reason: strong energy dependence of absorption
lengths
• measured intensity of photons between 1.1eV-1.40eV : ~3•10 -5
photons / avalanche electron-hole pair; estimated uncertainty: 2
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χ² -distribution of a scan in:
• temperature of photon spectrum
• intensity of photon spectrum
x
no unique solution of model parameters but
log scale
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4500K
Electron Lifetimes
2000K
Intensity of the photons is reduced by ~30%
if lifetime of the electrons in the non-depleted volume is non-zero
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