Nepomuk Otte 1

On the Efficiency of Photon Emission during Avalanches in Silicon

A. Nepomuk Otte

University of California in Santa CruzSanta Cruz Institute for Particle Physics

paying the conference fee

photon emission in avalanches(Sciacca, 2003)

2007 JINST TH 003work published in

wasMax-Planck-Institut für Physik, Munich

paying the hotel

supported by the American Astronomical Societypaying the flight ticket

Nepomuk Otte 2

Outline

• SiSi the SiPM Simulator

One example application of SiSi:

characterize photon emission, which results in optical crosstalk

Nepomuk Otte 3

SiSi*: The SiPM Simulator

*Elisabeth ”Sis(s)i” von Wittelsbach theempress consort of Emperor Franz Josephof Austria. She was born 1837 in Munich,Bavaria and murdered 1898 in Geneva,Switzerland

It is free!

nepomuk@scipp.ucsc.edu

send me an e-mail:

to make it most affordable:

a 3D Monte Carlo simulation package of SiPMfor the community

Nepomuk Otte 4

Study Photon Emission in Avalanches

The emission spectrum is uncertain:and so is the underlying physics

• spectral measurements differ

• absolute intensity/efficiency uncertain- direct measurement is difficult task- unit: photons emitted per avalanche carrier

An application of SiSi:

Why?

Nepomuk Otte 5

SiPM-Simulator: 3D-Geometry

geometrical description of a SiPM:• any number of cells / array layout • arbitrary

- depleted / undepleted volumes- avalanche region- insensitive regions- …

cross section of one cell390µm

42µm

21µm

2.5µm

non-depleted bulk

depleted and sensitive volume

avalanche region

depleted but non-sensitive volume

Nepomuk Otte 6

SiPM-Simulator: Treatment of Photons

ray-tracing of photons in the SiPM:

• surface reflections • wavelength dependent absorption

photon emission in avalanches:

• emission spectrum (free parameter)use Planck-spectrum

• intensity/efficiency (free parameter)• isotropic emission

creation of charge carrier

• diffusion (in non-depleted volume)

• drift (in depleted volume)

possible breakdown of another cell

Nepomuk Otte 7

Two Simulated Events

one cell triggered at random (blue)

SiPM with 24x24 cells

correlated firing of other cells optical crosstalkthe excess noise of SiPM

simulated deviceMEPhI / Pulsar from 2003

Nepomuk Otte 8

How to learn about Photon Emission?

1. take an existing device

+have a good relationship to the producer

2. trigger on dark counts and measure how often N cells are fired simultaneous(crosstalk distribution)

4. change free parameters temperature and intensity

until measured crosstalk distributions match

(minimizing χ²)

3. Repeat measurement

in the simulation

same data but different binning

MEPhI / Pulsar

Nepomuk Otte 9

Find Parameters that match

T = 4500 KTotal intensity = 1.45x10-4

photons per avalanche carrier

ResidualsCrosstalk Distribution

dark counts, which are not simulated

not a unique solution for Temperature and Intensity

Nepomuk Otte 10

Optical Crosstalk Photons: Photons that cause a breakdown of another SiPM cell

Precise knowledge of spectral shape not

required

after adjusting the intensity,different spectral shapes result in the same energy distribution of

optical crosstalk photons

2000K and 4500Kemission spectra

energy distribution of optical crosstalk photons

reduces the free parameters to one:the intensity of photon emission between

~1.1 and 1.4 eV

Nepomuk Otte 11

strong energy dependent absorption of photons in silicon

~10µm – 1mm absorption length= characteristic lengths of the SiPM

note the log-scale

Nepomuk Otte 12

Photon Emission during Avalanches in Silicon

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 SiPMhomogeneity of avalanche region and SiPM

introduces a systematic uncertainty by a factor of 2

integrating the emission spectrum 1.1eV …1.4 eV:

Nepomuk Otte 13

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

Nepomuk Otte 14

χ² -distribution of a scan in:• temperature of photon spectrum• intensity of photon spectrum

no unique solution of model parameters but

log scale

x

Nepomuk Otte 15

Electron Lifetimes

4500K 2000K

Intensity of the photons is reduced by ~30% if lifetime of the electrons in the non-depleted volume is non-zero