Towards a Pulseshape Simulation / Analysis Kevin Kröninger, MPI für Physik GERDA Collaboration...

Towards a Pulseshape Simulation / Analysis

Kevin Kröninger, MPI für Physik

GERDA Collaboration Meeting, DUBNA, 06/27 – 06/29/2005

Outline

Kevin Kröninger, MPI München GERDA Collaboration Meeting DUBNA, 06/27 – 06/29/2005

SIMULATION

Simulation Overview I


Simulation Overview II


• What happens inside the crystal? • Local energy depositions translate into the creation of electron-hole pairs

with Edep : deposited enery

Eeh : 2.95 eV at 80 K in Ge

• Egap = 0.73 eV at 80 K → ¾ of energy loss to phonons

• Corresponds to approximatly 600,000 e/h-pairs at 2 MeV

• Due to bias voltage electrons and holes drift towards electrodes

(direction depends on charge and detector type)

• Charge carriers induce mirror charges at the electrodes

while drifting

<N> = Edep / Eeh

→ SIGNAL

Drifting Field / Bias Voltage I


• In order to move charge carriers an electric field is needed

• Calculate field numerically: • 3-D grid with spatial resolution of 0.5 mm

• Define Dirichlet boundary conditions (voltage, ground)

→ depend on geometry (true coxial? non-true coxial? etc.)

• So far: no depletion regions, zero charge density inside crystal,

no trapping

• Solve Poisson equation ∆φ = 0 inside crystal using a Gauss-Seidel

method with simultaneous overrelaxiation

• Need approximatly 1000 iterations to get stable field

• Electric field calculated as gradient of potential

Drifting Field / Bias Voltage II


Drifting Field / Bias Voltage III


• Example: non-true coaxial n-type detector

Drifting Process


Mirror Charges – Ramo‘s Theorem


• Ramo‘s Theorem: • Induced charge Q on electrode by point-like charge q is given by

• Calculation of weighting field:• Set all space charges to zero potential

• Set electrode under investigation to unit potential

• Ground all other electrodes

• Solve Poisson equation for this setup (use numerical method explained)

Q = - q · φ0(x)Q : induced charge

q : moving pointlike charge

φ0 : weighting potential

Weighting Fields I


x

Weighting Fields II


• Example: true coaxial detector with 6 φ- and 3 z-segments

(Slices in φ showing ρ-z plane)

φ = 0° φ = 90°

φ = 180° φ = 270°

yx

z

Preamp / DAQ


• Drift and mirror charges yield charge as function of time

• Preamp decreases accumulated charge exponentially,

fold in gaussian transfer function with 35 ns width

• DAQ samples with 75 MHz → time window 13.3 ns

• Example:

(signal after drift, preamp and DAQ)(signal after drift)

Setups / Geometries / Eventdisplays I


• Full simulation of non-true coaxial detector

electrode

electrode

core

core

Cha

rge

Time

TimeC

harg

e

Cur

rent

Cur

rent

Setups / Geometries / Eventdisplays II


Setups / Geometries / Eventdisplays III


• Full simulation of true-coxial 18-fold segmented detector

Time

Cha

rge core

electrodes

Analysis Approach

Pulseshape Analysis in MC: Spatial Resolution I


• Is it possible to obtain spatial information of hits from

pulseshapes? In principal YES! • Risetime of signal (10% - 90% amplitude) is correlated with radius

of hit due to different drift times of electrons and holes

• Relative amplitude of neighboring segments is correlated to angle

• Events with more than one hit in detector give ambiguities

• Studied in Monte Carlo with 2-D 6-fold segment detector,

no DAQ, no sampling

Pulseshape Analysis in MC: Spatial Resolution II


• Spatial information of radius and angle

Pulseshape Analysis: SSE/MSE Discrimination I


• Do 0νββ signals differ from background signals? • Background mainly photons that Compton-scatter: multiple hits

in crystal → Multisite events (MSE)• Signal due to electrons with small mean free path: localized energy

deposition → Singlesite events (SSE)• Expect two ‘shoulders‘ at most from SSE and more from MSE

• Count number of shoulders in current• Apply mexican hat filter with integral 0 and different widths (IGEX method)

• Count number of shoulders: ≤2 : SSE

>2 : MSE

Pulseshape Analysis: SSE/MSE Discrimination II


Pulseshape Analysis: SSE/MSE Discrimination III


• Fraction of SSE and MSE for different filter widths

Separation of SSE/MSE in principle possible, combine with information from neighboring segments

Identified as SSE Identified as MSE

SSEMSE

Filter width Filter widthF

ract

ion

of E

vent

s

Fra

ctio

n of

Eve

nts

Data to Monte Carlo Comparison

Data to Monte Carlo Comparison I


• Data from teststand (see X. Liu)

• Later on used for SSE selection

Source

Data to Monte Carlo Comparison II


• Teststand data vs. Monte Carlo

Energy [MeV]Energy [MeV]

Energy [MeV]

• General agreement • No finetuning yet• Next: pulseshapes without any additional selection criteria

Data to Monte Carlo Comparison III


• Comparison of pulseshapesC

harg

e

Cha

rge

Data Monte Carlo

Data to Monte Carlo Comparison IV


• Comparison of pulseshapesC

urre

nt

Cur

rent

Data Monte Carlo

Data to Monte Carlo Comparison V


• Comparison of pulseshapes

Cur

rent

Cha

rge

Data to Monte Carlo Comparison VI



Charge amplitude Current amplitude

Data to Monte Carlo Comparison VII



Risetime [ns]

Conclusion


• First approach towards a simulation of pulseshapes

• Different geometries / fields available

• Package available and linked to MaGe

• Pulseshape analysis to further reduce background via

SSE/MSE identification is feasible → need sampling rate

as large as possible (1 GHz ↔ 1 ns possible?)

• Data to Monte Carlo comparison using teststand data

yields coarse agreement → finetune parameters of simulation

Towards a Pulseshape Simulation / Analysis Kevin Kröninger, MPI für Physik GERDA Collaboration...

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