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BEGe pulse shape simulation
Matteo Agostini, Alberto Garfagnini, Calin A. Ur,
Enrico Bellotti, Assunta Di Vacri, Luciano Pandola
September 30th, 2009
Universita di Padova
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Outline
Outline
1 The simulationI. The dynamics of electrons and photonsII. Signals induced by the charge motion inside the detectorIII. The total charge pulse and the preamplifier response
2 Validation of the simulation
3 MSE and SSE simulated signals
4 Summary
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The simulation
The simulation structure
I. The dynamics of electrons and photons (MaGe)
<– the production processes of charged particles and photons–> the position and the type of the interaction with the germanium crystal–> the energy loss in each interaction
II. Signals induced by the charge motion inside the detector (MGS)
<– interaction coordinates–> trajectories–> signal induced on the electrodes
III. The total charge pulse and the preamplifier response
<– the energy loss in each interaction<– the signals induced by each interaction<– the preamplifier transfer function (PTF)–> the total charge pulse convolved with the PTF
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The simulation
II. Signals induced by the charge motion inside thedetector - Trajectories
Mobility Model
vh = µh(r, E) · E ve = µe (r, E) · E
– Electron mobility [L. Mihailescu]– Hole mobility [B. Brynell]
Field Computation
∇2φ(r) = −
ρ(r)
ε→ E(r) = −∇ (ϕ(r))
– cathode at 0 V, anode at 3500 V– vacuum grounded chamber– detector fully depleted: ρ(r) = eNA(r)
Trajectory Computation
r(t + ∆t) = r(t) + v(r(t)) · ∆t
where ∆t = 1 ns
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The simulation
II. Signals induced by the charge motion inside thedetector - Trajectories
Mobility Model
vh = µh(r, E) · E ve = µe (r, E) · E
– Electron mobility [L. Mihailescu]– Hole mobility [B. Brynell]
Field Computation
∇2φ(r) = −
ρ(r)
ε→ E(r) = −∇ (ϕ(r))
– cathode at 0 V, anode at 3500 V– vacuum grounded chamber– detector fully depleted: ρ(r) = eNA(r)
Trajectory Computation
r(t + ∆t) = r(t) + v(r(t)) · ∆t
where ∆t = 1 ns
4 / 11BEGe pulse shape simulation
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The simulation
II. Signals induced by the charge motion inside thedetector - Trajectories
Mobility Model
vh = µh(r, E) · E ve = µe (r, E) · E
– Electron mobility [L. Mihailescu]– Hole mobility [B. Brynell]
Field Computation
∇2φ(r) = −
ρ(r)
ε→ E(r) = −∇ (ϕ(r))
– cathode at 0 V, anode at 3500 V– vacuum grounded chamber– detector fully depleted: ρ(r) = eNA(r)
Trajectory Computation
r(t + ∆t) = r(t) + v(r(t)) · ∆t
where ∆t = 1 ns
holeselectronscathode
anode
40
35
30
25
20
15
10
8070
6050
4030
2010
8070
6050
4030
2010
4 / 11BEGe pulse shape simulation
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The simulation
II. Signals induced by the charge motion inside thedetector - Signal induced on the electrodes
Signal induced on a electrode
Shockley-Ramo Theorem :
Q(t) = −qφw (r(t))
where φw (r(t)) is the weighting potential.
The weighting potential is defined as the electric potential calculated when the considered
electrode is kept at a unit potential, all other electrodes are grounded and all charges inside the
device are removed.
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The simulation
III. The total charge pulse and the preamplifierresponse
Preamplifier transfer function
the averaged output pulses is differentiatedby simply shifting the signal by one sampleand subtracting it from the original signal
Total charge pulse and convolutionwith the PTF
– the total charge pulse of a SSE is thesum of the electron pulse and the holepulse– the total charge is convolved with theexperimental transfer function
MSE
the total charge pulse of a MSE is the sumof the SSE signals weighted by the energytransfered in each interaction
pre outputpre input
time [ns]
adc
counts
36000032000028000024000020000016000012000080000
25000
20000
15000
10000
5000
0
transfer functionpreamplifier output
time [ns]
adc
counts
12001000800600400
12000
10000
8000
6000
4000
2000
0
6 / 11BEGe pulse shape simulation
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The simulation
III. The total charge pulse and the preamplifierresponse
Preamplifier transfer function
the averaged output pulses is differentiatedby simply shifting the signal by one sampleand subtracting it from the original signal
Total charge pulse and convolutionwith the PTF
– the total charge pulse of a SSE is thesum of the electron pulse and the holepulse– the total charge is convolved with theexperimental transfer function
MSE
the total charge pulse of a MSE is the sumof the SSE signals weighted by the energytransfered in each interaction
e pulseh pulsemgsmgs + pre
time [s]
adc
counts
4.5e-074e-073.5e-073e-072.5e-072e-071.5e-071e-075e-080
0.06
0.05
0.04
0.03
0.02
0.01
0
-0.01
6 / 11BEGe pulse shape simulation
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The simulation
III. The total charge pulse and the preamplifierresponse
Preamplifier transfer function
the averaged output pulses is differentiatedby simply shifting the signal by one sampleand subtracting it from the original signal
Total charge pulse and convolutionwith the PTF
– the total charge pulse of a SSE is thesum of the electron pulse and the holepulse– the total charge is convolved with theexperimental transfer function
MSE
the total charge pulse of a MSE is the sumof the SSE signals weighted by the energytransfered in each interaction
0
200
400
600
800
1000
1e-07 2e-07 3e-07 4e-07 5e-07 6e-07
adc
counts
[a.u
.]
time [s]
0.7 MeV SSE (46,34,26)1.3 MeV SSE (28,34,16)2.0 MeV MSE
6 / 11BEGe pulse shape simulation
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Validation of the simulation
The validation measurements and the Averagingalgorithm
The validation was carried out by comparing directly the simulated and theexperimental signals:
241Am colimated source ⇒ well localized events close to the detector surface;
∼ 600 s acquisitions for each position
averaging up the experimental signals ⇒ very low noise
The averaging algorithm steps:
1 the experimental signal(sampled at 10 ns) is resampledat 1 ns interpolating theoriginal points with a linearfunction;
2 the resampled signal is fittedwith the average in order toobtain the best possible timealignment;
3 if the average rms is minorthan the threshold value, theresampled and shifted signal isaccepted in the average.
experimental pulseaverage pulsesimulated pulse
time [s]
adc
counts
1e-068e-076e-074e-072e-070-2e-07
500
450
400
350
300
250
200
150
100
50
0
-50
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Validation of the simulation
Radial scanning
–> 241Am source –> 2 mm collimator –> 600 s acquisitions for each position
cathodeanode
40
35
30
25
20
15
10
8070
6050
4030
2010
8070605040302010
exp data35 mm30 mm25 mm20 mm15 mm10 mm0 mm
time [s]
adc
counts
8e-077e-076e-075e-074e-073e-072e-071e-07
500
400
300
200
100
0
The holes are dragged to the center of the detector and then drift to the p+ contact
with a common trajectory
⇒ Significant differences are expected to occur only in the first rising part of the
pulses
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Validation of the simulation
Circular Scanning
–> 241Am source –> 1 mm collimator –> 500 s acquisitions for each position
We study the rise time as a function of the angle.–> To observe variations we used the rise time between 1% and 90%
experimental datasimulated data
angle [deg]
rise
tim
eva
riat
ions
[ns]
36031527022518013590450
30
20
10
0
-10
-20
experimental datasimulated data
simulated data + shift
rise time [ns]
rise
tim
e[n
s]
8006004002000200400600800
1000
800
600
400
200
0
200
400
600
800
Although the experimental data show a behaviour coherent with the simulation,
the agreement is only qualitative.
⇒ the result is remarkable taking into account the problems related to the
identification of the time corresponding to the 1% of the maximum amplitude
9 / 11BEGe pulse shape simulation
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MSE and SSE simulated signals
MSE vs SSE
holeselectronscathode
anode
40
35
30
25
20
15
10
8070605040302010
80 70 60 50 40 30 20 10
SSE → 2 MeVMSE → 0.5 MeV+0.4 MeV+1.1 MeV
-20
-15
-10
-5
0
5
10
0 1e-07 2e-07 3e-07 4e-07 5e-07 6e-07 7e-07 8e-07 9e-07
adc
counts
[a.u
.]
time [s]
Second Derivate
0
10
20
30
40
50
60
70
80
90
adc
counts
[a.u
.]
First Derivate
0
200
400
600
800
1000
1200
1400
adc
counts
[a.u
.]
0.5 MeV SSE (66,34,26)0.4 MeV SSE (46,34,26)1.1 MeV SSE (28,34,16)2.0 MeV MSE2.0 MeV SSE (28,34,16)
10 / 11BEGe pulse shape simulation
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Summary
Summary
Results:
The simulated data show a good agreement with the average experimentalsignals;
we have achieved a deeper insight into the peculiar shapes of the BEGedetector signals and the time dependence of the pulses from the interactionposition;
a preliminary study of the BEGe pulse shape discrimination performance wascarried out by using the simulation providing excellent results.
Future works:
fully validate the simulation by performing a inner scanning of the detector;
include in the MaGe simulation a library of the simulated pulses;
investigate the BEGe geometry by studying which are the geometryparameters that provide the most accurate pulse shapes.
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Summary
BEGe detector
71 mm
p+ contact (read–out electrode)
n+ contact
p-type Ge
3500 V
0 V
groove
31
mm
Al endcapwindow
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Summary
DAQ systems
PRE
BEGe
N2
AMPLIFIER
Ortec 672
ETHERNIM
DIGITIZER
N1728B
PC
GAMMAVISION
PC
TUC software
processing
PULSES
Digital signal
(Gast MWD)
SPECTRA
ENERGY
93 Ω
50 Ω
ADC
14 / 11BEGe pulse shape simulation
Summary
Characterization measurements - Resolution
1332125011731100
105
104
103
102
101
digitalanalogue
Energy [keV]
counts
2500200015001000500
106
105
104
103
102
101
Energy [keV] Analogue DAQ system Digital DAQ systempeak counts FWHM [keV] peak counts FWHM [keV]
1173 259899 (510) 1.529 (0.002) 224857 (506) 1.520 (0.002)1332 225023 (474) 1.617 (0.002) 200137 (518) 1.607 (0.003)
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Summary
Characterization measurements - Linearity
digital electronicsanalogue electronics
Energy [keV]
chan
nel
300025002000150010005000
10000900080007000600050004000300020001000
0
digital electronicsanalogue electronics
Energy [keV]
300025002000150010005000
Energy [keV]
Ener
gy
[keV
]
25002000150010005000
1
0.5
0
-0.5
-1
16 / 11BEGe pulse shape simulation
Summary
Characterization measurements - Preamplifier
HV
Detector
Qin
A
Cf
Rf
V0
stage 1:
integrator amplifier
stage 2:
pole zero network
stage 3:
output buffer
T.P.
93 Ω
50 Ω
Energy
Timinig
17 / 11BEGe pulse shape simulation
Summary
Characterization measurements - Preamplifier noise
HV
Detector
Cf
Rf
stage 1:
integrator amplifier
in
νn
18 / 11BEGe pulse shape simulation
Summary
Characterization measurements - Preamplifier noise
corner frequency
Frequency [kHz]
Pow
er[a
rbitra
ryunits]
10000100010010
9
8
7
6
5
4
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Summary
Validation of the MaGe simulation - Absorption
position [mm]
counts
6040200-20-40-60
0.001
0.0008
0.0006
0.0004
0.0002
0
experimental dataMC
position [mm]
counts
20151050-5-10-15-20
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
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Summary
Validation of the MaGe simulation - Bariumspectrum
MC + backgroundexperimental data
Energy [keV]
counts
450400350300250
103
102
101
100
10−1
10−2
10−3
Energy [keV]
counts
1 · 1034 · 1022 · 1021 · 102
103
102
101
100
10−1
10−2
21 / 11BEGe pulse shape simulation