1. Towards pulse shape calculation and analysis for the GERDA experiment Kevin Kröninger, MPI für Physik International School of Nuclear Physics, Erice 2005 Introduction GERDA Calculation of Pulseshapes Pulse shape Analysis Conclusion

2. The GERDA Experiment Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Aim: Observation of neutrinoless double beta decay with a sensitivity of 50 meV → Talk by Stefan Schönert Idea: Germanium as source ( 76 Ge) and detector Use bare crystals in liquid N or Ar Key: Background reduction (to ≤ 10 -3 counts/kg/keV/y) Setup: 21 detectors arranged in a 3x7 hexagonal pattern Each crystal weighs approx. 2.4 kg (86% enriched in 76 Ge) Cryogenic vessel inside water tank (neutron and gamma shield) Gran Sasso underground Laboratory (cosmic ray shield)

3. Germanium Crystals Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Proposed: n-type detectors with lithographically made segmentation Detector segmentation: 6 φ x 3 z = 18 segments per detector Crystal setup (strings) GERmanium Detector Array Anti-coincidence requirement between segments discriminates multiple scattering from local energy deposition Further information can be gained from the pulse shapes 8 cm

4. Background Sources Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Signal: Background ( 60 Co): T 1/2 =10 25 y Monte Carlo first year statistics Background sources: Cosmogenically produced 68 Ge and 60 Co U/Th contamination, 210 Pb on surface Neutrons (rad. decay, cosmic muons) Signatures: Signal has two electrons in final state → local energy deposition (SSE) Background sources mostly gammas with energies larger than 2 MeV Compton scattering dominant interaction → multiple scattering (MSE)

5. Development of electrical Signal I Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 = E dep / E eh Δφ = ρ/ε r [cm] E [V/cm] Holes Electrons Local energy deposition Signal development: Local energy deposition translates into creation of electron-hole pairs with E dep : deposited energy E eh : 2.95 eV at 80 K in Ge Electrical fields causes electrons and holes to separate and drift towards electrodes Drift time is O(400 ns) Charge carriers induce charges on electrodes during their drift Fields are calculated numerically solving Poisson’s equation ε : dielectric constant ρ : charge density (HPGe ~ 0.5·10 10 cm -3 )

6. Development of electrical Signal II Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Ramo’s Theorem: Induced charge Q on electrode by point-like charge q is given by Charge [a.u.] Time [ns] Q = - q · φ 0 (x) Q : induced charge q : moving pointlike charge φ 0 : weighting potential Calculation of weighting field: Set all space charges to zero potential Set electrode under investigation to unit potential Ground all other electrodes 1 2 1 2 Mirror charge trajectory

7. Development of electrical Signal III Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Full simulation of 18-fold segmented detector Time Charge Mirror charges Signal electrode

8. Pulse Shape Analysis I Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Information from pulse shapes used for SSE/MSE discrimination Gamma ray tracking (e.g. AGATA experiment) Position information from risetime and asymmetries of neighboring segments Radius [cm] Risetime [ns] Z [cm] Asymmetry top-bottom Angle [°] Asymmetry left-right

9. Pulse Shape Analysis II Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Analysis approach: Create library of well-known pulse shapes (position, energy) and compare to data Library pulse shapes calculated with reference points from data Define χ 2 : t k : time interval x : pulseshape x j : j th library pulseshape σ : resolution Sum over all electrodes s (for segmented detectors) and time intervals k Pick the library pulse j with the lowest χ j 2 Advantage: make use of all avail. information (compared to single value analysis) Essential: calculation has to be done for every crystal, cross-checks important ~

10. Pulse Shape Analysis III Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Resolution with library pulse shapes Δr [cm] dN/dΔr Δz [cm] dN/dΔz Example: SSE in unsegmented non-true coaxial n-type detector Resolution in z due to inhomogenous field in z (cap) No resolution in φ due to missing segmentation Library: steps of 0.5 cm in r and z resolution ~ 0.4 cm

11. Pulse Shape Analysis IV Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 SSE/MSE discrimination: 12% signal loss 50% background reduction log 10 Toy MC SSE/MSE events in unsegmented non-true coaxial n-type detector Estimate factor 2 for background suppression (segmentation not taken into account)

12. Teststands for Germanium Crystals Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Teststands at the MPI Munich are under construction: Test bare crystals in liquid nitrogen for handling, robustness, resolution (n-type and p-type) Investigation of detector properties such as dead layers, segmentation, crystal orientation effects, etc. in vacuum teststand Compare calculations/simulations with data p-type Liquid N2 teststand

13. Measurement of Crystal Orientation Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Additional effect: crystal orientation w.r.t device changes drift velocity Phenomenological model (Reik and Risken, 1950s) → anisotropic conductivity Effect included in charge transport calculation E [V/cm] Angle [°] Risetime [ns]

14. Conclusion / Summary Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Development of pulse shape calculations in progress, data/MC comparison on qualitative level ongoing SSE/MSE discrimination technique in place, data/MC comparison is to follow. Estimated factor of 2 (~4 with segmentation) additional background suppression for photons (main background) Estimated factor of ~5 for alpha particles on surface Teststands aimed at the understanding of detector properties and pulse shapes are under construction at the MPI Munich Outlook: Apply library analysis on true-coaxial detector with segmentation Include two-hit hypothesis for tracking and SSE/MSE discrimination

15. Backup I Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Bandstructure of germanium

16. Backup II Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Anisotropy effects Electron velocity [cm/s] E [V/cm]Angle (z, x-y-plane) [°] Angle (v, E field) [°]

17. Backup III Kevin Kröninger, MPI München Erice Summer School 2005 Erice, 16.09. – 24.09.2005 Matching of pulseshapes