Stefano Bertoldo COMSOL SIMULATIONS OF HPGe DETECTORS WITH

Stefano Bertoldo COMSOL SIMULATIONS OF HPGe DETECTORS WITH MULTIPLE CONTACTS Stefano Bertoldo 1

GOALS • • Laser annealed junctions Segmentation of junctions with good passivation Accurate simulation of the detector behavior Simulated signals from segments without a prior signal database Planar detectors to reduce computational and material cost. Stefano Bertoldo 2

DRIFT WITHOUT DIFFUSION Approximations: • Electric field not influenced by charges movement • Point charge POISSON EQUATION DRIFT WITH DIFFUSION Approximations: • Einstein relation (diffusion proportional to mobility) • Isotropic diffusion POISSON EQUATION Stefano Bertoldo 3

DRIFT WITHOUT DIFFUSION Details: • Rapid simulation of the electric field and Shockley-Ramo weight fields for all the segments plus the ground. • Rapid simulation of the charge (or current) induced on segments over time. • COMSOL self sustaining script for simplicity. • Stability over various geometries and event spots. Stefano Bertoldo 4

DRIFT WITHOUT DIFFUSION Details: • Rapid simulation of the electric field and Shockley-Ramo weight fields for all the segments plus the ground. • Rapid simulation of the charge (or current) induced on segments over time. • COMSOL self sustaining script for simplicity. • Stability over various geometries and event spots. Stefano Bertoldo 5

SINGLE CONTACT TRIAL MODEL Vd Ns Gnd P-type HPGe → Nb ≈ 1010 cm-3 ? CH 3 OH Passivation → Ns ≈ 109 cm-2 Stefano Bertoldo 6

FINITE ELEMENT MESH Polarization voltage δ = 0. 2 mm Rotation axis Passivation Ground Stefano Bertoldo 7

DEPLETION VOLTAGE Vd Stefano Bertoldo 8

DEPLETION VOLTAGE Vd=2300 V Vd Stefano Bertoldo 9

SURFACE TRAPS (m-2) z (mm) |E| Vd(V/m) x (mm) Stefano Bertoldo 10

CHARGE TRAJECTORIES 2300 V y 0 (mm) Electrons Holes GND Stefano Bertoldo 11

INDUCED CURRENT y 0 (mm) Stefano Bertoldo 12

INDUCED CHARGE y 0 (mm) Stefano Bertoldo 13

DRIFT WITH DIFFUSION MODEL Longitudinal diffusion Trasversal diffusion Electric field gradient T=95 K Prolated electron cloud and oblated hole cloud for p-type detectors Diffusion negligible within the charge collection time Pulse shape contribution -Numerical instabilities -Long computational times -Computationally expensive USE OF DRIFT WITHOUT DIFFUSION MODEL Stefano Bertoldo 14

DRIFT WITH DIFFUSION MODEL ELECTRONS Stefano Bertoldo HOLES 15

EXPERIMENTAL SIGNALS Model time x 2 Stefano Bertoldo 16

SEGMENTED p-TYPE DETECTOR 10 mm • Laser annealed junction • Methanol passivation • Optimizing the detector geometry. 10 mm δ ξ δ 2. 5 mm 1. 5 mm GUARD RING C 1 C 2 GUARD RING y x Stefano Bertoldo 17

GEOMETRY AND MESH 2 D simulation → central zone approximation 10 mm δc = 2 µm δb = 100 µm 10 mm Ground Passivation Ground Polarization voltage Stefano Bertoldo 18

DEPLETION VOLTAGE Vd=23 V Vd Stefano Bertoldo 19

REAL AND WEIGHTING POTENTIALS REAL POTENTIAL V Shockley-Ramo Theorem Weighting potentials FIRST CONTACT WEIGHTING POTENTIAL V SECOND CONTACT WEIGHTING POTENTIAL Stefano Bertoldo 20

CHARGE TRAJECTORIES GND GND y 0=1. 4 mm Electrons Holes 25 V x 0 (mm) Stefano Bertoldo 21

1 st CONTACT SIGNALS y 0=1. 4 mm 1 st 2 nd x 0 (mm) Stefano Bertoldo 22

2 nd CONTACT SIGNALS y 0=1. 4 mm 1 st 2 nd ← Cusp at (38 ns, -0. 3) x 0 (mm) Stefano Bertoldo 23

CHARGE TRAJECTORIES Electrons Holes x 0=5 mm 1 st 2 nd Stefano Bertoldo 24

1 st CONTACT SIGNALS 1 st 2 nd y 0 (mm) Stefano Bertoldo 25

2 nd CONTACT SIGNALS 1 st 2 nd y 0 (mm) Stefano Bertoldo 26

GAP DISTANCE SWEEP Guard ring 2 nd GAP 1 st Guard ring (5 mm, 1 mm) 0. 2 1. 8 Gap (mm) 0 V Stefano Bertoldo 25 27

CHARGE TRAJECTORIES GAP y 0=1 mm x 0=5 mm Electrons Holes 25 V Gap (mm) Stefano Bertoldo 28

1 st CONTACT SIGNALS 1 st Stefano Bertoldo 2 nd 29

2 nd CONTACT SIGNALS 1 st Stefano Bertoldo 2 nd 30

FUTURE DEVELOPEMENT • Model refinement: recombination and generation processes, surface conductivity, trap density calibration… • New passivation techniques • New segmentation geometries Rescaling well designed detectors to higher dimensions. Developing strip detectors: Stefano Bertoldo 31

Thank you for the attention! Stefano Bertoldo 32

Stefano Bertoldo COMSOL SIMULATIONS OF HPGe DETECTORS WITH MULTIPLE CONTACTS Stefano Bertoldo 33

DETECTOR PROCESSING Laser annealed junction Gold contact Photoresist lithography Chemical etching & passivation Stefano Bertoldo 34