1. TCAD Simulations of Radiation Damage Effects at High Fluences in Silicon Detectors with Sentaurus TCAD D. Passeri(1,2), F. Moscatelli(2,3), A. Morozzi(1,2), G.M. Bilei(2)
(1) Dipartimento di Ingegneria - Università di Perugia, Italy (2) Istituto Nazionale Fisica Nucleare - Sezione di Perugia, Italy
(3) IMM CNR Bologna, Italy

2. Outline Introduction: background.
TCAD radiation damage models: discussion.
Si bulk (p-type) substrate radiation damage model enhancement.
Simulation results and comparison with experimental data.
Conclusions and Future plans.

3. “University of Perugia” model
Hierarchical approach based on increasing number of deep-level recombination centres / trap states.
Comprehensive modelling of device behaviour of with fluence:
- depletion voltage, leakage current (a), “double peak” shaped electric field, charge collection efficiency,…
Meaningful and physically sounded parametrization.
Three levels with donor removal and increased introduction rate (to cope with direct inter-defect charge exchange – numerically overwhelmed effect).
n type and p type substrate
OK for fluences up to 1015 cm-2 1 MeV neutrons.

4. “University of Perugia” model (2)
More than 20 specific journal papers on TCAD radiation damage modelling …
[1] D. Passeri, P. Ciampolini, G.M. Bilei, and F. Moscatelli, Comprehensive Modeling of Bulk-Damage Effects in Silicon Radiation Detectors, IEEE Trans. on Nuclear Science, vol. 48, no. 5, October 2001.
[2] M. Petasecca, F. Moscatelli, D. Passeri, and G. U. Pignatel, Numerical Simulation of Radiation Damage Effects in p- Type and n-Type FZ Silicon Detectors, IEEE Trans. on Nuclear Science, vol. 53, no. 5, October 2006. 4

5. Old “University of Perugia” model
Hierarchical approach based on increasing number of deep-level recombination centres / trap states.
Comprehensive modelling of device behaviour with fluence:
- depletion voltage, leakage current (a), “double peak” shaped electric field, charge collection efficiency
Meaningful and physically sounded parametrization
Three levels with donor removal and increased introduction rate (to cope with direct inter-defect charge exchange – numerically overwhelmed effect).
n type and p type substrate
OK for fluences up to up to 1015 cm-2 1 MeV neutrons.

6. Old “University of Perugia” model
Hierarchical approach based on increasing number of deep-level recombination centres / trap states.
Comprehensive modelling of device behaviour with fluence:
- depletion voltage, leakage current (a), “double peak” shaped electric field, charge collection efficiency
Meaningful and physically sounded parametrization
Three levels with donor removal and increased introduction rate (to cope with direct inter-defect charge exchange – numerically overwhelmed effect).
n type and p type substrate
Ok for fluences up to 1015 cm-2 1 MeV neutrons.
A lot of work has been done since then (see TCAD model review).
Commercial TCAD tools (e.g. Synopsys Sentaurus, Silvaco Atlas).

7. TCAD radiation damage models (2)
Pennicard et al., Simulations of radiation-damaged 3D detectors for the Super-LHC, NIM A 592 (2008) 16–25 .
- 3 levels, increased n, p.
E. Verbitskaya et al., Operational voltage of silicon heavily irradiated strip detectors utilizing avalanche multiplication effect, JINST 7 C02061, 2012.
- 2 levels, avalanche multiplication, 1D (“analytical”) approach.
Dehli University [R. Dalal et al., Vertex , 23rd RD50 CERN, Nov. 2013]
- 5 levels + QF / 2 levels + QF + Qit.
RD50 Collaboration [T. Peltola PSD2014 / RESMDD2014]
- defect models used in Synopsys Sentaurus package tuned by R. Eber from [V. Eremin et al., Avalanche effect in Si heavily irradiated detectors: Physical model and perspectives for application, NIM A 658 (2011)] for Φeq=1.0 1015 cm-2 at fixed T=253 K;
- 3-level model within 2 μm of device surface + proton model in bulk.
...

8. New “University of Perugia” model

9. The simulated structure
p-type
ND = 31012 cm-3
 = 4 kohmcm
depth = 300mm
p+ ohmic contact layer effects…

10. The depletion voltage
The procedure used for the extraction of VDEP was the standard linear fitting cross point in the logC-logV (T=300K).
The resulting depletion voltages show a satisfactory agreement between simulation findings and experimental data [1].
[1] M. Lozano et al., Comparison of radiation hardness of P-in-N, N-in-N, and N-in-P silicon pad detectors, IEEE Trans. Nucl. Sci. 52 (5) (2005) 1468

11. The leakage current
The model predicts the increase of the leakage current with the fluence and the saturation of the current at full depletion voltage.
The calculated damage constant a = 3.710-17 A/cm is in good agreement with experimental data (4.0±0.1) 10-17 A/cm [2].
[2] M. Moll, Radiation damage in silicon particle detectors, Ph.D. Thesis, University of Hamburg, Hamburg, Germany (1999).

12. The electric field
The peculiar two-peak shape electric field profile at high fluences is reproduced.
The effect depends on the proper parametrization of the hole capture cross-sections for the VVV level (e.g. substrate effective doping variations and potential barrier at the p+ side) .

13. Charge generation
Heavy Ion charge generation <-> Minimum Ionizing Particle
The CCE has been evaluated by simulating a MIP crossing.
80 e/h pairs per µm in silicon.
The time varying device behavior was simulated (transient analysis), and the current at the readout electrode was integrated over 20 ns, after subtracting the leakage current, to find the total collected charge.

14. Charge collection: the stimulus (MIP)…
Time and space discretization of the generated charge…
Numerical issues in charge generation -> charge collection evaluation.
Poor time discretization
Proper time discretization
Good Landau shape
“Extra” time discretization
Pure Gaussian shape

15. Charge collection at T=300K, VBIAS=900V
The charge collection behaviour at T=300K of a 280 µm-thick n-in-p strip detector was simulated in order to match the conditions used in actual measurements, e.g. [3].
Experimental
Simulated
[3] M. Lozano et al., Comparison of radiation hardness of P-in-N, N-in-N, and N-in-P silicon pad detectors, IEEE Trans. Nucl. Sci. 52 (5) (2005) 1468

16. Charge collection at T=248K, VBIAS=500V
Charge collection behaviour at T=248 K of a 300 µm n-in-p [4].
VBIAS = 500V
[4] Affolder et al., Collected charge of planar silicon detectors after pion and proton irradiations up to 2.2x1016 neq cm2 " NIM A, Vol. 623 (2010), pp

17. Charge collection at T=248K, VBIAS=900V
Charge collection behaviour at T=248 K of a 300 µm n-in-p [4].
The effect of the avalanche generation at high fluences is pointed out.
VBIAS = 900V
[4] Affolder et al., Collected charge of planar silicon detectors after pion and proton irradiations up to 2.2x1016 neq cm2 " NIM A, Vol. 623 (2010), pp

18. Avalanche generation
[5] A. G. Chynoweth, Ionization Rates for Electrons and Holes in Silicon, Physical Review, vol. 109, no. 5, pp. 1537–1540, 1958.

19. Avalanche models

20. Avalanche model comparison
Fluence
2×1016
CCE (e)
4000
VanOverstraeten (def)
3900
Okuto
3800
Okuto mod
a=0.8
b=0.5
3863
a=2.0
b=1.0
3940
a=5.0
b=2.0
3972
Default mod
a=1.2106
3971
a=3.0106
3933
Lackner
3825
No Avalanche
2800

21. Charge collection at T=248 K, VBIAS=900V
VBIAS = 900V
[4] Affolder et al., Collected charge of planar silicon detectors after pion and proton irradiations up to 2.2x1016 neq cm2 " NIM A, Vol. 623 (2010), pp

22. Conclusions
Si bulk radiation damage modelling scheme, suitable for commercial TCAD tools (e.g. Synopsys Sentaurus).
Predictive capabilities extended to SLHC radiation damage levels (e.g. fluences > 1.0×1016 cm-2 1 MeV neutrons).
Further validation with experimental data comparisons.
Effect of the interface (Si/SiO2) trap states / charges.
Required parameters in TCAD
oxide-charge density interface
trap density distribution
type: acceptor or donor
Dedicated structures and measurements to extract these parameters
Application to the optimization of pixel detectors (3D detectors, 2D planar detectors, …)

23. Backup

24. Charge generation (2)
Minimum Ionizing Particle -> Heavy Ion charge generation.

25. Once upon a time... (1996)
Numerical analysis and physical modelling of semiconductor devices.
Modelling of the interaction between ionizing particle / silicon substrate compatible with BIM simulation scheme.
Grad can be distributed in time and space according to the numerical spatial and time discretization algorithms (HFIELDS UniBO)… 25

26. Radiation Damage Modeling
Numerical modelling of radiation damage effects in semiconductor devices.
Deep-level recombination centres / traps radiation induced.
Explicit contribution of the trapped charges to the charge density (modified Poisson equation):
Continuity equation for both free and trapped carriers: 26

27. TCAD radiation damage models (2)

28. Charge collection: electrons
Electron drift timeline (Ntrap = 1E12 cm-3, Vbias = 100V).
Fast collection by (positively) biased back contact. 28

29. Charge collection: holes
Hole drift timeline (Ntrap = 1E12 cm-3, Vbias = 100V).
Relatively slow collection by (grounded) top contact. 29

30. Trap effects on charge collection
Electron drift timeline (Ntrap = 1E14 cm-3, Vbias = 100V).
Effects of traps on electron concentrations -> higher density/recombination -> lower charge collection! 30

31. Electric filed profile (preliminar)
Electric field profile with 0.6 µm of oxide and fixed oxide charge=3x1012 cm-2