1. Radiation Damage in Sentaurus TCAD
David Pennicard – University of Glasgow

2. Overview Introduction to trap models
Radiation damage effects and defects
P-type damage model
Some example simulations
Sentaurus Device command file

3. Radiation damage introduction
High-energy particle displaces silicon atom from a lattice site
Results in a vacancy and an interstitial
Atom can have enough energy to displace more atoms
After damage is caused, most vacancy-interstitial pairs recombine
Left with more stable defect clusters, e.g. divacancy (V2)
Defect clusters affected by annealing conditions & impurities in the silicon
Defect clusters give extra energy states (traps) in bandgap
Increased leakage current
Increased charge in depletion region (increase in effective p-type doping)
Trapping of free carriers
Can simulate this in Sentaurus Device by modelling behaviour of trap levels directly
NB – when dealing with different types and energies of particle irradiation, scale fluence (particles / cm2) by non-ionizing energy loss. Standard is 1MeV neutrons.
See M. Moll thesis, Hamburg 1999

4. Traps in Sentaurus Device
A statement added to the Physics section can describe the traps:
Parameters
Acceptor: trap has –ve charge when occupied by electron, 0 charge when occupied by hole. (Donor has +ve charge when occupied by hole)
Level: specifies how we describe energy level. Here, we give the energy below the conduction band. EnergyMid gives the energy difference
Concentration: given in cm-3
Electron cross-section: proportional to probability of electron moving between trap and conduction band - σe
Hole cross-section: likewise, proportional to chance of carrier moving between valence band and trap level - σp
Physics (material="Silicon") {
Traps (
(Acceptor Level fromCondBand Conc=1.613e15 EnergyMid=0.42
eXsection=9.5E-15 hXsection=9.5E-14) ) }
Electron cross-section – proportional to empty trap capturing electron from conduction band
Hole – prob of trap containing electron capturing hole from valence band.
But, what about other processes? Electron from trap to conduction band, hole from trap to valence band?

5. Traps in Sentaurus Device
For each trap level, Sentaurus simulates:
Proportion of trap states occupied by electrons and holes
NB – “not filled by electron”=“occupied by hole”
This affects charge distribution, and so has to be included in Poisson equations
Rate of trapping / emission between conduction band and trap, and between valence band and trap
These then have to be included in the carrier continuity equations
Poisson
Electron continuity
Hole continuity

6. Increase in reverse leakage current
Leakage current increases with fluence, independent of substrate type
Leakage current reduced by annealing
α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis)
Also, temperature dependence. α normally given for 20C

7. Increase in leakage current
2 transitions involved:
Electron from valence band moves to empty trap, leaving a hole
Electron in trap moves to conduction band, giving conduction electron
Then, electron and hole are swept out of depletion region by field, avoiding recombination
Rate of production limited by less frequent step (larger energy difference)
Trap above midgap limited by rate of valence band->trap
Traps below midgap likewise limited by trap->conduction band
Rate drops rapidly with distance of trap from midgap
Deep level traps dominate Ec
Free electron produced
Trap
Emid
Hole produced Ev

8. Change in effective doping concentration
Effective p-type doping increases (giving type inversion in n-type silicon)
Dependent on material, particularly oxygen content and radiation type
for p-type (n-type also has “donor removal” effect)
My models match p-type Float Zone irradiated with protons

9. Change in effective doping concentration
Additionally, have both “beneficial annealing) in short term, and “reverse annealing” in long term
Typically, test detectors after beneficial annealing, to try to find stable damage level
All this implies very complicated defect behaviour!

10. Change in effective doping concentration
Charge state of defect depends on whether it contains electron or hole
Acceptor: -ve when occupied by electron
Donor: +ve when occupied by hole
Source of –ve charge that gives effective p-type appears to be acceptors above midgap
A small proportion of these traps are occupied by electrons
Number of traps occupied once again is highly dependent on distance from bandgap
Donors below bandgap can give +ve charge, but relatively minor effect Ec
Acceptor Trap
- -
Emid
Hole produced Ev

11. Charge trapping
Number of free carriers in device decays exponentially over time
Described by effective lifetime:
Experimentally, effective lifetime varies inversely with fluence (this has been tested up to 1015neq/cm2)
G. Kramberger, Trapping in silicon detectors, Aug , 2006, Hamburg, Germany

12. Charge trapping In equilibrium, traps above Emid are mostly unoccupied
Free electrons in conduction band can fall into unoccupied trap states
Likewise, traps below midgap contain electrons – can trap holes in valence band
Effect is less energy-dependent
Similar equations for holes Ec
Trap
Emid
Trap Ev
Afterwards, carrier can be released from trap
If trap levels are reasonably close to midgap, detrapping is slow
So, less effect on fast detectors for LHC

13. University of Perugia trap models
IEEE Trans. Nucl. Sci., vol. 53, pp. 2971–2976, 2006
“Numerical Simulation of Radiation Damage Effects in p-Type and n-Type FZ Silicon Detectors”, M. Petasecca, F. Moscatelli, D. Passeri, and G. U. Pignatel Ec
Perugia P-type model (FZ)
0.9
2.5*10-15
2.5*10-14
CiOi
Ec+0.36
Donor
5.0*10-14
5.0*10-15
VVV
Ec-0.46
Acceptor
1.613
2.0*10-14
2.0*10-15 VV
Ec-0.42
η (cm-1)
σh (cm2)
σe (cm2)
Trap
Energy (eV)
Type -
The paper here is the most recent publication from the University of Perugia, but their previous simulation papers are also useful for reference.
- - Ev
2 Acceptor levels: Close to midgap
Leakage current, negative charge (Neff), trapping of free electrons
Donor level: Further from midgap
Trapping of free holes

14. University of Perugia trap models
Aspects of model:
Leakage current – reasonably close to α=4.0*10-17A/cm
Depletion voltage – matched to experimental results with proton irradiation with Float Zone silicon (M. Lozano et al., IEEE Trans. Nucl. Sci., vol. 52, pp. 1468–1473, 2005)
Carrier trapping –
Model reproduces CCE tests of 300m pad detectors
But trapping times don’t match experimental results
Experimental trapping times for p-type silicon (V. Cindro et al., IEEE NSS, Nov 2006) up to 1015neq/cm2
βe= 4.0*10-7cm2s-1 βh= 4.4*10-7cm2s-1
Calculated values from p-type trap model
βe= 1.6*10-7cm2s-1 βh= 3.5*10-8cm2s-1

15. Altering the trap models
Priorities: Trapping time and depletion behaviour
Leakage current should just be “sensible”: α = 2-10 *10-17A/cm
Chose to alter cross-sections, while keeping σh/σe constant
Carrier trapping:
Space charge:
Modified P-type model
0.9
3.23*10-14
3.23*10-13
CiOi
Ec+0.36
Donor
5.0*10-14
5.0*10-15
VVV
Ec-0.46
Acceptor
1.613
9.5*10-14
9.5*10-15 VV
Ec-0.42
η (cm-1)
σh (cm2)
σe (cm2)
Trap
Energy (eV)
Type

16. Comparison with experiment
Compared with experimental results with proton irradiation
Depletion voltage matches experiment
Leakage current is 30% higher than experiment, but not excessive
“Comparison of Radiation Hardness of P-in-N, N-in-N, and N-in-P Silicon Pad Detectors”, M. Lozano et al., IEEE Trans. Nucl. Sci., vol. 52, pp. 1468– 1473, 2005
α=5.13*10-17A/cm
α=3.75*10-17A/cm
The leakage current is about 30% higher than experiment. These simulations do not attempt to model leakage current accurately – it’s only important that the leakage is physically reasonable.
Experimentally,
α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis)

17. N+ on p strip detector: CCE
At high fluence, simulated CCE is lower than experimental value
Looked at trapping rates using 1D sim – as expected
Trapping rates were extrapolated from measurements below 1015neq/cm2
In reality, trapping rate at high fluence probably lower than predicted
PP Allport et al., IEEE Trans. Nucl. Sci., vol 52, Oct 2005
900V bias, 280m thick
As mentioned earlier, the simulation assumes the trapping rate measured up to 1015neq/cm2 continues up to 1016neq/cm2. Other simulations which make the assumptions give similar results. Also, the experimental results themselves aren’t completely linear; the parameter beta drops slightly at higher fluences (see V. Cindro et al., IEEE NSS conference record, Nov 2006). Back of envelope – beta gives us 0.25ns effective lifetime, vsat=1E7 cm/s, get drift distance 25um, hence 2ke- signal.
From β values used, expect 25μm drift distance, 2ke- signal

18. Example - Double-sided 3D detector
Electrode columns etched from opposite sides of silicon substrate
Short distance between electrodes
Expect reduced depletion voltage and faster collection (less trapping)
Unlike most 3D devices, the double-sided 3D detector can be biased from the back side.
Because the depletion region grows outwards from the n+ column (which is etched from the front surface) the back surfacce is difficult to deplete.

19. Example - Double-sided 3D at 1016 neq/cm2
Plotted electric field in cross-section at 100V bias
Where the columns overlap, (from 50m to 250m depth) the field matches that in the full-3D detector
At front and back surfaces, fields are lower as shown below
Region at back is difficult to deplete at high fluence A.
1016neq/cm2, front surface
1016neq/cm2, back surface A. B.
100V
100V
Unlike most 3D devices, the double-sided 3D detector can be biased from the back side.
Because the depletion region grows outwards from the n+ column (which is etched from the front surface) the back surfacce is difficult to deplete.
Undepleted B.

20. Example - Collection with double-sided 3D
Slightly higher collection at low damage
But at high fluence, results match standard 3D due to poorer collection from front and back surfaces.
20% greater substrate thickness
Uniformity? Hadn’t considered this.

21. Sentaurus Device command file
See Sentaurus/Seminar/RadDamage:
StripDetectorRadDamage_des.cmd
StripDetectorRadDamage_Param_des.cmd
Traps added to silicon
Insert appropriate concentrations, or use a “Fluence” variable in Workbench
Physics (material="Silicon") {
# Putting traps in silicon region only
Traps (
(Acceptor Level fromCondBand
EnergyMid=0.42 eXsection=9.5E-15 hXsection=9.5E-14)
(Acceptor Level fromCondBand
EnergyMid=0.46 eXsection=5E-15 hXsection=5E-14 )
(Donor Level fromValBand
EnergyMid=0.36 eXsection=3.23E-13 hXsection=3.23E-14 ) ) }

22. Sentaurus Device command file
Extra variables can be added to “Plot”
Warning – trap models are sensitive to changes in the bandgap and temperature
Don’t change the “effective intrinsic density” model – alters bandgap
Likewise, keep using default 300K temp. (Strictly speaking this is slightly wrong, since the standard test temp should be 20C.)
Plot {
………
eTrappedCharge hTrappedCharge
eGapStatesRecombination hGapStatesRecombination }
Physics {
# Standard physics models - no radiation damage or avalanche etc.
Temperature=300
Mobility( DopingDep HighFieldSaturation Enormal )
Recombination(SRH(DopingDep))
EffectiveIntrinsicDensity(Slotboom)

23. Sentaurus Device command file
Oxide charge increases after irradiation
Electron-hole pairs produced in oxide – holes become trapped in defects in oxide, giving positive charge
Saturates fairly rapidly – 1012cm-2 is a normal value after irradiation, though some papers claim up to 3*1012cm-2
X-ray irradiation causes oxide charging, but little bulk damage
Other points
More complicated physics tends to give slower solving, and poorer convergence: may need to alter solve conditions (smaller steps etc)
For charge collection simulations, need to correct the integrated current to remove the leakage current
CV simulations give strange results!
Physics(MaterialInterface="Oxide/Silicon") {
Charge(Conc=1e12) }

24. Example files See Sentaurus/Seminar/RadDamage
StripDetectorRadDamage_des.cmd
Basic MIP simulation at 1015neq/cm2
This has already been run
You can look at the output files in the same folder
.dat files taken during IV ramp
.dat files taken during the MIP transient
.plt files
StripDetectorRadDamage_Param_des.cmd
_des.cmd file for a Workbench project
Use parameter “Fluence” to control the radiation damage
Uses #if statements to omit “Traps” statement and use lower oxide charge if Fluence is zero
Works with simple StripDetector.bnd/cmd files in Workbench folder