Radiation Damage in Sentaurus
TCAD
David Pennicard – University of Glasgow
01: Tutorial/StripDetector/n5_msh.grd : n5_msh.dat
0
Y [um]
10
20
30
DopingConcentration [cm^-3]
9.7E+17
40
2.9E+15
8.9E+12
50
-9.2E+12
-40
-20
0
X [um]
-3.0E+15
20
-1.0E+18
Overview
• Introduction to trap models
• Radiation damage effects and defects
• P-type damage model
• Some example simulations
• Sentaurus Device command file
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
Traps in Sentaurus Device
• A statement added to the Physics section can describe the traps:
Physics (material="Silicon") {
Traps (
(Acceptor Level fromCondBand Conc=1.613e15 EnergyMid=0.42
eXsection=9.5E-15 hXsection=9.5E-14)
)
}
• 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
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
 s .E    q( p  n  pDonorTrap  n AcceptorTrap  N D  N A )
1
n
 .J n  GSRH  RSRH  rnTrap 
0
q
t
1
p
.J p  GSRH  RSRH  rpTrap 
0
q
t
Increase in reverse leakage current
 Eg  1 1  
T 
I (T )  I (T0 ).  exp  
   
2
k
B
 T0 
 T T0  

2
I

Vol
Leakage current increases with
fluence, independent of substrate type
I
Vol
 
Also, temperature dependence.
α normally given for 20C
Leakage current reduced by annealing
α=3.99*10-17A/cm3 after 80 mins
anneal at 60˚C (M. Moll thesis)
 Eg
T 
I (T )  I (T0 ).  exp  
 T0 
 2k B
2
 1 1 
   
 T T0  
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
Ec
Free electron produced
Trap
Emid
• 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
Hole produced
Ev
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
N eff  N A0   eq
for p-type (n-type also has “donor removal”
effect)
My models match p-type Float Zone irradiated with protons
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!
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
Ec
- -
Acceptor
Trap
Emid
Hole produced
• Donors below bandgap can give +ve
charge, but relatively minor effect
 n  p vth, p

E
E
ne,Trap  N trap fn  N trap exp  t  
exp  t  
kT  n  v
kT 


n th, n
 i

Ev
Charge trapping
Number of free carriers in device decays exponentially over time
Described by effective lifetime:
n  n

 eff ,e
t
p  p

 eff , p
t
Experimentally, effective lifetime varies inversely with fluence (this has been
tested up to 1015neq/cm2)
G. Kramberger, Trapping in silicon detectors, Aug. 23-24, 2006, Hamburg, Germany
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
n
e
 nvth  e N traps
t
1
e
 vth  e N
e
e vthee
• 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
Ev
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)
Energy
(eV)
Type
Trap
σe
(cm2)
σh
(cm2)
η
(cm-1)
Acceptor
Ec-0.42
VV
2.0*10-15
2.0*10-14
1.613
Acceptor
Ec-0.46
VVV
5.0*10-15
5.0*10-14
0.9
Donor
Ec+0.36
CiOi
2.5*10-14
2.5*10-15
0.9
--
0
Conc(cm3 )  eq
• 2 Acceptor levels: Close to midgap
– Leakage current, negative charge (Neff), trapping of free electrons
• Donor level: Further from midgap
– Trapping of free holes
Ev
University of Perugia trap models
• Aspects of model:
α=4.0*10-17A/cm
I

Vol
– Leakage current – reasonably close to
– 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
1
e
•
•
eeq
e vthee
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
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:
e,h vthe,he,h


h


v
n

E

E




h
th
t
t


n

N
f

N
exp

exp


e
,
Trap
trap
n
trap
e


kT
kT

 
 
n
v
i e
th


Modified P-type model
Type
Energy
(eV)
Trap
σe (cm2)
σh (cm2)
η
(cm-1)
Acceptor
Ec-0.42
VV
9.5*10-15
9.5*10-14
1.613
Acceptor
Ec-0.46
VVV
5.0*10-15
5.0*10-14
0.9
Donor
Ec+0.36
CiOi
3.23*10-13
3.23*10-14
0.9
Comparison with experiment
• Compared with experimental results with proton irradiation
• Depletion voltage matches experiment
• Leakage current is 30% higher than experiment, but not excessive
P-type trap model: Leakage Current
P-typetrapm
odels: Depletionvoltages
0.30
600
Depletionvoltage(V)
500
450
400
Default p-typesim
M
odifiedp-typesim
350
-17A/cm
α=5.13*10
α=3.75*10-17A/cm
0.25
Leakage current (A/cm^3)
550
“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
0.20
0.15
0.10
0.05
Experimentally,
α=3.99*10-17A/cm3 after 80 mins
anneal at 60˚C (M. Moll thesis)
Experim
ental
300
0.00
0
1E+14
2E+14
3E+14
4E+14
Fluence(Neq/cm
2)
5E+14
6E+14
7E+14
0
1E+15
2E+15
3E+15
4E+15
Fluence (neq/cm^2)
5E+15
6E+15
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
25
Simulated strip
Experimental results
Charge collection(ke-)
20
PP Allport et al., IEEE Trans.
Nucl. Sci., vol 52, Oct 2005
900V bias,
280m thick
15
10
From β values used,
expect 25μm drift
distance, 2ke- signal
5
0
0.0
2.0
4.0
6.0
8.0
15
2
Fluence (10 neq/cm )
10.0
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)
Structure of double-sided 3D device
Seperate contact to
each n+ column
p-stop
Inner radius 10um
Outer radius
15um
Dose 10 13cm-2
Oxide layer
n+ column
250um length
10um diameter
p- substrate
300um thick,
doping 7*10 11cm-3
p+ column
250um length
10um diameter
55um pitch
On back side:
Oxide layer covered with metal
All p+ columns connected together
Example - Double-sided 3D at 1016 neq/cm2
A.
•
•
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
•
•
D o u b le - s id e 2d 3 D , p - ty p e ,
16
2, front surface
10
1e+n
1 6eq
n e/cm
q /c m , fro
n t s u rfa c e
A.
0
100V
100V
0
n+
n+
200
00
Z (m)
30
50
p+
30000
30000
B.
190000
170000
150000
130000
110000
90000
70000
50000
30000
20000
10000
5000
0
00
E le c tric
F ie ld ( V /c m )
250
250
Z (m)
E le c tric
F ie ld ( V /c m )
60
0
00
00
10
240
20
40
25 00
230
50
10
B.
70000
2500
D o u b le - s id e 2d 3 D , p - ty p e ,
16
2,
10
surface
1 e + 1n6 eq
n e /cm
q /c m , bback
a c k s u rfa
ce
p+
260
10
0
00
270
2500
280
Undepleted
290
190000
170000
150000
130000
110000
90000
70000
50000
30000
20000
10000
5000
0
70
0
25
D ( m )
50
300
0
25
D ( m )
50
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.
25
20% greater substrate
thickness
Standard 3D, 250m substrate
Double-sided 3D, 250m
columns, 300m substrate
Charge collection (ke-)
20
15
10
5
0
0.0
2.0
4.0
6.0
8.0
15
2
Fluence (10 neq/cm )
10.0
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 Conc=@<Fluence*1.613>@
EnergyMid=0.42 eXsection=9.5E-15 hXsection=9.5E-14)
(Acceptor Level fromCondBand Conc=@<Fluence*0.9>@
EnergyMid=0.46 eXsection=5E-15 hXsection=5E-14 )
(Donor Level fromValBand Conc=@<Fluence*0.9>@
EnergyMid=0.36 eXsection=3.23E-13 hXsection=3.23E-14 )
)
}
Sentaurus Device command file
• Extra variables can be added to “Plot”
Plot {
………
eTrappedCharge hTrappedCharge
eGapStatesRecombination hGapStatesRecombination
}
• 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.)
Physics {
# Standard physics models - no radiation damage or avalanche etc.
Temperature=300
Mobility( DopingDep HighFieldSaturation Enormal )
Recombination(SRH(DopingDep))
EffectiveIntrinsicDensity(Slotboom)
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
Physics(MaterialInterface="Oxide/Silicon") {
Charge(Conc=1e12)
}
• 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!
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
• Email: d.pennicard@physics.gla.ac.uk