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Radiation Damage in Sentaurus TCAD
David Pennicard – University of Glasgow
X [um]
Y[u
m]
-40 -20 0 20
0
10
20
30
40
50
DopingConcentration [cm^-3]9.7E+17
2.9E+15
8.9E+12
-9.2E+12
-3.0E+15
-1.0E+18
01: Tutorial/StripDetector/n5_msh.grd : n5_msh.dat
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:
• 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)
) }
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
0.1
0.1
)(.
t
prRGJ
q
t
nrRGJ
q
NNnpnpqE
pTrapSRHSRHp
nTrapSRHSRHn
ADapAcceptorTrDonorTraps Poisson
Electron continuity
Hole continuity
Increase in reverse leakage current
VolI
0
2
00
11
2exp).()(
TTk
E
T
TTITI
B
g
VolI
Leakage current increases with fluence, independent of substrate type Leakage current reduced by annealing
Also, temperature dependence. α normally given for 20C
0
2
00
11
2exp).()(
TTk
E
T
TTITI
B
g
α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis)
Increase in leakage current
Ec
Ev
Emid
Trap
• 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
Hole produced
Free electron produced
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
eqAeff NN 0
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
• Donors below bandgap can give +ve charge, but relatively minor effect
Ec
Ev
Emid
Acceptor Trap
Hole produced
- -
kT
Ev
v
n
nkT
ENfnNn t
nthn
pthp
i
ttraptrapTrape expexp
,
,,
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)
Charge trapping
eeff
nt
n
,
G. Kramberger, Trapping in silicon detectors, Aug. 23-24, 2006, Hamburg, Germany
peff
pt
p
,
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
Ev
Emid
Trap
Trap
ee
the v
trapsee
th Nnvt
n
Nv ee
the
1
• 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
University of Perugia trap models
0.92.5*10-152.5*10-14CiOiEc+0.36Donor
0.95.0*10-145.0*10-15VVVEc-0.46Acceptor
1.6132.0*10-142.0*10-15VVEc-0.42Acceptor
η (cm-1)σh (cm2)σe (cm2)Trap
Energy (eV)Type
Perugia P-type model (FZ)
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
Ev
-- -
0
• 2 Acceptor levels: Close to midgap– Leakage current, negative charge (Neff), trapping of free electrons
• Donor level: Further from midgap– Trapping of free holes
eqcmConc )( 3
• 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
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 300m pad detectors
• But trapping times don’t match experimental results
ee
the veqee
1
VolI
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
hehe
thhe v ,,
, Carrier trapping:
Space charge:
Modified P-type model
0.93.23*10-143.23*10-13CiOiEc+0.36Donor
0.95.0*10-145.0*10-15VVVEc-0.46Acceptor
1.6139.5*10-149.5*10-15VVEc-0.42Acceptor
η (cm-1)σh (cm2)σe (cm2)Trap
Energy (eV)Type
kT
Ev
v
n
nkT
ENfNn te
the
hthh
i
ttrapntrapTrape expexp,
Comparison with experiment
P-type trap models: Depletion voltages
300
350
400
450
500
550
600
0 1E+14 2E+14 3E+14 4E+14 5E+14 6E+14 7E+14
Fluence (Neq/cm2)
Dep
leti
on
vo
ltag
e (V
)
Default p-type sim
Modified p-type sim
Experimental
“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=3.75*10-17A/cm
• 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
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 1E+15 2E+15 3E+15 4E+15 5E+15 6E+15
Fluence (neq/cm^2)
Lea
kag
e cu
rren
t (A
/cm
^3)
Experimentally,α=3.99*10-17A/cm3 after 80 mins anneal at 60˚C (M. Moll thesis)
α=5.13*10-17A/cm
0.0 2.0 4.0 6.0 8.0 10.0
0
5
10
15
20
25
C
harg
e co
llect
ion(
ke-)
Fluence (1015neq/cm2)
Simulated strip Experimental results
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 predictedPP Allport et al., IEEE Trans. Nucl. Sci., vol 52, Oct 2005
900V bias, 280m thick
From β values used, expect 25μm drift distance, 2ke- signal
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)
Oxide layer
n+ column250um length
10um diameter
p-stopInner radius 10umOuter radius 15um
Dose 1013cm-2
55um pitch
p- substrate300um thick,
doping 7*1011cm-3
Seperate contact toeach n+ column
On back side:Oxide layer covered with metal
All p+ columns connected together
Structure of double-sided 3D device
p+ column250um length
10um diameter
Example - Double-sided 3D at 1016 neq/cm2
• Plotted electric field in cross-section at 100V bias• Where the columns overlap, (from 50m to 250m 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
30
00
0
300
00
10000
5000
2500
20000
D (m)
Z(
m)
0 25 50
0
10
20
30
40
50
60
70
19000017000015000013000011000090000700005000030000200001000050000
Double-sided 3D, p-type,1e+16neq/cm2, front surface
n+
p+
ElectricField (V/cm)
70
00
0
25000
2500
0
10000
2500
D (m)
Z(
m)
0 25 50
230
240
250
260
270
280
290
300
19000017000015000013000011000090000700005000030000200001000050000
Double-sided 3D, p-type,1e+16neq/cm2, back surface
n+
p+
ElectricField (V/cm)
A.
A.
B.
B.
Undepleted
100V 100V
1016neq/cm2, front surface 1016neq/cm2, back surface
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
0.0 2.0 4.0 6.0 8.0 10.00
5
10
15
20
25
Cha
rge
colle
ctio
n (k
e-)
Fluence (1015neq/cm2)
Standard 3D, 250m substrate Double-sided 3D, 250m
columns, 300m substrate
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”
• 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 hTrappedChargeeGapStatesRecombination hGapStatesRecombination
}
Physics {# Standard physics models - no radiation damage or avalanche etc.Temperature=300Mobility( 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
• 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)
}
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: [email protected]