Radiation Damage in Sentaurus TCAD

David Pennicard – University of Glasgow

X [um]

Y[u

m]

-40 -20 0 20

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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

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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

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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

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harg

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llect

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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

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Z(

m)

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19000017000015000013000011000090000700005000030000200001000050000

Double-sided 3D, p-type,1e+16neq/cm2, front surface

n+

p+

ElectricField (V/cm)

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00

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25000

2500

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10000

2500

D (m)

Z(

m)

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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

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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: d.pennicard@physics.gla.ac.uk