Band gap energy modelisaon in Silvaco TCAD Atlas Device ... · Silvaco TCAD Atlas Device simulator...

31stRD50Workshop(CERN)–20-22/11/2017

Bandgapenergymodelisa0oninSilvacoTCADAtlasDevicesimulator

M.BombenLPNHE&UPD,Paris-France

M.Bomben-BandgapenergymodelisaNoninSilvacoTCADAtlasDevicesimulator-31stRD50WS,CERN 1

Outline•  BandgapnarrowinginSilvaco

•  Reverse/forwardcurrentlevelvsbandgapandtemperature

•  SimulaNonofradiaNondamageandimpactofbandgapandtemperature–  Reversebias:depleNonvoltageandleakagecurrent–  Forwardbias:forwardcurrent

•  ConclusionsandOutlook


BANDGAPNARROWINGINSILVACO


BandgapnarrowinginSilvaco


Bandgapnarrowing:howitlookslike

1710 1810 1910 2010]-3 [cmtotN

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

[eV]

gE

Slotboom

Calculatedfrompreviousformula


Bandgapnarrowing:howitlookslike

1710 1810 1910 2010]-3 [cmtotN

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

[eV]

gE

Slotboom

CourtesyofMichaelMoll

Sentaurus

Notsizeabledifference


Teststructure:effecNvedopingconcentraNon

Bulk~5e16/cm3


Teststructure:bandgapenergyinsimulaNon


Teststructure:bandgapenergyinsimulaNon

Nohiddenadjustmentshere:itiswhatiscalculatedaccordingtotheformulas


TemperaturedependenceofEg•  BothSilvacoAtlasandSynopsysSentaurususethesame

parameterizaNonforEg(T)*:

•  Theverywellknowndifferencebetweenthetwoisthat:–  Eg(300K)=1.08eVinSilvacoAtlas–  Eg(0K)=1.1696eVinSynopsysSentaurus(óEg(300K)~1.12eV)

*S.M.Sze,Physicsofsemiconductordevices.JohnWiley&Sons,1981

*


HowdoEgchangewithtemperature?

250 260 270 280 290 300 310 320 330 340T [K]

1.06

1.07

1.08

1.09

1.1 [eV]

gE

C) = 1.102 eV° (-20 gE

C) = 1.093 eV° ( 0 gE

C) = 1.083 eV° (+20 gE

C) = 1.102 eV° (-20 gE

C) = 1.093 eV° ( 0 gE

C) = 1.083 eV° (+20 gE

Eg(0K)=1.124eV

Eg(300K)=1.08eV


SILVACOTCAD

Reminder:why1.08eV?


IntrinsicconcentraNonvstemperature

250 260 270 280 290 300T [K]

2

4

6

8

10

12

14

910×]-3

[cm

in / ndf 2χ 1.424e+14 / 8

Norm 5.314e+17± 4.718e+19 n 0± 2

[eV] aE 0.0005748± 1.132

/ ndf 2χ 1.424e+14 / 8Norm 5.314e+17± 4.718e+19 n 0± 2

[eV] aE 0.0005748± 1.132

ni(293.15K)=8.29x109cm-3ni(300K)=1.45x1010cm-3Egfixedat1.08eV

Consistentwithliterature


N.B.!Moreonthislater

IntrinsicconcentraNonvsbandgap


1.08 1.09 1.1 1.11 1.12 1.13EG300 [eV]

3000

4000

5000

6000

7000

8000

610×]3 [1

/cm

in / ndf 2χ 0.003659 / 4

] 3Norm [1/cm 0± 8.29e+09 Mult. Fact. 0.01204± 0.4999 Th. En. [eV] 0± 0.02526

[eV] gE 0.0007262± 1.08

/ ndf 2χ 0.003659 / 4] 3Norm [1/cm 0± 8.29e+09

Mult. Fact. 0.01204± 0.4999 Th. En. [eV] 0± 0.02526

[eV] gE 0.0007262± 1.08

Fit Function:

)Th. En.

)g

(Mult. Fact).(x-Eexp(-×Norm

C°T = 20 TCAD sim.fit

~-Eg/2kT=>OK!

BandgapnarrowinginSilvaco:summary•  BandgapnarrowingasafuncNonofdopingworksasexpected

•  Bandgapnarrowingwithtemperatureworksasexpected

•  IntrinsicconcentraNonscalingwithtemperatureworksasexpected

•  Andvalueat293.15KisinagreementwithliteraturewhenEg(300K)=1.08eVisused

•  IntrinsicconcentraNonscalingwithbandgapworksasexpected


REVERSECURRENTLEVELVSBANDGAP


Structure

200µmthick50µmwide

n+implantbulkconcentraNon


ReverseleakagecurrentvsEgandcarr.vel.

[V]biasV500− 400− 300− 200− 100− 0

[A/c

m]

leak

J

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.212−10×

defaultEG112Syn. Th. Vel.EG112 & Syn. Th. Vel.NO BGN

Eg=1.08eV

Eg=1.12eV

TheonlyrelevantparameterhereisEg


SimulatedleakagecurrentvspredicNon

PredictedI=qniAw/2/τg~1.6x10-13A

ni(293.15K)=8.29x109cm-3 τg~4x10-5sAw=1e-8cm3

SimulatedI~1.65x10-13A


èEverythingisconsistent

LeakagecurrentvsTemperature,Φ=0

]-11/T [K

I [A/

cm]

14−10

13−10

/ ndf 2χ 1.573 / 7Prob 0.9797

ref1.0/T 0± 0.003411 n 0± 2

aE 0.0003565± 1.13 refI 17− 9.064e±13 − 1.654e

/ ndf 2χ 1.573 / 7Prob 0.9797

ref1.0/T 0± 0.003411 n 0± 2

aE 0.0003565± 1.13 refI 17− 9.064e±13 − 1.654e

]-11/T [K

I [A/

cm]

14−10

13−10

/ ndf 2χ 1.52 / 6Prob 0.9581

ref1.0/T 0± 0.003411 n 0.3528± 1.919

aE 0.01666± 1.134 refI 16− 1.16e±13 − 1.654e

/ ndf 2χ 1.52 / 6Prob 0.9581

ref1.0/T 0± 0.003411 n 0.3528± 1.919

aE 0.01666± 1.134 refI 16− 1.16e±13 − 1.654e

Ivs1/TIevaluatedatVdepl+50V(VdepldoesnotdependfromT)

nfreetofloat

nfixedto2


LeakagecurrentvsTemperature,Φ=0

]-11/T [K

I [A/

cm]

14−10

13−10

/ ndf 2χ 1.573 / 7Prob 0.9797

ref1.0/T 0± 0.003411 n 0± 2

aE 0.0003565± 1.13 refI 17− 9.064e±13 − 1.654e

/ ndf 2χ 1.573 / 7Prob 0.9797

ref1.0/T 0± 0.003411 n 0± 2

aE 0.0003565± 1.13 refI 17− 9.064e±13 − 1.654e

]-11/T [K

I [A/

cm]

14−10

13−10

/ ndf 2χ 1.52 / 6Prob 0.9581

ref1.0/T 0± 0.003411 n 0.3528± 1.919

aE 0.01666± 1.134 refI 16− 1.16e±13 − 1.654e

/ ndf 2χ 1.52 / 6Prob 0.9581

ref1.0/T 0± 0.003411 n 0.3528± 1.919

aE 0.01666± 1.134 refI 16− 1.16e±13 − 1.654e

Ivs1/TIevaluatedatVdepl+50V(VdepldoesnotdependfromT)

nfreetofloat

nfixedto2

Ea~1.13eVn~2


EavsEg(300K)–Φ=0

(300) [eV]SilgE

1.08 1.085 1.09 1.095 1.1 1.105 1.11 1.115 1.12

[eV]

aE

1.13

1.135

1.14

1.145

1.15

1.155

1.16

1.165

1.17

TCAD Simulation

Linear fit

Ea=Eg(300)+0.05eV

Empiricalrule:


SILVACOTCAD

(Reversecurrent@-20Cscaledto20C)/I(20C)

[V]biasV500− 400− 300− 200− 100− 0

/I(29

3.15

K)

scal

edI

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02


±2%

RaNoofReversecurrentsscaledto20C

T [K]250 255 260 265 270 275 280 285 290

/I(29

3.15

K)

scal

edI

0.99

0.995

1

1.005

1.01

1.015

1.02

TCAD Simulation

Linear fit


1%theaccuracyonaverageoftherescaling

Slopeconsistentwith1Interceptconsistentwith0

ForwardcurrentbeforeirradiaNon

Bias Voltage [V]0 0.2 0.4 0.6 0.8 1

Curre

nt [A

/cm

]

0

0.02

0.04

0.06

0.08

0.1

0.123−10×

C°n-on-p diode, Forward current, t = 20

= 1.08 eVgE = 1.09 eVgE = 1.10 eVgE = 1.11 eVgE = 1.12 eVgE = 1.13 eVgE

Asexpected,largerbandgap=>lesscurrent


Forwardcurrent/I(1.08eV)beforeirradiaNon

EG300 [eV]1.09 1.1 1.11 1.12 1.13

I(EG

300)

/I(1.

08 e

V) @

293

.15

K

0.2

0.3

0.4

0.5

0.6

0.7

/ ndf 2χ 4.42 / 3Norm 1.655± 1.041

[eV] gE 0.04008± 1.081

/ ndf 2χ 4.42 / 3Norm 1.655± 1.041

[eV] gE 0.04008± 1.081 V=0.2Vt=20C

=Norm*exp(-EG300-Eg/kT)

Itscales,asexpected,withni2~exp(-Eg)


Reverse/forwardcurrentlevelvsbandgap:Summary•  ReversecurrentscaleswiththeexpectedfuncNonalform

•  TheacNvaNonenergytobeusedisEa=EG300+0.05eV

•  Rescalingofleakagecurrentworksat1%level

•  Forwardcurrentscalesasexpectedwithexp(-Eg/kT)


SIMULATIONOFRADIATIONDAMAGEANDIMPACTOFBANDGAPM.Bomben-BandgapenergymodelisaNoninSilvacoTCADAtlasDevicesimulator-31stRD50WS,CERN 28

RadiaNondamagemodelconsidered


EffectsofInterfaceDonorTrapStatesonIsolaNonProperNesofDetectorsOperaNngatHigh-LuminosityLHCF.Moscatellietal.IEEETRANSACTIONSONNUCLEARSCIENCE,VOL.64,NO.8,AUGUST2017“Perugia2017”inthefollowing

Reminder:inmypresentaNoninTorino*IhaveshowedthatgoodagreementbetweensimulatorsisfoundwhenEG300=1.08eVischosenandthethermalvelociNesarecorrectedàlaSynopsys*Bomben,28thRD50WS,Torino,June2016

Perugia2017,Φ=1x1015neq/cm2

0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.004

]-11/T [K

11−10

10−10

I [A/

cm] / ndf 2χ 6.478 / 7

Prob 0.4851 ref1.0/T 0± 0.003411

n 0± 2 aE 0.001179± 1.418 refI 13− 8.242e±10 − 4.232e

/ ndf 2χ 6.478 / 7Prob 0.4851

ref1.0/T 0± 0.003411 n 0± 2

aE 0.001179± 1.418 refI 13− 8.242e±10 − 4.232e

BeforeirradiaNonitwas1.13eV


α(20C)~4.2e-17A/cm

1.  NormalisaNoniscorrect2.  Scalingasexpected

ReweighNngleakagecurrentwithEa=1.48eV

250 255 260 265 270 275 280 285 290T [K]

0.995

1

1.005

1.01

1.015

Lea

kage

Cur

rent

Rat

io

ReweighNngisaccuratewithin1.5%


<I(rew

eightedat20C)/I(2

0C)>

Perugia2017,Φ=3x1015neq/cm2

0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.004

]-11/T [K

10−10

9−10I [

A/cm

] / ndf 2χ 14.56 / 7Prob 0.04208

ref1.0/T 0± 0.003411 n 0± 2

aE 0.000457± 1.411 refI 12− 1.021e±09 − 1.237e

/ ndf 2χ 14.56 / 7Prob 0.04208

ref1.0/T 0± 0.003411 n 0± 2

aE 0.000457± 1.411 refI 12− 1.021e±09 − 1.237e

At1e15itwas1.418eV


α(20C)~4.1e-17A/cm

1.  NormalisaNoniscorrect2.  Scalingasexpected

Extra:depleNonvoltagevstemperature

250 255 260 265 270 275 280 285 290 295T [K]

140

160

180

200

220

240 [V]

depl

V

- Perugia 20171510× = 1Φ

TCAD sim.fit

- Perugia 20171510× = 1Φ

TCAD sim.fit

- Perugia 20171510× = 1Φ

TCAD sim.fitpol2

Eg=1.08eV



250 255 260 265 270 275 280 285 290 295T [K]

140

160

180

200

220

240 [V]

depl

V

- Perugia 20171510× = 1Φ

TCAD sim.fit

- Perugia 20171510× = 1Φ

TCAD sim.fit

- Perugia 20171510× = 1Φ

TCAD sim.fitpol2

Eg=1.08eV

SimpleTaylorexpansion


Rather“faraway”fromEi


250 255 260 265 270 275 280 285 290 295T [K]

200

250

300

350

400

450

500

550

600

650 [V

]de

pl V - Perugia 20171510× = 3Φ

TCAD sim.pol2

Eg=1.08eV


Itworksatlargerfluencesaswell

DepleNonvoltagevsEG300


0 50 100 150 200 250 300 [V]biasV

0200400600800

10001200140016001800

3010×]-2

[F-2 C


t=20CPerugia2017Φ=1e15neq/cm2

Largerbandgapvalues

SmallerdepleNonvoltage

DepleNonvoltagevsbandgap


1.08 1.09 1.1 1.11 1.12 1.13EG300 [eV]

120

140

160

180

200

220 [V]

depl

V

/ ndf 2χ 7.539 / 3Norm [V] 170.8± 212.5 Mult. Fact. 0.00845± 0.3093 Th. En. [eV] 0± 0.02526

[eV] gE 0.06563± 1.081

/ ndf 2χ 7.539 / 3Norm [V] 170.8± 212.5 Mult. Fact. 0.00845± 0.3093 Th. En. [eV] 0± 0.02526

[eV] gE 0.06563± 1.081

Fit Function:

)Th. En.

)g

(Mult. Fact).(x-Eexp(-×Norm

- Perugia 20171510× = 1Φ

TCAD sim.

fit

t=20C

•  ~-Eg/3kT(?)•  pol2givesbezeragreement(notshownhere)

Leakagecurrentvsbandgap


1.08 1.09 1.1 1.11 1.12 1.13EG300 [eV]

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.459−10×

[A]

leak

I / ndf 2χ 0.02563 / 4

Norm. [A] 0±10 − 4.231e [eV] gE 0.0007232± 1.08

Mult. Fact. 0.02365± 0.9862

/ ndf 2χ 0.02563 / 4Norm. [A] 0±10 − 4.231e

[eV] gE 0.0007232± 1.08 Mult. Fact. 0.02365± 0.9862

t=20C

~-Eg/kT

Forwardcurrenta{erirradiaNon

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 [V]biasV

0

0.05

0.1

0.15

0.2

0.259−10×

Curre

nt [A

]

EG300 = 1.08 eVEG300 = 1.09 eVEG300 = 1.10 eVEG300 = 1.11 eVEG300 = 1.12 eVEG300 = 1.13 eV


It’saresistor...


Forwardcurrenta{erirradiaNon

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 [V]biasV

0

0.05

0.1

0.15

0.2

0.259−10×

Curre

nt [A

]

EG300 = 1.08 eVEG300 = 1.09 eVEG300 = 1.10 eVEG300 = 1.11 eVEG300 = 1.12 eVEG300 = 1.13 eV


It’saresistor...

ρ~2x105Ωcm=>veryclosetointrinsicmaterial


Expected;e.g.:G.Lutz,NIMA377(1996)234-243

Forwardcurrenta{erirradiaNonvstemperature

0.0034 0.0035 0.0036 0.0037 0.0038 0.00391/T [1/K]

12−10

11−10Curre

nt [a

.u.]


V=0.2VPerugia2017Φ=1e15neq/cm2


Forwardcurrenta{erirradiaNon,Eg=1.08EeV

0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.0041/T [1/K]

12−10

11−10

I(1.

08 e

V) @

0.2

V / ndf 2χ 8.312 / 7

Norm 0.0004225± 0.003821 [eV] aE 0.002437± 0.446

/ ndf 2χ 8.312 / 7Norm 0.0004225± 0.003821

[eV] aE 0.002437± 0.446

Eg=1.08eVV=0.2VPerugia2017Φ=1e15neq/cm2

AsimpleexponenNalisthebestapproximaNon

~exp(-Ea/kT)


SimulaNonofradiaNondamageandimpactofbandgap:Summary•  ReversecurrentsNllscaleswiththesamefuncNonalform

•  AcNvaNonenergyratherdifferent(1.48eV)=>Modeldependent?–  Tobecheckedwithothermodels

•  DepleNonvoltagedependenceon(T,Eg)“small”onrangestested–  DuetoposiNonoftrapswrtintrinsiceenergy–  Tobecheckedwithothermodels

•  Forwardcurrentscalesasexpectedwithbandgapandenergy


CONCLUSIONSANDOUTLOOK


ConclusionsandOutlook•  Despitethelowdefaultbandgapvalueat300KpredicNonsseemtobe

consistentinSilvacoAtlasdevicesimulator•  ReversecurrentscalesasexpectedwhenthecorrectacNvaNonenergy

isused•  Forwardcurrentscalesasexpected•  A{erirradiaNonthingsgetsmorecomplicated•  YetthecurrentscaleswithtemperaturewiththesamefuncNonalform•  Morefluences/modelstobeinvesNgated•  Extra:predicteddepleNonvoltagevstemperatureneedsmore

invesNgaNon(incontactwithPerugiagroup)•  Outlook:thesituaNonismoreclear;possibletomakerobustpredicNons•  SilvacousedandtobeusedforATLASdigiNzer•  CollaboraNonwithMPItoo;seenexttalkM.Bomben-BandgapenergymodelisaNoninSilvacoTCADAtlasDevicesimulator-31stRD50WS,CERN 45

Acknowledgements•  MichaelforsuggesNngstudiestofurtherunderstand“what’sgoingon”•  Rogelio,PerugiaandMPIgroupforgivingSilvacoachance•  LucianoBosisio(Uni.ofTrieste)forgreatdiscussions

•  LPNHEgroupforsupporNngme

•  Mygirlfriend(abiologist)forlisteningtomewhilege�ngmadatEG300defaultvalue

•  and...


THANKYOUFORYOURATTENTION


Backup


Reminder•  ItwaspointedoutthatSilvacothermalvelociNesvaluesaredifferent

fromsSynopsysones

There’safactorx2forSynopsysonelectronsthermalvelociNeswrttoholes


Forwardcurrenta{erirradiaNon,Eg=1.08EeV

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 [V]biasV

0

0.05

0.1

0.15

0.2

0.259−10×

Curre

nt [A

]

t = -20 Ct = -10 Ct = 0 Ct = 10 Ct = 20 C

Eg=1.08eVPerugia2017Φ=1e15neq/cm2


Perugia2017,Φ=1x1015neq/cm2–nfreepar.

0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.004

]-11/T [K

11−10

10−10

I [A/

cm] / ndf 2χ 0.04 / 6

Prob 1 ref1.0/T 0± 0.003411

n 1.218± 5.057 aE 0.05731± 1.274 refI 12− 1.09e±10 − 4.25e

/ ndf 2χ 0.04 / 6Prob 1

ref1.0/T 0± 0.003411 n 1.218± 5.057

aE 0.05731± 1.274 refI 12− 1.09e±10 − 4.25e


Perugia2017,Φ=3x1015neq/cm2–nfreepar.

0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.004

]-11/T [K

10−10

9−10I [

A/cm

] / ndf 2χ 0.3555 / 6Prob 0.9992

ref1.0/T 0± 0.003411 n 0.4646± 3.773

aE 0.02175± 1.328 refI 12− 1.474e±09 − 1.241e

/ ndf 2χ 0.3555 / 6Prob 0.9992

ref1.0/T 0± 0.003411 n 0.4646± 3.773

aE 0.02175± 1.328 refI 12− 1.474e±09 − 1.241e


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