A new model for the TCAD simulation of the silicon damage ... · In principle a full 3D simulation of the implantation and diffusion should be performed for the corner region. But

Joern Schwandt University of Hamburg04.06.2018 | Hamburg �1

A new model for the TCAD simulation of the silicon damage by high fluence proton

irradiation

—The Hamburg Penta Trap Model—

J. Schwandt, E. Fretwurst, E. Garutti, C. Scharf and G. Steinbrück

Institute for Experimental Physics University of Hamburg

32nd RD50 Workshop 4.06.-6.06.2018

Joern Schwandt University of Hamburg04.06.2018 | Hamburg

Introduction

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High-Luminosity LHC radiation level for the 1st pixel layer after 3000 fb-1 : • Φeq ≈ 2.3·1016 cm-2, dose ≈ 12 MGy

TCAD simulations of sensors are valuable in: • Avoiding designs mistakes • Understanding and predicting the performance of the sensor • Optimization for radiation hardness

Requirements: • Accurate models + parameters describing bulk and surface radiation damage in TCAD • Choice of correct boundary conditions

➡

Problems: • Currently available radiation damage models are not able to describe I-V, C-V and CCE

measurements on pad diodes simultaneously for fluences ≥ 1·1015 neq/cm2 • Is SRH valid (point vs. cluster defects)? • Accuracy and reproducibility of data

Measurement and simulation program for high fluences with the aim of the development of an accurate model


Radiation damage

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Bulk damage (NIEL): • Point and cluster defects in the silicon lattice ➡ Increase of leakage current ➡ Change of the space charge in the depletion

region, increase of full depletion voltage ➡ Trapping of drifting charge

• I-V, C-V and CCE on pad diodes

Al

p-Bulk

p+

n+ n+Al Al

passivationSiO2

passivation

p-stop p-stop

Air

3.2. Defect formation

Fig. 7 shows a qualitative example of a finalconstellation of di- and tri-vacancies. The total

numbers of the defects indicated in the plot shouldnot be compared with any NIEL scaling becausethe statistical fluctuations are overwhelminglylarge. Also the depth of the projections should be

X (Å)

Z (Å

)

Z=14, A=28E=50 keV505 Vacancies

0

100

200

300

400

500

600

0 100 200 300 400 500 600Y (Å )

Z (Å

)

-100

0

100

200

300

400

500

600

700

-100 0 100 200 300 400 500 600 700

Fig. 4. Spatial distribution of vacancies created by a 50 keV Si-ion in silicon. The inset shows the transverse projection of the sameevent.

0

0.2

0.4

0.6

0.8

1

0 0.5 1

36824 vacancies

x (µm)

y (µ

m)

0 0.5 1

4145 vacancies

x (µm)0 0.5 1

8870 vacancies

x (µm)

Fig. 5. Initial distribution of vacancies produced by 10 MeV protons (left), 24 GeV=c protons (middle) and 1 MeV neutrons (right).The plots are projections over 1 mm of depth ðzÞ and correspond to a fluence of 1014 cm# 2:

M. Huhtinen / Nuclear Instruments and Methods in Physics Research A 491 (2002) 194–215204

e-h pairscreatedby ionizing radiation

protonrelease

protontransport

SiSiO2

Not: deep hole

trapping (E')near interface

hopping transport ofhole through localizedstates in bulk SiO2

H+

Gate

Nit: interface trap

formation (Pb)

24 GeV/c protons 1 MeV neutrons

surfa

ce dam

age

bulk damage

Surface damage (Ionizing Energy Loss): • Build up of oxide charges, border and interface traps ➡ Increase of surface current ➡ Change of electrical field near to the Si-SiO2

interface ➡ Trapping near to the Si-SiO2 interface

• C-V/I-V on MOS capacitors, MOSFET and gate controlled diodes

In the following only bulk damage from protons and no surface damage ( 1 D problem)


Diode measurements

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Large and small diodes available from the CMS HPK campaign:

1. Material • p-type (p-stop, p-spray)

- Thinned float zone FTH200 (200 µm thick) - + MCz, Epi, deep diffused FZ

2. Irradiations • Protons 24 GeV/c

- Fluences: 0.3, 1, 1.5 , 2.4, 3 , 6, 7.75, 13•1015 neq/cm2

3. Measurements after 80min@60°C annealing (irrad. 2015) at T= -20°C and -30°C with reverse and forward bias applied • I-V up to 1000 V (reverse) and up to current limit of 0.5 mA

(forward) • C/G-V with 100 Hz - 2 MHz • TCT with 670 nm (red) and 1063 (IR) nm laser

Diode 5mm x 5mm

Diode 2mm x 2mm


Example Diode measurements

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Large diodes FTH200: • 24 GeV/c protons with fluences 3 , 6, 7.75, 13•1015 neq/cm2

• 80min@60 °C • T = -20 °C • CCE from TCT measurements with error below 10 %

Are we able to reproduce all measurements with simulations?

reverse

forward

3• 1015cm-2

I-V3• 1015cm-2

13• 1015cm-213• 1015cm-2

C-V6• 1015neq/cm2

100 Hz

2 kHz

100 kHz

CCE 6• 1015neq/cm2

reverseforward

IR

IRred rear

red frontreverse


TCAD

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Poisson

Electron continuity where

where

- Works by modeling electrostatic potential (Poisson’s equation) and carrier continuity equations

- Takes mesh, applies semiconductor equations + boundary conditions (in discrete form) and solves

Hole continuity

- Different versions of physics models are available (mobility, avalanche, tunnelling etc)

- Radiation damage will change the net recombination rate Rnet and the charge density due to ρtraps

7. Optimization of the AGIPD Sensor

(a) (b)

Figure 7.3.6.: Simulated boron profile for an energy of 70 keV, dose of 5 �1015 cm�2 annealed at 1025ıCfor 4 hours. The junction depth is 2:4µm and the lateral extension is 1:95µm.

around the vertical axis at x D 0µm and can be used in the device simulation for both edgesof the implant window if one performs a mirror transformation. For implant windows whichare larger than 10:0µm the depth profile at x D 0µm is continued to fill the lacking range. Asshown in the three-dimensional view in Figure 7.3.7 the mask for the implantation of a pixelhas corners which are spherical or spherical shell like depending on the radius at the corners.In principle a full 3D simulation of the implantation and diffusion should be performed for thecorner region. But this requires a large amount of main memory and runtime. One possibility touse the 2D simulated profiles, and this was done in this work, is to sweep the 2D profiles alongthe ring segment which defines the rounding at the corner. For large enough radii the differencebetween the 3D and the 2D simulated profiles with an following sweeping should be negligible.

I I N = 10i4cm-3

0.5

'I

I 1 1

- Abrupt junctions - - - - Linearly graded junctions

1.5 h

?L

3 0 0

2 1 6 2

0 0 100 200 300 400 500 6

T (K)

I0

Fig. 20 Normalized avalanche breakdown voltage versus lattice temperature, in silicon. The breakdown voltage generally increases with temperature. (After Ref. 19.)

Insulator J

\Cylindrical region

Spherical region

0.7

0.6

'2 0.5 8 $ 0.4 P '% 0.3 2

0.2

0.1

001 .02 .04 .06 0.1 0.2 0.4 0.6 1.0 q=rjlWD,,,

(c)

Fig. 21 (a) A planar diffusion or implantation process forms a junction curvature near the edges of the mask with rj the radius of curvature. (b) Three-dimensional view of the junction curvature showing the spherical region at the corners. (c) Normalized breakdown voltage of cylindrical and spherical junctions as a function of the normalized radius of curvature. (After Ref. 18.)

113

Figure 7.3.7.: Three-dimensional view of a planar diffusion or implantation process. At the edges of themask the junction is cylindrical and at the corners spherical. Picture taken from[27].

For good ohmic contact typically a nC-n junction on the backside of the sensor is formed.

28

TCAD (Technology Computer Aided Design): • Process simulation → doping profile • Device simulation → electrical behaviour

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<latexit sha1_base64="h/y0UjNyhtaO9K6DGOyEju8t7NQ=">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</latexit><latexit sha1_base64="h/y0UjNyhtaO9K6DGOyEju8t7NQ=">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</latexit><latexit sha1_base64="h/y0UjNyhtaO9K6DGOyEju8t7NQ=">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</latexit>

Jn = qnµnE+ qDnrn<latexit sha1_base64="Gg/eZIR4pqDYVnQChggbt9WbLPU=">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</latexit><latexit sha1_base64="Gg/eZIR4pqDYVnQChggbt9WbLPU=">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</latexit><latexit sha1_base64="Gg/eZIR4pqDYVnQChggbt9WbLPU=">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</latexit>

Jp = qpµpE� qDnrp<latexit sha1_base64="nrYxLUyUTbXh6pSajxMAj5iUqAw=">AAAC/HichVFNSxxBEH1OEj82iVnjMZcmi+DFZVaE6EEQoiKBgEJWBVeW7rF3M+xMzzjTKzHLkr/hH/AkXj16NX9Bf4uHvGlnA1GCPfTU61dVr6u6VBqFufX92zHvxctX4xOTU5XXb95Ov6vOvN/Nk34W6GaQREm2r2Suo9Dopg1tpPfTTMtYRXpP9T4X/r0TneVhYr7Z01QfxrJrwk4YSEuqXV1sWf3Dqs7gy7CdilVxnLbiPtGI3hiKBXEs1tumZaSKpEgr7WrNr/tuiaegUYIayrWdVO/QwhESBOgjhoaBJY4gkfM7QAM+UnKHGJDLiELn1xiiwtw+ozQjJNke/12eDkrW8Fxo5i474C0Rd8ZMgTnuTaeoGF3cqolz2nvun47r/veGgVMuKjylVVSccopfyVt8Z8RzmXEZOarl+cyiK4sOll03IetLHVP0GfzVWacnI9dzHoENF9mlhnLnE76AoW2yguKVRwrCdXxEK53VTsWUipJ6GW3x+qyHY248HupT0Fysr9T9naXa2nI570l8wEfMc6ifsIYtbLOMAGe4xg1+e7+8c+/Cu3wI9cbKnFn8s7yrP1D8oiM=</latexit><latexit sha1_base64="nrYxLUyUTbXh6pSajxMAj5iUqAw=">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</latexit><latexit sha1_base64="nrYxLUyUTbXh6pSajxMAj5iUqAw=">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</latexit>


Radiation damage modelling

�7

Radiation damage modelling: • Usually effective trap levels modelling

the measured identified point and cluster defects

• It is assumed that the traps obey SRH statistics (still valid at high fluences?)

• Parameters are dependent on the simulator (Synopsys TCAD, Silvaco)

Ec

Ev

Eg/2

trapping generation recombination

capt

ure cn

cp

en

ep

Ec

Et

Ev

Eg/2

emission

Ec

Eg/2

Ev

Ec

Eg/2

Ev

EA

ED

Example: 2 trap model → 6 parameter 1. Concentrations : NA , ND

2. Cross sections : σAe , σAh , σDe , σDh

⇢trap = q[NDfD �NAfA]<latexit sha1_base64="AOjphAkVywjhj/LbK0UP6f1p/38=">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</latexit><latexit sha1_base64="AOjphAkVywjhj/LbK0UP6f1p/38=">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</latexit><latexit sha1_base64="AOjphAkVywjhj/LbK0UP6f1p/38=">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</latexit>

Rnet =vhve�D

h �De ND(np� n2

i )

ve�De (n+ nieED/kT ) + vh�D

h (p+ nie�ED/kT )

+vhve�A

h �Ae NA(np� n2

i )

ve�Ae (n+ nieEA/kT ) + vh�A

h (p+ nie�EA/kT )<latexit sha1_base64="+tqs4bGjKo+X8oavC1IPkLeEPco=">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</latexit><latexit sha1_base64="+tqs4bGjKo+X8oavC1IPkLeEPco=">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</latexit><latexit sha1_base64="+tqs4bGjKo+X8oavC1IPkLeEPco=">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</latexit>

withfA =

ve�Ae n+ vh�A

h nie�EA/kT

ve�Ae (n+ nieEA/kT ) + vh�A

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�e = ve[�Ae NA(1� fA) + �D

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�h = vh[�Dh ND(1� fD) + �A

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{Trapping


state of the art

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3-trap Perugia parameters (F. Moscatelli et al IEEE Trans Nucl Sci 2017) for Synopsys TCAD

V2

V3

CiOi

Fluence depending!!


Protons<->Neutrons~1016

•  Fieldprofilescompared

•  Protonswithmore“doublejunc8on”,flaÇerfield,lesspeakedatjunc8on

TREDI,Paris,Feb22,2016 MarkoMikuž:E,μandτinirrad.Si

Edge-TCT measurements (M. Mikuž: Tredi,Paris, FEB 2016)

1000 V

state of the art

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Does it describe our data?

*) All simulations done with Synopsys TCAD (L-2016.3-SP1)

I-V C-V

reverse

forward1.3• 1016neq/cm2 1.3• 1016neq/cm2

data

Perugia

dataPerugia

Perugia

data 1kHz

data 455 Hz

• Reverse current too low• CV shows no frequency

dependence • CCE has not the correct

voltage dependence• No double peak

reverse

CCE

reverse

1.3• 1016neq/cm2

data RF

data IRdata RR

Perugia RF

Perugia RRPerugia IR

Electric field1.3• 1016 neq/cm2

1000 V

200 V


New Parameter Tuning

�10

Attempts for the determination of new damage parameters: • Simulation of the I-V, C-V and CCE with infrared of diodes for the fluences 3 , 6,

13•1015 neq/cm2 and using the optimizer of TCAD for the determination of the free parameters i.e. minimize the relative deviation between the simulations and measurements over a large voltage range or more precise: Minimize simultaneously for every fluence

with Isim simulated current, Imes measured current Csim simulated capacitance, Cmes measured capacitance CCEirsim simulated CCE, CCEirmes measured simulated

F =

Z �900V

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Imes

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Z �600V

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sim

C455Hzmes

)2 dV +

Z �600V

�5V(1� C1kHz

sim

C1kHzmes

)2 dV

+

Z �1000V

�200V(1� CCEirsim

CEEirmes

)2 dV<latexit sha1_base64="qby2E9JwJkZNf4R6GKaDzK5aQOo=">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</latexit><latexit sha1_base64="qby2E9JwJkZNf4R6GKaDzK5aQOo=">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</latexit><latexit sha1_base64="qby2E9JwJkZNf4R6GKaDzK5aQOo=">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</latexit><latexit sha1_base64="qby2E9JwJkZNf4R6GKaDzK5aQOo=">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</latexit>

• I-V and C-V are simulated in 1D (CPU time: ≈3 min) • CCE is simulated in 2D (r,φ) at 5 voltages (CPU time: ≈50 min)


HPTM

�11

Result of tuning: Hamburg Penta Trap Model (HPTM)

• Trap concentration of defects: N = gint · Φneq • Simulations for the optimization have been performed at T= -20 °C with:

1. Slotboom band gap narrowing 2.Impact ionisation (van Overstaeten-de Man) 3.TAT Hurkx with tunnel mass = 0.25 me (default value: 0.5 me) in case of the Ip 4.Relative permittivity of silicon = 11.9 (default value : 11.9)

• Both cross section for the E30K and the electron cross section for the CiOi were fixed ➔ 12 free parameter

• Optimization done with the nonlinear simplex method


I-V for different fluences

�12

I-V for fluences from 0.3 - 13•1015 neq/cm2 at T= -20 °C (for T= -30 °C see backup)I-V ratio simulation / data

• The simulation for 0.3 and 1•1015 neq/cm2 are extrapolations and the 7.75•1015 neq/cm2 is a interpolation (not included in the optimization)

• The simulations agrees with the measurements within 20% for all fluences and voltages


C-V for different fluences

�13

C-V for fluences from 0.3 - 13•1015 neq/cm2 at 455 Hz and T = -20 °C (for T= -30 °C see backup)

• The simulation for 0.3 and 1•1015 neq/cm2 are extrapolations and the 7.75•1015 neq/cm2 is a interpolation (not included in the optimization)

• The simulations agrees with the measurements within 20% for all fluences and voltages • Deviation at highest fluence and voltage maybe due to impact ionization • A better agreement between simulations and measurements is achieved at 1 kHz

1/C2-V ratio simulation / data


CCE vs. V (infrared)

�14

�1000 �800 �600 �400 �200 0

Voltage [V]

0.0

0.2

0.4

0.6

0.8

1.0

CCE

HPTM 3 · 1014 cm�2

HPTM 1 · 1015 cm�2

HPTM 3 · 1015 cm�2

HPTM 6 · 1015 cm�2

HPTM 8 · 1015 cm�2

HPTM 13 · 1015 cm�2

Data 3 · 1014 cm�2

Data 1 · 1015 cm�2

Data 3 · 1015 cm�2

Data 6 · 1015 cm�2

Data 8 · 1015 cm�2

Data 13 · 1015 cm�2

CCE vs. V for fluences from 0.3 - 13•1015 neq/cm2 with infrared laser and T = -20 °C (for T= -30 °C see backup)

CCE-V ratio simulation / data

• In the optimization only the voltages -200, -400,-600,-800 and -1000V were used • For all fluences the voltage dependence is good reproduced • At high voltages the simulations agrees with the measurements within 20% for all fluences

13• 1015cm-2

3• 1015cm-2

3• 1014cm-2

13• 1015cm-2

3• 1015cm-2


E-fields for different fluences

�15

Simulated E-field as function of position for different fluences at 1000V

E-field vs position

13• 1015cm-2

3• 1014cm-2

3• 1015cm-2

• Double peak structure for fluences ≥ 3•1015 neq/cm2 clearly visible • Peak field of ≈ 2•105 V/cm at the highest fluence ➔ impact ionisation


E-fields vs. voltage

�16

E-field vs. voltage 1.3• 1016neq/cm23• 1015neq/cm2

ve + vh vs. voltage


Trapping

�17

Trapping rates:

Fi g. 9. Tr appi ng pr obabi l i t i es, 1/ T, f or bot h hol es and el ec-t r ons as a f unct i on of f ast neut r on f l uence as measur ed by t heobser ved pul se wi dt h ( squar es) and t he cal cul at ed char ge

col l ect i on t i me ( ci r cl es) . -

ment t hose damaged det ect or s f or whi ch t he cur r entshape has been measur ed. Usi ng an anal yt i cal r el at i on-shi p f or t he dependence of car r i er mobi l i t y on t heel ect r i c f i el d, one can cal cul at e t he char ge col l ect i ont i me . Two r el at i onshi ps have been used f or A( E) ( f orei t her e or h) t aken f r omCanal i et al . [ 14] and Sze [ 15] .

The col l ect i on t i mes ar e t hen cal cul at ed i n t he samef or mal i sm of t he i nduced cur r ent shapes and f ound t obe

t e .

and

Te, h

0

d E( x, )V+ Te I n E( xf )

d E( x f )- + , r , I nVS

E( x, ) '

100 200 300 400

eq [ 1011 n/ cm2]

f or t he mobi l i t y r el at i onshi p f r omSze [ 15] , wher eEEO

eh 0 hNef fand i and f r ef er t o i ni t i al and f i nal val ues of posi t i on .

Fi g. 9 shows t he t r appi ng pr obabi l i t i es, 1/ T, f orhol es and el ect r ons as a f unct i on of f ast neut r on f l u-ence t hat have been der i ved t hr ough char ge col l ect i ont i mes det er mi ned by bot h met hods, di r ect measur e-ment of t he cur r ent pul se wi dt h and t he cal cul at edcol l ect i on t i me. Ther e appear s t o be r easonabl e agr ee-ment bet ween bot h met hods and a cl ear l i near i ncr easei n t r appi ng wi t h i ncr easi ng f l uence, as woul d be ex-pect ed.

Fur t her cal cul at i ons of char ge col l ect i on t i mes havebeen made usi ng eq. ( 5) and compar i sons wi t h t heobser ved col l ect i on t i mes f r om cur r ent pul se wi dt hsar e i n good agr eement . Al so, a second or der t er m hasbeen appl i ed t o eq. ( 4) f or cases when t c l T i s not «1

HW. Kr aner et al . / Use of si gnal cur r ent pul se shape

whi ch bet t er descr i bes t he char ge decr ement at hi ghf l uences .

6. Concl usi ons

I t has been obser ved f r om hol e cur r ent pul se shapesf or al pha par t i cl e i r r adi at i ons of f r ont ( p +) and back( n +) cont act s t hat t he maxi mumi n t he el ect r i c f i el d i nn- t ype j unct i on det ect or s r ever t s t o t he back cont actaf t er f ast neut r on f l uences > 8 X 10 12 n/ cmZ f or mea-sur ement s made weeks post - i r r adi at i on, i . e. , t her e be-i ng no sel f anneal cor r ect i on . Al t hough deep l evelcompensat i on and r emoval of shal l ow donor s must ber ecogni zed i n t hi s pr ocess, a compar i son of t he ob-ser ved cur r ent pul se shapes wi t h cal cul at ed shapes i s i nr easonabl e agr eement i mpl yi ng t hat t he l i near el ect r i cf i el d pr of i l e used i n t he cal cul at ed shapes i s st i l l appl i -cabl e. The obser vat i on of hol e cur r ent shapes f or al -phas i nci dent on t he l owf i el d cont act , t he back cont actor sour ce of hol e t r ansi t , has r eveal ed a sl ow, di f f usi vecomponent whi ch may be expl ai ned by t he shi el di ng oft he f i el d by t he i oni zat i on- pr oduced hol es or ananomal ousl y hi gh sur f ace concent r at i on of donor s - orbot h. Tr appi ng t i mes or i nver se t r appi ng pr obabi l i t i escan be easi l y der i ved f r om cur r ent pul se shapes andagr ee wi t h ot her measur ement s t hat i nvol ve cal cul at edcar r i er t r ansi t t i mes . Al i near r el at i onshi p of t r appi ngpr obabi l i t y wi t h neut r on f l uence i s obser ved, whi chsuggest s some caut i on i n assumi ng l i t t l e r educt i on ofchar ge col l ect i on f or det ect or s i r r adi at ed at f l uencesabove 10 14 n/ cmZ. Cal cul at ed cur r ent shapes can al soi ncl ude t he ef f ect of t r appi ng and det r appi ng wi t hr esul t s t hat ar e not unexpect ed .

Acknowl edgement s

Ref er ences

355

I t i s a pl easur e t o acknowl edge t he cont r i but i ons ofA. Hr i soho, S. Resci a, D. St ephani and V. Radeka i nassembl i ng and devel opi ng t he f ast cur r ent measur e-ment syst em. We have benef i t t ed f r om ver y hel pf uldi scussi ons wi t h V. Radeka, G. Li ndst r oem, J. Wal t er ,F. Lemei l l eur , P. Jar r on and E. Hei j ne.

[ 1] G. Li ndst r om, M. Benker t , E. Fr et wur st , T. Schul z andR. Wunsdor f , Pr oc. 1st I nt . Conf . on Cal or i met r y mHi ghEner gy Physi cs, i ds . D. F. Ander son et al . ( Wor l d Sci en-t i f i c, Si ngapor e, 1991) .

[ 2] D. Pi t zl , N. Car t ogl i a, et al . , pr esent ed at t he I EEENucl ear Sci ence Symposi um, Sant a Fe, NM, USA, 1991 .

[ 3] F. Lemei l l eur , M. Gl aser , E. H. M. Hei j ne, P. Jar r on andE. Occel l i , pr esent ed at t he I EEE Nucl ear Sci ence Sym-posi um, Sant a Fe, NM, USA, 1991 .

VI I I . RADI ATI ONDAMAGE

30CURRENT SHAPE MEASUREMENT

25 " ELECTRONS .O HOLES

n. a

f20 _ PULSE HEI GHT MEASUREMENT

IN " ELECTRONS1 C O HOLESu 15

10 0

5 0

0

Kraner et al NIMA 1993

Table 3The fitted lifetimes in the drift and their slopes, calculated atº

!"##20V

Diode !"

Slope of !"

!$

Slope of !$

no. (ns) (ns/100V) (ns) (ns/100V)

1 15.26$2.38 32.7 $9.05 31.16$6.05 11.24$6.342 9.60$2.03 9.64$3.01 16.21$2.31 5.20$1.885 5.14$0.77 7.41$2.00 15.10$2.42 8.63$3.193 2.67$0.11 1.36$0.18 7.00$0.26 1.80$0.184 3.14$0.63 2.59$0.68 15.28$4.32 8.52$6.34

sensitive to the details of the electric field at thep! side.

Omission of the "#! data from the fits led to

values of the fitted parameters similar to those inTable 3, but with larger errors.

It was preferred therefore to keep the "#! data,

but with reduced weight to allow for model imper-fections, in the following manner. The error on the"#! data points was increased by adding in quadra-

ture with the usual error a term which variedinversely with (º

%&'(!º

!"#) until the mean #! con-

tribution per data point for each of the three curveswas of the same order:

err!"$!#k!50!/(º%&'(

!º!"#

)!. (9)

The necessary values of k are shown in Table 4, andwith this modification the fit quality was good with#! per degree of freedom&1.0.

Another feature of the fits was the fact that thelifetimes in the plasma tended to come out higherthan the lifetimes in the drift (Table 4). Thisphenomenon may be due to trap filling by the high

Table 4A comparison of the fitted lifetimes in the plasma with the fittedlifetimes in the drift. Also shown are the values of k foundnecessary to overcome the systematic effect described in Sec-tion 6

Diodeno.

!#)'(*'"

!!+&,-"

(º!"#

#50)

!#)'(*'$

!!+&,-$

(º!"#

#50)k

1 2.43$0.83 0.85$0.54 0.0072 4.31$1.53 2.09$200 0.0075 4.04$1.48 1.04$0.83 0.0153 !#)'(*'

"PR$R !#)'(*'

$PR$R 0.015

4 10.5$8.6 3.1$1.6 0.0175

density carrier cloud in the region of the ionisationdeposition. Note also that the uncertainty in thefitted lifetime in the plasma was much greater thanthe possible uncertainty in the value of 27 ns fort"#

determined in Section 5.

7. Results

Plotted in Fig. 4 is the trapping probability ex-tracted from the fits against fluence for two differ-ent values of overdepletion. The difference between

Fig. 4. The trapping probability at º%&'(

"º!#20V and

º%&'(

"º!#100V for all five diodes versus fluence. The lines

show the $1$ interval; (a) is for electrons and (b) for holes.

L. Beattie et al./Nucl. Instr. and Meth. in Phys. Res. A 421 (1999) 502—511 509

Table 3The fitted lifetimes in the drift and their slopes, calculated atº

!"##20V

Diode !"

Slope of !"

!$

Slope of !$

no. (ns) (ns/100V) (ns) (ns/100V)

1 15.26$2.38 32.7 $9.05 31.16$6.05 11.24$6.342 9.60$2.03 9.64$3.01 16.21$2.31 5.20$1.885 5.14$0.77 7.41$2.00 15.10$2.42 8.63$3.193 2.67$0.11 1.36$0.18 7.00$0.26 1.80$0.184 3.14$0.63 2.59$0.68 15.28$4.32 8.52$6.34

sensitive to the details of the electric field at thep! side.

Omission of the "#! data from the fits led to

values of the fitted parameters similar to those inTable 3, but with larger errors.

It was preferred therefore to keep the "#! data,

but with reduced weight to allow for model imper-fections, in the following manner. The error on the"#! data points was increased by adding in quadra-

ture with the usual error a term which variedinversely with (º

%&'(!º

!"#) until the mean #! con-

tribution per data point for each of the three curveswas of the same order:

err!"$!#k!50!/(º%&'(

!º!"#

)!. (9)

The necessary values of k are shown in Table 4, andwith this modification the fit quality was good with#! per degree of freedom&1.0.

Another feature of the fits was the fact that thelifetimes in the plasma tended to come out higherthan the lifetimes in the drift (Table 4). Thisphenomenon may be due to trap filling by the high

Table 4A comparison of the fitted lifetimes in the plasma with the fittedlifetimes in the drift. Also shown are the values of k foundnecessary to overcome the systematic effect described in Sec-tion 6

Diodeno.

!#)'(*'"

!!+&,-"

(º!"#

#50)

!#)'(*'$

!!+&,-$

(º!"#

#50)k

1 2.43$0.83 0.85$0.54 0.0072 4.31$1.53 2.09$200 0.0075 4.04$1.48 1.04$0.83 0.0153 !#)'(*'

"PR$R !#)'(*'

$PR$R 0.015

4 10.5$8.6 3.1$1.6 0.0175

density carrier cloud in the region of the ionisationdeposition. Note also that the uncertainty in thefitted lifetime in the plasma was much greater thanthe possible uncertainty in the value of 27 ns fort"#

determined in Section 5.

7. Results

Plotted in Fig. 4 is the trapping probability ex-tracted from the fits against fluence for two differ-ent values of overdepletion. The difference between

Fig. 4. The trapping probability at º%&'(

"º!#20V and

º%&'(

"º!#100V for all five diodes versus fluence. The lines

show the $1$ interval; (a) is for electrons and (b) for holes.

L. Beattie et al./Nucl. Instr. and Meth. in Phys. Res. A 421 (1999) 502—511 509

Beatie et al NIMA 1999

electrons holes

• For HPTM the trapping probability of electrons a factor 3 higher than for holes

• Similar to old alpha TCT measurements but different to new red laser TCT measurements

• Effect know since Brodbeck et al NIMA 2000, but not investigated further

electrons G. K. et al

holes G. K. et al

electrons HPTM

holes HPTM


Comparison with strips

�18

Charge collection measured with strip sensors (data from Affolder et al NIMA 2010)

• Float zone silicon• 300 um thick sensors• 80 um pitch• T = -25 °C • 90Sr source

• 5 AC coupled strips simulated• 80 e-h/um generated

Collected charge vs. fluenceSimulated structure


TCAD + pixelaV

�19

sensor geometry doping radiation damage model

TCAD simulation

electrical field map

particle tracking e/h pair generation

(with delta-electron)

charge transport signal calculation

(with trapping)

read out electronic simulation

test beam analysis

test beam data

Synopsys TCAD

PIXELAV (M. Swartz) ROOT

C++ / Python program

boundary conditions

trapping rates


First Comparison with pixels

�20

Collected charge vs voltage for 2•1015 neq/cm2 and 150 um thick sensors

Simulations: • T = -15 °C • Noise: 170 e • Threshold: 1000 e

• FE-I4 data from S. Terzo Phd thesis 2015 • Data from non-annealed sensors

simulations


Summary

�21

• New measurements (IV, CV, CCE) on highly irradiated diodes are available • A comparison of the measurements with TCAD simulations using the Perugia

trap parameters shows a large disagreement • Attempts are made to develop a new model by fitting I-V, C-V and CCE

measurements using the optimizer of TCAD • The Hamburg Penta Trap Model gives a significantly better and consistent

description of a large set of measurements of pad diodes irradiated with protons in the fluence range from 3•1014 neq/cm2 to 1.3•1016 neq/cm2

• First application of HPTM in strip sensor simulations and to pixel sensors in combination with PIXELAV are encouraging

Thank you for your attention!

End of the epicycles?To do: • Improve temperature dependence of HPTM by introduction of

temperature depending cross sections for Ip • Reduction from 5 to 4 defects? There are indication that H220

is not needed. • Differences in trapping rates by red laser and alpha particles


I-V and C-V at T=-30°C

�22

C-V for different fluence at 455 HzI-V


CCE at T=-30°C

�23

CCE-V for different fluence (infrared) at T = -30 °C

Documents

A new model for the TCAD simulation of the silicon damage ... · In principle a full 3D simulation of the implantation and diffusion should be performed for the corner region. But