Outline

14th RD50 - Workshop on Radiation hard semiconductor devices for very high luminosity colliders, Freiburg, Germany, 3-5 June 2009

Contributions of Electrons and Holes to Total Collected Charge in

Heavily Irradiated Si Pad and Strip/Pixel Detectors: A

Comparison Simulation Study

Zheng Li

Brookhaven National Laboratory, Upton, NY, USA

*This research was supported by the U.S. Department of Energy: Contract No. DE-AC02 -98CH10886 and it is within the frame work of CERN RD39 and RD50 Collaborations

Outline1. The simplified Model of Electric and Weighting Fields: analytical solutions for collected charge

2. Simulation Results in Analytical Forms and plots

3. Increased Hole Contribution in Collected Charge in Heavy Irradiation Environments

4. Some Approximations

5. Summary

Simplified Model of Electric and Weighting Fieldsanalytical solutions for collected charge

Weighting field:

,

Electric Field:

10

)( )(

)0( )(

1

)(

0

0

0

dxPPdP

PxPdP

xEW

EW (x0)

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

0

E (x0)

x0L d

0E

0)( 0 EEd

0

0) ( )( E

)0( E)(

00

000 dxL

LxxE

)(0 LdL

VE

P is the segmentation pitch

d the detector thickness, or depletion depth

Region 1 Region 2

e h

n+ p+

Real field

Real weighting field

Simplified Model of Electric and Weighting Fields

Two typical cases:

,

Strip/pixel front, Junction front (SFJF)

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0E

0EEd

n+ p+P-type

Electric field

Weighting field

0

Strip/pixel front, Junction back (SFJB)

P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0EEd

0E

n+ p+P-type

Electric field

Weighting field

0

Region 1 Region 2

Simplified Model of Electric and Weighting Fields

Carrier drift velocity:s

dr vtxE

txE

dt

tdxtxv

/)((1

)(()())((

,

eqeq nnt

scm /1051 27

Trapping time constant:

Depletion Depth: eqneff

eff

ΦNeN

Vw 02.0 ,

2 0

Induced current by a

Charge layer at x0:00 x

d

Q

Total collected charge:

ms/e' 80 )( ,0

,0

0, tt

t

hedrW

t

hedrW

he evExevExd

Qtdi

]dt dt [/'800 00

0

d t t

hdrW

t t

edrW

hdr

t

edr

t evEevEdxmseQ

Basic equations

Simulation ResultsSolutions

We can obtain analytical solutions for collected charges:

)(

)(

)])(1([)]1)(1([)]1()[(/'80

)(

)]()1[()]1()[(/'80

)(

)1(/'80

1,1,2,2,2,1,

1,1,1,1,

1,

2,1,2,1,2,2,

1,1,1,

1,1,

PL

PdP

eeevveevvevLdvmse

PdP

eeevevPLvmse

PdP

evPvmseQ

tedrt

edrt

edrt

edrt

edrt

edr

tedrt

edrt

edrt

edr

tedr

v

L

v

PL

v

Ld

tedrt

edr

v

PL

v

Ld

tedrt

edr

v

Ld

tedrt

edr

v

L

v

P

v

PL

tedr

v

PL

tedr

tedr

v

P

tedr

tedr

e

)( )]}1)(([

)]1)(1([)]1([{)(

1/'80

)]}1)(1([)]1()[({)(

/'80

)]1()[()(

/'80

2,1,1,

1,1,1,

2,1,1,

2,

1,2,

1,1,1,1,

1,2,1,1,

2,2,

PLeeevv

eevvevPvPdP

mse

eevvevPLvPdP

mse

evLdPdP

vmseQ

thdrt

hdrt

hdr

thdrt

hdrt

hdr

thdrt

hdrt

hdr

thdr

v

Ld

v

L

v

PL

thdrt

hdr

v

PL

v

P

thdrt

hdr

v

P

thdrt

hdr

v

Ld

v

PL

thdrt

hdr

v

PL

thdrt

hdr

v

Ld

thdr

thdrh

Electrons:

Holes:

Where: 0,,

2,0,,

1, , EvEv hehedr

hehedr

),)), (,,,,,( hewordVLPfQ

)(0 LdL

VE

Plots

We can make some plots for some typical cases:

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

8000.0

9000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)

Total Collected Charge

Qe

Qh

Strip or pixel detectorn+ strips/pixel on the front, junction on the front (SFJF) d = 100 um, P = 40 um, L=1/2d, V= 500V

P= 40 µm, = 0.01L=1/2d, = 0.3

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0E

0EEd

n+ p+P-type

Electric field

Weighting field

0

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

8000.0

9000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh

Strip or pixel detectorn+ strips/pixel on the front,junction on the back (SFJB) d = 100 um, P = 40 um, L=1/2d, V= 500V

P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0EEd

0E

n+ p+P-type

Electric field

Weighting field

0

SFJB

P= 40 µm, = 0.01L=1/2d, = 3.33

a) SFJF b) SFJBFig. 5 Collected charges for a strip or pixel detector with a) junction on the strip side (SFJF), and, b) junction on the backside (SFJB). The high-weighting field is 100 times more than the low one ( = 0.01), and high-electric field is 3 times more than the low one ( = 0.3 for JF, and

3.333 for JB).

The total collected charge is a little bit lower, but not by much if the low E-field region at the strip side is not too low.

Simulation Results

Plots

a) SFJF b) SFJBFig. 5 Collected charges for a strip or pixel detector with a) junction on the strip side (SFJF), and, b) junction on the backside (SFJB). The high-weighting field is 100 times more than the low one ( = 0.01), and high-electric field is 30 times more than the low one ( = 0.03 for JF,

and 33.33 for JB).

The total collected charge much lower if the low E-field region at the strip side is very low.

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

8000.0

9000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


P= 40 µm, = 0.01L=1/2d, = 0.03

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0E

0EEd

n+ p+P-type

Electric field

Weighting field

0

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

8000.0

9000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0EEd

0E

n+ p+P-type

Electric field

Weighting field

0

SFJB

P= 40 µm, = 0.01L=1/2d, = 33.33

Simulation Results

Plots

a) SFJF b) SFJB

Zero total collected charge if there is no E-field near the strip side.

0.0

500.0

1000.0

1500.0

2000.0

2500.0

3000.0

3500.0

4000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0dE

00 E

n+ p+ (before SCSI)n

Electric field

Weighting field

0

SFJBp+ n+ (after SCSI)n

P= 40 µm, = 0.01L=1/2d, = 1x107

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


P= 40 µm, = 0.01L=1/2d, = 1x10-8

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0E

0dE

n+ p+P-type

Electric field

Weighting field

0

Partial depletion cases:

Half of total collected charge if only half of the detector is depleted.

Simulation Results

Detector thickness dependence:

0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

20000.0

22000.0

24000.0

26000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


d = 300 µmP= 40 µm, = 0.01L=1/2d, = 0.03

x0P d

)(

1

PdPE Max

W

)( PdPE Min

W

L

0E

0EEd

n+ p+P-type

Electric field

Weighting field

0

0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

20000.0

22000.0

24000.0

26000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

20000.0

22000.0

24000.0

26000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


0.0

2000.0

4000.0

6000.0

8000.0

10000.0

12000.0

14000.0

16000.0

18000.0

20000.0

22000.0

24000.0

26000.0

0.E+00 2.E+15 4.E+15 6.E+15 8.E+15 1.E+16

Fluence (neq/cm^2)

Co

llec

ted

Ch

arg

e (

e's

)


Qe

Qh


d = 200 µmP= 40 µm, = 0.01L=1/2d, = 0.03

d = 75 µmP= 40 µm, = 0.01L=1/2d, = 0.03

d = 50 µmP= 40 µm, = 0.01L=1/2d, = 0.03

a) b)

c) d)

The thickness the detector, the more contribution of e’s to Q at low fluences At high fluences (>5x1015neq/cm2), total collected charge are almost the same and contribution by holes are approaching those of e’s for all thickness >P.

Simulation Results

Detector segmentation/pitch dependence:

0200400600800

100012001400160018002000220024002600

0 20 40 60 80 100 120 140 160

Pitch (P, um)

Co

llect

ed C

har

ge

('e's

)

Q

Qe

Qh

Strip or pixel detectorn+ strips/pixel on the front,junction on the back (SFJF) d = 150 um, L=1/2d, V= 1500V

1x1016 neq/cm2

For P 60 µm, the hole contribution is about 43% due to P >> dCCE or dt

For P < 60 µm, the hole contribution decreases as the P approaches dCCE or dt

tstdrtCCE vvdd )(or

Increased Hole Contribution in Collected Charge in Heavy Irradiation Environments

P d

n+ p+P-type

Weighting field

0 dCCE

dt

tstdrtCCE vvdd )(or

P dCCE

P d

n+ p+P-type

Weighting field

0 dCCE

dt

tstdrtCCE vvdd )(or

P >> dCCE

Detector segmentation/pitch dependence: Explanations

For P >> dCCE or dt,

(cases of high radiation, or large pitch)

hole contribution is compatible to that of electron

For P dCCE or dt,

(cases of low radiation, or very small pitch)

hole contribution is much smaller than

that of electron


Detector bias voltage dependence:

0

400

800

1200

1600

2000

2400

100 1000 10000 100000

Bias voltage (Volts)

Co

llec

ted

Ch

arg

e (

'e's

)

Q

Qe

Qh

Strip or pixel detector, SFJF

1x1016 neq/cm2

P = 40 µmd= 150 µm, = 0.01L=1/2d, = 0.03

500 5000 50000

For V 1000 volts, Q reaches more than 90% of the maximum

For P = 40 µm, the hole contribution is about 36%


Some Approximations

Partially depleted detector: E-field in region 2 is zero ( =0 ), w = L

)(

)(

)]()1[()]1()[(/'80

)(

)1(/'80

1,1,1,1,

1,

1,1,1,

1,1,

PL

PLP

eeevevPLvmse

PLP

evPvmseQ

tedrt

edrt

edrt

edr

tedr

v

L

v

P

v

PL

tedr

v

PL

tedr

tedr

v

P

tedr

tedr

e

)(

)]}1)(1([)]1([{)(

1/'80

)]1()[()(

/'80

1,1,1,

1,

1,1,1,1,

1,1,

PL

eevvevPvPLP

mse

evPLvPLP

mseQ

thdrt

hdrt

hdr

thdr

v

PL

v

P

thdrt

hdr

v

P

thdrt

hdr

v

PL

thdrt

hdr

h

x0P d

)(

1

PLPE Max

W

)( PLPE Min

W

L(or w)

0E

0dE

n+ p+P-type

Electric field

Weighting field

0

Some Approximations

At high fluences (SLHC):

eCCEt

edr

e dmsevmseQ /'80/'80 1,

hCCEt

hdr

h dmsevmseQ /'80/'80 1,

)(/'80 hCCE

eCCE ddmseQ

At 1x1016 neq/cm2: dCCE = 20 µm:

Q ~ 3200 e’s

)](6

11[

1,1,0

thdrt

edr

pad v

L

v

LQQ

Some Approximations

At low fluences ( 1015 neq/cm2)

For pad detectors:

For fully depleted pad detectors:

)](6

11[ )](

6

11[ 0

1,1,0

thCCE

eCCEt

hdrt

edr

pad d

d

d

dQ

v

d

v

dQQ

Summary1. A simple model has bee developed to simulate segmentated Si detectors

2. Analytical solutions can be obtained for colleted charge

3. Contribution of hole to the total colletected charge increases with radiation fluence in a n+ segmentation Si detector

4. At SLHC fluences close to 1x1016 neq/cm2, contribution of hole to the total colletected charge is comparable to that of electrons

5. At SLHC fluences, total collected charge can be appriximated as:

6. To improve radiation hardness, carrier trapping distance has to be increased --- e.g. by pre-filling of the traps, or decrease carrier drift distance (3D)

),)), (,,,,,( hewordVLPfQ

)(/'80 hCCE

eCCE ddmseQ

Collected charges simulated with real weighting field

Documents

Outline