analytical approach for 3d detectors engineering

Analytical approach for 3D detectors engineering

Vladimir Eremin, Elena Verbitskaya

Ioffe Physico -Technical Institute of Russian Academy of Sciences

St. PetersburgRussia

RD50 13-th meeting, CERN, 10-12 November, 2008

Outline

1.Typical constructions of 3D detectors 2.Electric field in 3D detectors3.Radiation effects in 3D detectors4.Conclusions

Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008

J/O-J/O

J/O-SiO2

J/O-Osurf J-Osurf

J-O/Osurf

Typical 3D detector constructions

Junctioncolumn (J)

Ohmickcolumn (O)

Front side

Back side


The Large Scale Model and operational parameters

Cylindrical p+-n junction

Sphericalp+-n junction

The depleted radius (Rd)

Sensitive volume (S)

The pinch-off voltage (Vpf)

The maximum operational voltage (Vm)


The critical regions of 3D detectors

Sphericalr0

Rd

Cylindrical


The main equations

0

01

effNq

dr

dr

dr

d

r

0

022

1

effNq

dr

dr

dr

d

r

1

2)(

2

0

0

r

Rr

NqrE deff

r0 Rd


r0

Rd

1

3)(

3

0

0

r

Rr

NqrE deff

The electric field distribution around the column

r0

Rd0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

0 0.001 0.002 0.003 0.004 0.005

Radius, u

Ele

ctr

ic f

ield

, V

/cm

Neff=1012cm-

3

r0=5uRd=50u


0.0E+00

5.0E+02

1.0E+03

1.5E+03

2.0E+03

2.5E+03

3.0E+03

3.5E+03

4.0E+03

4.5E+03

0 0.001 0.002 0.003 0.004 0.005

Radius, u

Ele

ctr

ic f

ield

, V

/cm

The pinch-off voltage

2pfRS

2

0

2

0

2

0

0 1ln4 pf

pfpf

effpf R

r

r

RR

NqV

MCZ: 1k cmNeff=4x1012cm-

3

r0=5uRpf=50u

r0

Rpf

Vladimir Eremin

78.04/


0

2

4

6

8

10

12

14

16

18

20

0.E+00 2.E-03 4.E-03 6.E-03 8.E-03 1.E-02

Rpf, cmV

pf,

V

The full depletion voltage

2pfRS

2

0

2

0

2

0

0 1ln4 a

r

r

aa

NqV efffd

MCZ: 1k cmNeff=4x1012cm-

3

r0=5uPitch=a=40u

r0

Rpf

Vladimir Eremin

78.04/


0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

1.6E-04

0 5 10 15 20 25 30

Bias, VS

, cm

2

Vpf Vfd

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

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

Fluence, n/cm2

Em

ax

, V

/cm

The maximal electric field and pinch- off voltage increase with

fluence

1

2

2

00

0

0max r

Rr

NqE pfeff

β=1.7e-2

Cylindrical part

Neff=βxF

0.0E+00

1.0E+02

2.0E+02

3.0E+02

4.0E+02

5.0E+02

6.0E+02

7.0E+02

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

Fluence, n/cm2

Vp

f, V

2

0

2

0

2

0

0 1ln4 pf

pfpf

effpf R

r

r

RR

NqV


MCZ: 1k cmr0=5uRpf=50u

Effect of 2D and 3D focusing on the breakdown voltage

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.01 0.10 1.00

r0/(Rd-r0)

Vb

r/V

br(

pla

na

r)

r0

Rd

Cylindrical

Spherical

Vbr(cyl)=0.4Vbr(planar)

Vbr(spher)=0.18Vbr(planar)

E

x

r0/Rd = 10

2D, 3D

1D


The breakdown characteristics of 3D planar detectors at different

fluences

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+12 1.E+13 1.E+14 1.E+15 1.E+16

Concentration, cm-3

Bre

ak d

ow

n v

olt

ag

e,

V

1.E+01

1.E+04

1.E+07

1.E+10

1.E+13

1.E+16

1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19

Fluence, cm-2


Configuration

Type Break-down

Response Dead volume

Technology

DS

SS

SS

DS

SS

J/O-J/O

J/O-Osurf

J-Osurf

J-O/Osurf

J/O-SiO2

Conclusions

Vladimir Eremin

1. The simple analytical equations can be applied for the engineering of 3D detectors2. At fluence of 1e16 neutrons/cm2 the pinch-off voltage is close to the breakdown voltage for cylindrical junction.3. The type of 3D detectors J-O/Osurf with the dead ends of junction and Ohmick columns is promising for the high fluence application

Thank you for you attention


analytical approach for 3d detectors engineering

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