Semi-Analytical 3D solution for assessing radial collector ...
Analytical approach for 3D detectors engineering
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Transcript of 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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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)
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
The critical regions of 3D detectors
Sphericalr0
Rd
Cylindrical
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
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RD50 13-th meeting, CERN, 10-12 November, 2008
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/
RD50 13-th meeting, CERN, 10-12 November, 2008
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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
Vladimir Eremin RD50 13-th meeting, CERN, 10-12 November, 2008
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
RD50 13-th meeting, CERN, 10-12 November, 2008