Download 9_LI__RD-50-6-09-rev2

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
Outline
1. 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 Fields
analytical solutions for collected charge
EW (x0)
Weighting field:
1

 P   (d  P)

EW ( x0 )  


 P   (d  P )
0  1
(0  x 0  P )
Real weighting field
1
EWMax 
P   (d  P)
(P  x0  d )
,
P is the segmentation pitch
EWMin 
d the detector thickness, or depletion
depth
0
x0
P

P   (d  P)
d
E (x0)
Electric Field:
Real field
(0  x 0  L )
E 0
E ( x0 )  
 E 0 ( L  x 0  d )
Region 1
E0
(   0)
Region 2
n+
p+
e
E0 
h
V
L   ( d  L)
Ed  E0
0
L
x0
d
(  0)
Simplified Model of Electric and Weighting Fields
Two typical cases:
Strip/pixel front, Junction front (SFJF)
Strip/pixel front, Junction back (SFJB)
,
n+
EWMax 
n+
p+
P-type
1
P   (d  P)
p+
P-type
EWMax 
Electric field
Weighting field
1
P   (d  P)
Electric field
Weighting field
Ed  E0
E0
Region 1
E0
Region 2
Ed  E0
EWMin 
0
P
L
x0
d

P   (d  P)
EWMin 
0
P
L
d

P   (d  P)
Simplified Model of Electric and Weighting Fields
Basic equations
v dr ( x(t )) 
Carrier drift velocity:
w
Depletion Depth:
,
1
Trapping time constant:
Induced current by a
Charge layer
Q0
x0 at x0:
d
t
20V
,
eN eff
N eff  0.02  Φneq
    neq  5  10 7 cm 2 / s   neq
t
t


Q0
t
e,h
e,h
e,h
di (t ) 
x0  EW  vdr  e  80 e' s/m  x0  EW  vdr  e  t
d
d
Total collected charge:
dx(t )
E ( x(t )

dt
1  E ( x(t ) / v s
t edr
Q   80e' s / m  dx0  [  EW  vdre  e
0
0

t
t
h
t dr
dt   EW  vdrh  e
0

t
t
dt ]
Simulation Results
Solutions
We can obtain analytical solutions for collected charges:
Electrons:
Q e  80e' s / m  vdre ,1 t
80e' s / m  vdre ,1 t
80e' s / m 
P  v  (1  e
e
dr ,1 t

P
e
vdr
,1 t
)
P   (d  P)
[( L  P )  v  (1  e

e
dr ,1 t

LP
e
vdr
,1 t
)]  v  [(1  e

e
dr ,1 t
LP
e
vdr
,1 t
)  (e

P
e
vdr
,1 t
e

L
e
vdr
,1 t
)]
P   (d  P)
v  [( d  L)  v  (1  e
e
dr , 2 t

e
dr , 2 t
d L
e
vdr
,1 t
)]  v  [v
e
dr ,1 t
 (1  e
e
dr , 2 t

d L
e
vdr
, 2 t
)(1  e


LP
e
vdr
, 2 t
)]  v  [v
e
dr ,1 t
 (1  e

e
dr , 2 t
P   (d  P)
( L  P)
Holes:
d L

vdrh , 2 t
v
h
Q  80e' s / m 
 [( d  L)  vdr , 2 t (1  e
P   (d  P)
h
80e' s / m 

P   (d  P)
{v  [( L  P)  v  (1  e
h
dr ,1 t
h
dr ,1 t

h
dr , 2 t
)] 
LP
h
vdr
,1 t
)]  v
 [v  (1  e
h
dr , 2 t
h
dr ,1 t
P

LP
h
vdr
,1 t
)(1  e
P
LP

d L
h
vdr
, 2 t
 h
 h
 h
1
v 
v 
v 
80e' s / m 
{vdrh ,1 t [ P  vdrh ,1 t (1  e dr,1 t )]  vdrh ,1 t [vdrh ,1 t (1  e dr,1 t )(1  e dr,1 t )] 
P   (d  P)
 v
Where:
 [v  (e
h
dr , 2 t
h
dr ,1 t

LP
h
vdr
,1 t
e

L
h
vdr
,1 t
)(1  e

d L
h
vdr
, 2 t
)]}
( L  P)
vdre,h,1   e,h  E0 , vdre,h, 2   e,h  E0
Q  f ( P, , L,  ,V , d (or w)),  e ,  h )
E0 
V
L   ( d  L)
)]} 
d L
e
vdr
, 2 t

)(e
LP
e
vdr
,1 t
e

L
e
vdr
,1 t
)]
Simulation Results
Plots
We can make some plots for some typical cases:
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.
8000.0
p+
P-type
EWMax 
P= 40 µm,  = 0.01
L=1/2d,  = 0.3
1
P   (d  P)
Electric field
Weighting field
E0
5000.0
Ed  E0
4000.0
Min
W
E
0
3000.0
P
L
x0
d


P   (d  P)
6000.0
Fluence (neq/cm^2)
8.E+15
1.E+16
1

P   (d  P)
Electric field
Weighting fiel
Ed  E0
4000.0
E0
EWMin 
3000.0
1000.0
6.E+15
p+
P-type
5000.0
1000.0
4.E+15
SFJB
n+
E
2000.0
2.E+15
P= 40 µm,  = 0.01
L=1/2d,  = 3.33
Max
W
2000.0
0.0
0.E+00
Total Collected Charge
Qe
Qh
7000.0
n+
6000.0
Strip or pixel detector
n+ strips/pixel on the front,junction on the back (SFJB)
d = 100 um, P = 40 um, L=1/2d, V= 500V
8000.0
Total Collected Charge
Qe
Qh
7000.0
Collected Charge (e's)
9000.0
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 100 um, P = 40 um, L=1/2d, V= 500V
Collected Charge (e's)
9000.0
0.0
0.E+00
0
2.E+15
4.E+15
6.E+15
P
8.E+15
L
d

P   (d  P)
1.E+16
Fluence (neq/cm^2)
a) SFJF
b) SFJB
Fig. 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).
Simulation Results
Plots
The total collected charge much lower if the low Efield region at the strip side is very low.
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 100 um, P = 40 um, L=1/2d, V= 500V
8000.0
Collected Charge (e's)
n+
EWMax 
7000.0
1
P   (d  P)
P= 40 µm,  = 0.01
L=1/2d,  = 0.03
SFJB
Electric field
Weighting field
E0
4000.0
Ed  E0
EWMin 
0
3000.0
P
L
Total Collected Charge
Qe
Qh
p+
P-type
6000.0
Strip or pixel detector
n+ strips/pixel on the front,junction on the back (SFJB)
d = 100 um, P = 40 um, L=1/2d, V= 500V
8000.0
Total Collected Charge
Qe
Qh
7000.0
5000.0
9000.0
x0
d

P   (d  P)
Collected Charge (e's)
9000.0
6000.0
5000.0
n+
p+
P-type
1
EWMax 
P   (d  P)
P= 40 µm,  = 0.01
L=1/2d,  = 33.33
Electric field
Weighting field
Ed  E0
4000.0
3000.0
EWMin 
E0
2000.0
2000.0
1000.0
1000.0
0.0
0.E+00
2.E+15
4.E+15
6.E+15
Fluence (neq/cm^2)
8.E+15
1.E+16
0.0
0.E+00
0
2.E+15
4.E+15
P
6.E+15
L
8.E+15
d

P   (d  P)
1.E+16
Fluence (neq/cm^2)
a) SFJF
b) SFJB
Fig. 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).
Simulation Results
Plots
Partial depletion cases:
Half of total collected charge if only half of the
detector is depleted.
5000.0
Zero total collected charge if there is no E-field
near the strip side.
4000.0
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 100 um, P = 40 um, L=1/2d, V= 500V
Strip or pixel detector
n+ strips/pixel on the front,junction on the back (SFJB)
d = 100 um, P = 40 um, L=1/2d, V= 500V
3500.0
4000.0
n+
P-type
Collected Charge (e's)
EWMax 
P= 40 µm,  = 0.01
L=1/2d,  = 1x10-8
3000.0
2000.0
p+
1
P   (d  P)
3000.0
Weighting field
E0
0
P
L
Total Collected Charge
Qe
Qh
Electric field
x0
EWMin 
d
Ed  0

P   (d  P)
SFJB
Collected Charge (e's)
Total Collected Charge
Qe
Qh
2500.0
2000.0
n
n+ (after SCSI)
n+
n
p+ (before SCSI)
P= 40 µm,  = 0.01
L=1/2d,  = 1x107
EWMax 
1
P   (d  P)
Electric field
Weighting field
Ed  0
1500.0
E0  0
1000.0
1000.0
p+
EWMin 
0
P
L
d
500.0
0.0
0.E+00
2.E+15
4.E+15
6.E+15
8.E+15
Fluence (neq/cm^2)
1.E+16
0.0
0.E+00
2.E+15
4.E+15
6.E+15
8.E+15
1.E+16
Fluence (neq/cm^2)
a) SFJF
b) SFJB

P   (d  P)
Simulation Results
24000.0
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 300 um, P = 40 um, L=1/2d, V= 500V
20000.0
Collected Charge (e's)
16000.0
24000.0
Total Collected Charge
Qe
Qh
22000.0
18000.0
26000.0
d = 300 µm
P= 40 µm,  = 0.01
n
L=1/2d,  = 0.03
p+
P-type
EWMax 
14000.0
1
P   (d  P)
Electric field
Weighting field
E0
12000.0
10000.0
16000.0
d = 200 µm
P= 40 µm,  = 0.01
L=1/2d,  = 0.03
14000.0
12000.0
10000.0
8000.0
8000.0
Ed  E0
EWMin 
6000.0
0
P
L
x0
d

6000.0
P   (d  P)
4000.0
4000.0
2000.0
2000.0
0.0
0.E+00
Total Collected Charge
Qe
Qh
20000.0
18000.0
+
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 200 um, P = 40 um, L=1/2d, V= 500V
22000.0
Collected Charge (e's)
26000.0
Detector thickness dependence:
2.E+15
4.E+15
6.E+15
8.E+15
0.0
0.E+00
1.E+16
2.E+15
20000.0
Collected Charge (e's)
16000.0
24000.0
Total Collected Charge
Qe
Qh
22000.0
18000.0
26000.0
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 75 um, P = 40 um, L=1/2d, V= 500V
d = 75 µm
P= 40 µm,  = 0.01
L=1/2d,  = 0.03
12000.0
10000.0
16000.0
12000.0
10000.0
8000.0
6000.0
6000.0
4000.0
4000.0
2000.0
2000.0
4.E+15
6.E+15
Fluence (neq/cm^2)
c)
8.E+15
1.E+16
d = 50 µm
P= 40 µm,  = 0.01
L=1/2d,  = 0.03
14000.0
8000.0
2.E+15
1.E+16
Total Collected Charge
Qe
Qh
20000.0
18000.0
14000.0
0.0
0.E+00
8.E+15
Strip or pixel detector
n+ strips/pixel on the front, junction on the front (SFJF)
d = 75 um, P = 40 um, L=1/2d, V= 500V
22000.0
Collected Charge (e's)
24000.0
6.E+15
b)
a)
26000.0
4.E+15
Fluence (neq/cm^2)
Fluence (neq/cm^2)
0.0
0.E+00
2.E+15
4.E+15
6.E+15
8.E+15
1.E+16
Fluence (neq/cm^2)
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.
Increased Hole Contribution in Collected Charge in Heavy Irradiation Environments
Collected Charge ('e's)
Detector segmentation/pitch dependence:
2600
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Strip or pixel detector
n+ strips/pixel on the front,junction on the back (SFJF)
d = 150 um, L=1/2d, V= 1500V
16
2
1x10 neq/cm
0
20
40
60
Q
Qe
Qh
80
100
120
140
160
Pitch (P, um)
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
d CCE (or d t )  vdr  t  vs  t
Increased Hole Contribution in Collected Charge in Heavy Irradiation Environments
Detector segmentation/pitch dependence: Explanations
n+
p+
P-type
Weighting field
n+
Weighting field
P >> dCCE
P  dCCE
d CCE (or d t )  vdr  t  vs  t
d CCE (or d t )  vdr  t  vs  t
0
dCCE P
dt
p+
P-type
d
0
P dCCE
dt
d
For P >> dCCE or dt,
For P  dCCE or dt,
(cases of high radiation, or large pitch)
(cases of low radiation, or very small pitch)
hole contribution is compatible to that of electron
hole contribution is much smaller than
that of electron
Increased Hole Contribution in Collected Charge in Heavy Irradiation Environments
Detector bias voltage dependence:
Strip or pixel detector, SFJF
Collected Charge ('e's)
2400
1x1016 neq/cm2
2000
1600
Q
Qe
1200
Qh
800
P = 40 µm
d= 150 µm,  = 0.01
L=1/2d,  = 0.03
400
0
100
500
1000
5000 10000
50000 100000
Bias voltage (Volts)
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
Q e  80e' s / m  vdre ,1 t
80e' s / m  vdre ,1 t
P  v  (1  e
e
dr ,1 t

P
e
vdr
,1 t
)
P   ( L  P)
[( L  P)  v  (1  e
e
dr ,1 t


LP
e
vdr
,1 t
)]  v  [(1  e
e
dr ,1 t

LP
e
vdr
,1 t
)  (e

P
e
vdr
,1 t
e

L
e
vdr
,1 t
)]
P   ( L  P)
( L  P)
n+

p+
P-type
EWMax 
1
P   ( L  P)
Electric field
Weighting field
E0
EWMin 
0
Q  80e' s / m 
h

P   ( L  P)
v  [( L  P)  v  (1  e
h
dr ,1 t
h
dr ,1 t
P

P

P   ( L  P)
L(or w) x0
d
LP
h
vdr
,1 t
Ed  0
)] 
P
LP
 h
 h
 h
1
vdr ,1 t
vdr ,1 t
v 
h
h
h
h
80e' s / m 
{vdr ,1 t [ P  vdr ,1 t (1  e
)]  vdr ,1 t [vdr ,1 t (1  e
)(1  e dr,1 t )]}
P   ( L  P)
( L  P)
Some Approximations
At high fluences (SLHC):
e
Qe  80e' s / m  vdre ,1 t  80e' s / m  dCCE
h
Qh  80e' s / m  vdrh ,1 t  80e' s / m  dCCE
e
h
Q  80e' s / m  (d CCE
 d CCE
)
At 1x1016 neq/cm2: dCCE = 20 µm:
Q ~ 3200 e’s
Some Approximations
At low fluences ( 1015 neq/cm2)
For pad detectors:
Qpad
1 L
L
 Q0 [1  ( e
 h )]
6 vdr ,1 t vdr ,1 t
For fully depleted pad detectors:
Qpad
1 d
d
1 d
d
 Q0 [1  ( e
 h )]  Q0 [1  ( e  h )]
6 vdr ,1 t vdr ,1 t
6 dCCE dCCE t
Summary
1. A simple model has bee developed to simulate
segmentated Si detectors
2. Analytical solutions can be obtained for colleted
charge
Q  f ( P, , L,  ,V , d (or w)),  e ,  h )
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: Q  80e' s / m  ( d e  d h )
CCE
CCE
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)
Collected charges simulated with real weighting field
Induced charge
n+/p/p+, P=50 um, Ps =40 um, d =500 um, Neff=8E11/cm3, V=1000V
1E16 neq/cm2
3.0E+03
Induced charge (e's)
2.5E+03
2.0E+03
Hole
1.5E+03
Electron
Total
1.0E+03
5.0E+02
0.0E+00
0.0E+00
2.0E-10
4.0E-10
6.0E-10
t (s)
8.0E-10
1.0E-09