Download Document

Charge collection in X-ray pixel detectors
based on SI-GaAs doped with Cr
G.I.Ayzenshtata, M.V.Bimatovb, O.P.Tolbanovc, A.P.Vorobievd
a Science
& Production Enterprise “Semicond. Dev. Research Inst”, Tomsk, Russia
b Tomsk State University, Tomsk, Russia
c Siberian Physical Technical Institute, Tomsk, Russia
d State Science Center “High-Energy Physics Institute”, Protvino, Russia
Introduction
The charge collection in a pixel detector and output current shape
were investigated for LEC SI-GaAs in the works by P.J.Sellin,
M.G.Bisogni and others.
The purpose of our work is to simulate a current and charge signal
in the pixel detector after X-ray absorption at various positions
in the detector for GaAs compensated by Cr.
This material distinctive features are:
• an uniform electric field distribution through the detector;
• much longer lifetime of an electron than of a hole (τe >> τh).
The material characteristics:
The mobility and lifetime values of charge carriers are:
µh = 200 cm2/Vs, µe = 1500 cm2/Vs
τh  0.2 ns, τe  10 ns,
The electron velocity depends nonlinearly on the electric field
strength:
ve = µeE when E < 5 kV/cm; ve = 7.5•106cm/s when E > 5 kV/cm
A Formula for the pixel current
The following formula was obtained for calculation of the
current induced on a pixel by a moving charge:

q( t )
i pixel 
v( t )  f (R  x, R  y)  f (R  x, R  y) 
4
k  
 f (R  x, R  y)  f (R  x, R  y)
where R=D/2 is half pixel size, x and y are the horizontal coordinates,
q and v are the charge value and the charge velocity respectively;
function f is:
ab l 2k  a 2  b 2
f (a , b )  2 2
l k (l k  a 2  b 2 )  a 2 b 2


l 2k
1  2
2
2
l

a

b
k


l k  z  h  2kh , k=0,±1,±2,…
where z is the perpendicular coordinate, h is the detector thickness.
z
x
y
(1)
(2)
D=100µm
thickness=500µm
x
The currents induced on irradiated and neighbouring pixels
(the capture was neglected)
µe = 1500 cm2/Vs , µh = 200 cm2/Vs
The pixel contacts are cathodes
the irradiated pixel
the neighbouring pixel
0,8
0,4
The side view of the detector:
the neighbouring
pixel
the irradiated pixel
Current, A
z
D=100µm
0,0
thickness=500µm
-0,4
0
10
time, ns
20
The conclusion: The negative current pulse arises
in the neighbouring pixel
The current induced on the pixel tacking
into account the capture
lifetimes of the charge carriers:
τh  0.2 ns
τe  10 ns
The pixel contacts are cathodes
The pixel contacts are anodes
without the capture
3
Current, A
Current, A
0,4
without the capture
with the capture
0,2
0,0
0
5
10
15
time, ns
20
25
with the capture
2
1
0
0
1
2
time, ns
3
Pixel contacts should be anodes (for SI – GaAs:Cr)
Dependences of CCE on the photon absorption depth
for events occurring under the pixel center
CCE, %
75
50
The pixel contacts are cathodes
Pixel width:
D = 150 m
D = 100 m
D = 40 m
25
0
100
The pixel contacts are anodes
75
CCE, %
100
50
Pixel width:
D = 150 m
D = 100 m
D = 40 m
25
0
0
250
500
Position z from planar contact, m
0
250
500
Position z from planar contact, m
z
500µm
0
Pixel contacts should be anodes (for SI – GaAs:Cr)
The dependences of CCE on the photon absorption depth
for events occurring at various distances from the pixel center
CCE, %
60
x = 48 m
40
20
80
40
20
0 100 200 300 400 500
Position z from planar contact, m
x = 52 m
15
60
0
0
0
30
100 absorption depth = 350m
CCE, %
m
x=0
m
5
3
=
x
CCE, %
80
25
50
75
x, m
100
0
x = 60 m
x = 100 m
-15
0 100 200 300 400 500
Position z from planar contact, m
the examined pixel
the examined pixel
z
z
x=50µm
x=100µm
0
x
0
Signal induced on the next nearest pixel is negligible.
x
Mean charge collected on the pixel
as a function of the detector thickness
The charge averaged over all photons incident on the detector cell
The pixel contacts are anodes
4000
30keV
<Q> , e
3000
60keV
2000
1000
0
0
Pixel width:
D = 150 m
D = 100 m
D = 40 m
500
1000
detector thickness, m
1500
There is an optimal detector thickness for the mean collected charge.
Its value is determined by the photon energy and the drift length of
charge carriers.
Conclusions
The formula for the current induced on the square pixel by a
moving charge was obtained.
The negative current pulse arises in the neighbouring pixel.
The pixel contacts should be anodes in the detector based on
SI-GaAs compensated by Cr.
There is an optimal detector thickness for the mean collected
charge. Its value is determined by the photon energy and the drift
length of charge carriers.