study of electric field distortion and charge careers collection
DESCRIPTION
Study of electric field distortion and charge careers collection. f= U. f= 0. W. H. L. detector geometry. Electric field calculation in germanium. poisson equation for potential: boundary conditions: electric field:. Electric field calculation in germanium. - PowerPoint PPT PresentationTRANSCRIPT
Samuel Lago
Study of electric field Study of electric field distortion and charge distortion and charge
careers collection careers collection
Samuel Lago
detector geometrydetector geometry
L
W
H
U
0
U
0
0
Samuel Lago
Electric field calculation in germaniumElectric field calculation in germanium
poisson equation for potential:
boundary conditions:
electric field:
const
E
0
),,(2 zyx
gradE
Samuel Lago
Electric field calculation in germaniumElectric field calculation in germanium
three dimension poisson equation:
),,(
2
2
2
2
2
2 zyx
zyx
6.16
10854.8
:constant dielectric
120
0
r
r
Vm
C
zh
zyx
mNNCe
m
CeNNe
DA
DA
)(),,(
10 106.1
6.1)( :density charge
010
3
1619
33
Samuel Lago
3D detector geometry3D detector geometry
0
U
0x
0
x
0y
0y
0z
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
2D grid
3D grid
• The detector is devided into rectangular controlvolumes.
• The potential is approximated through the grid points in the center of every controlvolume.
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation:
),,(
2
2
2
2
2
2 zyx
zyx
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation:
KK VVdV
zyxdV
zyx ),,(
2
2
2
2
2
2
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation (source term):
2
2
2010 )
)((
),,(
zz
zz
KK
V
K
K
K
yxz
hz
dVzyx
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
KV
tne
bsw
dVzyx
yxz
zxy
zyx
yxz
zxy
zyx
),,(
discretization of poisson equation (left hand side):
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
))(( 2xOxxx PE
PE
e
discretization of poisson equation (left hand side):
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
:const
discretization of poisson equation (Dirichlet boundary):
0))(()())()(()(
)())()((
)())()(()(
))()((
)())()(()(
)(
222
2
2
xOxxxx
xxx
xxxx
xx
xxxx
x
x
eeww
wewW
eeww
ewP
eeww
wE
w
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
:constx
discretization of poisson equation (Neumann boundary):
constxOxxxx
xxx
xxxx
xx
xxxx
x
x
eeww
wewW
eeww
ewP
eeww
wE
w
))(()())()(()(
)())()((
)())()(()(
))()((
)())()(()(
)(
222
2
2
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation:
with all coefficients we get
and a linear system of equations
bA
baaaaaaa PBBSSWWTTNNEEPP
Samuel Lago
PotentialPotential
p-type detector
blocking contact on unsegmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
z
e-3, e-3
pixel-size: 10mm x 10mm
Samuel Lago
PotentialPotential
p-type detector
blocking contact on unsegmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
z
e-3, e-3
ce-3
pixel-size: 10mm x 10mm
c
Samuel Lago
PotentialPotential
p-type detector
blocking contact on unsegmented electrode
U = 4250 V
geometry :
0.06m x 0.06m x 0.02m
x
e-3, e-3
pixel-size: 10mm x 10mm
Samuel Lago
PotentialPotential
p-type detector
blocking contact on unsegmented electrode
U = 4250 V
geometry :
0.06m x 0.06m x 0.02m
x
e-3, e-3
pixel-size: 10mm x 10mm
Samuel Lago
PotentialPotential
p-type detector
blocking contact on segmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
z
e-3, e-3
pixel-size: 10mm x 10mm
Samuel Lago
PotentialPotential
n-type detector
blocking contact on segmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
z
e-3, e-3
ce-3
pixel-size: 10mm x 10mm
c
c
Samuel Lago
Depletion chargeDepletion charge
blocking contact on segmented electrode
z
pixel 6x6 mm 10x10 mm 14x14 mm 18x18 mm
z up 5828 3178 2212 1836
z down 6219 3588 2629 2258
x, y 7478 4250 3064 2601
const:1.0E-3 4015 2256 1614 1365
const:2.0E-3 8030 4511 3227 2729
Samuel Lago
Depletion chargeDepletion charge
blocking contact on unsegmented electrode
pixel 6x6 mm 10x10 mm 14x14 mm 18x18 mm
z up 2265 2265 2262 2251
z down 1813 1813 1811 1806
x, y 2499 2542 2570 2575
const:1.0E-3 1360 1359 1358 1352
const:2.0E-3 2719 2718 2715 2704
Samuel Lago
Pulse shapesPulse shapes
dtrEvrEU
qdQ
dQdQtQttQ
W
he
))(()(
)()(
Total charge at time "t"
Samuel Lago
Pulse shapesPulse shapes
=const=1.6E-3 ,)(
),,( 010 z
hzyx
Samuel Lago
Calculations with the LOAX geometryCalculations with the LOAX geometry
Samuel Lago
Calculations with the LOAX geometryCalculations with the LOAX geometry
Samuel Lago
OutlookOutlook
• investigation of the position resolution with (x,y,z) in n- and p-type detector
• calculatulation of potential and electric Field with (x,y,z) in COMSOL
• export Data for investigation of the position resolution in Fortran-Code