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
![Page 1: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/1.jpg)
Samuel Lago
Study of electric field Study of electric field distortion and charge distortion and charge
careers collection careers collection
![Page 2: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/2.jpg)
Samuel Lago
detector geometrydetector geometry
L
W
H
U
0
U
0
0
![Page 3: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/3.jpg)
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
![Page 4: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/4.jpg)
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
![Page 5: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/5.jpg)
Samuel Lago
3D detector geometry3D detector geometry
0
U
0x
0
x
0y
0y
0z
![Page 6: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/6.jpg)
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.
![Page 7: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/7.jpg)
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation:
),,(
2
2
2
2
2
2 zyx
zyx
![Page 8: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/8.jpg)
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
discretization of poisson equation:
KK VVdV
zyxdV
zyx ),,(
2
2
2
2
2
2
![Page 9: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/9.jpg)
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
![Page 10: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/10.jpg)
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
KV
tne
bsw
dVzyx
yxz
zxy
zyx
yxz
zxy
zyx
),,(
discretization of poisson equation (left hand side):
![Page 11: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/11.jpg)
Samuel Lago
Finite-Volume-MethodFinite-Volume-Method
))(( 2xOxxx PE
PE
e
discretization of poisson equation (left hand side):
![Page 12: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/12.jpg)
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
![Page 13: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/13.jpg)
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
![Page 14: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/14.jpg)
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
![Page 15: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/15.jpg)
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
![Page 16: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/16.jpg)
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
![Page 17: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/17.jpg)
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
![Page 18: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/18.jpg)
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
![Page 19: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/19.jpg)
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
![Page 20: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/20.jpg)
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
![Page 21: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/21.jpg)
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
![Page 22: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/22.jpg)
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
![Page 23: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/23.jpg)
Samuel Lago
Pulse shapesPulse shapes
dtrEvrEU
qdQ
dQdQtQttQ
W
he
))(()(
)()(
Total charge at time "t"
![Page 24: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/24.jpg)
Samuel Lago
Pulse shapesPulse shapes
=const=1.6E-3 ,)(
),,( 010 z
hzyx
![Page 25: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/25.jpg)
Samuel Lago
Calculations with the LOAX geometryCalculations with the LOAX geometry
![Page 26: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/26.jpg)
Samuel Lago
Calculations with the LOAX geometryCalculations with the LOAX geometry
![Page 27: Study of electric field distortion and charge careers collection](https://reader036.vdocuments.us/reader036/viewer/2022070401/5681372f550346895d9ebc67/html5/thumbnails/27.jpg)
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