1. Study of electric field distortion and charge careers collection
Samuel Lago

2. detector geometry L W H
f=U
f=0
Samuel Lago

3. Electric field calculation in germanium
poisson equation for potential:
boundary conditions:
electric field:
Samuel Lago

4. Electric field calculation in germanium
three dimension poisson equation:
Samuel Lago

5. 3D detector geometry
Samuel Lago

6. Finite-Volume-Method
The detector is devided into rectangular controlvolumes.
The potential is approximated through the grid points in the center of every controlvolume.
2D grid
3D grid
Samuel Lago

7. Finite-Volume-Method
discretization of poisson equation:
Samuel Lago

8. Finite-Volume-Method
discretization of poisson equation:
Samuel Lago

9. Finite-Volume-Method
discretization of poisson equation (source term):
Samuel Lago

10. Finite-Volume-Method
discretization of poisson equation (left hand side):
Samuel Lago

11. Finite-Volume-Method
discretization of poisson equation (left hand side):
Samuel Lago

12. Finite-Volume-Method
discretization of poisson equation (Dirichlet boundary):
Samuel Lago

13. Finite-Volume-Method
discretization of poisson equation (Neumann boundary):
Samuel Lago

14. Finite-Volume-Method
discretization of poisson equation:
with all coefficients we get
and a linear system of equations
Samuel Lago

15. Potential p-type detector blocking contact on unsegmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
r(z):
r0=1.0 e-3, r1=2.0 e-3
pixel-size: 10mm x 10mm
Samuel Lago

16. Potential p-type detector blocking contact on unsegmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
r(z):
r0=1.0 e-3, r1=2.0 e-3
rc=1.6 e-3
pixel-size: 10mm x 10mm r1 rc r1 r0
Samuel Lago

17. Potential p-type detector blocking contact on unsegmented electrode
U = 4250 V
geometry :
0.06m x 0.06m x 0.02m
r(x):
r0=1.0 e-3, r1=2.0 e-3
pixel-size: 10mm x 10mm
Samuel Lago

18. Potential p-type detector blocking contact on unsegmented electrode
U = 4250 V
geometry :
0.06m x 0.06m x 0.02m
r(x):
r0=1.0 e-3, r1=2.0 e-3
pixel-size: 10mm x 10mm r0 r1
Samuel Lago

19. Potential p-type detector blocking contact on segmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
r(z):
r0=1.0 e-3, r1=2.0 e-3
pixel-size: 10mm x 10mm
Samuel Lago

20. Potential n-type detector blocking contact on segmented electrode
U = 4000 V
geometry :
0.06m x 0.06m x 0.02m
r(z):
r0=1.0 e-3, r1=2.0 e-3
rc=1.6 e-3
pixel-size: 10mm x 10mm r1 r1 rc rc r1 r1 r0 r0
Samuel Lago

21. Depletion charge blocking contact on segmented electrode Samuel Lago 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
blocking contact on segmented electrode z
Samuel Lago

22. Depletion charge blocking contact on unsegmented electrode Samuel Lago
pixel
6x6 mm
10x10 mm
14x14 mm
18x18 mm
z up
2265
2262
2251
z down
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

23. Pulse shapes
Total charge at time "t"
Samuel Lago

24. Pulse shapes
r0=1.0E-3
r1=2.0E-3
r=const=1.6E-3
Samuel Lago

25. Calculations with the LOAX geometry
Samuel Lago

26. Calculations with the LOAX geometry
Samuel Lago

27. Outlook
investigation of the position resolution with r(x,y,z) in n- and p-type detector
calculatulation of potential and electric Field with r(x,y,z) in COMSOL
export Data for investigation of the position resolution in Fortran-Code
Samuel Lago