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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


discretization of poisson equation:

),,(

2

2

2

2

2

2 zyx

zyx

Samuel Lago



KK VVdV

zyxdV

zyx ),,(

2

2

2

2

2

2

Samuel Lago


discretization of poisson equation (source term):

2

2

2010 )

)((

),,(

zz

zz

KK

V

K

K

K

yxz

hz

dVzyx

Samuel Lago


KV

tne

bsw

dVzyx

yxz

zxy

zyx

yxz

zxy

zyx

),,(

discretization of poisson equation (left hand side):

Samuel Lago


))(( 2xOxxx PE

PE

e

discretization of poisson equation (left hand side):

Samuel Lago


: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


: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



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


U = 4000 V

geometry :

0.06m x 0.06m x 0.02m

z

e-3, e-3

ce-3


c

Samuel Lago

PotentialPotential

p-type detector


U = 4250 V

geometry :

0.06m x 0.06m x 0.02m

x

e-3, e-3


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


Samuel Lago

PotentialPotential

n-type detector


U = 4000 V

geometry :

0.06m x 0.06m x 0.02m

z

e-3, e-3

ce-3


c

c

Samuel Lago

Depletion chargeDepletion charge


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


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

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

Download - Study of electric field distortion and charge careers collection

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