JC and Marina 12/18/00 Pixel Detector Simulation with Magnetic Field Effects with magnetic Field o Deflection o Effective mobility o Non-constant Hall.

JC and Marina12/18/00

Pixel Detector Simulationwith Magnetic Field

Effects with magnetic Field

o Deflection

o Effective mobility

o Non-constant Hall mobility

Comparison with magnet run

Jianchun (JC) WangSyracuse University 2

Magnetic Field

ZZYYXXZ eBeBeBB,eEE

hole72.0

electron15.1EE

B1

B1V {Heff22

H

2Z

2H

Z

2Z

2H

XH2HZY

Y2Z

2H

YH2HZX

X B1

BBBtan

B1

BBBtan

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Deflection in Magnetic Field

n+

n

p+

-V

0 V

eeee

ee

e

ee

ee

ee

B y

BHX tan

Effect of magnetic field Effect of incident angle

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Deflection in Magnetic Field

Assumption: H = constant eff =

The charge distributions are the

same with B or

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Effective Mobility

2

22H

eff

Tesla1

B01.01

B1

1

Very small effect:

B field Cloud drifts slower Larger Spread

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E-dependent Mobility

Larger E Smaller Hall Smaller deflection

P+ side larger E N+ Side

Smaller E

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Effect of Magnetic Field

With non-constant Hall(E), and eff

The charge distributions are slightly different

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Conclusion

We Don’t expect the magnetic field will

reduce the ratio between two-pixel

clusters and one-pixel clusters

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Magnet Run

Track at 1.3 angle( ~ 0.242 Tesla )

Measurement: Rmin = 0.193

Simulation ( Qth= 2.5Ke ): Rmin = 0.250

What is wrong ?

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Magnet Run

Track at 1.32 ( 23 mrad ) ( ~ 0.245 Tesla )

Measurement: Rmin = 0.193

Simulation ( Qth= 4.0Ke ): Rmin = 0.197

Just to Play around

But there is no other evidence that threshold was wrong

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Magnetic Field

Measured with Gauss meter: 45A 0.585 Tesla

Assume overall scale of the magnetic field uncertain

Use MC simulation to fit 0.517 Tesla (error?)

Error of Hall factor (Hall/ =1.15) can make up the difference

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Summary

MC simulation accurate both for drift and B field simulation

Magnet Run data is not fully understood yet

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Lorentz Angle

Lorentz angle is not a constant along z, shown are overall effects

Larger bias voltage

Larger E field

Smaller mobility

Smaller Lorentz angle

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Lorentz Angle Comparison

Uapplied(V) Udepletion(V) deffective(m) Lorentz( )

MC

ATLAS

MC

ATLAS

MC

ATLAS

MC

ATLAS

Magnetic field: 1.4 Tesla

Udepletion is calculated with effective thickness of the sensor

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Diffusion Constant

Reduce Teff from 390K to 300K

Reduce fraction of doublet by 1.4%

Einstein equation:

D = k T / q

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Angular Fit with Distribution

FPIX0-PstopNormal Incidence Data

MC: 0.5 interval, interpolation between points

Normal incident data: = (1.77 0.09)

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Angular Fit with Distribution

10° Data

5° Data 15° Data

20° Data

FPIX0-Pstop

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Detector Inclination Angle

Nominal Angle ( ) 0 5 10 15 20 30

Minuit Angle ( ) 0.25 6.00 11.0 15.9 21.1 30.4

Fit Angle ( ) 1.77 7.50 12.6 16.4 20.1 N/A

In Minuit fit, the beam is assumed to normal incident on the first SSD, the overall rotation of the detector can not be fitted

In fit, interpolation between MC points (0.5° interval) is used

The error from the fit is about 0.1°, which should be smaller than error from MC model