Ph.D. defense The measurement of the Lorentz angle in the BTeV pixel detectors: the new PCI based...

Ph.D. defensePh.D. defense

The measurement of the Lorentz angle The measurement of the Lorentz angle in the BTeV pixel detectors: in the BTeV pixel detectors:

the new PCI based DAQ, the setup and the resultsthe new PCI based DAQ, the setup and the results

Lorenzo UpleggerLorenzo Uplegger

Milano 26/01/2004

BTeV main goalsBTeV main goals

• Study of the beauty baryons

• Research of new phenomena beyond the Standard Model

• Definitively the measurement of the elements of the Cabibbo-Kobayashi-Maskawa matrix

The BTeV experiment will investigate one of the most fundamental problems of elementary particle physic, the CP violation. Some of the most important aspects of this kind of physics are:

• CP violation in b and c quark sector

• Measurement of the mixing phenomena of the B0s meson

BTeV main goalsBTeV detector layoutBTeV detector layout

•Pixel dimensions 50 m x 400 m •Plane dimensions 10 cm x 10 cm •Gap between stations 4.25 cm•Total number of stations 30•Total number of planes 60

Pixel vertex detectorPixel vertex detector

• The pixel detector will operate in a high magnetic field, so the position reconstructed by the pixels is shifted by the effect of the Lorentz force acting on the charge carriers in the silicon.


• Thus I worked on the development of a setup which allowed me to measure the Lorentz angle.

• The effect on the carriers depends upon the different irradiation doses absorbed by the detector. Since the irradiation dose is greater close to the beam than in the outer regions of the pixel plane, different corrections must be applied in order to keep a good track resolution.

• I covered many aspects of the design and implementation of this new PCI based DAQ and I will first discuss all the features required by the test-beam needs.

DAQ for pixelsDAQ for pixels• Since the pixel detectors will be tested in a 120 GeV beam this year, the work was mainly directed to build a complete read-out system for test-beam studies but flexible enough to allow laboratory bench-test studies and in particular the Lorentz angle measurement.

• Furthermore the DAQ system has been designed with enough flexibility to accommodate the strip readout chip as well.

( I would recall that my group is responsible for the construction of the strip forward tracker )

1. Measure the spatial resolution of the sensors before and afterirradiation

2. Time-Walk studies

3. Test the read-out chip (ROC) in the real BTeV working conditions• data-driven mode

4. Build events using only the temporal information (time-stamp) associated to pixel cells without the aim of an external trigger

Test-beam main goalsTest-beam main goals

Experimental setupExperimental setup


•FPIX0

•FPIX1

•preFPIX2Tb

telescope

detectors under test

DAQdedicated

PC

Detector Mezzanine-card PCI card



Readout &processes monitor PCI

extender

Read-out architectureRead-out architecture


DATA

BCO CLOCK, READ CLOCK…

DATA

BCO CLOCK, READ CLOCK …


DATA

DATA

Experimental setupExperimental setupDATA

DATA

DATA

DATA

DATA

DATA

PCI BUS

Readout process

DAQ main featuresDAQ main features

Data1

Data2

Data3

Data5

Data4

Data6

Data7

Data8

Data11

Data10

Data9

Data12

EVENT

Readout process


noise

noise

Readout process


noise

noise

noise

Data1

Data4

Data6

Data11

Data10

Data7

Data8

Readout process


noise

noise

noise

Data1

Data4

Data6

Data11

Data10

Data7

Data8

noise

Data1

Data4

Data10

Data7

Data1

Data2

Data3

Data5

Data4

Data7

Data10

Data9

Data12

?????

Data1Ts 2

Data2Ts 2

Data5Ts 2

Data6Ts 2

Data7Ts 2

Data8Ts 2

Data9Ts 2

Data3Ts 2

Data4Ts 2

BCO

time-stamp

DAQ main featuresDAQ main features132 ns

123456

Data1Ts 2

Data2Ts 2

Data6Ts 2

Data7Ts 2

Data8Ts 2

Data4Ts 2

Data1Ts 5

Data2Ts 5

Data6Ts 5

Data7Ts 5

Data8Ts 5

Data9Ts 5

Data4Ts 5

Data3Ts 5

Data5Ts 5

Data1Ts 5

Data2Ts 5

Data6Ts 5

Data7Ts 5

Data8Ts 5

Data9Ts 5

Data4Ts 5

Data3Ts 5

Data5Ts 5

Data1Ts 2

Data2Ts 2

Data6Ts 2

Data7Ts 2

Data8Ts 2

Data4Ts 2

Data9Ts 2

Data3Ts 2

Data5Ts 2

The read out system works in absence of an external trigger

The data collection from the different pixel detectors is therefore asynchronous

The DAQ must assemble the events in asynchronous mode

Events are built using the time-stamp information


• It is important that the data flux from pixels to PCI is not hampered by the read-out system, which transfers data to the PC.

ALTERA FPGA FirmwareALTERA FPGA Firmware• This read-out is data driven: data are collected as soon as there is a hit above threshold in the detector

1. FPGA firmware2. PC Read-out software

• In order to balance the different acquisition rates between the detectors, PCI cards and the PC, we took particular care in the design of the

ALTERA FPGA FirmwareALTERA FPGA Firmware

Readout process

Bank0 Bank1

FPGA

Shared memory

Consumer

Disk writerTime

Interrupt handler

Reset interrupt

PCI card working mechanismPCI card working mechanism

Readout process

Bank0 Bank1

FPGA Interrupt handler

Reset interrupt

Shared memory

Consumer

Disk writerTime


Readout process

Bank0 Bank1

FPGA

Shared memory

Consumer

Disk writerTime

Interrupt handler

Reset interrupt


• This process of periodic memory swap and transfer to a shared memory continues indefinetely.

• We have several PCI cards playing this swap game in parallel: in order to be able to build events at a later stage, we needed a syncronization mechanism to keep the event builder as simple as possible.

• By synchronizing the swapping of all the memories we can build events in a very simple and immediate way.


Interrupt handler A

Interrupt handler B

Interrupt handler C

Interrupt handler n

0 1Banks

1. The PCI card C redirect immediately the data flux to the other empty memory

Readout working mechanismReadout working mechanism

2. The interrupt handler of the PCI card C forces the other cards to swap and then starts flushing its content to the host PC

Each PCI card has its own interrupt-handler process listening for the memory-full signalLet’s suppose, for instance, that the PCI card C is the first being filled up.

3. The other cards start flushing their (partially) filled memory banks to the host PC.

0 1Banks Readout working mechanismReadout working mechanism

1. The PCI card C redirect immediately the data flux to the other empty memory

2. The interrupt handler of the PCI card C forces the other cards to swap and then starts flushing its content to the host PC

Each PCI card has its own interrupt-handler process listening for the memory-full signalLet’s suppose, for instance, that the PCI card C is the first being filled up.

Interrupt handler A

Interrupt handler B

Interrupt handler C

Interrupt handler n

0 1Banks Readout working mechanismReadout working mechanism

A0C0 … n0B0

• This architecture guarantees that events with contiguous time-stamps belong to buffers which are also contiguous in the read-out process.

Interrupt handler A

Interrupt handler B

Interrupt handler C

Interrupt handler n

0 1Banks

A0C0 … n0B0

Readout working mechanismReadout working mechanism

A1C1 … n1B1

• This architecture guarantees that events with contiguous time-stamps belong to buffers which are also contiguous in the read-out process.

Interrupt handler A

Interrupt handler B

Interrupt handler C

Interrupt handler n

0 1Banks

BUFi BUFi+1

A0C0 … n0B0 A1C1 … n1B1

Readout working mechanismReadout working mechanism• This architecture guarantees that events with contiguous time-stamps belong to buffers which are also contiguous in the read-out process.

• Events with the same time-stamp are contained within the boundaries of this overall buffer (BUFi), or at least in the next one, BUFi+1, but not in BUFi+2, making the event-builder an implementation of a sorting algorithm.

Interrupt handler A

Interrupt handler B

Interrupt handler C

Interrupt handler n

EventBuilder

Shared Memory

(unordered data)

Event buffer

(ordered data)

Timestamps:

Event

• Every hit with a new timestamp starts a new event (column) in a buffer• Other hits with the same time-stamp are appended to the right column in the buffer • When the analysis of the BUFFER i+1 is over, it is reasonable to assume that there are no more data related to an event that begun in BUFFER i.

Event builderEvent builder

DAQ conclusionDAQ conclusion• We built a DAQ system that will be used for the upcoming test-beam

• I covered many aspects in the design and implementation of this DAQ:1. I collaborated on the software development2. I personally took care of the FPGA programming

• I was then able to use this read-out system to measure the Lorentz angle in the silicon pixel detector

• I will show now the measurement and the results that I obtained…

E

L

X

Z280m

L effective = X/Z

Optical Fiber

Focusing Lens

Blue LED Light

~2m

B

X0 XL

Pixeldetector

Lorentz angleLorentz angle

Optical FiberFocusing Lens

EBlue Light

B


X

Y Bias E(V)B(KGauss)

Lorentz displacement400 m

50 m

• Pixel size in the Y direction= 400 m • Pixel size in the X direction = 50 m

• B parallel to the Y direction• Bias E along the Z direction

Lorentz displacement mainly in the X direction


• The blue light illuminated several cells in two different columns.• With a threshold scan I was able to know the charge collected in each cell.• Knowing the charge, I could calculate the Center of Gravity of the cluster: a bidimensional point, X and Y.

YX

50 m 400 m

MeasurementsMeasurements

C.o.G. =

i

ii

PHxPH

B > 0B < 0

We expect displacements linearly proportional to the magnetic field and symmetric respect to the sign of the B field.Instead here is what I measured

X-measurementsX-measurements

B KGauss

x [

m]

Displacements are present even with B 0. Also in this case they are in the same direction reversing themagnetic field.

B > 0B < 0

Y-measurementsY-measurements

B KGauss

x [

m]

The reason for this effect can be due to:1. a movement of the apparatus caused by magnetic attraction 2. a residual hysteresis in the ferromagnetic parts of the

apparatus3. a combination of the previous two

• I excluded residual hysteresis effects by performing a full set of measurements along a complete hysteresis cycle and checking the reproducibility of the measurements. I didn’t observe any appreciable differences between measurements at the same B value at different points of the hysteresis cycle

• So I tried to investigate a possible movement due to the attraction of parts of the apparatus by the magnet

InvestigatingInvestigating

Since the Lorentz displacement is an odd function of the magnetic field, while any movement due to magnetic attraction is an even function of it, by taking the sum of the measured positions at opposite values of the magnetic field one can cancel the contribution of the Lorentz effect, and, vice-versa, by taking the difference one can cancel the mechanical effect.

( XB +X-B)/2 or ( YB +Y-B)/2 = Mechanical movement ( XB -X-B)/2 or ( YB - Y-B)/2 = Lorentz displacement

How to measure the mechanical movement?How to measure the mechanical movement?

This movement exists, as shown by the following histograms, and is proportional to the module of the magnetic field as expected,but it should not depend on the value of the BIAS voltage.I checked this by fitting all the movements to a common line (RED)

100 V

350 V300 V250 V

200 V150 V

400 V

Measured mechanical X-movementMeasured mechanical X-movement

Even in this view exists a unique movement that can fit all data witha good ²( ²/d.o.f = 1.14 ) even if it is not as good as in X

100 V

350 V300 V250 V

200 V150 V

400 V

Measured mechanical Y-movementMeasured mechanical Y-movement

• Taking the difference ( XB - X-B)/2 we then find the Lorentz displacement.• For consistency we have to check that the Lorentz displacement be strictly linear with the magnetic field.• We can easily see that now the movement is linearly proportional to the magnetic field and it decreases, as expected, increasing the Bias voltage.

Lorentz X-displacementLorentz X-displacement

100 V

350 V300 V250 V

200 V150 V

400 V

6m

7.8m 6.8m

m

5.5m 5m

9m

In the Y direction instead we can fit the data with a straight line, within the errors, but the movement doesn’t scale as expected with the Bias voltage. Nevertheless the residual Lorentz displacement in this view is very small (B is almost parallel to Y) and practically comparable with the errors.

ONLY1 m

Lorentz Y-displacementLorentz Y-displacement

100 V

350 V300 V250 V

200 V150 V

400 V

Position finding algorithmPosition finding algorithm• Since the position is deduced by computing the charge cluster center of gravity from binned pixel cells, an indetermination is introduced in the measurements by the finite size of the cells.• I investigated this effect by assuming a shape for the LED light given by a gaussian fit to the charge collected on the pixel cells

X-correctionX-correctionThe final correction curve is given by the following

plot• X = Measured Center of Gravity coordinate• Y = Corrected coordinate value

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X-corrected mechanical movementX-corrected mechanical movementThe correction is really tiny for the mechanical movement.

100 V

350 V300 V250 V

200 V150 V

400 V

Corrected Lorentz X-displacementCorrected Lorentz X-displacement

100 V

350 V300 V250 V

200 V150 V

400 V

While for the Lorentz displacement the correction is ~1m at most

The same procedure has been applied to Y-coordinate where the effectis sizable due to the large discretization (400 m).I assumed the same LED shape as in X and I verified it rotating the optical fiber of 90 degrees

Y-correctionY-correction

Corrected Y-mechanical movement Corrected Y-mechanical movement

100 V

350 V300 V250 V

200 V150 V

400 V

Corrected Lorentz Y-displacementCorrected Lorentz Y-displacement

100 V

350 V300 V250 V

200 V150 V

400 V

1.6 m 2.6 m 1.5 m

1.5 m 0.8 m 1.8 m

1.2 m

Final Lorentz displacement at 2.8 KGaussFinal Lorentz displacement at 2.8 KGaussCombined X and Y displacement at different bias voltages

L

Lorentz displacement

Comparison with theoryComparison with theory

• The Lorentz angle is proportional to the magnetic fieldL = H Bwhere the proportionality factor, , is the Hall mobility which is related to the drift mobility viaH = rH ·

The Hall factor, rH, is a dimensionless value determined to berH = 1.15 for electrons, while the mobility can be well described by the empirical formula

=

)1 +( EEC)( 1/

• E is the electric field in the sensor• ,EC, are parameters determined empirically and are well measured at 300° K = 1450cm²/V·sEC = 7240 V/cm = 1.30

• I will compare the measured effective Lorentz angle as defined byL effective = X/Z with what expected from theory

Comparison with TheoryComparison with Theory

P+ implant

n+ n+ n+n+dVV db /)(

dVV db /)(

E

z

dVV

dz

dV

zE depbiasdep

1

2)(

• The electric field in the sensor can be well approximated by the following formula

L = dX/dZ = B dX = B dZ

…so it’s easy to calculate the trajectory of the carriers in the silicon

BdzrBdzX

d

H

d

HcEzE

0 10

/1)(

0

d n

Lorentz displacement at 2.8 KGauss

ResultsResults

² = 1.22

L

Effective Lorentz angle extrapolated at 1.6 Tesla

Bias: 100 Angle: 11.9 ±0.14 ± 0.3 Theory: 11.92Bias: 150 Angle: 10.6 ±0.16 ± 0.3 Theory: 10.4Bias: 200 Angle: 9.19 ±0.15 ± 0.3 Theory: 9.13Bias: 250 Angle: 8.02 ±0.15 ± 0.3 Theory: 8.1Bias: 300 Angle: 7.23 ±0.14 ± 0.3 Theory: 7.25Bias: 350 Angle: 6.83 ±0.16 ± 0.3 Theory: 6.56Bias: 400 Angle: 6.21 ±0.15 ± 0.3 Theory: 5.97

ResultsResults

L

I can even measure the three parameters, , 0 and Ec, by fitting my measurements with the theory model.The fit is reported in the plot and the returned parameters are0 = 1486 ± 123 = 1.19 ± 0.24 EC = 7706 ± 550

ResultsResults

( 0 = 1450 ) ( = 1.30 ) ( EC = 7240 )

ConclusionsConclusions• The measured Lorentz angle agrees very well with the previous measurements. -For instance, I obtain 9.3º ± 0.14º± 0.3º at 1.4 T and 150 V, to be compared with 9º ± 0.4º ± 0.5º measured by ATLAS

• I was able to measure the theory parameters which are in good agreement with those reported in literature.

• The scaling of the Lorentz angle with the bias voltage (i.e. mobility) follows the expectations

• The next step will be the measurement with irradiated detectors

• In the end, with a relatively simple apparatus, I was able to accurately measure the Lorentz angle.

BACK UP SLIDES

In order to improve the determination of the X displacement I add a correction in the X-direction performing a MonteCarlo simulation that takes into account this effect.

Data analysisData analysis

2. The mean value of these gaussians has been plotted in (a)

(a)

1. I generated a sample of 10,000 gaussians with fixed width and amplitude taken from the data sample shown in figure

3. For each chosen gaussian, the shape as been superimposed on a grid of pixels at fixed positions, and the fraction of gaussian area overlapping each bin has been computed. The mean values of these redistributed charges (C.o.G) have been computed and plotted in (b)

(b)


4. For each generated gaussian, the difference betweeen the input value (peak position of the gaussian) and the computed mean value after discretization is plotted in (c). The spread turns out to be of the order of 1m

5. Finally I obtained the correlation curve between continuous beam spot and the corresponding computed values from discretized quantities. See (d)

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474 = 23,4% 1548 = 76,6%

To improve the determination of the center of gravity in Y I verified, rotating the optical fiber of 90 degrees, that the distribution of the light was almost the same in X and Y. So I could learn from the more precise determination of the X position also a correction to apply to the Y.


130 344 483 504 378 183

Beam Axis50 m

400 m

X Plane

Y Plane

50 m

400 m


Ph.D. defense The measurement of the Lorentz angle in the BTeV pixel detectors: the new PCI based...

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