2008 JINST 3 P06004

PUBLISHED BY INSTITUTE OFPHYSICS PUBLISHING AND SISSA

RECEIVED: May 27, 2008ACCEPTED: June 6, 2008

PUBLISHED: June 19, 2008

Characterization of the ALICE Silicon Drift Detectorsusing an infrared laser

G. Batigne, a∗ S. Beolé, a E. Biolcati, a E. Crescio, b D. Falchieri, c G. Mazza,b

F. Prino, b† A. Rashevsky, d L. Riccati, b A. Rivetti, b S. Senyukov a and L. Toscano b

aDipartimento di Fisica Sperimentale dell’Università di Torino and INFN, Torino, ItalybIstituto Nazionale di Fisica Nucleare - Sezione di Torino, Torino, ItalycDipartimento di Fisica dell’Università di Bologna and INFN, Bologna, ItalydIstituto Nazionale di Fisica Nucleare - Sezione di Trieste,Trieste, ItalyE-mail: prino@to.infn.it

ABSTRACT: The Inner Tracking System of the ALICE experiment at LHC uses Silicon Drift De-tectors in two cylindrical layers located at radial distance of ≈ 15 and≈ 24 cm from the beamaxis. The spatial resolution of silicon drift detectors canbe strongly affected by inhomogeneities ofthe doping concentration, temperature effects and non-linearity of the drift potential distribution.Before the detector commissioning, an extensive study and characterization of all the produceddetectors has been performed. For this purpose, a specific measuring station, based on a lasermapping system, has been developed.

KEYWORDS: Particle tracking detectors; dE/dx detectors.

∗now at SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS/IN2P3, Nantes, France†Corresponding author

c© 2008 IOP Publishing Ltd and SISSA http://www.iop.org/EJ/jinst/

mailto:prino@to.infn.it

2008 JINST 3 P06004

Contents

1. Introduction 1

2. The SDD module 22.1 The silicon sensor 32.2 Front-end electronics 4

3. Laser test setup 43.1 Calibration of the setup 53.2 Choice of the laser wavelength 73.3 Mapping trajectory 73.4 Data taking conditions 8

4. Drift speed 9

5. Residual maps 105.1 Measurement of the residual map 105.2 Correction for the systematic deviations of the measured points 13

6. Conclusions 16

1. Introduction

Large area Silicon Drift Detectors (SDDs) [1 – 3] are used to equip the two middle layers of theInner Tracking System (ITS) [4] of the ALICE experiment at the LHC. They have been chosen dueto their good spatial resolution, capability of unambiguous two-dimensional position determinationand possibility to provide the energy-loss measurement needed for particle identification. Theoperating principle of SDDs is based on the measurement of the time necessary for the electronsproduced by an ionizing particle crossing the detector to drift from the generation point to thecollecting anodes, by applying an adequate electrostatic field. The first coordinate is obtained fromthe centroid of the charge distribution along the anodes, while the distance of the crossing pointfrom the anodes is determined by the measurement of the drifttime. The transport of electrons,in a direction parallel to the surface of the detector and along distances of several centimetres, isachieved by creating a drift channel in the middle of the depleted bulk of a silicon wafer. The driftspeed is proportional to the electric field E and to the electron mobility µe: v = µeE.

To reach the required spatial resolution of∼30 µm, it is necessary either to have a drift fieldwith an excellent uniformity over all the sensitive region of the detector, or to correct for the system-atic errors caused by its non-uniformity. A non-uniformityof the drift field along the drift direction

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Figure 1. Scheme of the SDD module.

alters the linear relation between the drift time of the electrons and the distance of the particlecrossing point from the anodes, thus introducing an uncertainty on the drift axis coordinate. On theother hand, the presence of a parasitic transversal field in the wafer induces deviations of the elec-tron trajectories from the ideal linear path. These deviations are responsible for systematic errorson the anodic coordinate.

The presence of non-uniformity effects, caused by systematic fluctuations of the doping con-centration, has been observed since 1999 on SDD prototypes tested with particle beams [5 – 7].A non-uniformity of the drift potential can be also caused bythe leakage current [8] which is thedark current generated by lattice imperfections both in thedepleted silicon bulk and on the detectorsurface. These imperfections are essentially impurities or damages to the crystal structure whichmay be introduced during the wafer processing and detector production or as a result of detector ir-radiation. The hole component of the leakage current entersin the cathodes and alters the linearityof the potential distribution along the voltage divider andconsequently makes the linear relationbetween the drift time and the drift distance to be non-linear, but rather parabolic.

A test station, based on a laser mapping system, has been set-up at the INFN Technologi-cal Laboratory in Torino (Italy) for the detailed study and characterization of the SDD modulesproduced for ALICE [9].

2. The SDD module

The basic building element of the SDD sub-system of the ITS, the SDD module [9] is sketched infigure 1. It consists of a silicon sensor and two hybrids hosting the front-end electronics.

The hybrid circuits are connected to the detector anodes through micro-cables. Each hybridis connected to a Low Voltage Card (LV) which provides individual power supply regulation andsignal interfacing to the data-reduction electronics. Thehigh voltage (HV) is supplied by a specificHV cable, which connects the detector to a HV card. An external voltage divider is placed on

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(a) (b)

Figure 2. Photograph of the SDD module: (a) upper-side, (b) underside.

the HV card. It biases some cathodes to specific reference voltages through the “transition cable”,placed on the underside detector surface. A “wrap-around” cable carries cathodes biasing from oneside of the detector to the other.

The total number of SDD modules in the ITS is 260.

2.1 The silicon sensor

The silicon detectors [10] are produced by Canberra Semiconductors on a 300µm thick 5" NeutronTransmutation Doped (NTD) wafer with a resistivity of 3 kΩ.cm. The active area of each SDD is7.02×7.53 cm2 and it is split into two adjacent 35 mm long drift regions, each equipped with 256collecting anodes (294µm pitch) and with integrated voltage dividers for the drift and the guard re-gions. The detector has a bidirectional structure, in whichthe electrons drift from a central cathodetowards two linear arrays of anodes, placed at the two opposite edges of the detector (see figure 3).

For each half-detector there are 291 drift cathodes with a pitch of 120µm. The drift cathodeclosest to the anodes will be referred to as "‘#291"’ in the following.

Since the drift speed is very sensitive to the detector temperature variation (v∝ T−2.4) themonitoring of this quantity is performed by means of three rows of 33 implanted point-like MOScharge injectors [11, 12].

The maximum voltage is acquired by the central cathode and gradually decreases going to-wards the two collection regions close to the anodes. The detector biasing is obtained with a set ofintegrated high-voltage dividers made of p+ implants. Each integrated resistor connecting adjacentdrift cathodes has a nominal value of 170 kΩ. Some cathodes are also connected to the externalvoltage divider on the HV card. On the underside detector surface, in front of the anode lines, aset of "‘pull-up"’ cathodes beyond the cathode #291 have been designed so as to ensure optimalcharge collection. They are biased at a higher voltage with respect to cathode #291. A mediumvoltage MV is applied to the cathode #291 in order to fully deplete the sensor in the collectionregion. The biasing voltage of the central cathode is given by HV = MV + 291∗Vgap, whereVgapis the inter-cathode voltage drop. The nominal drift fieldEd=667 V/cm corresponds to a potentialdifference of about 8 V between adjacent drift cathodes (8 V/gap).

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injector line

active area

guard region

anodes

drift

dire

ctio

n

Figure 3. Scheme of the SDD detector designed for ALICE. The three horizontal dashed lines in eachhalf-detector represent the injector lines.

2.2 Front-end electronics

The front-end electronics is composed by three ASICs, two ofthem (named PASCAL and AM-BRA) are located on the front-end hybrid and the third (namedCARLOS) on an external boardplaced at the end of the mechanical structure supporting thedetectors. PASCAL [13] performsthe preamplification, analog storage and analogue-to-digit conversion. The preamplifier dynamicrange is 32 fC, which corresponds to the maximum signal charge expected, eight times the chargereleased by a minimum ionizing particle. The amplifier output is sampled at a frequency of 40.08MHz by an analog ring memory with 256 cells for anode. The memory depth of 256 time binscorresponds totmax=6.4 µs, and taking into account the maximum drift distance on the sensor of35 mm, the resulting minimum drift speed isvmin ≈5.5µm/ns. AMBRA [13] is a digital four-eventbuffer performing data derandomisation and transmission to the CARLOS [13] chip, which is usedfor zero-suppression and data compression.

3. Laser test setup

The experimental setup used for the laser test of the SDD modules is sketched in figure 4. Themain goal of this test is to measure the systematic deviationbetween the position where charge isreleased in the detector and its reconstructed coordinates. Charges are created in the SDD sensitivevolume by means of a laser which can be remotely moved over thewhole detector surface. Thelaser light is carried through an optical fiber and it is focused on the SDD surface by means of a lenslocated at the end of the fiber. At the exit of the lens, the laser beam has a 9◦ opening angle witha 5µm waist. A video system composed of a CCD camera, a mirror and alens with 1.2 cm focaldistance is used to visually check the positioning of the SDDmodule and to align the laser spotwith the detector plane. This video system and the laser lensare mounted on three stages controlledby a Newport MM4006 multi-axis motion controller. The commands to the motor controller aregiven via a Labview interface running on the acquisition PC which executes a series of defined

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DAQ PC

trajectory

XYZ motor stages

optical fiber980 nm laser

to cathode #0

to cathode #291

(0−2368 V)

HV power supply

(0−2368 V)MV power supply

LV power supply(0−5 V)

trigger

DG2020

trigger

XYZ motor stagestrigger Data

trigge

r

yz

x

CARLOSrx board

trigger

Data Data

CARLOS

Data

CCD cameraMirror

Figure 4. Scheme of the experimental setup.

movements (called trajectory from now on) over the detectorsurface and generates a trigger pulseto fire the laser in definite positions. One important featureof this controller is that the pulses canbe generated when the motors are moving, thus limiting the error on the position and decreasingthe measurement time.

The pulse generated by the MM4006 is sent to a Sony/Tektronics DG2020 data pattern gener-ator. The DG2020 is used to generate both the 40 MHz clock for the front-end chips and the signalpulses (synchronized to this clock) which are used to trigger both the acquisition and the laser whenreceiving the trigger pulse from the motor controller. The front-end chips, after receiving the trig-ger, transmit the data to the acquisition system via opticallinks. The acquisition system is basedon the official hardware and software tools specifically developed for the ALICE experiment: aCARLOS chip for zero suppression [13], a CARLOSrx board [13], a DRORC acquisition card aswell as DATE [14] acquisition program are used.

The coordinate system is also shown in figure 4 and it is definedaccording to the conventionsused in ALICE software: x and z axes are on the detector plane directed respectively along driftand anode coordinates, while y is orthogonal to the detectorplane.

3.1 Calibration of the setup

In order to have an accurate measurement of the systematic effects on the space coordinates re-constructed by the SDD detector, the position where the laser hits the detector should be known asprecisely as possible.

The video system allows to check the planarity of the detector and the orthogonality of themotor movements along the x and z axes (i.e. on the detector plane). The planarity of the detectoris evaluated by checking the focal distance along the y axis in the 4 corners of the sensitive areaof the detector: variations below 100µm have been observed for all the tested modules. The angle

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0.2

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1

1.2

1.4

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(a) (b)

Figure 5. One of the 4 cross marks used for detector alignment. (a) Picture taken with the camera. (b)Charge collected (ADC units) during a laser scan of the detector surface (each pixel has a size of 5µm by5µm).

between x and z motors is found to differ from the expected 90◦ by 0◦5′17′′, representing a deviationof 100µm on a distance of 7 cm (i.e. the size of an SDD module). This last effect has been takeninto account to define the laser trajectories.

The alignment of the detector with the laser spot is obtainedby means of the video systemexploiting four cross shaped reference marks engraved on the metalizations of the 2 cathodes #219on both sides of the sensor at≈ 2 cm from the 2 detector edges.

The precise determination of the distance along x and z axes between the laser spot and cameracentral point has been determined from the offset of the the coordinates of one of these crosses asmeasured with the video system (see figure 5a) and with a laserscan with 5µm step. It should benoted that the crosses are visualized with a laser scan because they are cut in the metalization andtherefore laser light is reflected by the surrounding metalization resulting in small collected charge,while this charge is large in correspondence of the cross mark. The charge collected as a functionof the position on the detector is shown in figure 5b: the crossmark results clearly visible in theimage, thus allowing to measure the offset between laser spot and camera center with a precisionof about 5µm.

Furthermore, one should determine the y offset between the laser and the camera focal dis-tances. This is obtained by repeating the scans at differentdistances between the laser lens andthe detector and choosing the one with sharper edges of the cross mark, which corresponds to theminimum size of the laser spot. The obtained precision on this y offset is≈ 25 µm.

The incident angle of the laser has also been precisely measured by performing a scan in frontof an anode at different distances along y axis. The value of this angle has been found to be about6◦ which corresponds to a laser spot displacement of 10µm for a change of 100µm in the positionof the detector due to non planarity of the detector. This incident angle of the laser beam couldalso widen the area of charge creation within the 300µm of silicon wafer thickness. This effect is

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however limited because of the high refractive index of the silicon (nSi = 3.56 for λ ≈ 1000 nm):the angle of laser light in the wafer is reduced to≈ 1.6◦ and consequently the systematic shift onthe mean position of the ionization zone is limited to about 4.5 µm.

Finally, the time precision of the trigger signal should be taken into account. The MM4006module generates at given positions a pulse which triggers both the acquisition and the laser througha DG2020 module. The precision of the signal generation at a motor speed of 10mm/s is about 1µm and the time jitter between the acquisition trigger and thelaser pulse has been measured to beless than 0.1 ns. This jitter implies a negligible effect on the laser spot position, while (consideringa drift speed of 8µm/ns) it introduces an uncertainty on the position along thedrift direction ofabout 0.8µm.

Taking into account all these effects, the set-up allows to reach a resolution of about 11µm onthe laser spot position, i.e. the point where the charge is created within the detector. This value ismuch less than the expected intrinsic resolution of the detector (∼ 30µ m), so the setup is preciseenough to study the systematic deviation on the reconstructed points in the SDD modules.

3.2 Choice of the laser wavelength

The wavelength of the laser light has to be carefully chosen.Figure 6 shows the collected clustercharge as a function of laser position on the surface of the SDD module for two wavelengths(λ = 1060 nm (a) andλ = 980 nm (b)). The dark vertical lines correspond to the injector lines, thehorizontal ones to dead anodes. The transition cable located on the opposite side of the detector(see figure 2) is clearly visible when a wavelength of 1060 nm is used. This is a consequenceof the fact that the penetration depth of photons in silicon with a resistivity of 3 kΩ· cm is about800 µm for λ = 1060 nm and≈ 100 µm for λ = 980 nm [15]. Hence, the 980 nm wavelengthlaser is almost fully absorbed in the detector volume whereas only a small fraction of the 1060 nmwavelength laser is absorbed. So, with the 1060 nm laser, a significant fraction of photons reachesthe transition cable on the other side of the detector and is reflected by its metal lines, thus wideningthe charge creation volume and possibly introducing a systematic error on position measurements.

3.3 Mapping trajectory

The laser trajectory used to map a detector is shown in figure 7: for each anode coordinate the laseris moved along the drift direction starting from one edge of the detector and reaching the oppositeside. Then a movement along anode coordinate is done and a newline along the drift coordinatemoving in the reverse direction is taken.

The choice of moving along several lines parallel to the drift direction is dictated by the neces-sity of having the same drift speed for all the laser points measured for each anode, so as to have arobust calculation of the drift distance starting from the measured drift time. With such a trajectory,the laser events at the same anode coordinate are collected in about 7 seconds thus reducing theeffects of possible changes of ambient and detector temperature on the drift speed.

The laser moves along several lines each placed between two adjacent anodes. Each line iscomposed of 581 points (1 at each cathode) along the drift direction, i.e. with a step1 of 120 µm,

1The step of the scan along the drift coordinate is forced to integer multiples of 120µm by the fact that the laser isreflected by the cathode metalizations and therefore it should be fired in the 30µm inter-cathode space.

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Drift coordinate (mm)-30 -20 -10 0 10 20 30

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Figure 6. Collected charge vs. laser position on the detector surface. a): λ = 1060 nm. b):λ = 980 nm.

x

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Figure 7. Laser trajectory for SDD mapping

corresponding to the cathode pitch. Along the anode coordinate a step of 294µm (correspondingto the anode pitch and resulting in 257 map lines) has been chosen for first tests, while in theconstruction phase a doubled step (588µm, 128 map lines) has been used. The total number oflaser events is therefore 149317(74368) for 257(128) linesmap, giving a raw data size of about22(11) GB for each map. The motor speed is set to 10 mm/s, resulting in an event rate of about 90Hz. The time duration of a map is 40(20) minutes for the 257(128) line trajectory.

3.4 Data taking conditions

All the detectors constructed for the ALICE ITS have been tested and mapped at standard condi-tions of Ed=667 V/cm and without air flux for detector cooling. Afterwards, on a sub-sample of14 working detectors chosen among the spare ones not mountedon the ALICE ITS, a systematic

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HV [V] MV [V] Vgap [V] Edrift [V/cm]

-2368 -40 8 667-2082 -45 7 583-1791 -45 6 500-1645 -45 5.5 458

Table 1. Voltage configurations used for the systematic study.

study of the performance at different biasing voltages and air flux values has been performed. Thedifferent values of biasing voltage are summarized in table1 together with the corresponding driftfield value and inter-cathode voltage drop. When the high voltage (HV) is decreased, the mediumvoltage (MV) is increased to 45 V in order to maintain on the pull-up cathodes the potential thatprovide optimal charge collection efficiency. The operation at lower values of HV guarantees lesscritical working conditions for the system, in particular for what concerns heat dissipation and elec-tronic stability. The minimum value of drift field used is dictated by the need of keeping the driftspeed larger than 5.5µm/ns.

The behaviour of the drift speed with air cooling on the detector surface has also been studied.For this purpose a small (radius of≈ 3 cm) fan has been located near the sensor, parallel to the driftcoordinate eight centimetres far from the voltage divider.The fan could operate at different voltagevalues (ranging from 0 to 12 V), provided by an external powersupply. Each fan voltage valuecorresponds to a different rotation speed and consequentlydifferent air flux on the detector surface.

4. Drift speed

The electron drift speed is used to calculate the position ofthe crossing particle along one of thetwo coordinates and it is a critical parameter in silicon drift detectors because of its temperaturedependence. The drift speed in each SDD module is actually influenced by temperature gradientsin the silicon bulk produced by the voltage divider heating and the presence of air fluxes. More-over, during SDD operation in the ALICE ITS, the drift speed may be affected by temperaturespatial gradients in the ITS volume as well as by temperaturevariations with time due to ambienttemperature changes during the day (which should be howeverlimited in the ALICE pit).

A systematic study of the drift speed behaviour in differentexperimental conditions (withdifferent biasing voltages and in presence of air fluxes) hasbeen performed using the laser mappingsystem. The electron drift speed is measured from the correlation between the known laser positionalong the drift axis and the drift time measured by the SDD, asshown in figure 8, where the timecoordinate measured by the SDD is expressed intime bins(1 time bin = 25 ns).

The drift speed can be easily obtained as: vd = 1/(s · 25ns), being s the slope parameterobtained by fitting the correlation curve with a straight line. As noted above, a large leakage currentmakes the relation between the drift time and the drift distance to be non-linear, but rather parabolic.

Starting from the drift speed the electron mobility can be evaluated asµ = vd/Ed. In figure 9the results obtained for the drift speed (a) and for the mobility (b) as a function of the anode numberfor different values of the biasing voltage (respectively 8V/gap, 7 V/gap, 6 V/gap and 5.5 V/gap)are shown. As expected, the drift speed decreases with the lowering of the biasing voltage, which

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Laser position [mm]-35 -30 -25 -20 -15 -10 -5 0

Drif

t tim

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ime

bins

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slope = 4.658

/nsµ = 8.587 25 ns×slope 1 = driftv

Figure 8. Measured drift time (1 time bin = 25 ns) as a function of laser position along drift coordinate (0 isthe center of the detector) for a given anode.

corresponds to a lowering of the drift field. In the curves corresponding to the maximum drift field(8 V/gap), a dependence of the drift speed on the anode numberis clearly evident. This effect is dueto the presence of a temperature gradient in the silicon bulkalong anode coordinate. At the edges,because of the heat produced by the voltage divider, the temperature is higher and consequently themobility and the drift speed are lower, whereas it is lower (higher mobility and drift speed) in thedetector centre. This effect decreases for lower voltage biases. The relative difference between themaximum and the minimum value of the drift speed is of the order of 0.9% in the case of 8 V/gapand 0.4% in the case of 5.5 V/gap. It can be seen in figure 9(b) that the electron mobility increaseswith decreasing drift field, this effect can be understood asdue to a lower detector temperature atlower drift field as a consequence of the reduction of the heatproduced by the voltage divider whenlower HV values are used.

The results obtained for three different air flux values (corresponding to three different fanvoltage values, FV = 0, 6 and 10 V) are shown in figure 10, where the measured drift speed isplotted as a function of the anode number at the nominal driftfield of 667 V/cm. The drift speedbehaviour is not symmetric with respect to the detector center (as one could have expected) becausethe fan was positioned close to the side of the detector corresponding to the anode 0, for which thecooling effect was stronger. It can be seen that the average drift speed increases with increasingvalues of fan voltage, as a consequence of the stronger cooling effect.

5. Residual maps

5.1 Measurement of the residual map

The trajectory used for mapping a detector allows to measurethe systematic deviations between thereconstructed coordinates of the laser spot and the known laser position on a discrete grid of pointsspaced by 120µm along drift direction and by 294 (or 588)µm along anodes. For each laser shot,

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Anode number0 50 100 150 200 250

m/n

s]µ

Drif

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5

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8

8.5

9= 8 VgapV

= 7 VgapV

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]-1 s

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m1260

1270

1280

1290

1300

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= 8 VgapV

= 7 VgapV

= 6 VgapV

= 5.5 VgapV

(a) (b)

Figure 9. Drift speed (a) and electron mobility (b) as a function of theanode number for different values ofthe biasing voltage.

Anode number0 50 100 150 200 250

m/n

s]µ

Drif

t spe

ed [

8.2

8.4

8.6

8.8

9

9.2

9.4

FV=0V

FV=6V

FV=10V

Figure 10. Drift speed as a function of the anode number for three different conditions of air flux on thedetector surface, at the nominal drift field of 667 V/cm.

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Drift coordinate (mm)-30 -20 -10 0 10 20 30

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(a) (b) (c)

Figure 11. Maps of residuals along drift coordinates for 3 modules. (a): ideal detector; (b): detector withnon uniform drift field; (c): detector with doping inhomogeneities.

it is therefore possible to calculate the residuals along drift (x) and anode (z) coordinates as:

Rxi = xmeasi −x

lasi Rzi = z

measi −z

lasi (5.1)

wherexlasi andzlasi are the true laser positions (given by the motor controller)along drift and anode

coordinate for thei-th trajectory point, whilexmeasi andzmeasi are the reconstructed ones. In figure 11

three residual maps measured atVgap= 8V are shown for the drift coordinate: on the horizontal andvertical axes we report the position on the detector along drift and anode coordinates respectively(i.e.xlas andzlas) while in gray scale the corresponding measured residual along drift coordinate (inµm) is represented.

The map in figure 11 (a) is quite uniform and the measured residuals fluctuate in a range ofabout±30µm around zero without any significant dependence on the position on the sensor. Thisrepresents a typical case of a detector with a uniform drift field and without significant doping in-homogeneities. In figure 11 (b) the case of a detector with a non-linear voltage divider, resultingin a non uniform drift field is shown. It can be seen that in thiscase the measured residuals showa strong dependence on the drift distance, while all the anodes behave in the same way. It must benoted that this systematic bias does not affect the anode coordinate which is properly reconstructedfor detectors with non-linear voltage divider. Let us note that the white regions visible in the resid-ual map are due to dead anodes. Finally, in figure 11 (c) we showthe residual map for a detectorwith significant doping fluctuations. The circular structure which appears in the map of residualsis a consequence of the parasitic electric fields generated in the silicon bulk by the gradients ofdopant concentrations which shows the typical circular shape due to the rotating process used inthe growth of the silicon wafer. This systematic effect is ofcourse also present in the anode coor-dinate, since the parasitic fields deviate the electron cloud along bothx andzcoordinates: the mapof residuals along anode coordinate shows the same circularstructures observed in figure 11 (c) forthe drift distance.

In figure 12 the average profiles along drift coordinate of thethree residual maps shown infigure 11 are shown. A flat behaviour centered at zero is observed as expected for the ideal detector(a) and for the one with dopant fluctuations (c), because the circular structures visible in figure 11are on average canceled when projecting the residuals alongdrift direction. On the contrary, the de-

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Drift coordinate (mm)-30 -20 -10 0 10 20 30

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Figure 12. Projections of the residual maps along drift coordinates for 3 modules. (a) ideal detector; (b):detector with non uniform drift field; (c): detector with doping inhomogeneities.

Mean 0.1686

RMS 13.31

Kurtosis 3.427

m)µResidual (-200 -150 -100 -50 0 50 100 150 2000

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9000Mean 0.1686

RMS 13.31

Kurtosis 3.427

Mean 0.1051

RMS 34.65

Kurtosis 2.771

m)µResidual (-250 -200 -150 -100 -50 0 50 100 150 200 2500

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9000 Mean 0.1051RMS 34.65

Kurtosis 2.771

Mean -0.102

RMS 21.24

Kurtosis 1.032

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4500Mean -0.102

RMS 21.24

Kurtosis 1.032

(a) (b) (c)

Figure 13. Distributions of residuals along drift coordinates for 3 modules. (a): ideal detector; (b): detectorwith non uniform drift field; (c): detector with doping inhomogeneities.

tector with non-linear voltage divider (b) presents a systematic deviation from zero of the residualswhich depends on the drift distance.

Finally, in figure 13 we report the residual distributions for the same three detectors discussedabove. For the ideal detector (a) the residual distributionshows a Gaussian shape centered atzero, as it should be in absence of systematic effects which could bias the reconstruction of thelaser signal. The RMS of the distribution (≈ 15µm) represent the resolution of the detector alongthe drift coordinate. The detector with non uniform drift field (b) shows a clearly non-Gaussiandistribution of residuals with an average value different from zero. This bias is a consequence ofthe assumption of uniform drift speed along the whole drift length of the electron cloud. For thedetector with doping inhomogeneities (c), the distribution is Gaussian shaped and, as expected, hasa larger width (RMS= 21µm) with respect to the ideal case.

5.2 Correction for the systematic deviations of the measured points

It is clear that the presence of systematic effects such as the ones shown in figure 11 would dra-matically worsen the resolution of the SDD detectors and would introduce a significant bias in the

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las,0x las,1x las,2x las,3x

meas,0x

meas,1x

meas,2x

meas,3x

mx

corrx

Figure 14. Scheme of the correction of reconstructed position using the residual maps.

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Figure 15. Maps of residuals along drift coordinates for 3 modules after correction of systematic effects.(a): ideal detector; (b): detector with non uniform drift field; (c): detector with doping inhomogeneities.

reconstruction of the coordinates of a crossing particle. However, it is still possible to correct forsuch systematic effect if the map of residuals has been measured for each detector.

The correction procedure has been tested by repeating the laser scan of the detector surfaceand using the previously measured residual map to correct the reconstructed laser positions fromthe new measurement. When a particle crosses the sensor, a position (xm,ym) is recorded andthis position must be corrected using the maps of residuals.Since the maps contain the residualsmeasured on a discrete grid of laser shot points, an interpolation procedure is necessary. A schemeof such interpolation is shown in figure 14.

The measured coordinatexm along drift direction is included between two coordinates of thecorrection grid taken from the residual maps, in this casexmeas1 andx

meas2 . The true drift coordinate

of the position (xcorr) is obtained by using the equation of the straight line between the two points(xlas1 ,x

meas1 ) and (x

las2 ,x

meas2 ):

xcorr = xlas1 +(xm−x

meas1 )

xlas2 −xlas1

xmeas2 −xmeas1

(5.2)

The residuals obtained for the same three detectors, using the maps in figure 11 to correct thesystematic effects, are shown in figure 15. It can be seen thatthe systematic effects which werevisible in figure 11 are canceled by the correction based on the previously measured residual maps.

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Figure 16. Maps of residuals along drift coordinates for 3 modules measured atVgap= 6V after correctionof systematic effects. The correction is extracted from maps taken withVgap= 8V. (a): ideal detector; (b):detector with non uniform drift field; (c): detector with doping inhomogeneities.

Mean -0.5733

RMS 16.44

Kurtosis 15.99

m)µResidual (-150 -100 -50 0 50 100 1500

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7000Mean -0.5733

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Mean -0.5906

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Kurtosis 2.952

m)µResidual (-150 -100 -50 0 50 100 1500

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Mean -0.553

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Kurtosis 6.931

m)µResidual (-150 -100 -50 0 50 100 1500

1000

2000

3000

4000

5000

6000 Mean -0.553RMS 16.13

Kurtosis 6.931

(a) (b) (c)

Figure 17. Distribution of residuals along drift coordinates for 3 modules measured atVgap = 6V aftercorrection of systematic effects. The correction is extracted from maps taken withVgap = 8V. (a): idealdetector; (b): detector with non uniform drift field; (c): detector with doping inhomogeneities.

In figure 16 the residual maps measured with a lower drift field, Vgap= 6V, are shown. In thiscase the maps measured at the higher drift field (Vgap = 8V) were used to correct for systematiceffects. It can be seen that the systematic effects are curedboth in the case of non-linear voltagedivider and in the case of doping inhomogeneities also if thecorrection map is measured with adifferent drift field in the detector. This is a crucial result because it proves the possibility of usingthe residual maps measured with a given voltage configuration (e.g.Vgap= 8V) to correct the datataken with different values of drift field.

The same effect is illustrated in figure 17 by the distribution of the residuals for the threemodules under investigation: for the detector with non linear voltage divider (middle panel) theGaussian shape of the residual distribution is almost recovered with the correction thus obtainingan un-biased (i.e. centered at zero) distribution with better (RMS=16µm) resolution. Also forthe detector with non uniform dopant concentration the width of the residual distribution aftercorrection is smaller, thanks to the correction of the systematic effect due to parasitic fields.

The same analysis has been repeated at two other polarization voltages, namelyVgap = 7VandVgap= 5.5V and on 14 different detectors. As a summary of the obtained results we show in

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[V]gapV-7 -6.8 -6.6 -6.4 -6.2 -6 -5.8 -5.6 -5.4

m]

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[

0

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Reference range

Figure 18. RMS of the residual distributions as a function of the inter-cathode voltage gap; different symbolscorrespond to different tested detectors. The correction is extracted from maps taken withVgap= 8V.

figure 18 the RMS of the residual distributions after correcting with the residual map measured atVgap = 8V as a function ofVgap. The different symbols used in the figure correspond to differenttested detectors. The detectors are grouped in 5 categoriesaccording to their performance. Thehorizontal band in the range 11-18µm represents the RMS values obtained when correcting themeasured positions with a residual map collected with the same drift field. It should be notedthat these values are in good agreement with the expected systematic error of 11µm on the laserspot position. Hence, it quantifies the precision of our measurements which are influenced by thenon-perfect reproducibility of the alignment of the detector with the laser, by the motor precisionand by the fluctuations in the laser intensity. It can therefore be concluded that for most of thedetectors the performance does not deteriorate as a consequence of using a correction map extractedfrom measurements collected with different drift fields. Asalready stated before, this is of crucialimportance because it guarantees the possibility to operate the detectors mounted on the ALICEITS at different high voltage values.

It can be seen in figure 18 that four (out of 14) detectors do notexhibit the same constant per-formance at different voltages. The profiles of the residuals along drift coordinate of two detectorsrepresenting these four anomalous detectors are shown in figure 19. The results at twoVgap(namely8 and 6 V) values are superimposed. In figure 19 (a), a detectorwith large localized problems ofvoltage divider, resulting in residuals of several hundreds of microns is shown and a significantdifference in the residual profiles measured with two different drift fields is clearly visible. In fig-ure 19 (b) a detector with parabolic shape of the residual profile is shown, also in this case the shapeof the residual distributions depends on the applied voltage: the curvature of the parabola results tobe smaller at lower drift field.

The same study has been repeated on 5 detectors in three different conditions of cooling viathe fan. The measured map of residuals turned out to be independent of the air-flux.

6. Conclusions

A setup for characterizing the ALICE SDD detectors based on an infrared laser has been developedand optimized. All the detectors produced for the ALICE ITS have been tested and the maps ofresiduals has been measured and stored. A total number of 300modules has been measured, 260

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Figure 19. Projections of the residual maps along drift coordinates for the 4 values ofVgap. (a): detectorwith large localized problems of voltage divider; (b): detector with parabolic voltage divider.

of such modules have been selected for mounting on the ITS. The residual maps thus obtained willbe applied to correct the positions of measured clusters so as to reach the required SDD spatialresolution of∼30 µm in both anode and drift coordinates. On a sub-sample of 14 modules asystematic study of the performance as a function of detector bias voltage has been performed. Formost of the detectors, the performance is stable against lowering the drift field, thus allowing touse the residual maps measured at the nominal drift field of 667 V/cm without cooling air flux tocorrect the data collected in different conditions. For detectors with large localized imperfections inthe voltage divider, the measured residuals are observed tochange with the drift field. However, allthe detectors with such problems have been discarded and arenot present in the ALICE setup. Alsodetectors with parabolic shape of the voltage divider show adifferent behaviour when changing thedetector bias voltage.

Acknowledgments

We wish to thank the people helping us during the construction phase at the INFN TechnologialLaboratory in Turin. For the mechanic part: S. Coli, B. Giraudo, F. Cotorobai. For the electronics:M. Mignone, F. Rotondo. We wish to thank also the people involved in the assembly and bondingof the SDD modules, whose work was fundamental for the SDD project: F. Dumitrache, B. Piniand the teams from SRTIIE, Kharkov, the Ukraine. We are grateful to P. Giubellino, L. Ramello,S. Vallero and R. Wheadon for their help during the data taking and useful discussions.

References

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[4] ALICE collaboration,ALICE Inner Tracking System (ITS): Technical Design ReportCERN-LHCC-99-012, http://alice.web.cern.ch/Alice/documents.html

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[11] V. Bonvicini et al.,Characterising large area silicon drift detectors with MOSinjectors, Nuovo Cim.A 112 (1999) 137.

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[15] I. Abt et al.,Characterization of silicon microstrip detectors using aninfrared laser system,Nucl. Instrum. Meth.A 423 (1999) 303.

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