Dopant fluctuations in silicon wafers are responsible for systematic errors in the determination of the particle crossing point in silicon drift detectors. In this paper, we report on the first large scale measurement of this effect by means of a particle beam. A significant improvement of the anodic resolution has been obtained by correcting for these systematic deviations

Bondila, M

Bonvicini, V

Cerello, P G

Crescio, E

Giubellino, P

Hernández-Montoya, R

Kolojvari, A A

Montaño-Zetina, L M

Nilsen, B S

Nouais, D

Piemonte, C

Rachevsky, A

Tosello, F

Vacchi, A

Wheadon, R

Dopant fluctuations in silicon wafers are responsible for systematic errors in the determination of the particle
crossing point in silicon drift detectors. In this paper, we report on the first large-scale measurement of this effect by
means ofa particle beam. A significant improvement ofthe anodic resolution has been obtained by correcting for these
systematic deviations

D. Nouais

M. Bondila

V. Bonvicini

P. Cerello

E. Crescio

P. Giubellino

R. Hernandez Montoya

A. Kolojvari

L. M. Montano

B. S. Nilsen

A. Rashevsky

F. Tosello

A. Vacchi

R. Wheadon

Piemonte, Claudio

Archivio della ricerca - Fondazione Bruno Kessler

Correction of dopant concentration fluctuation effects in
silicon drift detectors

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Correction of dopant concentration fluctuationeects in silicon drift detectors.D. Nouais a,1, M. Bondila b, V. Bonvicini c, P. Cerello a,E. Crescio a, P. Giubellino a, R. Hernandez-Montoya a,2,A. Kolojvari a,3, L.M. Monta~no a,2, B.S. Nilsen d, C. Piemonte c,A. Rashevsky c, F. Tosello a, A. Vacchi c, R. Wheadon a,for the ALICE collaboration.aINFN Sezione di Torino, ItalybJyva¨skyla¨ University, FinlandcINFN Sezione di Trieste, ItalydThe Ohio State University, USAAbstractDopant fluctuations in silicon wafers are responsible for systematic errors in thedetermination of the particle crossing point in silicon drift detectors. In this paperwe report on the rst large scale measurement of this eect by means of a particlebeam. A signicant improvement of the anodic resolution has been obtained bycorrecting for these systematic deviations.Silicon drift detectors (SDDs) have been chosen to equip two layers of theinner tracking system of the ALICE[1,2] experiment at LHC due to theirvery good spatial precision and capability of unambiguous two-dimensionalposition determination in high multiplicity environments. In an SDD, underthe eect of an applied electric eld, the electrons liberated by the passage ofa particle drift along a direction parallel to the surface of the wafer to an arrayof collection anodes perpendicular to the drift direction. The drift velocity isproportional to the electric eld E and to the electron mobility µe: V = µeE.In this way, the distance of the crossing point from the anodes is determinedby the measurement of the drift time. The second coordinate is obtained fromthe centroid of the charge distribution across the anodes.1 Corresponding author. E-mail: nouais@to.infn.it2 also at CINVESTAV Mexico City, Mexico3 also at St.Petersburg University, St. Petersburg, RussiaPreprint submitted to Elsevier Preprint 31 May 2000To reach the spatial precision required in ALICE (about 30 µm along thetwo axes [1,2]), it is necessary either to have a drift eld with an excellentuniformity over all the sensitive region of the detector, or to correct for thesystematic errors caused by its non-uniformity. A non-uniformity of the eldalong the drift direction alters the proportionality between the drift time ofthe electron cloud and the distance of the crossing point of the particle fromthe anodes. This introduces an uncertainty on the drift axis coordinate. Onthe other hand, the presence of a parasitic transversal electric eld in thewafer induces deviations of the electron trajectories from the ideal linear pathas illustrated in g. 1. These deviations are responsible for systematic errorson the anodic coordinate. Such transversal deviations have been studied on aEdDrift fieldAnodesParasitic fieldE(x,y)∆ xImpact pointFig. 1. Sketch of an electron trajectory in a SDD in presence of a parasitic eldsuperimposed to the ideal drift eld.small area of a SDD, constructed on a floating zone wafer by using an infraredlaser [3,4].In this paper, we present the rst large scale study of these deviations, whichwe performed on an ALICE-D1 SDD prototype, produced on a 3 kΩ cm 5"n{type neutron transmutation doped (NTD) silicon wafer [2]. The NTD tech-nique has been chosen for its good uniformity of doping concentration. Thedetector active region is divided centrally into two separate zones each with a35 mm maximum drift path read out at the edge of the detector by 256 anodeswith a pitch of 294 µm. A detailed description of the ALICE SDD design isgiven in [5].The results have been obtained from the data analysis of a beam test per-formed in May 1999, with a 375 GeV/c pion beam of the SPS. The SDD,operated at a drift eld of 583 V/cm, was placed on the beam trajectory be-tween two microstrip telescopes which allow to predict the particle impact2point on the SDD with a precision of 5 µm r.m.s. The detector was read outusing the OLA chip [6], specially developed for this type of detector. An areaof about 19× 35 mm2, corresponding to 64 anodes, has been studied.This area has been divided in rectangles of 1 × 0.3 mm2. For each rectangle,we built the residual distributions between the anodic coordinate measured bythe SDD and the reference anode axis coordinate measured by the telescopes.The centroid of such local distribution is represented in g. 2 as a function ofthe position of the rectangle center.68101214161820220 5 10 15 20 25 30 35Drift distance (mm)Anode axis (mm)-250 -200 -150 -100 -50 0 50 100 150 200 250Systematic deviations (µm)Fig. 2. Systematic deviations of the anodic coordinate of the electron cloud centroidwith respect to the reference position of the crossing point of the particle, as afunction of the drift distance and the anodic coordinate. The dashed arcs, centredon the middle of the silicon wafer, are plotted to allow an eye estimate of the centralsymmetry of the observed deviations.Circular structures centred on the middle of the wafer (corresponding to thecentre of the detector) are clearly observed in this plot. This eect can beattributed to the radial dependence of the dopant concentration fluctuations[7]. A simple numerical calculation of electron trajectories has been performedin order to evaluate the amplitude of the fluctuations needed to explain suchdeviations. A radial sinusoidal dopant concentration variation with a 4mmspatial periodicity and a 2 % amplitude has been simulated, with the resultillustrated in g. 3. This preliminary result reproduces quite well the qualita-tive features and the amplitude of the deviations. In both the data and thesimulations, the amplitude of the deviations can be seen to increase with thedrift distance. This can be explained by the fact that the parasitic electric eldproduced by the dopant fluctuations is perpendicular to the drift eld at themaximum drift distance, and hence the deviation from the linear trajectoryis higher in this region. The amplitude of the dopant concentration variationsis of the same order of magnitude of those observed on identical wafers [8,9].Since the maximum systematic deviations have been measured to be of about300 µm, it is clearly indispensable to correct for this eect.The anodic resolution is dened as the r.m.s. of the residual distribution be-3681012141618200 5 10 15 20 25 30 35Drift distance (mm)Anode axis (mm)-250 -200 -150 -100 -50 0 50 100 150 200 250Systematic deviations (µm)Fig. 3. Systematic errors on the anodic coordinate as a function of the drift distancepredicted by simulating the electron trajectories in a drift electric eld with pertur-bations caused by dopant concentration fluctuations. The dopant concentration hasa radial sinusoidal dependence with a 4mm spatial periodicity and a 2% amplitude.tween the anode axis coordinates measured by the SDD and by the microstriptelescopes. In g. 4, the resolution as a function of the drift distance with andwithout corrections of the systematic deviations measured using the beam testdata are compared.0204060801001200 5 10 15 20 25 30 35Drift distance (mm)Resolution (µm)Fig. 4. r.m.s. of the residual distribution between the anodic coordinate of the elec-tron cloud measured by the SDD and the reference anodic coordinate given by thetelescope as a function of the drift distance, without any correction (open circles)and applying corrections of the systematic deviations (close circles). The contribu-tion of the microstrip telescopes to the resolution has not been deconvoluted.Applying the correction of the systematic deviation, an evident improvementof the resolution was obtained, in particular for the large drift distances. It isimportant to stress the fact that the systematic deviation map was built us-ing the same set of data that was used to construct the resolution curve. Thismeans that possible systematic errors coming from other sources, not neces-sarily stable during long periods or depending on the measurement procedure,4are also corrected.Since it would be dicult to measure the systematic deviations in the AL-ICE operating conditions, a preliminary study has been already performed inorder to built the correction map using an infrared laser in the laboratory.This study has been done on another large area SDD with a 200 µm anodepitch, also used during the beam test. The three anodic resolution curvesobtained without correction, and applying the correction maps measured inbeam test and by using the laser, are compared in g. 5. Even though the pro-01020304050607080901000 5 10 15 20 25 30Drift distance (mm)Resolution (µm)Fig. 5. Anodic resolution of a 200µm anode pitch SDD as a function of the driftdistance, without any correction (open circles), applying the corrections measuredusing the laser (close squares), and applying corrections measured in beam test(open squares).cedure is still to be optimized, the laboratory setup and the readout systemwere very dierent from the beam test experimental conditions, and severalmonths passed between the two measurements, a relevant improvement of theresolution has been obtained using the laboratory measurement.We wish to thank F. Piuz and P. Martinengo from CERN for the use of themicro-strip telescope and for their assistance during data taking. R.H. wishesto thank Conacyt from Mexico and ICTP from Trieste (Italy) and L.M.M.wishes to thank Conacyt for nancial support.References[1] ALICE Collaboration, CERN/LHCC, 95/71[2] ALICE Collaboration, CERN/LHCC, 99/12[3] A. Vacchi et al., Nucl. Instr. and Meth. A306 (1991) 1875[4] A. Castoldi et al., J. Appl. Phys. 71 (7) (1992) 3593[5] A. Rashevsky et al., these proceedings[6] W. Dabrowski et al, Nucl. Phys. B 44 (1995) 637[7] W. von Ammon and H. Herzer, Nucl. Instr. and Meth. 226 (1984) 94[8] S. Beole et al., Nucl. Instr. and Meth. A360 (1995) 67-70[9] S. Beole et al., submitted to Nucl. Instr. and Meth.6

Correction of Dopant Concentration Fluctuation Effects in Silicon Drift Detectors

Correction of Dopant Concentration Fluctuation Effects in Silicon Drift Detectors

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