Study of Various Anode Pad Readout Geometries ina GEM-TPC

Jochen Kaminski, Steffen Kappler, Bernhard Ledermann, Thomas Müller and Michael Ronan

Abstract— The use of a Time Projection Chamber (TPC) basedon Gas Electron Multipliers (GEMs) as a central tracker inparticle-physics experiments is being studied by several groups.Compared to the conventional multi-wire readout this combinationoffers a number of advantages such as intrinsically suppressed ionfeedback, high granularity and decoupling of gas amplificationstage and readout geometry. The fast signal of GEMs and thereduction of the transverse diffusion in parallel magnetic fieldsgive a good spatial resolution. However for short drift distancesand high magnetic fields this may lead to signal sizes muchnarrower than the pad size and thus to a degradation of the spatialresolution. We have studied the use of different pad geometriesto improve the performance of the detector in the small diffusionlimit.

Index Terms— Time Projection Chamber, TPC, GEM, padstructure, spatial resolution.

I. INTRODUCTION

THE International Linear Collider (ILC) will collide elec-trons and positrons at a center of mass energy rangingfrom 90 GeV up to 1 TeV. The goal is to perform preci-sion measurements in this wide energy range. A vast physicsprogram ranging from the study of known particles like Z-and W-bosons, and top-quarks to the search of new physicssuch as electro-weak symmetry-breaking and Supersymmetryare accessible.

This ILC goal puts stringent demands not only on theaccelerator but also on the detector. The central tracking sys-tem has to meet challenges for which a large volume TimeProjection Chamber (TPC) [1] is well suited. In particular thelarge number of space points with good spatial resolutions andhence the excellent momentum resolution, as well as the precisemeasurement of the energy deposited by the particles alongthe tracks are essential features of a TPC and are vital forthe overall performance of the detector. Additionally, a TPCassures a minimum amount of material, excellent homogeneityand very high granularity - all of which are key issues in anyparticle-physics experiment. The use of a micro-pattern basedreadout such as the Gas Electron Multiplier (GEM) [2] willsignificantly improve the performance of the TPC. Compared

Manuscript received November 15, 2004.Jochen Kaminski, Bernhard Ledermann and Thomas Müller are with In-

stitut für Experimentelle Kernphysik, Karlsruhe University, Germany. (e-mail:jochen.kaminski@iekp.fzk.de)

Steffen Kappler is with Rheinisch Westphälische Technische Hochschule,Aachen, Germany.

Michael Ronan is with Lawrence Berkeley National Laboratory, Berkeley,USA.

Fig. 1. Photograph of the prototype GEM-TPC with front-end electronics(FEE) and support frame

to the conventional multi-wire readout of a TPC these devicesoffer a number of advantages of which the intrinsic suppressionof the ion backflow is most important. With a multi-GEMreadout a suppression factor of 10 � � is routinely achievedpromising a continuous running mode without the need for agating grid. Yet another important characteristic is the collectionof the electrons released from the lowest GEM by a pad readoutleading to a fast and narrow signal. Therefore, the transversesignal size is mainly dominated by the diffusion processes inthe drift region, while the gas amplification stage adds only acomparatively small constant width.

This reduction in cluster size improves the spatial resolutionand the multi-track separation in the transverse as well as in thelongitudinal direction. However, in a low diffusion regime suchas high magnetic fields, short drift distances and gas mixtureswith low diffusion the transverse cluster size can become sosmall, that only a single pad per row collects the completesignal. In this case the spatial resolution degrades to p

��� ���,

where p is the transverse pitch of the pad, i.e. the width of thepad plus a thin gap needed to separate two pads electrically. Toavoid this undesirable effect the pad geometry can be adaptedso that charge sharing is always achieved.

The influence of a small diffusion on various pad geometriessuch as rectangular, rhombus and chevron shaped pads has beenstudied. Throughout this paper only the transverse single-pad-row spatial resolution will be discussed. As an extrapolation

TABLE IPROPERTIES OF GAS MIXTURES - THEORETICAL COMPUTATION BY

GARFIELD INTERFACE TO MAGBOLTZ [5]

prototype large scale system (LS)

Ar-CH � (95:5) Ar-CH � -CO (93:5:2)magnetic field 1 T 4 T

ionization per 6 mm 55 e 55 e

drift field 60 V/cm 240 V/cm

drift velocity 3.85 cm/ � s 4.55 cm/ � strans. diff. 116.8 � m/ � �� 70.0 � m/ � ��

we will refer to values of the large scale system (LS) describedin the Technical Design Report of the TESLA-project [3].Here a TPC in a 4 T magnetic field with a maximum driftlength of 250 cm from the central cathode to either readoutendcap and a radius of 162 cm is described. For this study tworecommendations are of central importance: For several reasonsthe gas mixture was suggested to be Ar-CH � -CO � (93:5:2), andthe pad geometry was restricted to

���������mm. The latter

choice was motivated by the number of space points needed(200) and the maximum number of electronic channels allowed(����������� �

).

II. EXPERIMENTAL SETUP

To test and optimize a TPC with GEM readout a small andflexible prototype chamber was designed and constructed at theInstitut für Experimentelle Kernphysik (Karlsruhe, Germany).The detector is shown in Fig.1 together with the front-endelectronics. The chamber consists of three parts - a cathodeplane, a drift cylinder and a readout endcap - all of whichcan easily be replaced. A detailed description of the detectoris given in [4]. For the studies presented in this paper a driftcylinder with a length of 25 cm was chosen and the endcapwas mounted with a double GEM gas amplification stage. Thetransfer gap between the two GEMs and the induction gapbetween the lower GEM and the readout board were both set to2 mm. Electrical potentials were applied so that field strengthsof 2.5 kV/cm and 3.5 kV/cm respectively were formed. Toreduce the transverse diffusion as far as possible a gas mixtureof Ar-CH � (95:5), a drift field of 60 V/cm and a magneticfield of 1 T were chosen resulting in a transverse diffusioncoefficient of 116.8 ! m/ � " � (see Table I). Comparing thisvalue (prototype) with that of the large scale system (LS), whichoperates at 4 T, one finds that an equivalent cluster size isreached after the following drift distance:#%$'&)(+*-,/.1032'4 �6587:9;� A@B>A@DC6

an average noise level of about 4.5 ADC-units and degradedthe overall signal to noise to an average value of 7.

III. ANALYSIS METHOD

In a large scale detector pads are arranged in concentric cir-cular rows. High energetic particles coming from the collider’sinteraction point will pass radially through the TPC, and theirtracks are therefore in parallel with the radial component of thepads. Due to the magnetic field lower energetic particles willbe curved, and their tracks projected on the readout endcapwill have inclinations with respect to the radial direction. Forthe analysis of physics event at the interaction point a preciseknowledge of all track parameters is of utmost importance.Since track parameters are determined in general by fitting ahelix to the space points reconstructed in every pad row, alarge number of rows and a reliable and accurate measurementand reconstruction of space points in each row are important.E.g. the momentum resolution of the detector based on theGlückstern equation scales with [ MFO/\ � � ] , where [ M1O/\ is thespatial resolution of each row and

]the number of rows.

For an easier analysis of the data the geometrical layoutof the prototype detector has been changed to a right-angledcoordinate system, where the y-coordinate corresponds to theradial direction of the large scale detector and the x-coordinateto the angular direction. In analogy to the large scale detector,the particle beam of the test facility was directed quasi-parallel to the detector’s y-coordinate. Small inclinations oftracks with the y-coordinate are denoted with angle ^ . Duringreconstruction the position of the charge cloud, which will alsobe refered to as a cluster, is determined for each pad row with acenter of gravity method (COG). A combinatorial track finderthen merges these clusters to tracks, and a linear regressionalgorithm1 determines the track parameters. Since the detectorserves as a tracking as well as a testing device during thespatial resolution study, special attention has to be given toreach an unbiased result. Therefore, a target row is defined andexcluded from the aforementioned track fit. Then the shortestdistance of the cluster reconstructed in the target row to thetrack is determined, and its projection onto the x-coordinategives the cluster’s residual. These residuals are corrected forrow specific offsets, that are mostly due to inhomogeneitiesin the magnetic field. Finally, one has to consider that theCOG-algorithm is not optimized for narrow Gaussian chargedistributions. It shifts the reconstructed cluster position towardsthe center of the pad. To measure and correct the effect, thecluster position is determined in dependence on the pad fractionindependently of the pad position. These fractions are 100 !wide and run from the left pad border (-1 mm) to the rightpad border (+1 mm). Then the residuals are determined forevery fraction of the pad individually. Fig. 3 shows such adistribution for the pad fraction between -0.3 mm and -0.2mm. This Gaussian-shaped distribution has a small standarddeviation and is shifted by an offset of about 210 ! m from the

1Note: Due to the short y-dimension of the area covered by pads (72 mm) andthe large bending radius of R = _`Fa b�c = 17 m the track curvature is negligible.

Fig. 3. Distribution of residuals for all clusters with a x-position on the padbetween -0.3 mm and -0.2 mm. The data were taken with the rectangular padgeometry, an effective gas gain of d�e f-gihAf b and a drift distance of 7.5 cm.

Fig. 4. Rectangular pads 2 Z 6 mm : offset of residual distribution dependenceon the pad x-position.

center. Fig. 4 shows the offsets in dependence on the x-positionson the pad for various effective gas gains, track inclinationsand drift distances of the track. If the residuals are correctedfor these offset and combined to a distribution independent onthe cluster position, a narrow peak is obtained. In Fig. 5 thesum of two Gaussian functions is fitted to this distribution. Thereason for the combination of a narrow and a wide Gaussianfunction is given at the end of the section. A weighted averageof the two values gives the final result of (166.4 j 1.2) ! m.

To determine the spatial resolution [ from the residual width[ M1S�k , the contribution from the track uncertainty [ P?M1l6mon has tobe taken into account according to [ �M1S�k ( [ �qp [ �P?M1l6mon . Thetrack uncertainty is approximated by [ P?MFlNmon ( rs t , where N

Fig. 5. Rectangular pads u-Zqv mm : distribution of residuals at an effectivegas gain of dwZxhAf b , a drift distance of 7.5 cm and a track inclination y = -2 z - after correcting for offset due to pad x-position.

Fig. 6. Rectangular pads u{Z|v mm : spatial resolution dependence on thecluster’s pad x-position. The lines are to guide the eye.

is the average number of pad rows considered in the track fit.Combining both equations a correction term depending onlyon N is obtained, and the spatial resolution is determined by:[ � ( [ �M1S�k ��} ] �8} ] p �~/~i�

Analog to the offset in Fig. 4 also the width of the residualsor the spatial resolution can be plotted in dependence on thex-positions on the pad. Fig. 6 shows the plot for rectangularpads with various effective gas gains, track inclinations and driftdistances. For clusters that are closer to the edge of the pad theresiduals are much smaller, since they have sufficient chargesharing with the neighboring pad. In contrast clusters closer tothe middle of the pad have a higher probability to hit only onepad, and in the reconstruction they are then shifted to the centerof the pad. Therefore, also the distribution of clusters over the

Fig. 7. Number of tracks per fraction of pad dependence on the cluster’s padx-position. The lines are to guide the eye.

x-position of a pad is not homogeneous as expected, but showsa strong accumulation of clusters in the center (see Fig. 7).Combining the information of Fig. 6 and Fig. 7 it becomesclear, that the two Gaussian functions fitted to Fig. 5 representthe narrow distribution of clusters closer to the pad border andthe wider distribution of clusters at the middle of the pad.

IV. DISCUSSION OF PAD GEOMETRIES

The quantification of the spatial resolution depends on manyparameters. Notably the effective gas gain and the track incli-nation ^ have to be taken into account, if results should becompared. The influence of the effective gas gain is shown inFig. 8. The spatial resolution improves with the gain, because inmore and more events the charge collected by the neighboringpads raises above the electric noise and sufficient charge sharingfor a good reconstruction of the clusters is obtained. At higheffective gas gains the spatial resolution converges to a limitresulting from the fact that all clusters show charge sharing.The spatial resolution in dependence on the track inclination isshown in Fig. 9. It degrades with an increasing track inclination,which is due to the angular pad effect (see ref. [10]). For theresults presented in the following, the effective gas gain willbe quoted, and the track inclination will be -2 , if not statedotherwise.

A. Rectangular Pads -��x����x�

The rectangular geometry is the baseline design of theTESLA-TDR and the simplest implementation of the require-ments stated in the last paragraph of section I. The resultsobtained with this pad geometry have been discussed aboveand only a short summary shall be given. The dependency ofthe transverse spatial resolution on the cluster’s x-position onthe pad is shown in Fig. 6. As expected the charge sharingbecomes better for higher gains and longer drift distances, that

Fig. 8. Staggered rectangular pads: transverse spatial resolution dependenceon effective gas gain. The lines are to guide the eye.

Fig. 9. Rectangular pads uZv mm : transverse spatial resolution dependenceon track inclination y .means region of degraded spatial resolution becomes smaller.For drift distances of 17.5 cm and an effective gas gain ofU����'���

the spatial resolution is rather homogeneous with asmall deviation at the center. Under these conditions a finalresult of (148 j 2) ! m is reached.

One peculiarity of this pad geometry shall be discussedin the following. If charge clouds are narrow, and the trackinclination ^ becomes small (e.g. 0.4 ), the spatial resolutionimproves drastically. Fig. 6 shows that under these conditionsclusters in the center of the pad give a better residual widththen clusters closer to the edge, which is in contrast to thegeneral aforementioned behavior. It originates from an ’artificalalignment’ by the reconstruction: If a track passes along one

Fig. 10. a) rectangular pads: illustration of ’artifical alignment’ of narrowtrack with small inclination, b) rhombus pads: illustration of charge collecting,c) comb-like pads: illustration of tracks leading to identical charge ratios onneighboring pads

column of pads, and a significant number of clusters is shiftedto the center of the respective pad, then also the track will bealigned in parallel to the y-coordinate and at the center of thispad column resulting in very small residuals (see Fig. 10a).To avoid this bias the beam was mainly aligned for a trackinclination of ^� � .B. Staggered Rectangular Pads

A simple modification of the rectangular pad geometry isthe staggered design. Here every second row is shifted to oneside by half the pitch of pads. Tracks with small inclinations^ thus have a high probability of charge sharing in at leastevery second row. Therefore the spatial resolution improves, ifthe cluster is closer to the edge (see Fig. 11). If the clusterapproaches the center of a pad the offsets are larger than inthe non-staggered case and the spatial resolution for centralclusters becomes worse. Because of insufficient charge sharingthe cluster is shifted to the middle, and since the middle ofthe two consecutive pad rows is not identical, the clusters arezig-zagging around the actual track position. This circumstancecan be seen in Fig. 12, where the residuals are plotted versusthe x-position on the pad and the residuals of the previous row.The offset in dependence on the position can clearly be seenby the z-shape of the distribution. The ”Z” is a bisecting linethrough the origin if the distribution is projected in the residual-residual-plane.

The ’artificial alignment’ of clusters in tracks with smallinclinations has not been observed.

C. Rhombus Pads

The rhombus pads have a maximum width of 2 mm anda maximum height of 12 mm giving an equivalent pitch in

Fig. 11. Staggered rectangular pads: transverse spatial resolution dependenceon pad x-position. The lines are to guide the eye.

Fig. 12. Residual of target row versus residuals of row above target row andpad x-position.

both directions and an identical area per pad compared to thedesigns mentioned above. The spatial resolution in dependenceon the x-position shown in Fig. 13 behaves similar to the oneof the staggered rectangular pads. However, the final result of(225 j 3) ! m for a drift distance of 7.5 cm and an effective gainof 6.2

�;�� is somewhat worse. This originates from the line-

oriented analysis, that does not exploit the good charge sharingof neighboring pads in different rows. However, an asymmetriccharge collection is enhanced by the analysis: If a track passesclose to the center of the pad, in comparison with the staggeredrectangular pads a larger amount of charge is collected by thecentral pad, whereas a much smaller fraction is collected bythe neighboring pad of the same row (see Fig. 10b). This leadsto a higher number of clusters that are shifted to the pad center

Fig. 13. Rhombus pads: transverse spatial resolution dependence on pad x-position. The lines are to guide the eye.

and the final result degrades.

D. Chevron Pads

The chevron pads are also characterized by a��x��x�

mmarea and feature one tine with an angle of �VU . Even though itwas demonstrated by Monte-Carlo simulations [11] that a largernumber of tines will perform better, this design was chosen forreasons of easier manufacturing. Fig. 14 shows that the spatialresolution is rather homogeneous over the pad width, and alsothe number of tracks is better distributed. However, the spatialresolution is not as good as in the case of rectangular andrhombus pads. This results from the asymmetric shape of thepads and can be improved by taking the pad response functioninto account.

E. Comb-Like Pads

The comb-like pads are based on the idea to connect thinstrips so that large area interconnected pads are created. In ourimplementation we have combined four 500 ! m wide stripsto pads with a width of 3 mm but a pitch of only 2 mm.In this way charge sharing is also possible for clusters in thecenter of the pad. As can be seen in Fig.15 this works ratherwell giving comparable spatial resolution of about 180 ! mfor both drift distances of 7.5 cm and 17.5 cm at the center.However, the spatial resolution degrades towards the border tomore than 300 ! m. The reason for this is illustrated in Fig. 10c:The three track positions indicated by the vertical lines givean identical charge ratio on the neighboring pads and lead tounresolvable ambiguities. This could be improved by changingthe pad design to a significantly increased number of muchthinner strips.

Fig. 14. Chevron pads: transverse spatial resolution dependence on pad x-position. The lines are to guide the eye.

Fig. 15. Comb-like pads: transverse spatial resolution dependence on padx-position. The lines are to guide the eye.

F. ”3+1”-Pads

This pad geometry is characterized by two different padtypes: one 18 mm long pad and three 6 mm long pads arelocated side by side. Due to this combination the pitch ofboth pad types can be reduced to 1.33 mm, while retaining anaverage pad area of 12 mm

�. During the analysis the long pad

is considered as three short pads, and its charge is distributedaccording to the charge distribution of the six surroundingshort pads. The spatial resolution displayed in Fig.16 shows nosignificant degradation towards the center of the pad. But thereis an improvement in spatial resolution at central hits on thepad for longer drift distances and higher gains. This indicates

Fig. 16. ”3+1”-pads: transverse spatial resolution dependence on pad x-position. The lines are to guide the eye.

Fig. 17. Long rectangular pads 1.27 Z 12.5 mm : transverse spatial resolutiondependence on pad x-position. The lines are to guide the eye.

that these clusters hit three pads above noise, whereas clusterson the edge hit only two pads. There is also no significantoffset in the residual distribution dependent on the cluster’s x-position on the pad. Despite the reduced pad width the spatialresolution does not improve, since the large primary chargelocated on the long pads saturates the electronic channels evenat modest effective gas gains.

G. Long Rectangular Pads -����� Uq�x�����G� ��x�

This pad layout differs from the ones mentioned before, asit does not comply with the requirements stated in sectionI. All of the strips have a length of 12.5 mm increasing thecollected primary statistics from 55 electrons to 115 electronsper row and thus improving the spatial resolution by a factor

TABLE IICOMPARISON OF RESULTS WITH THE PAD GEOMETRIES TESTED.

pad geometry spatial resolution in � m spatial resolution in � mfor 7.5 cm drift for 17.5 cm drift

rectangular pads 158 2 148 22 Z 6 mm dZhAf b - hie 6z d�e uTZhAf b - e 6z

staggered 183 2 152 2rectangular pads ve�h-Z�hAf b - ue�h z dZ�hAf b - hie v z

rhombus pads 225 3 198 2ve uwZ�hAf b - ue d z wZ�hAf b - hie v zchevrons pads 289 2 263 3d�e�h-Z�hAf b - ue d z ve vTZhAf b - e�h zcomb-like pads 289 5 239 3ve wZ�hAf b - ue f z ve {ZhAf b - ue z

”3+1” pads 208 3 213 3d�e vwZ�hAf b - ue�h z d�e vTZhAf b - ue zrectangular pads 63 3 78 1

1.27 Z 12.5 mm 4.3 ZhAf b - fe z ve dwZhAf b - fe zof t't?A (  F ¡/¡   �G�VU . The width of the pads hasbeen chosen for geometrical reasons to be 1.27 mm giving atotal area of 15.9 mm

�per pad. This pad geometry has been

extensively tested before (see [7] and [8]) and therefore onlya reference measurement at 17.5 cm has been performed (Thevalue for 7.5 cm in table II has been extrapolated from datapresented in [8]). The spatial resolution for higher gains showsno dependency on the x-position on the pad (see Fig. 17) andthe offsets and distribution of tracks are constant over the pad’swidth. The overall performance is very good with values of}U3W j �~ ! m. Previous measurements have shown, that thisresult is further improved for shorter drift distances, however astrong dependency on track inclinations exists.

V. CONCLUSION

We have designed and experimentally tested seven differentpad geometries in the small diffusion limit. In this paper thesingle-pad-row transverse spatial resolution is discussed. Afterdescribing the analysis method and the pad geometries, thespatial resolution in dependence on the x-position on the pad ispresented. A comparison of the overall spatial resolution includ-ing the specific effective gas gain and track inclination is listedin Table II. As expected the long rectangular pads performedbest. But the best results for 6 mm long pads are achievedfor standard and staggered rectangular pads. For all other padgeometries the center of gravity-method does not seem to beappropriate to determine spatial resolution. Considering the truepad response function and a larger number of pad rows willimprove the overall performance of the detector.

ACKNOWLEDGMENTThe authors would like to thank Norbert Meyners from

DESY for helping with test beam related issues and providingthe magnet, the FLC-group of DESY and especially T. Behnkeand M. Ball for supporting this project in many ways, D. Karlenfor modifying the electronics and T. Barvich for building thedetector and parts of the equipment.

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