A complete simulation of a triple-gem detector

A complete simulation of a triple-gem detector W. Bonivento, A. Cardini, D. Pinci Abstract Since some years the Gas Electron Multipliers (GEM) based detectors have been proposed for many different applications, in particular in high-energy physics and astrophyisics experiments and medical imaging. Many experimental measurements and tests have been performed to investigate their characteristics and performances. To achieve a better understanding of the behavior of such a detector the computer simulation is a very important tool. In this paper a complete and detailed simulation of a triple-gem based detector is described. A method has been developped to take into account all the processes from the ionization machanism up to the signal formation and electronic response. The results obtained are compared with experimental data and a very good agreement is achieved. Keywords GEM, Garfield, Simulation. I. INTRODUCTION A Gas Electron Multiplier (GEM) [1] is a kapton foil, copper clad on each side, perfored with an high surface-density of holes. A potential difference of the order of 500 V applied between the two copper electrodes generates an electric field as high as 100 kv/cm into the holes which may act as multiplication channels for the electrons created in a gas by an ionizing particle. The gain in the channel is of the order 100 Ξ 200, but only a part of the secondary electrons can leave the GEM foil and the effective gain results of about 20Ξ100. Multiple GEM s structures, allowing to reach higher total gain (10 4 Ξ 10 5 ), are used to build detectors for charged particles and photon. In order to study the properties of a triple-gem based detector a full and detailed simulation has been performed. At first single GEM characteristics have been investigated by using Maxwell [2] and Garfield [3]. The properties of a complete triple-gem based detector have been then derived by developping a Monte-Carlo method. The read-out electronics behavior has also been simulated by means of Spice [4] in order to compare the simulation results with experimental data. II. THE SINGLE GEM SIMULATION A. The model The Standard GEM (bi-conical holes with external diameter of 70 μm, internal diameter of 50 μm disposed with a pitch of 140 μm on staggered rows) operating in an Ar/CO2/CF4 (60/20/20) gas mixture has been simulated and studied. A.1 The electric field configuration To calculate the electric field map of a voltage supplied GEM in an external electric field a 3D-model has been built in Maxwell. This model (Fig. 1), based on an elementary unit with dimension of 400 121 70 μm 3, is made by a 50 μm thick kapton clad on each side (b and c in the figure) with 5 μm thick copper in a parallelepipedic box. It is possible to reproduce W. Bonivento is with CERN, PPE Division, 1211 Geneva 23, Switzerland. A. Cardini is with INFN Sezione di Cagliari, S. S. Monserrato-Sestu, 09042 Monserrato (Ca), Italy. D. Pinci is with INFN Sezione di Cagliari, S. S. Monserrato-Sestu, 09042 Monserrato (Ca), Italy (telephone +39 070 675 4840, e-mail: Davide.Pinci@ca.infn.it). Fig. 1. GEM foil elementary unit layout used in Maxwell. different electrostatic configurations by changing the boundaryconditions on the surfaces a; b; c and d. Maxwell calculates, by finite elements method, the resulting electric fields maps. About 31,000 thetraedrons have been used in this model resulting in an error on the system electrostatic energy (which can be also exactly calculated) lower than 0:04%. In the field map only the components tangential to the box lateral faces of the electric field are taken into account. In this way an entire GEM foil is obtained by periodically repeating this elementary unit. A.2 The gas mixture The gas mixture properties have been calculated using the following simulation tools: ffl Magboltz [5] has been used to compute the electrons drift velocity and the longitudinal and transverse diffusion coefficients; ffl Heed [6] calculates the energy loss through ionization of a particle that traverses the gas and allows to simulate the clusters production process; ffl Imonte 4.5 [7] has been used to compute the Townsend and attachment coefficients. The calculated electron drift velocity as a function of the electric field is shown in Fig. 2 compared with experimental data [8]. The distribution of the number of primary clusters produced by a minimum ionizing particle in a3mmgap, shown in Fig. 2, gives an avarage value of about 15 clusters/3 mm. B. GEM electron transparency Due to the diffusion effect and electric field lines defocusing (i.e. some electric field lines above the GEM do not enter into the holes) some electrons hit the upper GEM electrode (Fig. 3 ). Into the channel a part of electrons will be captured by the kapton because the diffusion effect, or by the lower copper 0-7803-7324-3/02/$17.00 2002 IEEE 273

It is important to outline that the properties of one side of the GEM appear to be only marginally influenced by the electric field on the other side. Fig. 2. Ar/CO 2 /CF 4 (60/20/20) gas mixture properties. : drift velocity obtained from experimental measurements [8] and from Garfield simulation. : distribution of the number of primary clusters in a 3 mm gap obtained from Garfield simulation. side because a poor extraction capability of the electric field below (Fig. 3 ). Therefore the GEM electron transparency T represents a very important parameter to be studied. Fig. 4. Efficiencies dependence on drift field and on transfer field. III. THE GEM GAIN To study the single GEM gain, into the channel avalanches are simulated by using a Monte Carlo method from Garfield. (Fig. 5). In order to aveluate correctly the gain is of crucial relevance Fig. 3. Example of simulated processes: electron hitting the upper electrode; electron absorbed in a GEM channel. In order to evaluate the behavior of T as a function of the various electric fields simple studies have been performed. Electrons have been produced in a uniformly random position on a surface 150 μm above the GEM (where the equipotential surfaces are completely flat) and then a process of Monte Carlo drift has been generated. The ratio (number of e entering)/(number of e generated) will be indicated as collection efficiency ffl coll while the ratio (number of e extracted)/(number of e into the channel) will be indicated as extraction efficiency ffl extr and are related to T : T = ffl coll ffl extr The electric field above the GEM will be indicated as the drift field and the one below as the transfer field. ffl in Fig. 4 the dipendence on the drift field is shown. The ffl coll decreases at high drift field due to the defocusing effect, while ffl extr doesn t depend strongly on this parameter. ffl in Fig. 4 is shown the behavior for different transfer fields. Due to a best electrons extraction capability the ffl extr increases at high transfer fields. Fig. 5. Simulated avalanche developping in a GEM hole. to take into account the diffusion effects which can make the electrons reach the regions close to the kapton where the higher electric field results in a higher multiplication. The distribution of the number of secondary electrons leaving the GEM obtained by generating 1000 electrons on a surface 150 μm above a GEM with a U gem of 450 V is shown in Fig. 6. For each single primary electron, large gain fluctuations have been found. The average number of secondary electrons produced will be indicated as intrinsic gain μ G intr while the average number of secondary electron extracted will be indicated as the effective gain μ G eff. It results that: μg eff = μ G intr T The dipendences of μ G intr and μ G eff on the U gem values are shown in Fig. 7 and. 274

A. Clusterization and electron drift The number, the position and the size of the clusters created has been calculate by using Heed. Starting from the creation point, for each primary electron a drift process is simulated and the arrival time (t d ) on the first GEM is recorded. The general expression for the probability-distribution of the creation point distance from the first GEM x for the cluster j, when n is the average number produced, is [9]: A n j (x) = xj 1 (j 1)! nj e nx It is possible to calculate (knowing the drift velocity v d ) the arrival time probability-distribution: Fig. 6. Distribution of the number os secondary electrons extracted from the GEM foil. P j (t d )=v d A n j (vt d) In particular for the first cluster (the nearest to the first GEM) P1(t d )=v d ne nvt d ff1(t) =1=nv d Fig. 7. μg intr and μg eff as a function of the GEM voltage supply. where ff1(t) gives the intrinsic limit for the time resolution of a GEM-based detector when the first cluster is always detected. It depends only on the gas mixture properties and for the one used in the simulation is ff1(t) =2:2 ns. B. Detector gain For each primary electron the total gain is calculated. The total multiplication of any single electron of a cluster containing m primaries is given simply as the product of random extracted values g eff from the effective single GEM gain distribution. In this way each cluster produced in the ionization gap becomes a cloud of n tot electrons where: IV. THE TRIPLE-GEM DETECTOR SIMULATION Starting from the single GEM simulation the properties of a triple-gem based detector have been derived. The detector model used as reference for the simulation and for the comparison is the prototype tested on beam by the LHCb-muon group [11]. The geometric and electric configuration and the read-out electronics paramenters are here summarized: ffl 3 standard GEM staked one above the other, with U gem2=u gem3=390 V; ffl 3 mm drift gap with E d =3 kv/cm; ffl 2 mm transfer gaps with E t1=e t2=4 kv/cm; ffl 1 mm induction gap with E i =5 kv/cm; ffl discrete-componets read-out electronics with peaking time of 8 ns and sensitivity of 10 mv/fc. To evaluate the signal produced by a charged particle crossing the detector, the following physical processes have to be taken into account: 1. Clusterization and electrons drift in the drift gap; 2. Multiplications and electron transparency of each GEM; 3. Charge transfer in the transfer gaps; 4. Drift in the induction gap, signal formation and electronics response. n tot =(± m i=1 gi eff1 ) g eff2 g eff3 In the first GEM different gains are evaluated for each primary electron of a cluster. Due to the large number (' 30) of the secondary electrons leaving the first GEM the gains in the following GEM have been approximated with an average value which is the same for each electron. C. Charge transfer The transfer times (i.e. the times to cover the transfer gaps) t t1 and t t2 have also been calculated by the sum of random extracted values from the distributions of the electron drift times in the two transfer gaps. The electrons cloud in the simulation arrives at the last gap at a time T0 after the track crossing, given by: T0 = t d + t t1 + t t2 The total arrival time spread can be calculated as: ff(t0) =ff(t d ) Φ ff(t t1) Φ ff(t t2) From the simulation, has been found ff(t t1) =ff(t t2) ' 0.5 ns (which is due to diffusion effect). Hence the main contribution to the ff(t0) is expected to be given by ff(t d ). 275

D. Signal formation The signal is induced on the readout anode by the electrons motion in the induction gap. The current that flows into an electrode k due to a moving charge q can be calculated using the Ramo s theorem [10]: I k = q~v(x) ~ E k (x) V k where the E ~ k (x) is the electric field created by raising the electrode k to the potential V k (all other electrodes being at 0 V). In particular if V k =1 V, the resulting electric field is called weighting field ( E ~ w k ) and the Ramo s theorem becomes: I k = q~v(x) ~ E k w (x) Due to the induction gap thickness E ~ w k (x) in this detector is almost constant. As expected from Ramo s theorem a single electron induces a constant current of -14 pa for about 11 ns. E. The electronics simulation To simulate the electronics response Spice has been used to evaluate the trasfer function of the read-out electronics. By using the convolution method the signal due to a charge moving in the last gap as appear on the electronics output has been calculated. The total signal due to a minimum ionizing particle can be calculated by the convolution of signals due to each electrons cloud starting at various T0 (Fig. 8). It is possible to see: 1. the signal rise due to the arrive of the first electrons in the last gap; 2. the flat part of the signal due to the constant E ~ w ; 3. the duration time (about 30 ns) wich is the drift time in the ionization gap. resolution. From electronics rise time t r (' 6 ns) the upper 3 db frequency f h could be calculated from the relationship [12]: f h t r ' 0:35 which gives f h =60 MHz. The noise frequency distribution has been approximated as flat up to 3 f h and then setted to 0. The noise amplitude has been chosen to be gaussian distribuited with mean 0 and RMS tuned to reproduce the ADC spectra pedestal RMS (' 30 counts) recorded on the test beam with a sensitivity of 50 fc/count and a gate of 200 ns. V. SIMULATION RESULTS Using the method and tools described in previous sections, the detector main characteristics have been simulated and studied in details. A. Detector total gain A first study has been performed on the detector total gain (i.e. the 3-GEM gain and the electronics gain). The total charge spectra have been calculated as a function of U gem1. The simulated total charge has been found to be lower than the experimental one by a factor 3 in the whole range U gem1 = 400 V! 450 V. Taken into account this averall recalibration factor a very good agreement between simulation and experiment data has been obtained. The charge spectra obtained with U gem1= 420 V are shown in Fig. 9. In Fig. 10 the simulation total charge spectra peak positions are compared with the experimental ones. The indipendence of the recalibration factor on U gem1 suggests that it could be mainly due to an underestimation of the electronics gain in charge. Also the calculated 3-GEM gain could be lower than the real one, as found also in other works [13]. Detailed understanding of this discrepancy is being studied. Fig. 9. Experimental and simulated detector total charge spectra. F. The noise Fig. 8. Signal due to a track from the simulation. A very important role in the detector performances is played by the electronics noise which in particular decreases the time B. Detector efficiency and time resolution The total effieciency and the 25 ns time-window efficiency have been then calculated. These parameters are very important for the proposal to use GEM based detectors for trigger in the LHC experiments. To abtain correct values for the efficiency in the narrow timewindow the so called bi-gem effect has to be included. This effect is due to the possibility that the ionization produced in the first transfer gap could be amplified by the second and third 276

C. Conclusions A big effort has been necessary to abtain a correct modelization of this new kind of detector by using the Maxwell and Garfield tools. The results obtained, after a recalibration of the total (3-GEM and read-out electronics) gain of a factor 3, show a very good agreement with the experimental data. This indicates that the method developed can be used to achieve a better understanding of the behavior of the GEM and to optimize the detector characteristics (geometry, gas mixture, electric fields configuration...) in order to optimize the real detector performances. Fig. 10. Position of the Landau distribution peaks from experimental data and simulation. GEM enough to be discriminated resulting in an out of time (i.e. early) TDC hit, which worses the time resolution. The experimental fraction of events due to bi-gem effect is 1.3 % while from the simulation a value of 1.4 % has been found and subtracted from the narrow time window efficiency. In Fig. 11 are shown the behaviors of the experimental and simulated total and in a 25 ns time-window efficiencies as a function of U gem1 with a discriminator threshold of 12 mv. REFERENCES [1] F.Sauli, GEM: A new concept for electron amplification in gas detectors, Nucl. Instrum. Meth. vol A386, p. 531, 1997. [2] Maxwell 3D Field Simulator. User s Reference. Avaible: http://wwwinfo.cern.ch/ce/ae/maxwell/maxwell.html. [3] R. Veenhof, Garfield, a drift chamber simulation program, Version 7.04 Nucl. Instrum. Meth. vol A419, p. 726, 1998. Avaible: http://consult.cern.ch/writeup/garfield. [4] PSpice circuit analysis software. User s Guide. MicroSim Corporation. [5] S. Biagi, Magboltz, a program to solve the Boltzmann transport equations for electrons in gas mixtures, Version 2.0 CERN. Avaible: http://consult.cern.ch/writeup/magboltz. [6] I. Smirnov, HEED, a program to compute energy loss of fast particle in a gas, Version 1.01, CERN. Avaible: http://consult.cern.ch/writeup/heed. [7] S. Biagi, Nucl. Instrum. Meth. vol A273, 1998. [8] U. Beker et al. Gas R&D Home Page. Avaible: http://cyclotron.mit.edu/drift. [9] F. Sauli, Principles of operation of multiwire proportional and drift chamber, CERN 77-09, 1977. [10] S. Ramo, Currents induced in electron motion, in Proc. IRE 27, 584 (1939). [11] G. Bencivenni et al., A triple GEM detector with pad readout for inner region of the first LHCb muon station, LHCb 2001-051. [12] P.W. Nicholson, Nuclear electronics. [13] A. Sharma, 3D simulation of charge transfer in a Gas Electron Multiplier (GEM) and comparison to experiment, Nucl. Instrum. Meth. vol A454, p. 267, 2000. Fig. 11. Experimental and simulated total and in a 25 ns window detector efficiency as function of U gem1. The simulation seems to reproduce very well the experimental efficiencies and time performances. 277