Simulation of the energy resolution dependence on the geometry of Micromegas detectors Max Chefdeville, NIKHEF, Amsterdam TPC Jamboree, Aachen, 16th March 2007

Overview Introduction The simulator Drift field and cathode voltage Why looking at the gain fluctuations? Any room for energy resolution optimization? The simulator Parameters: geometry/gas/fields Program steps Analysis Drift field and cathode voltage Gas mixtures of interest: P10, Ar/CF4, pure CF4 Simulation predictions: On the field ratio & transverse diffusion On the hole Ø, amplification gap, grid thickness Conclusions

Looking at gain fluctuations Goals: investigate the single electron response of the Micromegas detector for the pixel readout TPC of the ILC Optimize Micromegas geometry for good energy resolution With a pixel readout anode: Collection efficiency must be maximum Gain fluctuations must be known How many avalanche will end up above the threshold? Gain fluctuations composed of: Single electron response or avalanche fluctuations (exponential, Polya) Gain RMS over the Micromegas hole (Micromegas geometry) Investigate the fluctuations from the geometry Should depends on How much is the gain fluctuating over a hole? FIELD MAPS How centered the e- enter the hole? MONTE CARLO

Simulation parameters Detector geometry: Hole pitch / diameter Grid thickness Amplification gap Field shape Amplification field Drift field Field ratio (i.e. focusing) Gas properties: Transverse diffusion Townsend/attachment coef. Gain(x,y) MAXWELL 3D GARFIELD G, ΔG/G, collection P(x,y) MAGBOLTZ

Simulation steps Standard geometry Create a field map Square pattern of round-shaped hole Create a field map Use 4-fold symmetry (actually 8-fold) Define geometry Set voltages on electrodes (E fields) Run field solver Read the map in GARFIELD Release single e- at the cathode No focusing yet (E = Ez) Drift & amplify e- in a given gas until collection Create a drift line according to diffusion and a user defined step (~1 μm) Integrate Townsend & attachment along line NO 3D spatial development of avalanche Write gain & coordinates of start/end points AND (x,y) grid crossing point coordinates

Analysis Output from GARFIELD (x,y,z)I, (x,y,z)g, (x,y,g)f, G Make histo. of grid crossing point coordinates Hole entrance position distribution Calculate the collection efficiency Determine the gain as a function of the hole entrance point Gain spatial dependence Calculate the gain mean & variance over the hole Determine the gain distribution experienced by the e- (Gain spatial distribution) x (entrance distrib.) Quantify fluctuations from the field un-uniformity

Drift field and cathode voltage First attempt, one wants Ed @ cathode: take Vd = Ed.Dgap + Vg yields too large Ed Cathode not far enough from the grid “feels” the anode potential Va > Vg especially for large hole Ø and low Ed Enlarge the cell Use the effective potential of the grid Veff = Σx Σy V(x,y,z=zgrid) / N Stick to large Ed, i.e. low field ratio Set Ea = 80 kV/cm, Ed = 1 kV/cm Vc Vg ED Va

Gas mixtures At the end, compare gain with data Try experimentally used gas Ar/He/iC4H10/CO2/CH4/CF4 No Penning effect No Ar/ethane, Ar/iC4H10 mix. No secondary e- from photo-effect on the grid Not too high amplif. field (< 80 kV/cm) Can we simulate the effect of diffusion? Field from 1 kV/cm to 10 kV/cm at the hole entrance Use low/high transverse diffusion mixtures Selection: Ar 10% CH4 σt from 225 to 240 μm.cm-1/2 Ar 10% CF4 σt from 100 to 180 μm.cm-1/2 Pure CF4 σt from 40 to 80 μm.cm-1/2

Focusing versus diffusion Gain fluctuations are minimized if e- enter the hole at the same location. Monte Carlo quantify the size of the entrance area as a function of transverse diffusion focusing “high” diffusion “low” diffusion field ratio = 80 field ratio = 470

Focusing versus diffusion Gas: P10, Ar/CF4 90/10, CF4 Geometry Hole Ø 25 μm Hole pitch 50 μm Agap 50 μm Grid thickness 1 μm Fields Ea = 80 kV/cm Ed = 170 V/cm α = 470 Ed = 1000 V/cm α = 80 In a high diffusion gas, focusing is reduced Hole entrance distribution ~ flat No effect of the field ratio At low diffusion, focusing affect the gain RMS RMS lower at higher field ratio Effect of collection efficiency is being understood (not shown here) Mean gain doesn’t depend on the focusing Gain RMS reduced for low diffusion gas

The hole diameter Relevant parameter is the ratio of hole diameter over hole pitch Ø/p At Ø/p < 0.5 Low/high collection eff. Depends on focusing Uniform field and thus gain At Ø/p > 0.5 High collection eff. Low/large gain RMS Ø = 37.5 μm Ø/p = ¾ G_RMS = 23.5 % Ø = 12.5 μm Ø/p = ¼ G_RMS = 6.8 %

The hole diameter Previous slide: If one look at spectrum of 200 e- Collection improves with hole Ø Gain RMS over hole degrades with Ø If one look at spectrum of 200 e- Is there an optimum Ø? Translate collection eff. into resolution e.g. for 200 e- signals if collec = 70 %, σc ~ 4.6 % At higher field ratio, the collection efficiency should be constant down to smaller hole diameters Should find a minimum of energy resolution at high field ratio

The grid thickness For thicker grid field gets lower inside the hole Decreases collection efficiency field may gets less homogeneous in the avalanche gap Reduces the gain but no effect below 5 μm thicknesses Increases Gain RMS Drop less severe for low diffusion gas t = 1 μm (left) Gain = (1264 +/- 30) RMS = (14.0 +/- 0.3) % t = 5 μm (right) Gain = (1298 +/- 30) RMS = (19.0 +/- 0.4) %

The grid thickness At the end Collection plateau then degradation with thickness The higher the field ratio, the larger the plateau Gain RMS degrades little below 5 μm Resolution dominated by collection efficiency

The amplification gap Modify the gap thickness and keep the fields constant Variable gain Same focusing/diffusion Collection constant Relevant parameter is the ratio of the hole diameter to the amplification gap Ø/Agap. Ø/Agap << 1 Low gain RMS Gain mean increases with gap G = exp(α.gap) Gain RMS decreases with gap Condition to met: Agap >> Ø Agap = 30 μm Ø/Agap = 5/6 G_RMS = 19.9 % Agap = 50 μm Ø/Agap = 1/2 G_RMS = 14 %

Summary First results on gain, resolution and collection understood. Limited to low field ratios for now Effect of gain variation over the hole not striking Resolution dominated by collection efficiency Design rules at low field ratio are contradictory Maximum collection: Grid as thin as possible Hole diameter ~ hole pitch Minimum Gain RMS over the hole: Hole diameter smaller than 1 4th of the pitch Amplification gap larger than 2 times the hole diameter Situation should be clearer at high field ratio Check how large the cell can be without losing field computing accuracy

Thanks for your attention

The amplification gap At full collection efficiency Resolution governed by the amplification gap Resolution plateau for Agap>>Ø In our case, field ratio = 80 Full collection only for CF4 Constant collection efficiency