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**M. Chefdeville NIKHEF, Amsterdam MPGD, Hawaii 07**

Measurements and modeling of the ion backflow properties of integrated Micromegas (MP3-2) M. Chefdeville NIKHEF, Amsterdam MPGD, Hawaii 07

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**Overview Introduction Measurements Simulations Conclusion**

GridPix detectors InGrid, an integrated Micromegas Ion backflow of InGrid Measurements Experimental set-up Results Simulations 2D, 3D Monte Carlo 1D, 2D, 3D Numerical calculation Conclusion

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**The Gridpix detector Readout gas volume by means of pixels**

Edrift Readout plane Gas volume particle The Gridpix detector Readout gas volume by means of pixels Small input capacitance High granularity Micromegas-based amplification High electric field faced by the chip Single electron sensitivity Broad range of application from HEP (TPC, VTX) to Rare events detection and X-ray polarimetry Edrift Eamplif. Grid + (Pillars) + Pixels

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**The Gridpix detector Demonstrated to work in 2004 Issues**

Fraction the 14x14 mm2 Medipix2 pixel area ~ 7 mm Demonstrated to work in 2004 Issues Gas detectors do spark sensitive to gas discharges Large Micromegas pillar Ø detection area loss Pixel pads and grid holes misaligned efficiency loss Grid hole and pixel pitches ≠ periodic variation of efficiency Moiré pattern

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**InGrid, an integrated Micromegas**

Solve the alignment / pillar Ø / pitch issues by integrating the Micromegas onto the chip Wafer post-processing Grid geometry fits the chip Pillar Ø ~ 30 μm Very good grid flatness Minimum gain fluctuations Extremely good resolution of 11.7 % 5.9 keV in Ar 10% CH4 Ion backflow properties recently studied 2 cm Ø pillar 11.7 % FWHM

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**Ion backflow in Micromegas**

Intrinsic low BF as most of the field lines in the avalanche gap end on the grid Number of ions arriving on the grid depends on: Shape/size of the field line funnel Ion formation positions Grid geometry Ratio of the Amplification to Drift fields Longitudinally: Townsend coefficient Transversally: Electron diffusion Ion drift lines EDrift EAmplif. Electron avalanches

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**Size of the field line funnel**

SA Sd EDrift EAmplif. Gauss theorem: ∫funnelE.dS = 0 For D and A fields: ED.SD = EA.SA SA, SD funnel length (1D) or cross section areas (2D,3D) in Amplification and Drift regions Thus: SA = SD . ED / EA = SD / FR FR, field ratio Increasing field ratio FR (EA ↑ or ED ↓) SD ↑ (up-bounded by hole pitch) SA ↓ (no lower bound) Above certain field ratio FR, SD = p*p: SA = p*p / FR the backflow fraction ↓ like 1/FR and ↑ like p2

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**Measuring the ion backflow fraction of Micromegas**

Definition, for a single e- induced avalanche, the backflow fraction is: back-flowing ions / total number of ions i.e. ions collected on the cathode / ions on the anode Experimentally, the ion backflow fraction BF is: BF = (Ic - Ip) / Ia = Ib / Ia Ic: cathode current Ip: primary current Ia: anode current Constraints: Measurable primary currents Accurate measure of Ib (very small at high field ratio) Should operate the detector: Under relatively high irradiation (strong e- radio source / X-ray gun) High gains Ip -Ip Ia Ib

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**Measuring the ion backflow fraction of InGrid**

2 cm Ø InGrid have a small area (π cm2) Recombination in drift region may occur if charge density is too high No field cage: electric field not uniform on the grid edges (effect ↑ at low Drift fields) Collection loss Limit the minimum drift field (maximum FR) Therefore: Moderate irradiation and small gains measure small currents (Ip ~ tens of pA) Use guard electrode around the grid + strong source collimation

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**Experimental set-up X-ray gun up to 12 keV photons, 200 μA**

Operated at 9 keV energy (50 μA) 10 keV photo e- range ~ 1 cm in Ar Collimator is 2 cm thick with a 3 mm Ø hole Guard electrode 1 mm above the grid Adjustable voltage Cathode/Anode current measurements Voltage drop through 92 MΩ resistor Zinput = 1 GΩ, ΔI = 1 pA Voltage drop through 10 MΩ resistor Zinput = 100 MΩ, ΔI = 100 pA Reversed polarities: Cathode at ground, grid and anode at positive voltages No field between detector window and cathode Gas mixture: Ar:CH4 90:10

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**Experimental set-up X-tube Collimator Voltmeters Gas chamber**

Electronics

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**Detector geometries 4 different hole pitches**

20, 32, 45 and 58 μm 20 & 32 μm pitch grids have pillars inside holes 45 & 58 μm pitch grids have pillars between holes 3 different amplification gap thicknesses 45, 58 and 69 μm ± 1 μm Operated at 325, 350 and 370 V Amplification fields of 72, 60 and 53 kV/cm Gains of 200, 550 and 150 Diffusion coef. of 142, 152 and 160 μm/√cm Avalanche width of 9.5, 11.6 and 13.4 μm

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**Measurements in Ar:CH4 90:10**

Vary field ratio FR from 100 to 1000 Drift field from ~ 500 V/cm down to few ~ 50 V/cm At high FR (low Drift field), primary e- loss due to field distortions Stop at FR ~ 1000 Fit curve with BF = p0/FRp1

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**Measurements with 45 μm gap InGrids**

BF = p0/FRp1 Gain ~ 200 σt = 9.5 μm 20 μm pitch p1 = 1.01 32 μm pitch p1 = 0.90 45 μm pitch p1 = 0.96 58 μm pitch p1 = 1.19 At given field ratio and ion distribution, the backflow fraction ↓ with the pitch

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**Measurements with 58 μm gap InGrids**

BF = p0/FRp1 Gain ~ 500 σt = 11.6 μm 20 μm pitch p1 = 1.08 32 μm pitch p1 = 1.02 45 μm pitch p1 = 1.01 58 μm pitch p1 = 1.21 BF < 1 ‰ At given field ratio and ion distribution, the backflow fraction ↓ with the pitch

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**Measurements with 70 μm gap InGrids**

BF = p0/FRp1 Gain ~ 150 σt = 13.4 μm 32 μm pitch p1 = 1.14 45 μm pitch p1 = 1.13 58 μm pitch p1 = 1.28 BF < 1 ‰ At given field ratio and ion distribution, the backflow fraction ↓ with the pitch

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**Summary of the measurements**

At given field ratio, the backflow fraction ↓ with the ion distribution width and ↑ with the hole pitch

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**Simulations Monte Carlo Numerical calculation**

Calculate the electric field in 3D with MAXWELL3D Simulate avalanche development within GARFIELD with MAGBOLTZ calculated Townsend and diffusion coefficients Count the number of back-flowing and total ions Can be used to determine the funnel shape Numerical calculation Assume homogeneous amplification field Assume field line funnel shape and area Calculate ion distribution in 1D/2D/3D with MAGBOLTZ calculated Townsend and diffusion coefficients Integrate the distribution over the field line funnel length/area/volume

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3D Monte Carlo Finite element mesh restricts the study to “large” funnel size (> 0.25 μm) OK for low FR Not suitable for studying the effect of geometry on the backflow fraction Requires a lot of field maps to be solved Time consuming However, can be used to check assumption for the numerical calculation Reveal the field line funnel shape Alike hole shape? Round? Square?

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3D Monte Carlo Finite element mesh restricts the study to “large” funnel size (> 0.25 μm) OK for low FR Not suitable for studying the effect of geometry on the backflow fraction Requires a lot of field maps to be solved Time consuming However, can be used to check assumption for the numerical calculation Reveal the field line funnel shape Alike hole shape? Round? Square?

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**Numerical calculations**

Ion distributed along anode axis or over anode plane with and without longitudinal development X model Gaussian distribution Funnel is an interval of length L2 = L1 / FR = pitch / FR X-Z model Gaussian x exponential distribution G(x,σ(z)).e(α.z) Funnel is a rectangle of area S2 = GAP.L2 = GAP . pitch / FR XY model Gaussian distribution G(x,y,σ(GAP)) Funnel is a circle of area S2 = S1 / FR = pitch2 / FR XY-Z model Gaussian x exponential distribution G(x,y,σ(z)).e(α.z) Funnel is a cylinder of volume V2 = GAP . S2 = GAP . S1 / FR = GAP . pitch2 / FR X model X-Z model XY model

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**Ion backflow in the 1D,2D & 3D models**

In all models, the backflow fraction reaches a minimum plateau equals to 1/FR Ion backflow from neighboring holes Reducing pitch or increasing ion distribution width further does not help In “Z” models, more ions are generated in the funnel Increase of backflow fraction Z-dimension can be neglected at high gains

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**Simulations and results**

Backflow trend in good agreement with the XY-Z simulation Though, measurements show 0.5 to 1 % offset Errors on σt for data points, or α for simulated points?

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Conclusions Backflow fraction of few per mil reached in Ar:CH4 90:10 gas mixture with 20 μm hole pitch InGrids Measurements and simulations: Good understanding of dependence on hole pitch and gas diffusion Still discrepancies on the trend of backflow w.r.t. field ratio Further studies, decrease the backflow further Double stage grid (TwinGrid) Measure backflow fraction in under-quenched gas mixtures

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**Acknowledgements NIKHEF**

Harry van der Graaf, Fred Hartjes, Jan Timmermans, Jan Visschers, Marten Bosma, Martin Fransen, Yevgen Bilevych Twente Cora Salm, Joost Melai, Jurriaan Schmitz, Sander Smits, Victor Blanco Carballo Saclay D. Attié, P. Colas, I. Giomataris

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