1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. Size of the field line funnelSA 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

8. 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

9. 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

10. 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

11. Experimental set-up X-tube Collimator Voltmeters Gas chamber
Electronics

12. 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

13. 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

14. 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

15. 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

16. 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

17. Summary of the measurements
At given field ratio, the backflow fraction ↓ with the ion distribution width
and ↑ with the hole pitch

18. 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

19. 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?

20. 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?

21. 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

22. 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

23. 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?

24. 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

25. 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