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Digital primary electron counting: W, Fano Factor, Polya vs Exponential

Study the efficiency of single electron detection and measure gain fluctuations using Polya and Exponential models. New technique for F measurement with GridPix and TimePix chips. Experimental results and conclusions on detection efficiency and gain distribution.

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Digital primary electron counting: W, Fano Factor, Polya vs Exponential

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  1. Digital primary electron counting: W, Fano Factor, Polya vs Exponential M. Chefdeville, NIKHEF, Amsterdam RD51, Paris, 13-15 October 2008

  2. Introduction • Motivations • Study single electron detection efficiency of GridPix detectors • What are the gain fluctuations? Polya/Exponential-like • Two approaches • Measure the single electron response (difficult) • Measure energy resolution, primary statistics (W & F) then deduce gain fluctuations • New technique to measure F: count primary electrons from 55Fe quanta conversions

  3. 55Fe X-ray E0 5.9 and 6.5 keV Photo-e- Auger-e- TimePix chip 55Fe quanta conversions seen by GridPix After large drift distance, primary e- separate and can be counted InGrid Gas mixture: Ar/iso 95/5

  4. 55Fe X-ray E0 5.9 and 6.5 keV Photo-e- Auger-e- TimePix chip 55Fe quanta conversions seen by GridPix Photo-peak (photo-e and Auger-e) Escape peak (only photo-e) 2 conversions 3 conversions Raw spectrum Look at the escape peak only (smallest number of primary electrons)

  5. 55Fe X-ray E0 5.9 and 6.5 keV Photo-e- Auger-e- TimePix chip Measurements of W and F What is measured is the mean and variance of the number of detected electrons (Nd, Vd) Correction for limited collection and detection efficiencies yield Np and Vp W = E0 / Np F = Vp / Np Collection and detection eff. should be known Np , Vp Nc , Vc Nd , Vd

  6. pixel threshold Detection efficiency κ = ∫t∞ p(g).dg Exponential fluctuations: κ(g) = exp (-t/<g>) Polya-like fluctuations: parameter m=1/b ~ 2 with √b the relative rms κ(2,g) = (1+2.t/<g>) . exp(-2.t/<g>) Detection efficiency will be determined by fitting κ(g) to (Nd,Vgrid) data points

  7. 40 μm hole diameter Detectors Two measurement periods • Timepix chip # 1: • Standard InGrid • Low event statistics • Timepix chip #2 : • Increased event statistics • New GEMGrid structure • Filter out 6.5 keV with Cr foil 30 μm hole diameter • Chamber geometry: • 10 cm field cage • Guard electrode surrounding the chip • (inside chamber)

  8. Timepix #1 Timepix #2 Measured spectra at -330 V 5.9 and 6.5 keV escape events (event ratio ~ 7:1) 5.9 and 6.5 keV escape events (event ratio ~ 50:1)

  9. Peak position and grid voltage Asymptotic value of Nd gives the number of collected electrons Nc Polya fit works very well where exponential one (not shown) fails! Nc = 115 e- Nc = 102 e- • Compatible with the smaller hole diameter of InGrid #2 • Contribution from collection efficiency to peak width now known

  10. W and F in Ar/iso 95/5 at 2.9 keV Assume full collection efficiency of detector #1 Np = Nc = 115 ± 2 e- Extrapolation to 5.9 keV photo-peak straightforward Np = 230 ± 4 e- W = 25.2 ± 0.5 eV Peak width measured with detector #2 corrected for detection and collection eff. (87 %) RMS(Np) ~ 4.3 % Compatible with literature W = 25.0 ± 0.6 eV F = 0.250 ± 0.010 Ar/iso 20/80 – 1253 eV X-rays from Pansky. et al. J. Appl. Phys.79 (1996) 8892 F = 0.21 ± 0.06

  11. Conclusion • Method works well in our experimental conditions of large gap/transverse diffusion and small number of primary electrons. • Fit of Polya parameters to data points works very well, exponential gain distribution yield inaccurate results. • Next steps: study of W, F and gain fluctuations in other gas mixtures.

  12. Thanks for your attentionAcknowledgements: all fellows fromNIKHEF-AmsterdamSC-TwenteCEA/Irfu-Saclay

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