Image Sensor Dark Current Non Uniformity modeling using GEANT 4

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2 Image Sensor Dark Current Non Uniformity modeling using GEANT 4 C. Inguimbert 1, T. Nuns 1, D. Falguère 1 1) ONERA- DESP, Toulouse center, France

3 Deffects in semiconductor CCDs, CMOS and IR imagers (increased dark current & hot Puce de niveau 2 Arial pixels, 18 Random Telegraph Signals Puce de niveau 2 Arial 16 Solar array (RTS)) Puce de niveau 3 Arial 14 (power loss) Optocoupler (charge transfer ratio (CTR) degradation) LED & Laser diodes (light output degradation) Bipolar and III-V transistors (gain degradation & increased leakage currents) Photodiode (photocurrent loss & dark current increases) 3

4 Deffects in semiconductors : Carrier transport degradation Conduction band Trap level Valence band holes Recombination Generation Scattering Trapping Mobility reduction Conductivity reduction 4

5 Image sensors degradation HOT PIXELS Hot pixels critical For star trackers Dark signal Distribution 1.E+06 Geant4 : 185 MeV Count / Jdark (na/cm²) -1 1.E+05 JADE measurements : 185 MeV protons/cm² 0.E+00 2.E+01 3.E+01 4.E+01 Jdark (na/cm²) Nuclear reactions Damage cascade Dark current Different number of nuclear reactions initiated in each pixel (Poisson's Law) Different recoil nuclei Initiating different damage cascade Non uniform increase in dark current 5

6 Existing modelling approach Analytical approach (P.W. Marshall, C. J. Dale, E. A. Burke, IEEE Trans. Nucl. Sci., Dec ) Gaussian or Gamma shape are assumed recoil damage distribution Parameterised using average Damage energy (NIEL) and variance Nuclear inelastic reactions roughly simulated Many recoil nuclei with different mass (different range) can be produced Border Crossing effect is neglected The damage is suposed to be confined in the pixel Supposed to work for pixels greater than ~10 µm side What about pixels of a few µm? 6

7 DSNU Modelling 1.E+06 Geant4 : 185 MeV Count / Jdark (na/cm²) -1 1.E+05 JADE measurements : 185 MeV protons/cm² Pixel design Geant4 modelling Damage pixel databank 0.E+00 2.E+01 3.E+01 4.E+01 J dark (na/cm²) DSNU modelling FASTRAD GDML Depleted zone = sensitive detector G4Binary - nuclear reaction model G4screenedNuclearRecoil - Coulombic damage of cascade G4XWrapperProcess - Cross section Biasing Central pixel irradiation Storage : number of displacements in the impacted pixel + Its neighbours Number of nuclear reactions randomly selected In a Poison distribution For each reaction the damage in the irradiated pixel + its neigbours is randomly selected in the Precalculated dataset Each pixel is impacted by a number of nuclear interactions depending on the incident fluence that follow a Poison's distribution 50 µm Dead zones + substrate + upper layers 7 Atomic displacements Typicaly nuclear reactions Irradiated area Pattern produced by GEANT4 simulation

8 DSNU : Comparison with E2V JADE measurements Good predictions High accuracy that evidences "abnormal" events that standard approaches are not able 1.E+06 Geant4, 120 MeV 1.E+06 1.E+05 JADE measurements : 120 MeV 1.E+05 Geant4 : 185 MeV Count/ jobsc (Lsb/s) protons/cm² Count / Jobsc (Lsb/s) -1 JADE measurements : 185 MeV protons/cm² 1.E+00 1.E E Jobsc (Lsb/s) 1.E-01 Discrepancy due partly to coulombian scattering Discrepancy partly due to nuclear elastic events Ionizing dose J obsc (Lsb/s) Publication IN RADECS 2012

9 DSNU : Enhancement effect 1.E protons/cm² 1.E+05 1 interaction/pixel 10 interactions/pixel Count Geant4 : 120 MeV, events Probability for Poisson's law. 1.E+00 1.E-01 1.E-02 1.E-03 Geant4, 120 MeV, events JADE measurements : 120 MeV 1.E-04 Poisson's law 1.E Jobsc (Lsb/s) 1.E-05 Evidences of "abnormal" events Enhancement phenomena 9

10 Border Crossing effect analysis The distribution of damage through the neighours pixels changes the shape of the DSNU This phenomenon appears for pixels of a few µm side. Cas test 2 Pixel size : 5x5x1 µm Damage Distribution pixel size : 5x5x1 µm Cas test 4 Pixel size : 5x5x1 µm Pixels relative damage in % Cas test 3 Pixel size : 5x5x1 µm Pixels number S1 S2 S3 S4 S5 Pixel number Pixels relative damage in % Pixels number S1 S2 S3 S4 S5 Pixel number Number of displacements Pixels relative damage in % Pixels number S1 S2 S3 S4 S5 Pixel number 10

11 Conclusions and perspectives Original 3D Monte Carlo approach for DSNU prediction Very good predictions knowing only the size of the pixels Border crossing evidence for small pixels (few µm side) Improvement of the model in progress Nuclear elastric scattering Coulombic scattering Potential SPENVIS application for image sensor degradation prediction?! 11