Detector chain calibration strategy for the Euclid Flight IR H2RGs

Keywords: Euclid, NISP, HgCdTe, H2RG, non-linearity, latency, reciprocity failure, trapping

Euclid is an ESA mission to map the geometry of the Dark Universe with a planned launch date in 2021. 1 Two primary cosmological probes, weak gravitational lensing and baryonic acoustic oscillations, are implemented through a VISible imager (VIS) and a Near-Infrared Spectrometer and Photometer (NISP). The ground characterization of the NISP Flight Sensor Chip Systems (SCS) followed by the pixel response calibration aims to produce all informations to correct and control the accuracy of the signal. This work reports on the ground characterization of the NISP detector chain. The detector and electrical effects are likely to generate statistical fluctuations and systematic errors on the final flux measurement. The analysis strategies to maintain the pixel relative response accuracy within 1% is proposed in this work. The Euclid NISP test flow is presented and the main concerns of the detector chain calibration, such as non-linearity, charge trapping and de-trapping are discussed on the basis of the analysis of the flight detectors characterization data.

INTRODUCTION

The NISP focal plane is composed of a 4x4 mosaic of Sensor Chip Assemblies (SCAs). The SCAs are 16 HgCdTe detectors produced by Teledyne Imaging Sensors. They are commonly named H2RG. [START_REF]Teledyne imaging sensors, hawaii-2rg technical manual[END_REF] The cut-off has been tuned to 2.3µm. The readout electronic of the SCAs are 16 SIDECARs called in NISP, the Sensor Chip Electronics (SCE). [START_REF]Teledyne imaging sensors, sidecar asic technical manual[END_REF] The ground characterization performed by the NISP detector team was dedicated to the calibration of the pixel response. The NISP characterization and data analysis aim to produce pixel maps for different purposes:

• to verify the detector chain performances,

• to feed the internal detector chain calibration pipeline,

• to feed the processing pipeline of the Science Ground Segment,

• to feed the detector chain simulation.

The signal extracted from the NISP detector chain is obtained by measuring a non-destructive readout of the pixel. This readout mode is called Sampling up the Ramp (SUTR). The in-flight readout mode of the NISP is a particular mode of SUTR: the MultiACCumulation (MACC) mode which minimizes the on-board processing keeping the ability to produce a Quality Factor of the signal sent to the ground. The MACC readout mode is illustrated in figure 1. This conference paper presents in section 2 the main requirements on the detector chain calibration accuracy and the products (pixel maps) that the NISP detector team is foreseen to deliver from the ground characterization campaign. Section 3 deals with the description of the test flow. First, the content of the characterization is described and then the execution of the test flow performed at CPPM in 2017 and 2018 is summarized. Section 4 deals with the main objective of this paper, namely the pixel response calibration strategy. Section 4.1 presents the methods while section 4.2 shows preliminary results obtained from Flight Run data.

NIR DETECTOR CHAIN CALIBRATION ACCURACY REQUIREMENTS

Requirements

The main motivation for a precise detector chain error measurement is the control of the systematics on the fluxes of the sources. The detector chain error is defined as the systematic error (Req. 1%) on the correction of the pixel response. The correction functions aims to rectify the value of the slope of the ramp modified by detector and electronic effects. These effects include bias drift, dark current, non-linearity in the charge and the voltage domains, trapping (persistence) and de-trapping of charge carriers, electronic cross talk between readout channels, inter-pixel capacitance contribution from the neighbour pixels, and intra-pixel variations.

Operable pixels From the survey efficiency flows down the requirement on the percentile of operable pixels (Req. = 95%) for science. Non-operability can be either a permanent or a transient feature. In the category of permanently inoperable pixels for science we intend to consider:

• pixels disconnected from the MUX (mainly with a missing bump),

• pixels with Random Telegraph Signal (typical pixel with traps under the oxide of the gate of the pixel source follower),

• pixels not responding to light due to low quantum efficiency in each band of observation,

• pixels responding weirdly (pixel response to illumination which cannot be corrected by the non-linearity lookup table),

• hot pixels (defined for a given threshold on the master dark),

• pixels showing a baseline out of the useful range.

In the transient category of inoperable pixels we notice:

• the pixels showing a ramp with a primary or a secondary particle interaction within the sensitive substrate,

• the pixels identified as producing too high background signal originating from de-trapping,

• the pixels with a very high capture probability of charge carriers.

Characterization products Table 1 summarizes the expected products of the detector chain calibration pipeline which should be applied on ground characterization data.

NISP detector chain overview

This work is mainly focused on the most challenging contribution to the pixel calibration of the pixel response, i.e. the sensitivity of the non-linearity correction to the trapping/de-trapping effects.

Two additional Euclid papers on the conversion gain measurement per pixel and the pixels with Random Telegraph Signal are presented for this conference (see 4 and 5 ).

To characterize and correct the non-linearity of the pixel response it is important to underline different contributions of the transfer functions establishing the relation between the number of impinging NIR photons and the number of Analog to Digital Converter units (ADCu) or counts (cnt).

Pixel response calibration strategy

The main idea driving the calibration strategy requires a method able to separate the measurement of the contribution of the transfer function in the charge domain and the electronic transfer function in the voltage domain. This hypothesis can be simplified by assessing that it is necessary to correct first the pixel response by all transfer function in the voltage domain before deriving any 'varactor' effect of the pn-junction (quadratic in first approximation) and then to study the trapping/de-trapping contributions in the charge carrier domain.

Our hypothesis is sustained by the repeated observation that a direct polynomial fit (orthogonal or not) of the pixel response obtained from 20 ramps under a stable illumination (better than 1%) are dependent of the traps states (free or occupied) and consequently dependent of the illumination history (dark, zodiacal background of 2 e/s or same flux). A typical standard deviation of the linear part of the fit (the expected true flux to be used to generate the correction lookup tables) obtained with a 4th order orthogonal polynomial fit is around 10% in a same pixel over 20 ramps of the same illumination within 1% (the stability is controlled by a cold photo-diode in the focal plan). Surprisingly the standard deviation over the ramps is too high compared with the expected standard deviation from the statistics and the readout noise although the residuals of the fit per ramp are good. This point will be discussed in section 4.

Detector chain scheme and transfer function of the components Figure 2 shows a simplified view of the main components contributing to the different effects responsible to the inaccuracy of the detector chain response calibration. Figure 3 summarizes in a more synthetic view the matching between the physical components and the transfer function of the signal.

The main components of the SIDECAR ASIC used for NISP readout are the 33 preamplifiers: 0 to 31 for the 32 channels of science and reference pixels and one channel to sample the feedback of the reference voltages. Data from channel 33 are called telemetry in what follows.

The main components of the Multiplexer bonded with the HgCdTe are the output buffers (one source follower per channel) and the source followers of the pixels (SF). Various components and effects are considered for the HgCdTe sensitive volume. The transfer function corresponding to the pn-junction (p-well to collect holes) is the charge to voltage conversion factor (CVF in µV/e-, also named the transimpedance gain). The sensitive volume, N-epi layer is responsible for two transfer functions which are the quantum efficiency (QE) and the charge collection efficiency (CCE). From an experimental point of view we are measuring the product of the two transfer functions. The first one is related to the ratio between the photo-generated carriers and the incoming photons. The second refers to the collection efficiency of the carriers by the depleted volume. This is a dynamical behaviour because of the relation between the density of free traps and the extension of the depletion volume during the integration time. This relation is also dynamical in the sense that the densities of traps susceptible to collect charge carriers and occupied traps susceptible to release charge carriers depend on the illumination history of the pixel. Figure 4 shows the flat field computed from two independent measurements: the quantum efficiency maps provided by the acceptance test of NASA and the Least Square Fit of the signal of the ramp for a stable and flat illumination around 90 e/s. The flat is normalized by the quantum efficiency map after dark subtraction to generate the illumination flat field image. This image should have a uniformity better than 1% on the full array since we have checked that the flatness of the illumination is better than 1% RMS. The right part of Figure 4 shows the residual dark after an illumination ramp. The two images are fairly correlated (same trapping and detrapping areas). The average flatness value in the 'smiley' shape is lower. This is interpreted as a lower QE (more precisely lower CCE) for this illumination after a dark acquisition than the QE taken from the NASA maps. It is not surprising we notice that the QE maps are measured with strong fluxes without darks interleaved. On the contrary the ramp used to compute the LSF of this flat field image follows a dark exposure. Then in this case the number of free traps is clearly higher. This is in favour of the need for a better control of trapping/de-trapping contribution to the signal measurement.

V in (Vrst) = h -1 (ADU) V in (Vref) = f -1 (ADU) V in (Vrst) = g -1 (ADU) V in (φ) = R -1 (ADU)
Different contributions to the non-linearity from the components In Figure 3 we see the transfer functions of the pixel response through the three components: the HgCdTe, the ROIC and the SIDECAR ASIC. To disentangle the non-linearity contributions, the circuitry configurations offer various possibilities to apply reference voltage at different stages of the detector chain. The different inputs are reported in Figure 3. Two of them are dedicated to verification (vrefmain, vreset with the reset switched off or open state) whereas the reset voltage on the gate of the source follower (SF) keeping the reset selection switched on is used to generate the electrical transfer function (g -1 (ADCu) = V of Figure 3) which includes all voltage contributions down to the digital conversion of the ADC.

DETECTOR CHAIN CHARACTERIZATION

Test flow overview

Definitions

The test flow of the ground characterization performed by the NISP detector team (from IN2P3 * ) has been specified through a dedicated terminology. This dictionary has been introduced to generate a synthetic and general description to script all possible runs used for the detector chain characterization. monitors the illuminations when it executes the list of the specified runs with dedicated detector configurations. At the end of each run the DAS generates a report on data quality checking (QC) based on pixel maps with systematic comparison between current and reference maps (absolute or relative). The Data QC functions produces few hundreds of histograms and pixel maps per run to validate the expectations from the scheduler point of view. The analyses are performed per pixel but also with spatial averages over rows, columns, channels and arrays to highlight some possible electronics features or instabilities. In summary, the DAS developed for the Euclid ground testing campaign can be seen as a scheduler of asynchronous distributed object or distributed functions over a network to produce a huge amount of Detector Data and to control and assess their quality.

# ADCu/fr

Runs of the test flow

When the test campaign started in 2017, the main programmatic requirement was on the maximum duration (50 days) allocated to the characterization per SCS. The test flow has been derived to match this time scale keeping the objective of 1% accuracy on the corrected pixel response. A list of runs presented in Table 2 has been established to cover as much as possible different illumination scenarios to generate the largest data set with trapping and de-trapping effects. The CPPM detector characterization laboratory developed 2 test facilities dedicated to the Euclid NISP ground characterization campaign. Each facility is able to characterize two detectors in parallel with the same illumination sequences and the same focal plan temperature. Therefore a Flight Run is composed of 45 days of tests with 4 SCS in parallel. We kept the naming convention used during the test campaign i.e. FR2 to FR5. It is not the purpose of this work to describe in details the characterization facilities. Nevertheless, to highlight the success of the test campaign and the effectiveness of the characterization facility in terms of hardware, software and human resources, the Figure 6 represents the yield of the test flow. Yield is derived from the number of frames effectively stored on disk as function of time. The dotted grey line represents the ideal acquisition campaign corresponding to a increase of the number of frames stored on disk if a continuous readout of frames is sustained during the full duration of the Flight Run campaign. Then the yield is the ratio between the true number of frames and the ideal one for a period standing from the first cold run to the last cold run of the scheduler. The main results illustrated in Figure 6 are reported in Table 3. An extremely high yield of 80% has been sustained during more that 4x50 days of testing, thanks to the huge human effort and to a well designed automation. The main delays observed during the test campaign are mainly due to general power blackout in the Marseille area due to storms and one important Pulse Tube failure. The second reason of delay was that tests with the mono-chromator (one for both) and the operating temperature changes (OTs = 100K, 90K, 85K, 80K) have not been automatized (see Figure 6 left for the temperature time lines per Flight Run). The data QC processing is automatically performed to report and to validate the run. This validation is based on a summary through tables with fail and warning flags for each variables computed and compared with reference values extracted from the history of the test flow. A screen shot of the data QC processing is shown in Figure 5 (right). The rationale for the pixel calibration flows down from the requirements mentioned in section 2.

Readout mode and SCE configuration

The data bandwidth sustained by the Data Acquisition Software enables a full readout and storage of all frames of the ramps for the 2 SCS in parallel. Therefore, sampling up the ramp was systematically used for the readout mode. It has been checked during the Pilot Runs that there is no difference in the noise properties between data taken with a MACC mode implemented inside the SIDECAR which not transmit the frames between the groups and data obtained in SUTR and computed off-line in the same MACC mode. This is not surprising since all frames are sampled by the ADCs even if the MACC mode is selected by the Euclid flight firmware loaded in the SIDECAR. A 15dB value of gain has been chosen for the preamplifiers with a single ended bus configuration. A bias of 500mV has been set between Dsub substrate voltage and the reset voltage of the P-well. With a 100 kHz pixel clock, the full frame (2048x2048) is read out in 1.4548s with 32 channels in parallel.

Baseline The in-flight information about the flux (See Ref. [START_REF] Kubik | A new signal estimator from the nir detectors of the euclid mission[END_REF] for the definition of the slope computation and the associated quality factor (QF) of the fit used in NISP) transmitted to the ground is constrained by telemetry/day budget. None of the group ADCu values is transmitted to the ground in science observation modes. It is then of relevant interest to have a determination of the baseline after reset and its scatter from ground tests (see Table 2 for details on this run). Possible reset anomalies are well traceable by comparing the mean value of the first frame to the mean value of the first group. The first two CDS are also compared. This noise has to be well controlled since it could contribute to the systematic error when a non-linearity correction is applied to the measured slope. Thanks to the large number of iterations (1000), the precision of this measurement allows to be well under the Reset noise per ramp.

Darks Darks acquisitions are of two types: short and long darks (see Table 2). Short darks with SUTR(500) are typically repeated 62 times for each operating temperatures (80K, 85K, 90K, 100K) to derive for each science MACC readout mode the master dark and the master noise of the slope after reference pixel subtraction. A larger value of 500 frames instead of the nominal 400 has been chosen in case of a necessity to increase the integration time for science observation during the mission. Reference from ground data will be available in this case.

Zodiacal background illumination Zodiacal background which is expected to be around 2 e-/s in-flight is of major importance to understand the steady states of the pixels since they will "see" in average such flux during at least 24 hours without higher illumination from stars or galaxies. A cycle with 60 iterations has been programmed at each OTs to produce a zodiacal reference data sample.

Electrical transfer function for non-linearity correction We have mentioned in section 2 that in order to build the non-linearity correction lookup tables for each readout mode it is necessary to measure the true linear flux with a systematic error lower than 1%. The methodology foreseen for NISP is defined in Ref. [START_REF] Kubik | Impact of noise covariance and nonlinearities in nir h2rg detectors[END_REF] This method uses a polynomial fit (orthogonal or not) up to the 4th degree. This should give enough accuracy on the "true" linear flux. As mentioned previously, the standard deviation of the true flux is observed to be for some type of acquisitions and for some groups of pixels twice higher than the expected Poisson and readout noise contributions. After many tests and analyses in a broad range of fluxes and various illumination histories (illumination preceded by a dark, a zodiacal background and an equivalent flux) we observed that it could become problematic to find a unique set of correction coefficients although the residuals of the fit were good and not structured along the ramp.

This observation leads us to try to disentangle different contributions to the non-linearity of the pixel response (V/V, e/V or trapping) in order to isolate the trapping and de-trapping contributions. We hope to be able to compute the "true" linear flux required by the non-linearity lookup table correction method with a better control of the systematic errors.

A second argument in favour of the (SF) transfer function method is that we will be able to verify the nonlinear behaviour of the pixel response with a pretty good statistical accuracy that is unreachable with low flux illumination due to the number of ramps required by the averaging (thousands of ramps).

A third argument for this method is that the baseline reset method can be executed in-flight and then could be useful for in-flight calibration or verification. This could be a complementary method to flat field obtained with the calibration unit.

The corresponding electrical runs dedicated to this measurement are identified as reset voltage runs since the electric transfer function is constructed by changing the reset voltage on different input stages of the readout chain. The different possibilities used for the flight Runs are reported in Figure 3.

Non linearity correction and trapping effects

The second objective is to develop a trapping and detrapping model either to mask the transient inoperable pixels or to correct the illumination. Indeed we expect by working on different states of occupied traps preceding the illumination, to develop a trapping and de-trapping model which will be able to fit as much a ramp of illumination with de-trapping and trapping of charge carriers as a dark or zodiacal ramp with de-trapping. Thanks to the data acquisition system which time stamps all event and frames all along the 45 days of acquisition, we expect to be able to constraint with many different illumination scenarios the parameters of the trapping and de-trapping model with a global fitting procedure.

For that purpose we define different scenarios repeated many times at many fluxes and at the 3 operating temperatures. The targeted fluxes are mainly those expected during the in-flight calibration with the NISP Calibration Unit (NI-CU fluxes are 28, 52, 90, 160, 280 e-/s) but lower fluxes are also tested with 30 iterations to reduce the relative precision below 1% per pixel. The illumination scenarios are described by the simple notation: (flux + short dark), (flux+long dark), (flux+zodiacal background), (flux+flux). See Table 2 for a detailed description of the non-linearity runs.

De-trapping effects (fast and slow components) The de-trapping model, that will be compatible with the trapping effects, will be based on two types of illumination patterns (see Figure 5 for the definition of a pattern). The ones with long dark (7274s) will be used mainly to measure the slow decay time constant and the ones with short darks (1163s) reproduced with a higher statistics. These runs, reported in Table 2, will be first used to fit the density of occupied traps versus the preceding illumination and the fast decay time constant.

De-trapping after saturation of the P-well High flux saturating the P-well of the diode (120 ke-with a Bias of 0.5V) are also executed with short and long darks (See Table 2) to measure the increase of trapping and de-trapping due surface states appearing as active due to disappearance of the collecting electric field profile or in order words the shrinking of the depletion volume.

Inter pixel capacitance (IPC) with single pixel reset method (SPR) The single pixel reset has been implemented into the Euclid flight firmware of the SIDECAR. With 64 different register configurations of the single pixel Grid the full array is covered in a short time (few hours). Then a per pixel IPC map is produced thanks to the DAS. Three runs with three different biases values (0.35V, 0.5V, 0.625V) have been produced to quantify the IPC sensitivity to the voltage difference between the two resets.

Temperature Sensitivity The in-flight passive cooling of the NISP focal plane does not allow to proceed with a ground testing at a single temperature since the OT is not predictable. Three operating temperatures have been chosen to cover the range of expected OTs with margins. The parameters used to correct the response function will be compared for the three OTs. To stay within the 45 days of testing per SCS, OT=80K and OT=90K cover fewer scenarios than OT=85K keeping at least the same statistics used for the nominal illumination fluxes of the NI-CU that will be available in-flight (20 iterations for each pattern and each nominal flux).

Preliminary Results from the Flight Runs

A systematic reporting on the 4 Flight Runs is out of the scope of this conference paper. We focus here on results which underline the pixel calibration strategy and show the tricky part of the pipeline.

V/V non-linearity correction

From pixel Source Follower to the ADC units A specific run dedicated to the V/V measurement has been applied (see Reset Sel ON in Figure 3). The pixel reset switch is represented in Figure 2. Using Telemetry measurement of the applied Reset voltage, it is straightforward to construct the pixel response function in Volt with a step of one LSB in the configuration bit word (∼2 mV/LSB).

It is nevertheless of prime importance to verified the linearity of the voltage applied in the range 0.3-0.8V before fitting the correction function. Both the -3dB gain set on the telemetry preamplifier and the setting value of the vrefmain voltage reference put the ADCu values in a small, central and linear range of the ADC.

To validate the linearity of the telemetry versus voltage, we have studied with a linear fit the telemetry value (ADCu) versus the configuration voltage or equivalently the configuration bit word. Once the linearity of the input voltages is verified the transfer function response is measured over the full ADC range with all necessary bit words of the DAC and measuring the baseline of the pixel over a number of ramps and a number of frames per ramp sufficient to minimize the errors due to the readout noise and the kTC noise. The results are presented in Figures 8 and9 where, for each degree of the polynomial function, the global residual of the fit and the zoom in the useful range for science (from the baseline of the pixel to 63000 ADCu) are plotted. We clearly see that the 4th degree is required to decrease the residuals below 0.1%. Next, we generated the ADCu to the source follower input voltage inversion function for the 4th degree polynomial. A systematic study on the cost and of the benefit of using of a higher polynomial order to gain one or two thousands of ADCu in the ADC saturation part will be performed. We are not fully convinced that the benefit from the increase of the dynamical range justifies the risk of a strong increase of the systematics after applying this correction.

e/V non-linearity correction

Applying the inverse transfer function translating ADCu into voltage on the gate of the pixel SF gives access to the e/V transfer function. Under a strong illumination, covering the 16 bits ADCu range in typical spectroscopic ramp of 400 frames (565s), we expect to observe a typical varactor effect of a pn-junction. [START_REF] Sze | Semiconductor Devices: Physics and Technology[END_REF] Nevertheless, we notice that trapping and de-trapping contributions are dominant during the first 100 frames. To verify the e/V contribution to the pixel non-linearity we show in Figure 10 the residual to a linear fit of the pixel response for two groups of 64 pixels after and before the application of the SF inverse function presented in section 4.2.1. The two groups are reported in Figure 4. They are representative of two different populations with a strong and weak latency.

Figure 10 is very instructive if we compare the panels on the left with those on the right as they correspond to the after (left) and before (right) the application of the SF correction, respectively. The top and bottom panels correspond to two different groups of pixels (see squares in Figure 4) showing a difference in the measured latency of the order of two (higher persistence observed for the group of pixels corresponds to the residuals at the bottom of Figure 9). Important comments from this figure can be derived.

• The residuals without correction of electrical response (just a translation of ADCu into volt through a constant transimpedance gain and conversion gain ratio to keep the same units), the two plots on the right of Figure 10, show very different behaviours depending on the trap density. This confirms the fact that for some pixels a direct fit of the pixel under constant illumination with a 4th order polynomial will not be stable for different illumination history. This can explain the 10% RMS of the linear part of the fit observed on a full array.

• The high-end of the residuals for the non corrected data presents a broader dispersion among pixels. On the contrary, the corrected residuals present a very sharp dispersion. This is the proof of the effectiveness of the SF pixel correction and it shows that we face the non linearity of the pn-junction. It suggests a very sharp dispersion of the implants implying a sharp dispertion of the pn-junction capacitances (at least at the level of accuracy we are able to achieve). The distribution of the baseline is broad so that the high-end of each pixel for the same integrated flux will be in different part of the electrical transfer function. It is the root cause of the dispersion observed for non corrected ramps compare with the sharp dispersion observed for the corrected data.

Various strategies of generating the correction function of the pn-junction non linearity are under study. First method is to use the 200 last frames, where capacitive quadratic term dominates the trapping effects, to fit the e/V correction. An illumination with a flux of 160 e/s covering the full dynamical range of the ADC has been used to fit the quadratic function. This is the most straightforward and pragmatic method which works with the expected accuracy but with a risk of keeping a small contribution of trapping or de-trapping.

Another method, which is under study, is to use two others reset voltages with the reset switch turn off to fit the e/V correction. With these runs a non-linearity is extracted from data but it is difficult to unambiguously correlate this non-linearity in the voltage domain with the one observed and measured in Figure 10 (left panel). It might be due to the contribution of parasitic capacitances before and after the reset of such three transistors circuitry. Algebraically it should be manageable even if the design of the pixel is unknown. This method is under To illustrate the level of control that one able to achieve by applying a quadratic e/V transfer function, we show in Figure 11 the residuals of the fit of the flux applied only on the second part (high-end) of the data corrected by both V/V and e/V functions. The results are shown for several values of fluxes in the range expected in science observation. We notice that at the beginning of the ramp, the contribution of the trapping to the non-linearity increases with the absolute value of the flux. This linear increase in the zero point tends to tell us that, in first approximation, the trapping rate is constant for the low illumination range. This is not true for high fluxes (120-160 e/s). This feature has to be included in a trapping and de-trapping model which depends on the extension of the depletion volume. It was shown in section 4.2.2 that we are able to disentangle the trapping and de-trapping effects in the pixel response and the electrical (e/V and V/V) non-linearity contributions. This gives us the possibility to study systematically de-trapping/trapping models varying the number of trap types, the total number of traps, the trapping and de-trapping rates, the densities of traps, the number of free and occupied traps as a function of the illumination history. This work is at its beginning and the results shown in the following sections of this paper are for illustration purposes only. Dispersion of the fitted parameters for a large sample of pixels has not been yet computed. Such effort requires a important software development work. Nevertheless, we observed that for some pixels the fit does not converge properly.

A simple example of trapping and de-trapping model: two types of traps The first attempt is to verify if a unique model of trapping and de-trapping is able to cover a large spectrum of illumination histories with a broad range of illumination levels (from 2 to 240 e/s) and different types of patterns: (flux + short dark), (flux+long dark), (flux+zodiacal background), (flux+flux). The simple model of current versus time with trapping and de-trapping of charge carriers by two types of traps is defined by:

dq(t) dt = I q (t) = φ q - (x) φ q a 0 (x) σ a (x) + A (x) -a (x) 0 σ ā(x) e -(φqσ a (x) +σ ā(x) )t (1)
where q(t) is the charge carrier at time t, φ q the photo-conversion current or the dark current, a 0 (x) the number of free traps at t = 0 of type (x) (with x = 0, 1, 2, ...), A (x) the total number of traps of type (x), σ a (x) the probability that a free trap of type (x) to capture a carrier, σ ā(x) the de-trapping rate of occupied traps ā(x) of type (x).

Results on the fit of the pixel (2000,1063) from FR2 SCS 18628 are presented. Figures 13 to 15 (top panels) show for this pixel the V/V and e/V corrected CDS (points) and the corresponding fitted model (lines) of the ramps for four illumination patterns: (flux + short dark), (flux+long dark), (flux+zodiacal background), (flux+flux). The residuals of the fit with a model of trapping/de-trapping with two types of traps are plotted in the bottom of each panels. Illumination pattern is reproduced many times, therefore we can consider that, in a circular way, each ramp is the preceding or consecutive ramp of the other. This circularity condition can be used to compute a mean ramp over iterations of the patterns (typically 20 iterations). The temporal evolution can also be fitted since the time stamp of each frame as well the time stamp of the status of the illumination are recorded. Various scenarios of very long illumination history can be study per pixel. This solution is kept for future work since it requires a huge effort on the development High Performance Computing (HPC).

For all of them the same model is used with two types of traps (x=0, 1). For each illumination patterns the mean ramp is generated by averaging over the iteration of the same pattern. The residuals for all illumination patterns are within +/-5 e/s without any temporal structure.

A strategy to combine into the same fit all informations coming from all types of patterns and fluxes is under development for the pixel calibration pipeline.

Trapping and de-trapping for the two different latency areas Figure 12 shows the trapping behaviour for two pixels belonging into two different latency areas shown in Figure 4. A fair difference is observed in the non-linearity of the pixel response for the first 150s of the ramp with illumination. Trapping and de-trapping versus the illumination pattern Figure 13 shows the same illumination flux followed or preceded by 3 different illumination states: a short dark which allows de-trapping, a zodiacal illumination of 2 e/s or an illumination with the same duration and intensity. Two different behaviours are observed at the beginning of the ramps (100 first frames). CDS increases due to decraising of the trapping in the (dark+zodiacal background) acquisition pattern while it decreases in (flux + flux) acquisition pattern where the de-trapping component is dominant.

The first remark is that the model is able to fit both patterns with trapping and de-trapping with residuals showing no systematics in their temporal structure. This is of the first importance for measuring the true flux value. The discussion on the results has been focused on one of the most difficult task of the pixel response calibration pipeline. The trapping/de-trapping contributions to the non-linearity measurement has been raised and illustrated with Flight Run data.

A tentative to use correction functions both in the charge and voltage domains (e/V and V/V) of the pixel response has been proposed and illustrated.

Encouraging results on Flight Run data have shown that the tuning of various models of trapping/de-trapping could be used to develop a pixel response calibration pipeline as a function of the illumination history. This work is just at this starting point and we expect more than 2 years of work on data analysis, detector physics and software coding of the pipeline to reduce more than 400 TB of data.

Figure 1 .

 1 Figure 1. Scheme of the Multi ACCumulation (MACC) readout mode for one ramp. The spectroscopic observation with an effective integration time of 565s is read out with a MACC(15,16,11) . Photometric observation could be either a Fowler, MACC(2,16,D) or a MACC(G,16,D) with G=3,4 or 5. The frame time is 1.4548s

Figure 2 .

 2 Figure 2. Simplified schematics of the main components of the detector chain. All these components impact the response of the HgCdTe detector chain.

Figure 3 .

 3 Figure 3. Scheme of the main transfer functions of the pixel response corresponding to the main components of the readout chain and its electronics of Figure 2.

Figure 4 .

 4 Figure 4. Left: Flat Field computed from a stable flat illumination after dark subtraction and normalization by a QE maps obtained from the NASA acceptance test. The illumination follows a dark ramp. Right: image of the residual dark (right) after illumination. These images are taken from the data QC of SCA 18268 of Flight Run 2 on Pegasus.

Figure 5 Figure 5 .

 55 Figure5presents the generic description of encapsulation starting from the most general which is a run to the smallest building block: the exposure with a single ASIC configuration, one readout mode and one environment status. The pseudo-code of specification has been used to generate the a scheduler of the test flow covering the 45 days of the test flow. The fully automatized asynchronous data acquisition system (DAS) controls and

  Figure 6 illustrates the complexity of the test flow by showing on the left and in background colors the operating temperatures and on the right the illumination status versus time.

Figure 6 .

 6 Figure 6. Figures of Merits of the FR2 to FR5 characterization yields computed from the frames stored on disk (left) and the acquisition time (right). The ideal characterization corresponds to the straight line versus time standing for a continuous acquisition during more than 45 days devoted to the flight Runs. The color bands in the background shows the operating temperature of the SCAs (left) and the flux status of the illumination set up during the test flow (right). These measurement shows the complexity of the test flow. Pegasus and Andromeda are the names of the 2 cryostat of the CPPM test facility.

Figure 7 (Figure 7 .

 77 Figure 7. Left: Linearity of the Reset Voltage applied during electrical test on the Gate of the Source Follower with on state. Right: vreset difference of two consecutive voltage with one LSB flip (top) and the corresponding spectrum of the Fourier Transform (bottom). We clearly stress a bit flip effect of the DAC with the frequencies[START_REF] Racca | The euclid mission design[END_REF] 2 n with n = 1, 2, 3, ...

Figure 8 .

 8 Figure 8. Voltage response to Vreset SEL ON run of Pixel (2000,1036) of SCS 18628. The residuals to the fit with a 1th order polynomial is shown (bottom).

Figure 9 .

 9 Figure 9. Voltage response to to the reset run of Pixel (2000,1036) for SCS 18628. The residual of the fit with a 2nd order polynomial is shown in bottom left. The residual of the fit with a 4th order polynomial is shown in bottom right.

Figure 10 .

 10 Figure 10. Quadratic behaviour due to non-linearity of the pn-junction e/V non-linearity for a 160 e/s flux with a moderate trapping in the second part of the ramp. This part, dominated by e/V non-linearity, is used to fit a quadratic correction corresponding to the non-linearity of the pn-junction under illumination

Figure 11 .

 11 Figure 11. Top: slope corrected with e/V and V/V functions for various illumination intensities. The residuals to a linear fit show an increase of non-linearity due to trapping

Figure 12 .

 12 Figure 12. Trapping behaviour of two pixels taken from the two different latency areas shown in Figure 4. The configured flux are 57 and 160 e-/s and the pattern is (flux + short dark).

Figure 13 .

 13 Figure 13. Trapping behaviour for pixel (2000,1063) for a flux of 120 e/s and three illumination patterns: (flux+dark), (flux+zod. bkg) and (flux+flux)

Figure 14 .

 14 Figure 14. Trapping behaviour for pixel (2000,1063) for different fluxes and the acquisition pattern: (flux + short dark)

Figure 15 .

 15 Figure 15. Trapping behaviour for pixel (2000,1063) at 85K for acquisition pattern (flux + long dark) for slow decay time constant analysis.

  This work presented the pixel response calibration strategy of the NISP H2RG detector chains. The requirements on the calibration of the pixel response with an error budget has been introduced. It justified the test flow developed for the ground characterization of the SCS. The success of the characterization campaign has been demonstrated. The rationale for the measurements has been proposed and described in the context of the NISP characterization facility at CPPM. The acquisition sequences with various pattern of illumination and intensities have been described and justified.

Table 1 .

 1 NISP products: expected pixel maps produced by the detector chain calibration pipeline which will reduce data taken during the Flight Runs of the Euclid Consortium ground characterization campaign

	Product	Description	Destination
	master darks	dark in the science readout mode	SGS-NISP
	master noise	slope noise in the science readout mode	SGS-NISP
	nl LUT	non-linearity correction LUT (input: flux)	SGS-NISP
	la LUT	latency LUT for masking (input: previous flux)	SGS-NISP
	flat LUT	flat fielding LUT	SGS-NISP
	non-operable	mask of permanent non-operable pixels (all bads) SGS-NISP
	ipc	Inter Pixel Capacitance with Single Pixel Reset	SGS-NISP
	cg	conversion gain (cnt per e-)	SGS-NISP
	baseline	mean and STD of the first group after Reset	NISP
	dpix	disconnected pixels	NISP
	bad baseline	pixel with too high or too low baseline	NISP
	bad response	non-responding or badly responding pixels	NISP
	rts	pixels with Random Telegraph Signal	NISP
	trapping / de-trapping trapping coefficients (model)	NISP

Table 2 .

 2 List of the runs used during the test flow. Most of them are repeated at the three nominal operating temperature OT=90K,85K,80K

	Run type	Flux cfg	Pattern	# Iter.	calib. purpose
	name	(e-/s)	nb. ramps (stat 1%)
	Reset runs
	Baseline	0	16	1000	First Gr. + kTC
	Vrst	0	3	64/Vrst	non linearity
	SPR	0	SPR mode	16/Vrst	IPC per pixel
	Dark runs
	Dark sci.	0	500	50	Master dark
	Dark long	0	5000	4	RTS + ref. dark
	Flat runs
	Flux zodiacal bkg	2	400	60	non-linearity + latency short
	Flux	8, 16, 28, 52, 90	400	30 to 5	non-linearity + latency short
	Flux + short dark	4, 8, 16, 28, 40, 52	400 + 800	30 to 5	non-linearity + latency short
	-	60, 80, 90, 100, 120 400 + 800	20	non-linearity + latency short
	-	140, 160, 200, 280	400 + 800)	20 to 6	non-linearity + latency short
	High Flux + short dark 400, 600, 800,	100 + 1200 6	non-linearity + latency short
	-	1000, 1200, 1400	100 + 1200 6	latency short
	Flux + zodiacal bkg	8, 16, 28, 52, 90	400 + 800	20	non-linearity + latency short
	Flux + long dark	4, 8, 16, 28, 40	400 + 5000 5	non-linearity + latency long
	-	52, 60, 80, 90, 160	400 + 5000 5	non-linearity + latency long
	-	1200, 2000, 4000	100 + 5000 3	latency long
	Mono-chromator	50 -15 λs	400-100	5	spectral response
			7

Table 3 .

 3 Summary table of the 4 Flight Runs with SCS-Id, date, duration and the two Figures of Merit of the Euclid ground testing campaign of the Flight SCAs.

	FR Cryo SCS Id	Beg. time	Duration Runs Ramps Frames	FoM FoM
	#	And. 18# -18# date	days	#	#	#	acq.	frames
		Peg.		hh:mm:ss	hh:mm:ss				%	%
	2	A	249-278	2017-09-07 45	157	38683	2335668 89.4 85.9
				14:51:49	18:48:23
	2	P	268-284	2017-09-07 50	159	61840	2359329 83.0 78.3
				14:08:43	17:38:57
	3	A	269-452	2017-11-15 46	152	38582	2262438 84.9 81.7
				13:42:45	15:05:09
	3	P	453-632	2017-11-02 46	147	38560	2265078 85.2 82.0
				14:30:44	12:51:39
	4	A	280-282	2018-01-13 45	149	38818	2292593 88.8 85.6
				19:00:17	2:39:13
	4	P	285-548	2018-01-14 43	143	38619	2273113 92.1 88.6
				21:01:33	4:52:00
	5	A	221-267	2018-03-06 46	146	39573	2295328 86.5 83.2
				14:59:51	10:32:18
	5	P	272-458	2018-03-06 45	150	38634	2300413 88.2 84.9
				19:22:40	14:35:49
			4. DETECTOR CHAIN CALIBRATION
	4.1 Methods

4.1.1 Rationale for a pixel response calibration pipeline

ACKNOWLEDGMENTS

This project is funded by CNES and ESA. We would like to thanks the Detector Characterization Lab of the NASA Goddard Spatial Flight Center and the Euclid detector team of the NASA, Jet Propulsion Laboratory for


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Keywords: Single Event Upset, Flip-Flop, design, architecture, Readout circuit, CMOS, heavy ions

This work highlights the impact of design on the single event upset (SEU) sensitivity of D-Flip-Flops used in a readout circuit (ROIC) under heavy ions. New experimental data obtained at University of Louvain for several designs are presented. The SEE prediction tool MUSCA SEP3 is used to investigate the failure occurrences at the circuit level as a function of the design. In some cases, design specificities allow for increasing in the SEU robustness of the DFF. However, it appeared that cryogenic temperatures limit the impact of the design on the SEU sensitivity of DFFs. The results show a very limited impact of the temperature on the SEU occurrence, independent of the layout. These results are consistent with experimental data presented in recent works regarding SET and SEFI. These results allow for performing irradiation tests of CMOS IR detector (ROIC) at room temperature instead of cooling down the device during the SEE measurements.

I. INTRODUCTION HE use of CMOS (Complementary Metal Oxide

Semiconductor) functions and their reliability are a major concern for very integrated technologies. CMOS technology is really interesting because it leads to integrate with an image sensor several electronic functions such as a raw decoder, machine state, registers, and D-Flip-Flops (DFF). However, digital CMOS functions of image sensors are known to be sensitive to single event effects (SEE), such as single event transient (SET) and single event upset SEU [START_REF] Hopkinson | Radiation effects in CMOS active pixel sensor[END_REF]. SETs can be induced by various ionizing particles, i.e., heavy ions, protons, electrons. SETs and SEU can become critical for image devices and integrated circuits (IC) on-board in flight.

D-Flip-Flops are widely used in digital and computing devices, but are also used in the readout circuit (ROIC) of CMOS image sensors (CIS) as shown in Fig. 1 [2] [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. DFF are especially used for the digital function for the row counter, column counter and serial register. One of the challenges Manuscript received September 27, 2017; first revision received November 21, 2017; second revision received January 26, 2018, manuscript accepted January 30, 2018.

This work was supported in part by CNES, The French Space Agency, Toulouse, France L. Artola and G. Hubert with ONERA, The French Aerospace Lab, 31055 Toulouse, France (email: laurent.artola@onera.fr) S. Ducret, N. Ricard, with Sofradir, 38113, Veurey-Voroize, France. J. Mekki, with CNES, the French space agency, 31400 Toulouse, France. This work presents the impact of the design and the architecture of DFF on the SEU sensitivity under heavy ions at cryogenic temperatures. Table I summarizes the various designs and architectures of the DFFs tested during the irradiation test campaigns. The description of the reference DFF has been presented in L. Artola et al [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. The differences in the DFFs in terms of designs and architecture are illustrated by the number of n-MOS and p-MOS transistors and the number of inputs and outputs respectively. For confidential reasons, no more details can be provided.

First, the irradiation test setup performed at University Catholic of Louvain (UCL) is presented. Second, the SEU cross sections for each architecture and design are presented and discussed.

In addition, the discussions are completed using a fault injection approach based on SPICE (Simulation Program with Integrated Circuit Emphasis) simulations and the SEE prediction tool, MUSCA SEP3. The soft error prediction tool is based on a Monte-Carlo approach. It performs a full flow of simulations from the interaction of the radiation particles with the device down to the occurrence of SET in the circuit. The circuit response is determined by SPICE simulations. The tool is used to investigate the failure occurrences at the circuit level as a function of the design. Finally, the effects of the supply voltage on the SEU sensitivity trends are analyzed.

II. EXPERIMENT SETUP AND SEU DETECTION IN D-FLIP-FLOP UNDER HEAVY IONS

A. Single Event Upset detection in DFF

As reported in Table I, the DFFs can be classified in two categories: DFFs with 3 input signals and DFFs with five or higher input signals. These two categories will be referenced as classic and complex DFFs respectively. The DFF is synchronized on the rising edge of the clock signal. When TE is at low level, the DFF transfer the data of the D input to the Q output of the DFF; when TE is at high level, the DFF transfers the data of the secondary input signal, e.g. TI, on the output signal.

During the irradiation, a SEU has been considered when the output of the DFF chain changed from "1" to "0" or "0" to "1" depending on the stored logic state as illustrated in Fig. 2(b) by the white dashed circle.

B. Setup description SEU measurements

The devices under test (DUT) have been developed by Sofradir. The two test chips are designed with various DFF architecture chains as mentioned in [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. Each of the DFF chain are composed of 200 DFF cells in order to maximize the SET capture during irradiation tests as depicted in Fig. 3. Each of the DFF chain shares the Clock (set at 20MHz), Reset, Data The heavy ion tests were performed at the University Catholic of Louvain (UCL) for the two heavy ion cocktails. The CYClotron of Louvain la NEuve (CYCLONE) proposes different heavy ions species which are split in two "Ion cocktails", named M/Q= 5 and M/Q= 3.3. The heavy ion species have been presented in a previous work [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. The chamber has the shape of a barrel stretched vertically; its internal dimensions are 71 cm in height, 54 cm in width and 76 cm in depth. One side flange is used to support the board frame (25 x 25 cm²) and user connectors. The chamber is equipped with a vacuum system. In the case of the campaign the DUT is in a cryostat connected to the vacuum chamber in order to allow for cooling the temperature of the chip during the irradiation test.

The temperature of the chip was monitored and regulated, by means of an instrument from CNES, to a range of temperatures from 77 K to 300 K [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. The cooling system is based on a cryostat using liquid helium. The bias of the DFF chains was done in static and dynamic mode. In dynamic mode a fixed pattern was used (e.g. 01010101 …). The frequency of the clock signal was 20MHz. In this work only the static mode is presented and discussed. The bias scaling dependence of the SEU sensitivity of the various DFF architectures will be discussed in the final section of the paper.

During each irradiation run, a delatcher system was used on the DUT's power in order to detect latchup occurrence. Two runs dedicated to latchup detection have been done. The runs were performed at room temperature (300 K) with a fluence of 1x10 7 .cm -2 at 67.7 MeV.cm 2 .mg -1 . No single event latchup (SEL) was detected during the irradiation campaigns of the two test chips.

III. SINGLE EVENT UPSET IN DFFS UNDER HEAVY IONS

Fig. 4 shows the SEU cross section of DFFs with all architecture and design variations measured under heavy ions at 300 K. The irradiation tests have been done across temperatures from 70 K up to at 300 K with a bias condition of 5V. Note that SEU data for test-chip 2 is only available for 40 and 67.7 MeV.cm 2 .mg -1 . The wide variability of SEU cross section over 40 MeV.cm 2 .mg -1 is explained by the architecture and design variations of DFF. The impact of the architecture and design on the SEU sensitivity measured under heavy ions is investigated in the following section. A specificity of the design of the DFFs from test-chip 2 (DFF7 up to DFF11) is analyzed in the second part of the next sub-section.

A. Architecture and design dependence of the SEU sensitivity in D-Flip-Flops

Fig. 5 presents the SEU cross section measured on the four different designs of the two DFF categories: DFF1 (black squares), the reference DFF (black dots) as classic designs, DFF3 (black triangles) and DFF4 (black reversed triangles) as ). However, over 20 MeV.cm 2 .mg -1 , test results suggest that DFFs with classic designs are more sensitive than the DFFs with complex designs of the test-chip1. This point can be moderated and completed by the analysis of the SEU sensitivity as a function of the DFF area. Fig. 6 presents the SEU cross sections of eleven DFFs induced by heavy ions with a LET of about 32 and 40 MeV.cm 2 .mg -1 . It appears that two SEU sensitivity trends can be identified. First, an increase in the DFF area induces a decrease in the SEU cross section, except for a group of five DFFs (DFF7 up to DFF11). This increase in cell area is partially due to wider transistors which induces a higher drive current. A higher drive current is known to improve the SEU robustness of CMOS gates [START_REF] Artola | Comparative soft error evaluation of layout cells in FinFET technology[END_REF]. This point should be confirmed in the next section by an analysis at circuit level.

Second, the DFFs with areas between 1.5 and 1.7 use a different design rule. These designs are based on the same number of n-MOS and p-MOS transistors, as reported in Table I. This design specificity impacts the drive current of the floating nodes of the DFF. The floating nodes are known as potential critical areas for the occurrence of SEU in digital devices [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF], [START_REF] Hubert | Single-Event Transient Modeling in a 65-nm Bulk CMOS Technology Based on Multi-Physical Approach and Electrical Simulations[END_REF], [START_REF] Artola | Pulse quenching induced by multi-collection effects in 45 nm silicon-on-insulator technology[END_REF]. Fig. 7 presents the impact of the ratio between the number of n-MOS and p-MOS transistors on the SEU cross section of DFFs. The DFFs designed with a higher number of n-MOS transistors (black symbols) are less sensitive than the DFFs designed with the same number of n-MOS and p-MOS transistors (red symbols). This experimental data confirms the sensitivity trends observed in Fig. 6.

The analysis of the design effect on the SEU sensitivity will be completed at circuit level in the next section.

IV. FAILURE INVESTIGATION BY FAULT INJECTION

SIMULATIONS

MUSCA SEP3 is a soft error prediction tool based on a Monte-Carlo approach, which performs a full flow of simulations from the interaction of the radiation particles with the device down to the occurrence of the soft error in the circuit (in this work DFF). The transport and collection mechanisms of generated charges in semiconductors (e.g. silicon) are simulated by 3-D analytical models. The complete description of the modeling and simulation flow is reported in previous works [START_REF] Hubert | Single-Event Transient Modeling in a 65-nm Bulk CMOS Technology Based on Multi-Physical Approach and Electrical Simulations[END_REF], [START_REF] Hubert | Operational SER Calculations on the SAC-C Orbit Using the Multi-Scales Single Event Phenomena Predictive Platform (MUSCA SEP3)[END_REF], [START_REF] Artola | SEU Prediction From SET Modeling Using Multi-Node Collection in Bulk Transistors and SRAMs Down to the 65 nm Technology Node[END_REF]. These fault injection simulations are based on physical simulations and electric simulations. A SET current database based on bias voltage, layout, and fabrication process was generated from the physical simulations. Next this SET currents database is used for fault injection simulations using a SPICE simulator with the aim to estimate the soft error response of the circuit. For this work, the n-MOS and p-MOS transistor models are provided by Sofradir.

The validation of the relevance of the SEU sensitivity modeling has been validated in previous work for the reference DFF and the DFF1 at room temperature (e.g. 300 K) and down to 70 K [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF].

A. Effect of DFF design on SEU sensitivity trend

In order to confirm the global SEU sensitivity trend observed under heavy ion tests, SEU cross sections have been calculated at 300 K and 70 K.

Fig. 8 (a) presents the SEU cross sections calculated by the SEE prediction tool for two DFFs: the reference DFF (red dots) and DFF6 (black squares) under heavy ions. The SEU prediction tool emphasizes a higher SEU sensitivity for the classic design of the reference DFF than the complex DFF6, as observed with the experimental tests in Fig. 5. The same trend has been obtained for the DFF1 and DFF5. Fig. 8 (b) presents the same comparison of SEU cross section but with the logical state "0" stored in DFF6 and the reference DFF. The same comparison has been performed at 70 K as illustrated in Fig. 8(c) and Fig. 8(d) for the logical state "1" and "0" respectively. At 70 K, the effect of DFF design is very limited, especially at saturation of the cross section. It seems that cryogenic temperatures limit the impact of the design on the SEU sensitivity of DFFs.

B. Failure analysis at layout level at nominal voltage

A failure analysis at layout level has been performed on the DFF6 with the aim to show the specificities of critical transistors which allow a stronger SEU robustness. Fig. 9 presents the SEU sensitivity mappings obtained by simulations representative of heavy ions with various LETs in DFF6 at room temperature. Each colored symbol indicates the SEU sensitivity of DFF6 if a heavy ion strikes the layout at the corresponding location. After the simulations by the SET fault injection, three sensitive transistors have been identified on the design of DFF6, as shown in Fig. 9. The three critical transistors (2 p-MOS and 1 n-MOS) are linked to floating nodes: as well for the Source and the Drain electrodes. Moreover, the criticality of these transistors is highlighted because one of them controls the propagation of the clock signal in the DFF circuitry.

A comparison between the design of the reference DFF and DFF6/DFF5 reveals a critical point: the critical transistor which controls the clock signal is designed with a drive current higher by a factor of 2 in comparison to the reference DFF. A higher drive current is known to improve the SEU robustness of a CMOS gate [START_REF] Artola | Comparative soft error evaluation of layout cells in FinFET technology[END_REF]. Then, this design specificity of the DFF6 which increases in the cell area explains the lower sensitivity of DFF6 in comparison to the reference DFF.

C. Temperature effects on SEU occurrence

Recent works reported the limited impact of the cryogenic temperatures on the SEU sensitivity in the reference design of DFF [START_REF] Artola | Single Event Upset Sensitivity of D-Flip Flop of Infrared Image Sensors for Low Temperature Applications Down to 77 K[END_REF]. Fig. 10 presents the experimental measurements of SEU cross section of the DFF6 as a function of temperature for two values of LET. The results show a very limited impact of the SEU occurrence in the DFFs. The trend has been confirmed by simulation by the mean of MUSCA SEP3 tool coupled to SPECTRE simulations as shown in Fig. 11.

These results are consistent with experimental data presented in recent works regarding SET and Single Event Functional Interrupt (SEFI) [START_REF] Al Youssef | Single Event Transients in ReadOut circuitries at Low Temperature down to 50K[END_REF] [START_REF] Artola | Single Event Transient and Functional Interrupt in Readout Integrated Circuit of Infrared Image Sensors at Low Temperatures[END_REF].

p-MOS1 p-MOS2

n-MOS1

D. Prospective evaluation of the impact of the supply voltage reduction

It has been shown that a decrease in the supply voltage leads to an increase in the SEU sensitivity, independent of the technology's digital function [START_REF] Artola | Comparative soft error evaluation of layout cells in FinFET technology[END_REF] - [START_REF] De Aguiar | Evaluation of radiation-induced soft error in majority voters designed in 7 nm FinFET technology[END_REF]. For this technology, Sofradir has the opportunity to tweak the supply voltage of the D-Flip-Flop down to 3.3 V. However, it is interesting to note that the best trade-off performance has been obtained around 4.5 V. Fig. 12 presents the relative increase in SEU cross section depending on the core voltage SEU for a range of LET from 10 MeV.cm 2 .mg -1 up to 58.8 MeV.cm 2 .mg -1 for the DFF6 at state "1" at 300 K. An increase in the SEU cross section by a factor of two has been estimated for heavy ions with a LET range between 10 and 30 MeV.cm 2 .mg -1 . On the other hand, the increase in the SEU cross section at saturation (over 50 MeV.cm 2 .mg -1 ) is very limited: lower than 6% even at 3.3 V. Finally, an important point is the limited increase (lower than 30%) in the SEU cross section for the optimal supply voltage (4.5 V).

V. CONCLUSION

This work highlights the impact of design on the SEU sensitivity of D-Flip-Flips of a ROIC under heavy ions. New experimental data obtained at University of Louvain for several design and architectures are presented. The SEU sensitivity trends are discussed as a function of the DFF area, the design complexity and the number of n-MOS and p-MOS transistors. The analyses of the experimental measurements have been completed by a study at circuit level with the use of a fault injection tool. The simulations confirm the interest of wide transistor (2X drive current) which controls the clock signal. This wide transistor connected to the floating nodes of critical transistors improves the SEU robustness. This design specificity allows for increasing in the SEU robustness of the DFF. However, it appeared that cryogenic temperatures limit the impact of the design on the SEU sensitivity of DFFs. The results show a very limited impact of the temperature on the SEU occurrence, independent of the layout. The trend has been confirmed by simulation. These results are consistent with experimental data presented in recent works regarding SET and SEFI. These results allow for performing irradiation tests of CMOS IR detector (ROIC) at room temperature instead of cooling down the device during the SEE measurements.

Finally, a prospective evaluation of the effect of the supply voltage reduction has been done. It highlighted the relevant choice of Sofradir about the supply voltage used for their digital functions in the ROIC. In future works, the analyses of these six designs could be extended to the other DFF designs and architectures in order to generalize the highlighted mechanisms.

VI. ACKNOWLEDGMENT

The authors thank P. Garcia, G. Vignon from TRAD, and M. Boutillier from CNES for their work and their support for the radiation tests at UCL. (black squares) and 67.7 MeV.cm 2 .mg -1 (red dots) Fig. 12 Relative increase in SEU cross section depending on the core voltage SEU for a range of LET from 10 MeV.cm 2 .mg -1 up to 58.8 MeV.cm 2 .mg -1 for DFF6 at state "1" at 300 K Fig. 11 Simulations of the SEU cross section of DFF6 as a function of temperature for two LETs, 10 MeV.cm 2 .mg -1 (black squares) and 67.7 MeV.cm 2 .mg -1 (red dots)

  during the development process of space CIS is the best trade-Impact of D-Flip-Flop Architectures and Designs on Single Event Upset Induced by Heavy Ions L. Artola, G. Hubert, S. Ducret, J. Mekki, Ahmad Al Youssef, and N. RicardT

Fig. 1

 1 Fig. 1 Simplified schematic of the role of DFF in the digital function of ROIC

Fig. 2 (

 2 Fig. 2 (a) shows the nominal behavior of DFF5. The five input signals (SD, TE, TI, Clk, D) and the output signal, (Q), are presented. SD is the clear signal; TE is the selection signal of input data signals; D is the main input data signal; TI is the secondary input data signal; and Clk is the clock of the DFF; The DFF is synchronized on the rising edge of the clock signal. When TE is at low level, the DFF transfer the data of the D input to the Q output of the DFF; when TE is at high level, the DFF transfers the data of the secondary input signal, e.g. TI, on the output signal.During the irradiation, a SEU has been considered when the output of the DFF chain changed from "1" to "0" or "0" to "1" depending on the stored logic state as illustrated in Fig.2(b) by the white dashed circle.

Fig. 2 Fig. 3 :

 23 Fig. 3: Synoptic view of the 6 shift registers composed by 200 DFF cells designed by Sofradir for the two test vehicles

Fig. 5 1 Fig. 4

 514 Fig. 5 SEU cross section of DFFs of test-chip 1 for simple (black symbols) and complex (red symbols) designs as a function of LET at room temperature (300 K)

Fig. 7

 7 Fig. 7 SEU cross section of DFFs from test-chip2 as a function of the ratio between the number of n-MOS and p-MOS transistors.

Fig. 9

 9 Fig. 9 SEU sensitivity mappings obtained by fault injection simulation representative of heavy ions with a LET of 10 (blue), 20 (green), 32(red), 58.8 (white) MeV.cm 2 .mg -1 in the DFF6 (test-chip 1) at room temperature (300 K).

Fig. 10

 10 Fig. 10 Experimental measurements of the SEU cross section of DFF6 as a function of temperature for two LETs, 10 MeV.cm 2 .mg -1(black squares) and 67.7 MeV.cm 2 .mg -1 (red dots) Fig.12Relative increase in SEU cross section depending on the core voltage SEU for a range of LET from 10 MeV.cm 2 .mg -1 up to 58.8 MeV.cm 2 .mg -1 for DFF6 at state "1" at 300 K


A Belkadi

A Montillet

J Bellettre
email: jerome.bellettre@univ-nantes.fr

BIOFUEL EMULSIFIER USING HIGH VELOCITY IMPINGING FLOWS AND SINGULARITIES IN MICRO-CHANNELS

The objective of this work is to design an original microfluidic mixer for continuous emulsification of small fractions of water in a lipid phase. This system is aimed to be integrated on-line in the process so as to avoid the use of a surfactant. The targeted application is a better combustion of alternative biofuels in boilers, turbines or internal combustion engines in general. The developed micro-system which includes impinging flows and elbows, is performed on the basis of a specific design of micro-channels, adapted to the respective flow rates and the characteristics of the fluids to be emulsified (viscosity, surface tension). The variation of different parameters is tested in this study such as the nature of the lipid phase (viscosity, density, surface tension and components), the length of micro-channels in the elbow and the flow rate of the dispersed phase. The dispersion of water is much more efficient with this microsystem using gasoil rather than vegetable oil as the continuous phase.

INTRODUCTION

For the sake of a less polluted environment and the necessity of enhancing efficient consumption of energy, alternative fuels have to be developed and their combustion has to be improved. Some studies [START_REF] Jacques | The combustion of water-in-oil emulsions and the influence of asphaltene content[END_REF][START_REF] Mura | Effects of dispersed water droplets size in Microexplosion phenomenon for water in oil emulsions[END_REF][START_REF] Tarlet | Formulation and combustion of emulsified fuel: The changes in emission of carbonaceous residue[END_REF][START_REF] Attia | Influence of the structure of water-in-fuel emulsion on diesel engine performance[END_REF][START_REF] Kumar | A comparative study of different methods of using animal fat as fuel in a compression ignition engine[END_REF] show that the presence of a low fraction of finely dispersed water (droplets of the order of 5 to 10 µm) in the fuel lowers the combustion temperature and thus reduces emissions of polluting gasses and particles matters resulted from poor combustion. In this objective, the use of water as a dispersed phase in liquid biofuels is commonly promoted. The emulsified fuel is intended for powering internal combustion engines, turbines and boilers. The dispersed water plays a key role in a phenomenon called micro-explosion, where both thermal and mechanical effects allow optimizing combustion and reduction of emissions of polluting gases and particles. The ambition of this study is to provide a continuous emulsification system dedicated specifically to water in oil emulsification. The final applications concern the field of energy conversion, such as boilers, turbines or internal combustion engines in general. The continuous phase can be made of various sources such as petrodiesel, heavy fuel or lipid waste (waste vegetable oils, animal fats). The difficulties related to the envisaged applications are numerous such as the characteristics of the used fluids, their volumetric ratio in the emulsion and the need to design a compact process to treat sufficient flow rates for the energy plans target. This work was directed towards the proposal of a system based on the use of sub millimeter-sized channels (Dh < 1 mm). Research in the field of microfluidics is very active for two decades and shows particular interest for the development of emulsification processes [START_REF] Zhao | Two-phase microfluidic flows[END_REF][START_REF] Schubert | Product and formulation engineering of emulsions[END_REF]. The state of the art literature shows a significant number of studies dealing with emulsification processes, mainly applied to oil in water mixtures (o/w) [START_REF] Nisisako | A microfluidic crossflowing emulsion generator for producing biphasic droplets and anisotropically shaped polymer particles[END_REF][START_REF] Kiss | Formation of O/W emulsions by static mixers for pharmaceutical applications[END_REF]. Unquestionably, emulsification of water in oil (w/o), which is treated in this work, is more seldom studied as it requires optimization from an energy point of view. Two main reasons explain it: the continuous phase exhibits a viscosity which is, generally, several decades higher than that of the water. The ratio of the flow rates for the two phases is such that the emulsification process is consuming much more energy with w/o emulsion than o/w ones.

Generally, the maximal fraction of water that can be included before catastrophic inversion with w/o emulsions is about 20% [START_REF] Belkadi | Water-in-oil emulsification in a microfluidic impinging flow at high capillary numbers[END_REF][START_REF] Nisisako | Formation of droplets using branch channels in a microfluidic circuit[END_REF][START_REF] Nisisako | Droplet formation in a microchannel network[END_REF].

In particular, concerning the targeted applications, literature points out that small fractions of water (10% or less) are needed [START_REF] Tarlet | Formulation and combustion of emulsified fuel: The changes in emission of carbonaceous residue[END_REF][START_REF] Attia | Influence of the structure of water-in-fuel emulsion on diesel engine performance[END_REF][START_REF] Kumar | A comparative study of different methods of using animal fat as fuel in a compression ignition engine[END_REF].

A test facility was developed in this work in the aim to test the studied micro-systems in the emulsification conditions corresponding to the final applications (fluid properties and flow rates involved). During these tests, water was used as the aqueous phase in small amounts, not exceeding a fraction of 20 %. Sunflower oil or gasoil are tested as the continuous phase. Because of economic and environmental concerns related to the intended final application for this emulsification process (combustion), no surface agent is used.

EXPERIMENT AND PROCEDURES

Experimental facility

The used test bench is shown in Figure 1. This installation is equipped with double piston displacement pumps (ARMEN -APF-100-251, see Figure 1234). The maximum working pressure and flow rate of these pumps are respectively 25 bar and 100 ml/min (maximum speed available in the case of the use of water).

In order to measure the flow rates versus time, the experimental set-up is equipped with two weighing scales Sartorius -MSE2203 (see Figure 123456)) allowing a continuous acquisition of measured mass with an accuracy of ± 10 -3 g. The pressure measurement is ensured by two compact pressure transmitters Gems-3100. The measuring range of pressure sensor 0 -25 bar with an accuracy of ± 0.25% of full scale. The pressure sensors are connected to the emulsification loop between the pump and the inlet of the micro-system (Figure 123). The sensors measure the relative and static pressure for each of the two mixed phases. Connections between the pumps and the micro-system are made using fluoropolymer tubes (FEP) with an inner diameter (ID) of 1.55 mm and an outer diameter (OD) of 3.125 mm.

High speed visualization

For the purpose of analyzing the flow prevailing in the microsystem, a high speed visualization using "LaVision HighSpeedStar 6" camera is implemented.

Characteristics of the used fluids

The main characteristics of the fluids are recapped in Table 1. Sunflower oil and gasoil are respectively used as the continuous phase. It may be noticed that the viscosity of Sunflower oil at the ambient temperature is closed to that of heavy fuel at a temperature of about 60°C.

Table1. Main characteristics of the used fluids.

Liquids characteristics at 25 °C

Density Surface tension

Viscosity

ρ [kg/m3] σd/c / [mN/m] µ [mPa.s]

Control of emulsification quality

The quality of dispersion is checked using optical microscopy techniques. At each test, a sample of emulsion, is immediately analyzed (Figure 2) on a hemocytometer cell type made of PolyMethyl MethAcrylate (PMMA). Convergence of the statistics regarding mean diameter, d 10 , and its standard error,  exp , are controlled as the function of the number of analyzed water droplets.

The mean diameter d10 is defined as following:

Where "n" is the number of analyzed droplets di.

The expression for the experimental standard deviation, calculated for each size diameter, is given by the formula:

The arithmetic uncertainty for each mean droplet size calculation is given below:

Dimensionless numbers

Dimensionless numbers are useful to compare the different flow regimes in our experiments. The following parameters are used to identify the relevant forces involved in the microchannel for the drop formation:

-The capillary number expresses the ratio of viscous forces and interfacial forces: Ca = µc vm / σd/c.

-The Ohnesorge number estimates the ratio of the viscous forces and the combination of inertial forces and interfacial forces. In the case of dispersion, it characterizes simultaneously the deformation and transport (advection) imposed by the continuous phase (vegetable oil or gasoil) on the dispersed phase (water

): Oh = µ c / (ρ d d 10 σ d/c ) 1/2 .
-The Weber number is defined as the ratio of inertial forces on the interfacial forces: We = ρd vd 2 dd / σd/c.

MICRO-SYSTEM FOR W/O EMULSIFICATION

The developed microfluidic device is composed of two slabs of PMMA, held together with screws. An O-ring is disposed between slabs in order to ensure the sealing. The micro-channels are machined on a single slab, the second one is used as a cover.

The geometry and design of the microfluidic device core is presented in Figure 3. It consists of two crossing micro-channels featuring two inlet sections and two outlet sections. As shown in Figure 3, the channels have a square cross section and are designed to put oil and water streams in a head-on, impinging flow. The originality of the present work is that the section of water inlet is smaller than that of oil. In this configuration, an off-axis is responsible for the occurrence of a hydrodynamic structure called swirl [START_REF] Belkadi | Water-in-oil emulsification in a microfluidic impinging flow at high capillary numbers[END_REF].

As mentioned before, this micro-system is designed for continuous water in oil emulsification. One of the aims of this work is to study the influence of the fluid characteristics on the swirl. For this purpose, two liquids have been used as the continuous phase, respectively sunflower oil and gasoil.

In this work, a new original geometry is used, as shown in Figure 4, for which two different configurations are tested, respectively designated as (a) and (b). As formerly explained, both configurations offer a cross which is the seat of the frontal impact of two phases (dispersed and continuous phase). On each of the two channels of the emulsion is disposed one right bend. For both configurations, the cross section of the oil channel and emulsion channels is 600µm x 600µm. The cross section of the water channel is 300µm x 300µm. The only difference between the configurations (a) and (b) is the length. The distance between the intersection and the bend of configuration (a) is indeed two times longer than the same distance in configuration (b).

Result of dispersion

Table 2 summarizes the conditions and results of different tests obtained using the two configurations. Each series corresponds to a different flow rate of the dispersed phase while the flow-rate of the continuous phase is kept at the same order of magnitude for a given lipid phase. The pressure drop is respectively about 5 bars and 4 bars with configurations (a) and (b) using sunflower oil as lipid phase. Using gasoil, the pressure drop is respectively about 0.9 bar and 0.7 bar with the configurations (a) and (b). For each lipid phase, the maximal flow-rate available with the pump has been studied. This explains why the maximal flow rate with sunflower oil is lower than that of gasoil. An example of diameter distribution obtained (gasoil, configuration b, series 1) is plotted in the figure 5. The distribution of size is rather close to a log normal distribution, but it may be emphasized that the measurement of the diameter is limited by a physical cut off due to the use of an optical observation to characterize the droplets. Thus, droplets under 1-2 µm cannot be considered.

Figure 6 points out the effect of the continuous phase flow rate on the water mean diameter in the configuration (b). Mean diameter of droplets corresponding to the targeted range (5 to 10 µm) can be achieved with flow-rates of about 100 mL/min. Figure 7 allows comparing the performances of the two configurations using similar couples of lipid/water flow-rates. A better dispersion is obtained when using a continuous phase with a relatively low viscosity (gasoil). Compared to the results with configuration (a), it can be observed that shortening the length of channel is useful only with gasoil as continuous phase: mean diameters of droplets respectively obtained with the two configurations are not significantly different, except at the lowest water flow-rate studied. Concerning the sunflower oil phase, the efficiency of the configuration (a) is better, indicating an influence of the length of the channels on the dispersion. Table 3 recaps the covered ranges of the capillary number, weber number and Ohnesorge number. The level of the capillary number involved in this study is much higher than what is classically observed in the field of microfluidics. The values of the capillary number indicate that the viscous forces are higher than the interfacial ones in all the experiments. Concerning the inertial forces, they are mainly dominant compared to the interfacial ones at the higher flow-rates investigated. The variation of the Weber number in the studied range indicates that these experiments are implemented in a transitional flow regime. This is confirmed by the flow visualization experiments that are presented in the next section.

FLOW VISUALISATION

As mentioned, an experimental investigation using a high speed camera was applied to investigate the flow at the crossing and the outlet of the crossing of the studied micro-system (configuration (b) shown in Figure 4). Images of this investigation are shown in Figure 8.

The flow of the continuous phase (vegetable oil or gasoil) is maintained as constant as possible. The dispersed phase flow rate is strongly varied in order to study the influence on the flow topology and on the size of water droplet.

These images are obtained without the use of particles seeds or liquids tracers. The interface of the dispersed phase (water) and the continuous phase naturally appears as black color, due to the interaction of incident light and water/oil interface. This phenomenon is explained by redirection of the incident light beam which locally produces extinction on this interface. The difference between the two configurations lies in the difference of the length of the sections of the outlet channels. Each straight section (respectively located before and after the bend) is divided by a factor 2 in the configuration (b) compared to configuration (a). It is observed in our experiments that a longer length is more benefit in the case of sunflower oil as the mean diameter of the emulsion is smaller with this configuration, but the opposite effect is observed with using gasoil as the continuous phase. The length of the channel can have an importance regarding coalescence phenomena and mixing. As no surfactant is used, coalescence which mostly happens in long straight channels has to be avoided. In this work, the shortness of the channels is limited by technical constraints (the use of a seal to avoid leakages) and then can hardly be smaller than 10 mm, as in configuration (b). Secondly, it can be observed that the tested design of the micro-channels, whatever is the length of the outlet channels, is more efficient using a less viscous fluid. In these microsystems, the mechanisms of water dispersion are mainly enhanced by the impact of the fluids, and subsequently by the development of roll structures generated by a step present in the cross. As the value of the interfacial tension is similar for the two couples of fluids tested, the nature of the flow pattern mainly depends on the viscosity of the fluid. A previous study [START_REF] Mouheb | Numerical and experimental investigations of mixing in T-shaped and cross-shaped micromixers[END_REF] have shown that cross shape micromixers exhibit a good efficiency in mixing fluids of similar viscosities, particularly in the engulfment regime. This is observed in the present work in the case of the diphasic system gasoil/water (Fig. 8). In the case of sunflower oil/water diphasic system, the mixing of the two fluids is more difficult, thus roll structures persists along the outlet channels (Fig. 8) and the mechanism of dispersion is much less completed before the elbow than with the gasoil phase. At higher tested flow rates of water, intermittent structures which are Rayleigh instabilities can be observed (8.c and 8.d). These instabilities contribute to a better dispersion of water. The configuration (a) offers in this case a better development of these structures which leads to a better dispersion than in configuration b).

CONCLUSION

In the present work, an original liquid/liquid mixer is developed. This emulsifier is tested using two different continuous phase. Results show that emulsification with high velocity lipid phase flow allows the production of a fine emulsion (mean water drop diameter around 10 µm). Globally, a better dispersion of water is observed in the present study using gasoil as compared to vegetable oil. This study allows giving some indications concerning the design of micromixers for biofuels emulsification. The effect of the length of the channels has been studied in order to evaluate a possible lowering of the pressure drop while shortening them (configuration (b)). Using low viscous continuous phase like gasoil, the efficiency of the dispersion is not significantly increased using longer channels (configuration (a)) but the level of the pressure drop is relatively low, then the interest of shortening the length of the channel remains limited.

On the opposite, the dispersion of viscous continuous phase is more efficient using longer channels. In this case, Rayleigh instabilities are developed within the flow. They need time and length to grow up and disperse the water.

Tests with other geometries and fluids are under progress and will further improve the quality and the diversity of the emulsion produced in micro-channel for fuel preparation.

NOMENCLATURE

Figure 1 .

 1 Figure 1. Emulsification setup: (1)-Micro-system comprising a single bend at the emulsion channel, (2)-Water in oil emulsion, (3)-Pressure sensors, (4)-Piston pumps, (5)-Beakers containing water or continuous phase (oil or Diesel), (6)-Weighing scales, (7)-Fluoropolymer tubes (FEP) with ID = 1.55 mm and OD = 3.125 mm.

Figure 2 .

 2 Figure 2. Example of water in sunflower oil dispersion under an optical microscope.

Figure 3 .

 3 Figure 3. Design of the impinging zone localized in the crossing zone of the developed microfluidic devices [10].

Figure 4 .

 4 Figure 4. Schematic representation of the two micro-fluidic configurations tested.

  d10 e [µm] [ml/min] d 10 e [µm] [ml/min] Series 1 32 ±0,29 (76.4 -8.3) 23 ±0,22 (100 -7.5) Series 2 27 ±0,25 (81 -11.4) 15 ±0,19 (99.5 -10.5) Series 3 19 ±0,19 (75.2 -17.4) 13 ±0,18 (97.6 -15.9) Series 4 19 ±0,18 (70.5-22.3) 12 ±0,18 (97.7 -21) 18 (80.8 -17.6) 11 ±0,17 (99.2 -18.0) Series 4 29 ±0,16 (76.4 -23.7) 8,5 ±0,14 (99.1 -24.0)

Figure 5 . 1 )Figure 6 .

 516 Figure 5. water droplets distribution (gasoil, configuration b, series 1)

Figure 7 .

 7 Figure 7. Influence of the dispersed phase flow on the mean size of water droplets.

(Figure 8 .

 8 Figure 8. Flow topology for two different continuous phases using configuration (b).

Table 2 . Mean size of droplet determined in the dispersions obtained using the two different continuous phases.

 2

Table 3 . Explored range of dimensionless characteristic numbers using configuration (b).

 3

	Config. (b)		Series 1 Series 2 Series 3 Series 4
	Sunflower oil	We Oh Ca	0.06 1.6 3.37	0.10 1.76 4.18	0.14 2.18 4.54	0.31 1.96 4.62
		We	0.02	0.04	0.08	0.10
	Gasoil	Oh	1.01	1.03	1.05	1.22
		Ca	1.75	1.80	1.92	2.02