the species.

Its measurement is therefore a very powerful method to identify the physical nature of the defect.

Trap species like the O-Vacancy complex (or A-trap), with a characteristic energy of 0.17 eV or the multi-vacancy (V-V-V trap) at ≃0.20 eV, are expected to have the greatest impact on serial CTI in Gaia devices.

At the nominal Gaia CCDs temperature of -110 C, using Equation 5, the emission times of these species are of the order of a few to hundreds of microseconds, close to the serial readout sampling value.

Other common species, like the Phosphorous-vacancy defect mentioned earlier, characterized by an energy level below the conduction band of approximately 0.44 eV, have emission times too long to affect the serial readout process.

Once these defects capture an electron they remain filled for timescales much longer than the serial transfer process, and are said to be effectively ‘frozen’.

These species have no net impact on serial CTI.

In the first attempts at fitting the serial calibration data sets using CtiPixel, a fixed, nominal CCD temperature of -110 C was used for all the devices of the Gaia field of view.

This was based on preliminary analysis of the spacecraft telemetry indicating a generally stable temperature over the field of view.

A more detailed investigation of thermal variations has later shown differences of several degrees between devices, as well as seasonal and long-scale fluctuations.

Variation of up to 5 degrees in temperature over the field of view can lead to uncertainties in the estimates of the release timescale of fast trap species as the A-trap of up to 30% (see Equation 5).

The updated CCD temperature information has subsequently been introduced to the fitting model.

This change allowed the direct derivation of the characteristic energy level Et of the species from the fits, in place of the temperature-dependent emission times τe.

In CtiPixel, the amount of previously captured charge by traps that is released back into a pixel is determined for each trap species by multiplying the release probabilities of Equation 4 by the number of traps filled by captured electrons.

The total number of electrons released into a pixel is therefore calculated as:
R = �
Ri = �
(6)
i
i ρi ffilled,iPe,i
where ρi is the number density of the ith trap species, ffilled,i is the fraction of traps filled with a captured electron for that species, and Pe,i its emission probability.

CtiPixel simulates the serial readout process by updating the signal flux F(x) of every pixel for the charge losses (Equation 3) and the charge released by each trap species (Equation 1) during a serial readout pixel clocking cycle, and tracking the defects statistics updating the number of empty and filled traps.

The signal is then shifted by one pixel towards the readout node, and the calculations illustrated above are repeated, until the full readout register has been readout, and additionally evaluating the charge released by traps in the 20 (or 24 for AF1) post-scan pixels.

At this stage, the flux of the bottom line from the CCD image section is transferred into the serial register, and the process is repeated until the serial readout of the full calibration dataset has been completed.

The parameters of CtiPixel that are fitted using the serial calibration activities data sets are the traps number densities ρi, Article number, page 6
the capture parameters α of Equation 2 and the volume scaling β values, for each trap species.

The parameter β is allowed to change by species to account for possible variations in the spacial distribution of the different impurities in the silicon.

In addition, as mentioned earlier, during the initial fitting attempts the traps emission timescales τe (Equation 5) were also derived, employing the nominal Gaia temperature value of -110 C for all devices and epochs.

This choice was necessary as the complete telemetry from the temperature sensors over the Gaia focal plane wasn’t available at the time the project was started and the initial model was being developed.

In the refined CtiPixel implementation an epoch-dependent CCD temperature was used for each camera, derived from the spacecraft telemetry, allowing the direct fit of the characteristic energy level Et of different species.

In the model, the trap species parameters τe (or Et), α and β are set to be independent of time, as they are considered intrinsic characteristics of a defect type, while the traps number densities ρi are allowed to vary to track the increase of defects in the CCD caused by radiation.