physical volume occupied by the signal (its confinement volume Vc).

[Figure: Fig. 2: Example charge trails from three epochs of Gaia in–orbit serial CTI calibration activities. The mean level of the charge injection in the image section CCD columns is shown before the start of the post-scan measurements illustrating the 2 orders–of– magnitude range in the commanded blocks. A small increase in serial CTI is observed from early to late epochs in the mission time line, particularly for the release signature at longer timescales. These data come from device AF5 on row 5 near the middle of the focal plane array.]

The β parameter in Equation 2 models how Vc varies as a
charge injection flux over the entire serial register, calculated using a robust estimate of the measurements of the CI lines in a block, corrected by the residual bias evaluated from the prescan pixels. The sequence of serial transfer times for a specific CI line is retrieved using an utility that provides the dwell times (see previously) for the full readout process. The modelling of the readout starts by shifting the charge by one pixel toward the readout node. For every pixel of the serial register, the CtiPixel processing task evaluates the charge losses due to the traps and the number of electrons released by each trap species into the pixel (Li, and Ri, respectively, for the ith trap species), and updates the total number of electrons F in the signal at pixel x accordingly:
function of the source signals size F, so that Vc
VP = ( F
FW )β, where VP is the physical volume of the pixel and FW its full well capacity, in number of electrons. A β value of 1 is equivalent to the classic linear scaling of volume with number of electrons (the so called volume-driven model), while a β = 0 represents the regime in which a cloud of any size physically fills the entire pixel volume (the density-driven model mentioned earlier in the Section). The capture probability of the trap species i, Pc,i, (Equation 2), is used in CtiPixel to calculate the charge losses in a pixel in conjunction with the following quantities: the signal flux in the pixel F(x), the fraction of the pixel’s physical volume that the signal occupies (Vf = Vc/VP), the density ρi of each species, and the fraction of empty traps (fempty,i). To summarize,
(Ri −Li) (1)
F = F(x) + �
i
the total charge losses L in a pixel are therefore calculated as:
In CtiPixel the capture and the release of electrons by traps is modelled as stochastic processes, with a capture probability Pc and emission probability Pe specific to each trap type. The probability of a trap capturing an electron in a time interval t is a function of the signal flux F in the pixel:
L = �
Li = �
F(x)V f ρi fempty,iPc,i
(3)
i
i
The probability of a defect emitting a previously trapped electron has a characteristics emission time τe:
Pc = 1 −e−t
τc = 1 −e−αtFβ
(2) The capture parameter α in the above equation includes the trap cross section σ, the thermal velocity of the electrons vth, and the effective confinement volume Vc of the signal. The capture time constant τc is such that commonly, in classical radiation damage algorithms, the capture of an electron by a trap is assumed instantaneous (Pc = 1). In the case of Gaia, it is instead necessary to compute this probability explicitly, as its value can be smaller than one, in particular for the small charge packets of the faintest sources.
Pe = 1 −e−t
(4)
τe
that is a function of the specific trap energy level Et, the defect cross section σn and the CCD operating temperature T, expressed as:
Et kT
τe = e
(5)
χσnvthNc Article number, page 5 where χ is the entropy factor (≃1), vth the thermal energy of the electrons and Nc are the number of effective states in the conduction band.

The emission (or release) time varies greatly among trap types, as its value is very sensitive to the characteristic energy level Et of 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.