6.3 The Nature Of CTE Losses

CTE losses arise during the readout process, as the charge packet for each pixel is transferred pixel-by-pixel down the detector, in parallel, to the serial register.  As the packet moves through the silicon of the detector, it often encounters imperfections (traps) in the lattice that have been caused by radiation damage.  These traps can temporarily detain individual electrons.

Once an electron is trapped, it becomes separated from its original charge packet. This trapped electron is often released some time later during the readout and finds itself in an upstream pixel.  For this reason, CTE takes charge away from downstream pixels and deposits it into upstream pixels.  Visually, the effect results in “trails” of charge that extend out from sources in the direction opposite the readout amplifier.

Electrons are confined within pixels by the electrostatic potential well created by the electrodes.  Charge packets that have more electrons tend to occupy a physically larger volume within the pixel than smaller charge packets, on account of their self-repulsion pushing back against the pixel's potential well.  The larger volume occupied by larger charge packets provides a larger cross-section to traps as the packets are shuffled through the silicon lattice. For the WFC3/UVIS model we discuss below in Section 6.4, a cloud with ten electrons, for example, will see about 3 times more traps than a cloud with only 1 electron.  This illustration shows that even though losses increase in an absolute sense when we have more electrons in a cloud, the per-electron losses go down with increasing packet size.

Figure 6.1: Effect of Electron Traps

(Left) The dark line shows the cumulative number of traps in each column as a function of the size of the electron packet. The dotted line shows the extrapolation of the power law from the bright end. (Right) The derivative of the cumulative curve on the left, showing the marginal number of traps seen by the Nth electron in a packet.   The dashed line denotes where there is one trap per marginal electron.

Figure 6.1 shows the model recently constructed by WFC3 ISR 2021-09 (see DHB Section 6.4). The model was based on the analysis of dark exposures taken in late 2020, and specifically on the analysis of the blurring experienced by hot and warm pixels. On the left, we show the cumulative number of traps as a function of packet size. We see that a charge packet that contains just one electron will encounter 40 traps on its 2000-pixel journey to the serial register, if there is no background.  Clearly we should not expect such an electron to survive the journey.  A charge packet with ten electrons will encounter 100 traps and is also not likely to be detected.  

A packet with 100 electrons will encounter 150 traps.  Of course an isolated packet that starts with 100 electrons will not maintain that size all the way down, so in practice it will see fewer traps than this. Packets with 1000 electrons on zero background will lose only about 300 electrons, so over 70% of them will easily survive to the register.  Packets with 10,000 electrons on an image with no background will lose only about 6% of their electrons.

In the right panel of Figure 6.1 we show the marginal number of traps, i.e. the number of traps that would be seen by the Nth electron in a charge packet. The first electron will encounter almost 40 traps on its path to the readout register. As such, it has a very small chance of making the journey with its original pixel.  The second electron will see 20 traps, the third 15, and the tenth about 2.

Note that these curves cannot directly predict the original number of electrons from the observed number, since as a charge packet gets shuffled down the detector, it loses electrons and therefore its electron-loss-rate changes in a very non-linear way. It is also the case that downstream packets can “prefill” traps, such that upstream packets can be shuffled down the chip with fewer losses. CTE losses can also cause asymmetries in source shapes which is why a forward-modeling routine is required to reconstruct the pixel distribution.

The fact that the marginal losses drop sharply as a function of charge packet size means that if we have a small level of background in an image, many of the traps will be kept filled by the background and will not therefore affect the science photons above the background. The curve shows that if we have a background of zero in an image, then a marginal electron will see 20 traps, but if the background is 10, it will likely see less two traps. If the background is around 20, in fact, we find that a marginal science electron has about an 50% chance of making it to the readout register (as of late 2020).

Finally, we note that the delta-function charge packets that we have been considering in our study of warm pixels in dark exposures are of course not typical of science sources.  Even unresolved objects on UVIS have a point-spread-function shape (PSF), which means that the central pixel receives about 20% of the star's light and the immediately adjacent pixels each receive about 10% of the light.  As a consequence, the outer pixels of sources will fill some traps that the sources' inner pixels then will not have to encounter. This can increase the overall transfer efficiency of real-world sources over the delta functions we have access to in the darks.