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. The 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. Charge packets that have more electrons tend to occupy a physically larger volume within the pixel. As such, larger packets provide larger cross-sections 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. It is worth noting, however that even though losses increase in an absolute sense when we have more electrons in a cloud, the per-electron fractional 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 curve on the left. This shows the marginal number of traps seen by the Nth electron. The dip between 12 and 30 electrons shows the "sweet spot" background level, where the charge transfer is maximized at low background levels.

Figure 6.1 shows the model constructed by Anderson et al. (2012) (see the document on the CTE-Tools webpage and Section 6.4). The model was based on the analysis of dark exposures taken in August 2012, 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 20 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 60 traps and is also not likely to be detected. A packet with 100 electrons will lose 90, and something should therefore be detected at the readout register.

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 will lose only about 200 electrons, so 80% of them will survive to the register. Packets with 10,000 electrons on an image with no background will lose only about 4% of their electrons.

The behavior of this curve provides strong evidence for the presence of a "supplemental buried channel" or a "mini-channel”. The channel, a key design feature in the WFC3 chips, was constructed to confine small packets to a narrow channel within the silicon in order to minimize their exposure to charge traps. The first few electrons in this channel would inevitably see a large number of traps, but subsequent electrons would find themselves relatively shielded from losses, as traps have been partially filled by preceding electrons. The fact that the observed trend in Figure 6.1 is steeper than average on the left but flattens out in the middle is attributed to the mini-channel.

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 20 traps on its path to the readout register. As such it has a 10-12 chance of making the journey without being delayed. The second electron will see 12 traps, the third 4, and the tenth less than 1.

Note that this curve cannot 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. This can also cause asymmetries in source shapes. This is why a forward-modeling routine is required to reconstruct the pixel distribution. The fact that the marginal losses drop sharply as the charge packet gets larger means that if we have a small level of background in an image, then many of the traps will be kept filled by the background and will not therefore affect the science photons. The curve shows that if we have a background of zero in an image, then a marginal electron will see twenty traps, but if the background is 10, it will likely see less than one trap. If the background is around 12, in fact, we find that a marginal science electron has about an 80% chance of making it to the readout register (as of August 2012). This corresponds to the dip in the marginal distribution, which is related to the flattening in the cumulative distribution, and which is likely a consequence of the mini-channel.

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