Formation and diffusion of the electron cloud

When the photon interacts with a silicon atom in a detector an electron cloud is formed. If the interaction occured in the depleted layer, the electrons are pulled by the electric field and the cloud drifts into CCD potential wells, while spreading wider due to diffusion processes at the same time. If the cloud was formed in the undepleted bulk of silicon, the electrons diffues without a drifting component, where only the electrons that reach the border with the depleted region are carried by the electric field into the potential wells of the CCD. The final cloud size is an important parameter which determines how the charge of the cloud is split between adjacent pixels. We use the most common approach and calculate the final cloud radius r according to the formula  where r_i is the initial cloud radius, r_d is the cloud radius after the diffusion process. To calculate the diffusion radius for charge generated both in depleted and undepleted bulk we follow the paper of Hopkinson [Hopkinson1987]. For the initial cloud radius we use the results of Scholze&Ulm [Scholze and Ulm1994] if the interaction of the photon with the silicon atom did not occur near the Si-SiO₂ interface. Events which originate within a small distance from the surface lose some charge to the oxide layer and form a low energy tail of the response function. The treatment of such events is described in the subsection 4.3.2, the original cloud radius for them being much smaller than for the bulk events.

A different procedure is used for the charge clouds that are formed in the doped area of the channel stops. We have shown (see [Prigozhin1998]) that events originating in the p⁺ region of the channel stop suffer a charge loss and as a result form a shoulder on the low energy side of the main peak. Since the majority of the events in the channel stops is split between two adjacent pixels, this effect is most pronounced for the horizontally split events. A histogram of the horizontally split events (ASCA grades 3 and 4) at 1487 eV is shown in Fig.  4.129.
 

Figure 4.129: Histogram of the horizontally split events at 1487 eV

We have measured a fraction of the events in the shoulder relative to the total number of counts in the horizontally split histogram as a function of energy. The corresponding plot is shown on Fig. 4.130. It indicates that all the lossy events in the channel stop area come from a shallow region about 0.3 microns deep.

Figure 1.130: Ratio of the number of events in the shoulder to the total number of events in the horizontally split event histogram (triangles). Dotted line shows the calculated ratio assuming these events come from a layer of silicon 0.3 microns thick.

To take this phenomenon into account in our model for all charge clouds having their centers inside this region we introduce a loss which is a function of the cloud charge and the cloud center location. As a result our model can reproduce the low energy tail of the horizontally split events reasonably well.