2.1. EBS gain

Electron bombarded silicon (EBS) gain makes the CCD interesting for keV electron detection. Ionizing particles absorbed in silicon create electron-hole pairs at the average rate of one per 3.64 eV incident energy. This rate is average, not exact, due to energy absorption by the lattice. The variance in the number of electron-hole pairs created is given by the Fano factor for silicon (.1-.2) times the number of pairs created. When we use a CCD as a detector of ionizing particles, we would like to collect all of the electrons created. If these secondaries are created near or in the potential wells, as can be the case for X-ray absorption, we may be able to do so. Energetic electrons however, cannot travel far into silicon and in fact lose all of their energy long before they reach the wells⁸. Some secondary electrons recombine at the back surface rather than being collected. The fact that all electrons created are not accounted for means that the assumptions made in determination of the Fano factor are no longer valid⁹. The variance in the number of collected electrons is higher than just the Fano factor times the measured gain. It is beyond the scope of this paper to quantify the variation, however we will note that some additional "charge loss" noise of (at this point) unknown amplitude is added to every incident electron event.

2.2. Charge spreading

The process of electron multiplication occurs near the back surface of the device. From there the electrons diffuse until they are collected in the potential wells. During diffusion there is some lateral spreading, the extent of which is determined by the thickness of the silicon between the surface and the buried channel (typically 8-20 µm), and by the diffusion length of electrons in silicon. Although the resulting point spread function (PSF) of the CCD may be less than the PSF of the electron optics used to image the electrons in the first place, it is generally enough to keep all of the secondary electrons from being collected in one well even in the event of a central hit on a pixel. In fact, the likelihood of a split event is quite high. For a CCD with a 24 µm pixel and a Gaussian PSF of standard deviation 6 µm, there is a fifty-fifty chance of finding less than 65% of the secondary gain electrons in the pixel under impact. Even in the event of an impact centered on a pixel, only 93% of the secondaries are collected. At worst, for a corner hit, the secondaries are split four ways. Not only does this charge spreading have an impact on the spatial resolution of the CCD, but it also impacts its single electron detection capability as will be discussed later.

2.3 Radiation damage

Electron bombardment of silicon creates X-rays which propagate to, and damage, the gate insulator and silicon-insulator interface. This damage causes an increase in the dark current generation rate that is proportional to the number of X-rays generated. X-ray generation goes as about the 1.6th power of beam energy¹⁰, so a single electron will create about three times as much damage at twice the beam energy. Gain, however, is higher at twice the energy, so it takes fewer electrons to make a full well. Depending on the collection efficiencies at the energies in question, the damage per full well could actually go down.

With this background in mind we can go on to discuss the signal to noise ratio for single electron events.