# Initial Charge Cloud Generated by Photon Interactions

Compton scattering and the photoelectric interaction will transfer either part or all of the photon energy to the interacted electron. The electron loses its energy through scattering, ionization of atoms, and Bremsstrahlung radiation. Consequently, the interaction generates phonons (lattice vibration) or electron-hole pairs in CdTe or CZT. The process of the electron-hole pair *(N _{el})* generation could be modeled as a Poisson process. Since the number of electron-hole pairs is on the order of 10,000, the process could be approximated by a Gaussian distribution:

where the variance of the distribution, *FN _{eh},* illustrates the sub-Poisson behaviors of the process. For CdTe or CZT. the Fano factor

*F*is around 0.12 [5]. The mean,

*N*is equal to where

_{eh}*C*is the

FIGURE 13.2 (A-l) charge distribution for a single 31 keV electron; (A-2) charge distribution for

10.000 electrons with energy of 31 keV; (A-3) charge distribution for 100,000 electrons with energy of 31 keV; except the photon energy. (B-l), (B-2). and (B-3) are similar to that of (A-l), (A-2), and (A-3), respectively. The photon has energy of 91 keV.

energy needed for generating an electron-hole pair. For CZT, it is 4.64 eV. *E _{e}* is the photon energy, here we assume the detector absorb all the photon energy. For a 122-keV photon, there are around 26,300 electron-pairs produced by the photoelectric effect.

The initial charge cloud (electrons and holes) spatial distribution can be assumed to be the same as the electron energy deposition profile. For a single electron interaction, it is quite random, as shown in Figure 13.2. But when we evaluate the detector response, the average behavior of hundreds or even thousands of events will be considered. Figure 13.2 A and Figure 13.2B also show the charge distribution profile over 10 к and 100 к events with energy at 31 keV and 91 keV. The maximum distance that an electron can penetrate can be calculated by the КО radius in Eq. 13.2. However, it is significantly overestimated by charge cloud size. Figure 13.3 shows the radius covering 95% of the initial charge, which roughly equals to *0.42R _{Ko}.*