As zhermes notes photons trigger ionizing radiation detectors (of all sorts, not just silicon) by generating charged particles.
The processes by which this occurs are primarily scattering off of electrons, and at high enough energies by pair production. To a lesser extent scattering off of nuclei also contribute. As usual, a good reference is the chapter on "Passage of Particles Through Matter" (PDF link) in the Particle Data Book. The cross-section for various processes are shown in figure 30.15 of the 2012 PDB (figure number occasionally change, but the figure has been in there for a long time)
You might think that this would make distinguishing electrons and photons a challenge--especially at both will generate an electromagnetic cascade from there--and you would be right. However, if
- you have high spacial and energy resolution
- the energy of the track is high enough that the photon cross-section is dominated by pair-production (a few MeV and up)
then can be distinguished with reasonable certainty. You look at the energy deposition at the first few $\text{g cm}^{-2}$ of the track (less than one radiation length); most electrons will have a energy deposition around 1 minimum ionizing particle (MIP) in that range, while most photons exhibit 2 MIP (because the first interaction was probably a pair production).
If your spacial resolution is good enough and your detector diffuse enough, you may also be able to see the separation between the vertex and the onset of the cascade for photons, but this is difficult in many detectors. Anna v's answer suggests that this is the primary photon tag for ATLAS.
I believe that I heard in a talk that ATLAS also uses some geometric parameters of the shower in the ECAL to help with PID between electrons and photons, but can provide no reference. I'm not doing those big compound detectors right now and have not stayed abreast the details.