/ AbstractThe EDELWEISS-III direct dark matter search experiment uses cryogenic HP-Ge detectors Fully covered with Inter-Digitized electrodes (FID). They are operated at low fields ($<1\;\mathrm{V/cm}$), and as a consequence charge-carrier trapping significantly affects both the ionization and heat energy measurements. This paper describes an analytical model of the signals induced by trapped charges in FID detectors based on the Shockley-Ramo theorem. It is used to demonstrate that veto electrodes, initially designed for the sole purpose of surface event rejection, can be used to provide a sensitivity to the depth of the energy deposits, characterize the trapping in the crystals, perform heat and ionization energy corrections and improve the ionization baseline resolutions. These procedures are applied successfully to actual data.