Photon detectors play a central role in the quantification of the interactions of photons and electrons with matter, therefore their characterization is necessary for a wide range of experiments and applications. Accurate determination of the efficiency and response of these detectors requires lengthy and costly experiments. The many attempts to reduce the effort spent in this process using simulations with Monte Carlo codes obtained efficiency and response of the detectors that did not reach the required accuracy when not guided by complementary experiments. This work reports the methodologies we developed to obtain the response and efficiency of detectors with good accuracy, combining experiment, simulation and the construction of analytic functions. Both the simulations and the analytical expressions took into account physical parameters, such as crystal dimensions, thicknesses of dead layers and other components of the detector, which were measured, modeled and/or calculated to match, within the experimental uncertainty, the measured efficiency of collimated photon beams. Some of the these studies led to find one detection secondary effect not previously reported in the literature. The characterized detectors were used in several measurements of cross sections of the bremsstrahlung and the ionization of atomic inner shells with the São Paulo Microtron electrons beams, which brought new contributions to the study of the interactions of photons and electrons with matter.