  The build-factor is a magnitude which allows to correct the photon
exponential attenuation model to obtain the real value of a certain dosimetric
magnitude, like air exposure. Its main weaknesses are the dependences on the
response function of such a magnitude, the geometry, and the source
directionality. A formalism to deal with the first is presented in this work,
which leads to the definition of the differential build-up factor. Analog Monte
Carlo calculations were used to calculate this factor, as well as describing
its uncertainty, in the 30 keV to 10 MeV energy range for the most typical
materials up to 10 mean-free-paths. Coherent scattering and binding effects
were considered in the simulations, which make the results suitable for
calculations with the most complete descriptions of the attenuation
coefficients. Differences due to geometry, source directionality, and detector
response variability were typically found to be up to 30 % in the studied
range.
