An electrically cooled Broad Energy Germanium (BEGe) detector has been characterized in the energy range E$_{gamma}$ $sim$ 0.122 - 7 MeV by utilizing the $gamma$- rays emitted by a short-lived resonance state in $^{15}$O populated through $^{14}$N(p,$gamma$) reaction and standard radioactive source ($^{152}$Eu). The experimental results have been reproduced through simulations with GEANT4 code, including vendor specified detector geometry along with the detailed construction of the target holder flange, to delineate the effects of the holder at various energies and detector position. Later the efficiency with a bare point source has been simulated. It has been found that the electrically cooled BEGe detector is suitable for usage in the $gamma$-ray spectroscopy as well as for the study of resonance phenomena in nuclear astrophysics.
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