Parametric equation for the efficiency curve of germanium detectors

The simple equation used to calculate the intrinsic photopeak efficiency of a semiconductor germanium detector consisting of one factor which allows for the x-ray transmission through the window and another factor which takes into account the photoelectric interaction in the active volume of the detector has proved to be insufficient since it does not consider the escape of photons with characteristic line energies. An analytical expression embodying all physical processes for photon interaction, including the escape of characteristic photons, is proposed; such an expression corrects the simplified equation shown in modern textbooks. When the detector's thickness is known, the model can be reduced to an expression with one free parameter, which was chosen to be the equivalent beryllium thickness, in order to describe the attenuation of the incident photon beam. The value of the parameter is finally obtained by comparison of the tabulated Kα/Kβ as compared to the measured Kα/Kβ values for thin, high-purity samples. The efficiency curves for two cylindrical 5 and 7 mm thick germanium detectors were obtained with the sole assumption that photons escape from the upper, or radiation entrance, detector face. Finally, Monte Carlo simulations of the detection of x-rays with these detectors with an ad hoc developed program show that the proposed parametric function is useful to fit results over a broad range of energies.