Analytical response function for planar Ge detectors

We model the response function (RF) of planar HPGe x-ray spectrometers for photon energies between around 10 keV and 100 keV. The RF is based on the proposal of Seltzer [1981. Nucl. Instrum. Methods 188, 133-151] and takes into account the full-energy absorption in the Ge active volume, the escape of Ge Kα and Kβ x-rays and the escape of photons after one Compton interaction. The relativistic impulse approximation is employed instead of the Klein-Nishina formula to describe incoherent photon scattering in the Ge crystal. We also incorporate a simple model for the continuous component of the spectrum produced by the escape of photo-electrons from the active volume. In our calculations we include external interaction contributions to the RF: (i) the incoherent scattering effects caused by the detector's Be window and (ii) the spectrum produced by photo-electrons emitted in the Ge dead layer that reach the active volume. The analytical RF model is compared with pulse-height spectra simulated using the penelope Monte Carlo code.