The aim of semiconductor spintronics is to exploit the spin degree of freedom of electrons to add new functionalities to electronic devices and boost their performances. The development of assets with the ability of efficiently injecting, transferring and detecting spins is a first step towards this goal. In this sense, a well established spin injection/detection scheme relies on an heavy metal grown on the top of a Ge substrate. The semiconductor is exploited to photogenerate spin-polarized carriers making use of the optical orientation technique. These carriers are then transferred to the heavy-metal layer where spin detection occurs by means of the inverse spin-Hall effect. A key point to get quantitative information from the investigation of such a platform is the knowledge of the total spin transferred from the semiconductor to the heavy-metal layer. Here, we address this problem by employing both an analytical and a numerical spin drift-diffusion model.