The neutron spectrometer discussed in this work consists of a PIN diode coupled with a polyethylene converter. Neutrons are detected through the energy deposited by recoil-protons in silicon. The maximum detectable energy is -6 MeV and is imposed by the thickness of the fully depleted layer (300 microm for the present device). The minimum detectable energy which can be assessed with pulse-shape discrimination (PSD) is -0.9 MeV. PSD is performed with a crossover method and setting the diode in the 'reverse-injection' configuration (i.e. with the N+ layer adjacent to the converter). This configuration provides longer collection times for the electron-hole pairs generated by the recoil-protons. The limited interval of detectable energies restricts the application of this spectrometer to low-energy neutron fields, such as the ones which can be produced at facilities hosting low-energy ion accelerators. The capacity to reproduce continuous neutron spectra was investigated by optimising the electronic chain for pulse-shape discrimination. In particular, the spectrometer was irradiated with neutrons that were generated by striking a thick beryllium target with protons of several energies and the measured spectra were compared with data taken from the literature.