Silicon carbide detectors represent an alternative to diamond detectors for fast neutron detection in harsh environments, especially fusion plasmas. Previous studies on thin prototypes (either 10 μm or 100 μm thick) suggested that thicker active volumes might be better suited for spectroscopy measurements, due to the higher chance of retaining the neutron interaction products inside the active volume. Therefore, in this work two 250 μm SiC prototypes are tested with alpha particles following the same process conducted in the past for thinner prototypes. A stable detection is demonstrated, along an energy resolution that, if projected to DT neutrons, could become the lowest achieved so far with a SiC detector (1.3%). Some difficulties in reaching a full depletion are highlighted, as long as perspectives of a partial polarization operation of the detectors.