This paper describes a novel design to achieve sensitive and stable performance of an avalanche photodiode based on silicon carbide material. The design includes a field-stopping layer with limited extension, and junction termination, in order to achieve avalanche multiplication only in the central region of the device. Also, sensitivity is increased by the achievement of a rectangular field distribution, and full depletion of the absorption region by the onset of avalanche multiplication. Evaluation of devices produced with this design show that a low leakage current and a sharp and stable avalanche breakdown point around 120V is achieved. Optical responsivity to radiation of wavelength 200 to 400 nm is shown to increase with increasing applied reverse bias, until a factor of 8 increase is achieved at the breakdown voltage.