This paper describes a novel design for an avalanche photodiode based on silicon carbide material. The design is based on a SAM-APD, with the novel feature of a field-stopping layer with limited extension only to the anode edge. Simulation shows that avalanche multiplication is achieved only in the central region of the device, thus enabling stable performance, when this novel structure is coupled with junction termination. Also, increased sensitivity is enabled by the achievement of a rectangular field distribution and full depletion of the absorption region by the onset of avalanche multiplication. The design has been experimentally verified, with the demonstration of low leakage current and a sharp, stable avalanche breakdown point around 120V. Optical responsivity to radiation of wavelength 200 to 400 nm is shown to increase with increasing applied reverse bias. Comparison with simulation shows that this is probably limited by reflection of the incident radiation at the device surface and by recombination effects.