Photodetectors that produce detectivities close to the theoretical maximum detectivity include an electrically insulating substrate carrying a body of semiconductive material that includes a region of first conductivity type and a region of second conductivity type where the first region overlies and substantially covers the top and sides of the region of second conductivity type and where the junction between the first and second regions creates a depletion layer that separates minority carriers in the region of second conductivity type from majority carriers in the region of first conductivity type. These photodetectors produce high detectivities where radiation incident on the detectors has wavelengths in the range of about 1 to about 25 microns or more, particularly under low background conditions.