We suggest the use of crystal of BaF 2 as scintillator in Positron Emission Tomography (PET) with very high space resolution at the level of 1–2 mm. These crystals are prospective candidates to provide necessary cell granularity (crystal+photodetector) of 2×2 mm 2 and they possesses a very short decay time (∼0.8 ns) of the fast component in the emission spectrum. In order to detect this emission lying within deep ultra-violet (UV) spectral range with wavelengths 195–240 nm we propose to develop new type of photodetecting devices. These ones are based on wide band gap group-III nitride compounds (A 3 N) having an adjustable spectral sensitivity at wavelengths 210–360 nm and quantum efficiency 10–15%. The principal schemes of such devices based on A 3 N-nanoheterostructures emitting photoelectrons into vacuum or gaseous atmosphere and detector of photoelectrons are discussed in this paper. The photo-device with parallel-plane gas positron sensitive detector having time and position resolutions 1 ns and 500 μm, respectively, can work at counting rate up to 10 8 ph cm −2 s −1 .