The large polarization difference between AlN and GaN provides extremely high electron densities at the interface of AlN/GaN heterojunctions. In this work the growths of high-quality single AlN/GaN heterojunctions with RFMBE are reported, which leads to high-conductivity two-dimensional electron gases. The sheet densities can be tuned from ~5* 1012/cm2 to ~5*1013/cm2 by varying the AlN thickness from 2 - 7 nm. A critical thickness is observed beyond which biaxial strain relaxation and cracking of AlN occurs, and a degradation of carrier mobility is seen to occur at extremely high sheet densities. High-mobility windows are identified with different growth rates. Record low sheet resistances in the range of ~148 å_åü/sq has been achieved. Interface roughness scattering and strain relaxation are identified as the factors preventing lower sheet resistances at present. At low temperature, Shubnikov-de-Haas oscillations have been observed for the first time in single AlN/GaN heterojunctions. The MBE growth for multiple AlN/GaN heterojunctions are also studied. The electron energy states are calculated in the AlN/GaN superlattices which inductivelyto obtain give the miniband structures, for the design of intersubband emitters of detectors. Propagation of longitudinal acoustic phonons through AlN/GaN superlattices is simulated. Finally, phonon filters and phonon cavities are designed for efficient thermal engineering from nitride active layers.