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In AlN/InN/GaN-based semiconductors, the polar optical phonon energy is large (much larger than the thermal energy at room temperature). As a consequence, the dominant optical polar scattering occurs in two steps: photon absorption and re-emission (resulting in an effectively elastic scattering process). In high electric fields, an electron runaway plays a key role in determining the peak field and peak velocity in these compounds. The runaway effects are further enhanced in the two dimensional electron gas at the AlGaN/GaN or AlGaInN-InGaN heterointerfaces. As a result of the runaway and quantization effects, the peak electron drift velocity and peak electric field of the 2D electrons in compound semiconductors are smaller than for the 3D electrons in these materials. In very short (e.g. sub-0.1 micron) GaN-based structures, ballistic and overshoot effects become important. In a deep submicron structures, the ballistic effects in low electric fields reduce an apparent value of the low field mobility because of a finite electron acceleration time in the structure. In long channel devices, the electron mobility in AlGaN/GaN or AIGalnN/InGaN heterostructures at cryogenic temperatures is limited by acoustic scattering, electron transfer from 2D to 3D states, and by the alloy scattering. Relatively high values of the electron mobility and very high values of the 2D electron gas densities in nitride heterostructures also make them attractive candidates for plasma wave electronics devices operating in the terahertz range of frequencies.