AlGaN/GaN heterostructures were successfully grown with the AlIn(Ga)N back barrier at 900 degrees C. However, the atomic composition of the AlIn(Ga)N layer was strongly dependent on the growth pressure, which resulted in a different lattice constant of the layer. The AlIn(Ga)N back barrier grown at 400 Corr was almost lattice-matched to GaN layer. The AlGaN/GaN heterostructures with 10 and 15 nm-thick AlIn(Ga)N back barrier exhibited improved 2-DEG properties, compared to those of the conventional AlGaN/GaN heterostructure without the back barrier. The high electron mobility transistors (HEMTs) fabricated on the AlGaN/GaN heterostructure with a 15 nm-thick AlIn(Ga)N back barrier exhibited a very low off-state leakage current of similar to 2 x 10 (-7)A/mm which is about 1 order lower in magnitude than the value of the device without the back barrier. The AlIn(Ga)N back barrier is a promising candidate as an alternative to conventional AlGaN and InGaN back barrier.