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Compared to the AlGaN alloy, which can only be grown under tensile strain on GaN, the AlInN alloy is predicted by Vegard's law to be lattice-matched (LM) on fully relaxed GaN templates for an indium content of similar to 17.5%, i.e., it can be grown either tensely or compressively on GaN. The effect of strain on the polarization induced sheet charge density at the Al1-xInxN/AlN/GaN heterointerfaces is carefully investigated for 6 and 14 nm thick AlInN barriers including a 1 nm thick AlN interlayer. The barrier indium content ranges at 0.03