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We investigate terahertz plasmon-polariton (PP) resonances for hetero-structures (AlGaN/GaN, SiGe/Si/SiGe, AlGaAs/GaAs and InAlN/GaN) with grating coupler in order to find the optimal structure. We show a modeling work devoted to a parametric study (influence of geometry, temperature...) that the resonances are tunable in frequency allowing a control of the terahertz detection. The modeling shows that AlGaN/GaN and InAlN/GaN heterostructures present the highest PP resonances at 300K. Then we compare modeling with room temperature and cryogenic temperature FTIR measurements on group III-N heterostructures which are indeed the most promising.