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Influence of relaxation on the two-dimensional electron-gas (2DEG) in AlxGa1-xN/GaN/AlyGa1-yN double heterostructure (DH) is investigated by self-consistently solving the coupled Schrodinger and Poisson equations. The GaN channel layer is in compressive strain on a relaxed AlGaN lower barrier (LB) so as to improve the Al content in the AlxGa1-xN top barrier (TB) to be double that in the LB (y) and hence the 2DEG density is greatly improved. It is found that the 2DEG sheet density increases with increasing Al content in the TB and achieves a maximum NS=3.88×1013 cm-2 at x=0.88 (with y=0.38), even behind the onset of relaxation at x=0.76, indicating the dominant influence of the polarization effect and the quantum confinement effect. Further increasing x reduces NS due to significant relaxation. Taking relaxation, R, into account, the 2DEG sheet density increases with increasing Al content in the AlyGa1-yN lower barrier (LB), opposite to the case of fully strained.