We study both GaInN/GaN/AlGaN quantum wells with an asymmetric barrier structure grown on SiC substrate and GaN/AlGaN asymmetric double quantum well (ADQW) structures. In the first case, a time-resolved study reveals an enhanced oscillator strength when the AlGaN barrier is on top of the GaInN quantum well. In comparison to our previous study of the same structure grown on sapphire, we find that the sign of the field is the same in both cases: the field points towards the substrate. In the case of ADQW, we observed not only intrawell transitions of both a 4 nm and a 2 nm QW separated by a 2.5 nm AlGaN barrier but also an interwell transition between the two QWs in the photoluminescence. The lifetimes and emission energies of the transitions can be well explained by the existence of the piezoelectric field built in the QWs.