We discuss structural, optical and electrical properties of AlxInyGai-x-yN/
GaN heterostructures grown on sapphire and GH-SIC substrates. The incorpora
tion of In reduces the lattice mismatch in a much stronger way than the ene
rgy gap discontinuity. An In to Al ratio close to 1:5 should result in near
ly strain-free heterostructures. The incorporation of In and resulting chan
ges in the built-in strain in AlInGaN/GaN heterostructures strongly affect
the transport properties of the two-dimensional (2D) electron gas at the he
terointerface. Using the incorporation of In in order to increase the Al mo
lar fraction preserving the same value of strain should allow us to greatly
enhance the sheet carrier density at the AlGaInN/GaN heterointerface. Furt
her work on improving In incorporation techniques is needed in order to mee
t these expectations.