Near lattice matched Al0.81In0.19N/GaN heterojunction structures are compared with conventional Al0.3Ga0.7N/GaN heterojunctions in terms of the sheet density and mobility and their dependence on barrier and spacer layer parameters. With the insertion of an AlN spacer, the mobility of both structures is improved dramatically. Self-consistent solution of Poisson-Schrödinger equations was developed in order to determine the band structure and carrier distribution in these GaN based heterostructures in an effort to gain insight into the experimental observations. Surface donor states were included to account for the origin of electrons in 2DEG, which is treated as charge neutralization conditions in the simulation. Also the change in the piezoelectric polarization due to the electromechanical coupling effect, and shift of band gap caused by uniaxial strain were both included in the calculations. The calculated sheet density is close to the measured values, especially for the AlGaN samples investigated, but a notable difference was noted in the AlInN cases. The discrepancy is confirmed to be caused by the existence of a Ga-rich layer on the top of AlN spacer during the growth interruption, which can split the 2DEG into two channels with different mobilities and lower the overall sheet density. When the modifications made necessary by this GaN layer are taken into account in our model for the AlInN barrier case, the calculations match with the experimental data. When the spacer thickness increase from 0.3 to 3 nm, the total sheet density was found to slightly increase experimentally, which agreed with the theoretical prediction.