Abstract: 
GaN based High Electron Mobility Transistors have shown great promise for the future high frequency and high-power applications. The most interesting feature of these devices is the presence of a two-dimensional electron gas (2DEG) density of the order of 1013 cm-2 at the AlGaN/GaN interface. This is attributed to the presence of strong piezoelectric as well as spontaneous polarization effects. In the last few years, it has been shown that the presence of donor states at the AlGaN surface is the main source of the electrons in the 2DEG. Furthermore, SiN passivation produces a perturbation in the distribution of these surface donor states, affects the 2DEG density ns, and therefore the resulting device properties. The use of an AlN spacer between GaN and AlGaN also helps to improve electron mobility values as well as increase 2DEG by inducing a very strong piezoelectric polarization due to the large lattice mismatch between AlN and GaN. Mathematical modeling is required for device design and understanding of the formation of the 2DEG and the Surface barrier height (SBH, qΦB) in different GaN based material stacks such as AlGaN/GaN, AlGaN/AlN/GaN, SiN/AlGaN/GaN and SiN/AlGaN/AlN/GaN. In this abstract, we present a brief review of the developed mathematical framework for these material stacks. This has been described in terms of two surface donor parameters i.e. the donor density (no) and the donor level (Ed). The detailed relationships between the model parameters no and Ed and the observable quantities ns and qΦB are obtained by accounting precisely for the electrostatics throughout the structure. Assuming charge conservation and solution of Poisson’s equation with appropriate boundary conditions gives self-consistent solutions for the above-mentioned structures. The presented modeling is able to predict the experimental observations in GaN heterostructures and can be used for optimized design.