Schrodinger-Poisson Modeling of Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$N/GaN Heterostructures Employing Tailored Depth-Dependent Aluminum Concentration for Polarization Grading*

Polarization-gradient profiling of Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$N/GaN heterostructures in the vertical (depth) direction, achieved by deliberate spatial tailoring of the aluminum concentration profile, can be used to control the spatial structure of the conducting electron gas in high electron mobility transistors. In particular, the typical two-dimensional electron gas of abrupt heterostructures can exhibit a more three-dimensional distribution in graded structures. This offers the possibility of improved device linearity through deliberate vertical heterostructure engineering, which can minimize or compensate for various scattering mechanisms that contribute to nonlinearity. Schrodinger-Poisson modeling (i.e., the Hartree approximation) is used to study the electron density profiles that result from such deliberate grading, and how those profiles evolve with the application of biasing vertical electric fields across the heterostructure. Implications of the results on device linearity will be discussed. Comparisons between the electron density profiles predicted by the Schrodinger-Poisson modeling and those obtained by density-gradient theory will be made in selected examples.