GaN-based heterostructures: electric--static equilibrium and boundary conditions

In the GaN-based heterostructures, this paper reports that the strong electricfields induced by polarization effects at the structure boundaries complicate theelectric--static equilibrium and the boundary conditions. The basic requirements ofelectric--static equilibrium for the heterostructure systems are discussed first,and it is deduced that in the application of the coupled Schr"{o}dinger--Poissonmodel to the heterostructures of electric--static equilibrium state, zero externalelectric field guarantees the overall electric neutrality, and there is no need tointroduce the charge balance equation. Then the relation between the screening ofthe polar charges in GaN-based heterostructures and the possible boundary conditionsof the Poisson equation is analysed, it is shown that the various boundaryconditions are equivalent to each other, and the surface charge, which can be usedin studying the screening of the polar charges, can be precisely solved even if onlythe conduction band energy is correctly known at the surface. Finally, through thecalculations on an AlGaN/GaN heterostructure with typical structure parameters bythe coupled Schr"{o}dinger--Poisson model under the various boundary conditions,the correctness of the above analyses are validated.