The behavior of two-dimensional electron gas density, induced by spontaneous and piezoelectric polarization, in non-intentionally doped GaN=AlxGa1-xN=GaN heterostructures with very thin barriers has been studied. The sheet carrier concentration, Ns, induced by polarization charges was determined self-consistently from the coupled Schr odinger and Poisson equations, by taking into account the image and exchange-correlation potential and by considering ÿve energy levels. As a result, the physical values such as potential distribution, subband energies, wave function, Fermi level, total sheet density and occupation of di erent subbands have been obtained and discussed for di erent capping and barrier layer thickness and temperatures. The numerical results show: (a) the formation of the quantum well in GaN, when x (the Al composition in barrier) =1, is possible for every AlN thin barrier thickness, but when x ¡ 1, the minimum barrier thickness necessary for the formation of the well is depended on x. Also when x = 1, depending upon two-dimensional electron gas sheet density, Ns, the number of occupied levels of the well, can be one, two or even three, (b) the above-mentioned values are almost highly sensitive to capping layer thickness.
The temperature evolution of the sub-band occupation number shows that there is still an e cient conÿnement even at very high temperature (900 K) for a thinner capping layer system.