It is assumed that in modulation-doped heterojunctions the 2D electron gas is in thermodynamical equilibrium with an external reservoir. In a quantizing magnetic field energy gaps appear in the density of states of the 2D system. This produces, when the magnetic field B increases, oscillations of the density of the free 2D electrons, because of the transfer of electrons into (and out of) the reservoir. It is shown that these oscillations of N , induce the formation of plateaus of the Hall resistivity exy with the exact quantization in h/ie2 and vanishing values of the resistivity exx, when the Fermi energy is between Landau levels. The model developed in the triangular well approximation accounts well for the width and shape of the Hall steps and for the eXx behaviour in a magnetic field, in a large range of temperatures.Nous supposons que, dans les heterojonctions a modulation de dopage, le gaz d'electron bidimensionnel est a l'equilibre thermodynamique avec un reservoir exterieur. En presence d'un champ magnetique quantifiant, des "gaps" d'energie apparaissent dans la densite d'etats de ce systeme 2D. Ceci provoque, lorsque le champ magnetique B croit, des oscillations de la densite N , d'electrons libres 2D, ii cause du transfert d'electron dans (et hors de) ce reservoir. Nous montrons que ces oscillations de N , induisent, lorsque I'energie de Fermi est entre deux niveaux de Landau, dune part la formation de plateaux de la resistivite de Hall exy presentant la quantification exacte en h/ie2 et d'autre part des zones dans lequelles la resistivite exx tend vers zero. Le modele developpe dans I'approximation du puits triangulaire rend bien compte, dans une large gamme de temperatures, de la largeur et de la forme des "marches" de Hall ainsi que de la variation de ex, en fonction du champ magnetique.

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We develop a theoretical model of charge equilibrium in modulation-doped GaAlAs/GaAs heterojunctions in which the presence of donor-like interface states is considered. Assuming that the electrons occupy the first and second electronic subbands we calculate the charge transfer in the heterojunction as a function of the temperature, taking into account the metastable character of the Si donors in the GaAlAs-doped layer. We show that interface states, the density of which depends on the growth process and on the sample quality, play an important role in the temperature dependence of the charge equilibrium and allow us to explain the variation of the density of the 2D electrons with the temperature. On this basis we investigate in detail the scattering mechanisms, in order to account for the mobility limitation in the low-temperature range (T < 10 K). In this case too the role of interface states is found to be crucial. All the calculations are performed within the generalized variational subband wavefunction model.

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