Quasi-two-dimensional electron gas at metallic densities

We consider the three-dimensional electron gas confined by a strictly two-dimensional homogeneous positive charge density at $z=0$. Within the Hartree-Fock approximation, we study the mode structure in the confined direction in the metallic regime. We find that for rₛ<1.3 (rₛ<2.5) the unpolarized (polarized) electron gas starts to populate also the first-excited state in the z direction.