Hartree and exchange energy in populated semiconductor quantum wells

The relative importance of the various contributions entering the energy of an electron gas in a quantum well is estimated on the basis of a very simple model in Hartree-Fock approximation. The situation here studied corresponds to an uncompensated electron gas inside the well. Kinetic and electrostatic energy may then cancel each other for some characteristic value of the well thickness, thus enhancing the importance of exchange. The roles of inter versus intrasubband terms, of subband population and of subband structure are discussed.