Many-body carrier interaction effects in quantum wells

Many-body carrier interaction effects shift the ground- and excited-state subband energy levels of quantum wells. We derive carrier-carrier Coulomb exchange and direct interaction energies as a function of carrier density, quantum well composition, and well width. For values of these parameters of physical interest, the excited-state exchange energy is small compared to the ground-state exchange energy. Our expressions for the ground- and excited-state direct interactions yield considerably smaller energy values than those reported by previous investigators. This is due to the fact that in our derivations we differentiate between quantum well width, carrier doping width, and ground- and excited-state wave function effective confinement lengths. Direct interaction energies increase linearly with carrier density, and for large carrier densities substantially negate exchange interaction effects. We illustrate carrier-carrier interaction effects for the heavy-hole subband of electrically neutral, p-type, isolated strained-layer ${\mathrm{Ge}}_{\mathrm{x}}$ ${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ /Si quantum wells.