Exchange-correlation induced energy-level shift in quantum wells with strain

The energy-level shift due to exchange-correlation effects for a quasi-two-dimensional InxGa1−xAs/InGaAsP quantum well systems is studied as a function of the sheet carrier density for different biaxial compressive strain. We have calculated the leading-order self-energy within the random-phase approximation, by solving a 4×4 Luttinger-Kohn Hamiltonian for the consideration of the valence-band nonparabolicity of strained layer. We have found that the correlation energy, as well as the exchange energy significantly contributes to the energy-level shifts and these shifts grow with the increases of the biaxial compressive strain and the sheet carrier density. Our calculations show that for the biaxial compressive strain of 0.47%–1.02% the negative shift ratios of the band-gap energy are about 3.9%–4.6% and 7%–8.4% at sheet carrier densities of ns=1×1012 cm−2 and ns=1×1013 cm−2, respectively.