GaAs quantum structures: Comparison between direct pseudopotential and single-band truncated-crystal calculations

Abstract

A single-band approach for semiconductor clusters which accounts for the nonparabolicity of the energy bands was recently used by Rama Krishna and Friesner [M.V. Rama Krishna and R.A. Friesner, Phys. Rev. Lett. 67, 629 (1991)]. We compare the results of this method (denoted here as single-band truncated-crystal, or SBTC, approximation) with a direct pseudopotential band-structure calculation for free-standing hydrogen-passivated GaAs quantum films, wires, and dots. The direct pseudopotential calculation, which includes coupling between all bands, shows that isolated GaAs quantum films, wires, and dots have an indirect band gap for thicknesses below 16, 28, and at least 30 Å (8, 14, and at least 15 ML), respectively; beyond these critical dimensions the transition becomes direct. A comparison of the SBTC approximation with the direct pseudopotential calculation shows that (i) the confinement energy of the valence-band maximum is overestimated by the SBTC method, because the zero-confinement character of this state is neglected; (ii) the confinement energy of the Γ-derived conduction state (direct band gap) is slightly overestimated by the SBTC approximation, mainly because of the assumption of infinite potential barriers at the boundaries; (iii) the confinement energy of the X-derived conduction state (indirect band gap) is severely underestimated by the SBTC method; (iv) while the SBTC approximation predicts ‘‘quantum deconfinement’’ (i.e., reduction of gap as size is reduced) for the direct gap of thin GaAs quantum wires, such effect is not present in the direct pseudopotential calculation.