Successes and failures of thek⋅pmethod: A direct assessment for GaAs/AlAs quantum structures

Abstract

The k⋅p method combined with the envelope-function approximation is the tool most commonly used to predict electronic properties of semiconductor quantum wells and superlattices. We test this approach by comparing band energies, dispersion, and wave functions for GaAs/AlAs superlattices and quantum wells as computed directly from a pseudopotential band structure and using eight-band k⋅p. To assure equivalent inputs, all parameters needed for the k⋅p treatment are extracted from calculated bulk GaAs and AlAs pseudopotential band structures. Except for large exchange splittings in the in-plane dispersion for thin superlattices, present in pseudopotential calculations but absent from the k⋅p results, we find generally good agreement for heterostructure hole bands within ∼200 meV of the GaAs valence-band maximum. There are systematic errors in band energies and dispersion for deeper hole bands (all other than hh1 and lh1) and significant qualitative and quantitative errors for the conduction bands. Errors for heterostructure conduction states which are derived from the zinc-blende Γ point diminish as length scales increase beyond ∼20 ML, while significant errors persist for L- and X-derived states.