Tight-binding and k·p models for the electronic structure of Ga(In)NAs and related alloys

Abstract

We review how the tight-binding method provides a particularly useful approach to understand the electronic structure of GaInNAs alloys, and use it to derive a modified k•p model for the electronic structure of GaInNAs heterostructures. Using the tight-binding model, we first confirm that N forms a resonant defect level above the conduction band edge in Ga(In)As. We show that the interaction of the resonant N level with the conduction band edge accounts for the strong bandgap bowing observed in GaInN x As 1−x , in agreement with experimental analysis but contrary to some theoretical interpretations. We then use a Green function model to derive explicitly the two-level band-anti-crossing model describing the interaction between the resonant states and the conduction band edge in ordered Ga(In)N x As 1−x . We extend the Green function model to show that the conventional k•p model must be modified to include two extra spin-degenerate nitrogen states, giving a 10-band k•p model to describe the band structure of GaNAs/GaAs and related heterostructures. We describe how this 10-band model provides excellent quantitative agreement with a wide range of experimental data and finally discuss briefly the effects of disorder on the electronic structure in dilute nitride alloys.

Band anticrossing in dilute nitrides

“…32,33 It has been argued that the conventional k·p model must be modified to include two extra spin-degenerate nitrogen states as to use ten bands to describe the electronic band structure of GaNAs/GaAs and related heterostructures. In addition, detailed studies on the nearest-neighbor environment of the substitutional N atoms in…”

Photoluminescence spectroscopy of bandgap reduction in dilute InNAs alloys

“…However, PL still has to be interpreted with caution, since at low temperatures it can originate from the tail of localized states at the band edge associated with any disorder in the alloy. 15 The InNAs epilayers were coherently grown to a thickness of 300 nm on InAs͑001͒ substrates by MBE using a turbopumped Vacuum Generators V80 system equipped with an Oxford Applied Research ͑OAR͒ HD25 rf plasma nitrogen source. The samples were all grown with a substrate temperature of 375°C.…”

“…3. The change in the effective N level due to the increased concentration of N pairs with increasing x content is accounted for by E N ͑x͒ = E N0 − ␥x, 15 where E N 0 = 1.48 eV is the isolated N resonant state and ␥ = 2.00 eV. 20 The parameters for the k·p Hamiltonian were determined by fitting the resulting E ± subbands to the tight binding band structure of InN x As 1−x .…”

Electron dynamics in InNxSb1−x

“…The interaction of the extended ⌫ states of the conduction band of the host semiconductor with the localized N-induced resonant states results in the formation of two nonparabolic subbands E Ϫ and E ϩ whose dispersion is modeled using a modified k"p Hamiltonian. 4 The E Ϫ band has mainly conduction band-like character, whereas the E ϩ subband is due to the E N -like states. The parameters for the modified k"p Hamiltonian have been determined by fitting the resulting E Ϯ subbands to the tight binding band structure of InN x Sb 1Ϫx .…”

“…Details of the tight binding calculation can be found in Ref. 4 and references therein. The dispersion of the E Ϯ subbands can be determined by finding the eigenvalues of the 2ϫ2 determinant…”