A further source of disorder must be considered when analyzing the quaternary alloy, Ga1−yInyNxAs1−x. The nature of the isolated resonant state changes with local environment, depending on the average number of In and Ga atoms neighboring each N atom [42,43]. To investigate this variation, we took a number of 216-atom supercell structures, in which we constrained the central group V site to have a given number, m, ofindium nearest neighbors (m=0 to 4) [43], and then placed In atoms at random on the remaining sites to give an overall indium fraction of y=0.25.
We found, for the structures considered, that EN varies approximately linearly from EN=1.52 eV for four Ga neighbors to EN=1.75 eV for four In neighbors. The value of EN depends weakly on the atomic arrangement in the second shell of group III neighbors, but the calculated effect for a range of supercell calculations indicates that the atomic arrangement in the second shell only shifts EN by ~±0.021 eV, down by an order of magnitude on the effects of variations in the nearest-neighbor environment. The matrix element linking the N resonant state and the conduction band edge is calculated in the tight-binding method to vary between 2.00 x1/2 eV (for a structure where all N have four Ga neighbors) to 1.35 x1/2 eV (for a structure where all N have four In neighbors), with the conduction-band-edge energy, Ec, in the 2×2 matrix of Equation 3.1 then varying between 1.10 eV and 1.11 eV for the 216-atom supercells considered, and the band-gap between 0.95 eV and 1.04 eV as the number of In nearest neighbors m increases from 0 to 4. The average interaction in a larger unit cell containing a mixture of nearest-neighbor environments is then given by an appropriately weighted average of the above parameters. This justifies the construction of an effective two-band model to describe the variation of conduction-band-edge energy and energy gap in quaternary GaInNxAs1−x alloys, but the magnitude of the parameter β in the interaction term βx1/2 and the value of EN will vary, depending on the average N cation nearest-neighbor environment [25]. The experimentally observed blueshift in the energy gap of many GaInNAs samples with mild thermal annealing [25,39–41] can then be explained by local atomic rearrangements leading to an increase in the average number of In neighbors about each N atom [59–61].
ROSSANA HERNANDEZ
Electrónica del estado solido
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