Electronic Structure

Electronic Structure of Ga(In)NAs

Electronic Structure_Dilute_NitridesEnergy gap versus composition of GaNAs
GaInNAs has an anomalously large band gap bowing, markedly different to conventional semiconductors, and of interest both from a fundamental perspective and also because of its significant potential device applications. Our models explain this unusual behaviour [1], and confirm the potential of this novel material for GaAs-based lasers emitting at telecomm wavelengths [2].

Fig. 1 Variation of energy gap (lower curve) with composition in GaNxAs1-x.

Physics of GaInNAs band-gap bowing.
Because a N atom is very different to an As atom (40% smaller; much more electronegative), an isolated substitutional N atom introduces a resonant defect state in GaAs, at energy EN about 200 meV above the GaAs conduction band edge, Ec. The band-gap bowing in GaNxAs1-x is then explained in terms of a Band Anti-Crossing (BAC) interaction between the N resonant states and the conduction band edge. Our tight-binding calculations validate this unusual behaviour [1,3], and show that the conduction band dispersion in GaNxAs1-x is very well described in terms of interactions between a distribution of nitrogen resonant states and the host matrix (GaAs) conduction band.

 

The two-level BAC model treats all N defect states as being at the same energy. Using this 2-level model there is one significant set of experimental data which cannot be explained, namely the observed composition dependence of the conduction band edge (CBE) effective mass in Ga(In)NAs alloys. The BAC model predicts a smoothly varying enhancement of the CBE mass compared to GaAs. It provides a good estimate of the measured mass at very low N compositions (x < 0.05%), but significantly underestimates the mass in GaNxAs1-x for x > 0.1%, and fails to describe its non-monotonic behaviour. In Fig. 2 below, the filled data points are the experimental results, measured by Masia and co-workers at University of Rome "La Sapienza" [4,5]. The open data points were calculated including an accurate theoretical model for the full distribution of N defect levels. The results show that the unexpectedly large electron effective mass values observed in many GaNAs samples are due to hybridisation between the conduction band edge and nitrogen cluster states close to the band edge. Because the density of cluster states varies with energy, we predict and find a non-monotonic behaviour in the effective mass with hydrostatic pressure in many GaNAs samples. Based on this understanding of GaNAs band structure, we have been able to extend the model to treat a wide range of different dilute nitride alloys [5] and also to address the electronic structure of other extreme alloys such as Ga1-xBxAs [6].

LCINS effective mass vs composition for GaNAsFIG. 2: Measured values of the electron effective mass as a function of the N concentration. Several untreated (full circles) and H-irradiated (full diamonds) samples are considered. Error bars indicate the uncertainty on the mass values (in some case the uncertainty is within the symbol size). Open squares are the effective mass values calculated by the model of Ref. 3, the dotted line is a guide to the eye. An abscissa axis break at x=0.70% has been introduced for ease of comparison. .

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