domingo, 25 de julio de 2010

Local N-Environment and Fine Structure of the Band Gap

In the following, we will focus on the rearrangement of the local N environment. In many samples grown by MOVPE or MBE, there are indications of changes of the local N environment from a configuration with four Ga nearest neighbors (nn) to configurations with more In nns . This change of the local N environment can be detected by changes of the local vibrational modes of N in (Ga,In)(N,As) in Raman or infraredabsorption spectra . Very convincing evidence for such changes is obtained by Raman spectroscopy close to the E+ resonance with excitation energies of 2.18 eV  and 1.92 eV or by infrared absorption. Recently, these findings were also confirmed by X-ray absorption spectroscopy. It is worth mentioning that under certain growth and annealing conditions, there do not seem to be significant changes of the nn environment of N in (Ga,In)(N,As), i.e., the four-Ga environment dominates even after annealing .

To reach a better understanding of the effect of the nitrogen nn environment on the band structure of Ga1−yInyNxAs1−x, full sp3s* tight-binding supercell calculations have been performed, in which the central group V site was constrained to have a given number m (=0 to 4) of In nns. In atoms were placed at random on the remaining sites to give the desired overall y. The Hamiltonian was written as H1=H0+ΔH, where H0 is the Hamiltonian for (Ga,In)As, and ΔH is the change due to N incorporation. Pairs of supercells H0 and H1 were defined by placing As and N, respec-tively, onto the central group V site. Calculating separately the wavefunctions ψc0 and ψc1 for H0 and H1, one canderive a nitrogen resonant level wavefunction ψN. This allows one to relate the supercell calculations to the simple level repulsion model by VNc=<ψN |H1|ψc0>, EN=<ψN|H1|ψN>, and Ec=<ψc0|H1|ψc0>. Details of the model are given in Refs. [17,25] and Chapter 3 of this volume. These results are corroborated by other
theoretical models.

For each y, the EN for the five nn configurations are equally spaced with the value for four-Ga nns being always about 220 meV lower than that of four-In nns. Such strong dependence of the energy of isolated, strongly localized impurities on the nn environment is common. Calculations, where the atomic arrangement in the second group III shell and higher shells was altered, only shift EN by ±20 meV. This agrees with experiments on Ga(As,P):N, where a broadening of 30 meV of the localized N state is observed due to disorder on the group V sublattice. The derived matrix element VNc linking the N resonant state and the conduction band edge varies between about 2.00 eV·x1/2 for four- Ga nns to about 1.35 eV·x1/2 for four-In nns, i.e., the strength of the perturbation of the crystal decreases with increasing number of In nns. The large differences of the five nn environments of N are also reflected in the derived conduction-band-edge energies E−. For each y at x=1%, the E− values for the five nn configurations are evenly spread over an energy range of about 80 meV below the corresponding unperturbed Ec of (Ga,In)As, with that for fourGa nns being lowest in energy.
                                                 ROSSANA HERNANDEZ
                                       ELECTRONICA DEL ESTADO SOLIDO

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