Chemically ordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ alloys: Spontaneous formation of natural quantum wells

We combine transmission electron microscopy, high-resolution x-ray diffraction, cathodoluminescence, and photoluminescence experiments with first-principles calculations to study the formation, thermodynamic stability, structural, and optical properties of chemically ordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ alloys $(0<x<1)$. Our results reveal that group-III-nitride surfaces exhibit chemically highly sensitive adsorption sites at step edges and that these sites can be used to kinetically engineer chemically ordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ alloys. The ordered alloys have unique properties: (i) the band gap is redshifted up to $110\mathrm{meV}$ with respect to the disordered alloy of the same composition and (ii) the band gap reduction is caused by localization of the band edge wave functions in the GaN layer. Ordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ thus can be seen as a natural quantum well structure where electrons and holes are localized and confined in monolayer GaN quantum wells.

Figure 1

Model of a monatomic superlattice consisting of alternating AlN and GaN layers. Group-III atoms at $B2$ $\left(T1\right)$ sites form two (one) bonds with the N atoms in the layer below. Growth of ordered alloys may occur by preferential incorporation Al (Ga) at $B2$ $\left(T1\right)$ sites at the exposed facet, and by the lateral movement of this facet across the surface.

Figure 2

(a) and (b) Distribution of order domains in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ $(x=0.56)$ before and after annealing at high temperature and high pressure. Cross-sectional transmission electron dark-field images are taken with order-sensitive 0001 reflection under dark-field conditions [the corresponding electron diffraction patterns are shown in (c) and (d), respectively]. (a) Order domains in the as-grown samples appear bright. Dark areas are disordered regions. Clear 0001 spots can be seen in the electron diffraction pattern taken along $1\overline{1}00$. (b) No order is present after annealing, as indicated by the absence of the respective order spots in the electron diffraction.

Figure 3

(Color online) Photoluminescence (PL) and cathodoluminescence (CL) data of ordered and disordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ samples. (a) Transmission electron microscopy cathodoluminescence spectra taken at $90K$ of ordered (as-grown) and disordered (annealed) samples under identical excitation conditions. The CL peak of the ordered sample is redshifted but has an increased full width at half maximum. (b) CL peak position of ordered and disordered samples throughout the whole range of Al concentration. The redshift of ordered samples with respect to the disordered ones is maximum for an Al fraction around $x=0.5$.

Figure 4

(Color online) Contour plots of the valence band states in ordered and disordered ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ $(x=0.5)$. (a) For the $1\times 1$ ordered structure a strong localization of the valance band state at N atoms bound to three Ga atoms (i.e., in the GaN layer) can be seen. (b) For the disordered sample the wave function is no longer confined to the GaN layer and thus more delocalized.