Hexagonal AlN: Dimensional-crossover-driven band-gap transition

Motivated by a recent experiment that reported the successful synthesis of hexagonal $\left(h\right)$ AlN [Tsipas et al., Appl. Phys. Lett. 103, 251605 (2013)], we investigate structural, electronic, and vibrational properties of bulk, bilayer, and monolayer structures of $h$-AlN by using first-principles calculations. We show that the hexagonal phase of the bulk $h$-AlN is a stable direct-band-gap semiconductor. The calculated phonon spectrum displays a rigid-layer shear mode at $274 {\text{cm}}^{-1}$ and an $E_g$ mode at $703 {\text{cm}}^{-1}$, which are observable by Raman measurements. In addition, single-layer $h$-AlN is an indirect-band-gap semiconductor with a nonmagnetic ground state. For the bilayer structure, $A{A}^{\prime }$-type stacking is found to be the most favorable one, and interlayer interaction is strong. While $N$-layered $h$-AlN is an indirect-band-gap semiconductor for $N=1-9$, we predict that thicker structures $\left(N\ge 10\right)$ have a direct band gap at the $\Gamma$ point. The number-of-layer-dependent band-gap transitions in $h$-AlN is interesting in that it is significantly different from the indirect-to-direct crossover obtained in the transition-metal dichalcogenides.

Figure 1

Top and tilted-side views of atomic structures of bulk (a) wurtzite and (b) hexagonal AlN (top panel), and their electronic band dispersion (lower panel).

Figure 2

Phonon dispersion of bulk $h$-AlN.

Figure 3

Monolayer $h$-AlN band diagram within PBE and HSE06 (left panel), partial density of states (middle panel), and the band decomposed charge densities of the band edges (right panel). Sections of 3D charge density that represent the connection to the neighboring cells are filled with blue color.

Figure 4

(a) Possible stackings between two layers of $h$-AlN. (b) Layer-layer interaction energy for different stackings. (c) Interlayer-spacing-dependent band dispersion of $A{A}^{\prime }$ stacked two layers of $h$-AlN.

Figure 5

Evolution of electronic band dispersion of $N$-layer $h$-AlN.

Figure 6

The evolution of the bonding charge density of $h$-AlN for monolayer, bilayer, 3-layer, 8-layer, and 15-layer. Sections of 3D charge density that represent the connection to the neighboring cells are filled with blue color.