Three-dimensional (3D) GaN is a III-V compound semiconductor with potential optoelectronic applications. In this paper, starting from 3D GaN in wurtzite and zinc-blende structures, we investigated the mechanical, electronic, and optical properties of the 2D single-layer honeycomb structure of GaN ($g-\mathrm{GaN}$) and its bilayer, trilayer, and multilayer van der Waals solids using density-functional theory. Based on high-temperature ab initio molecular-dynamics calculations, we first showed that $g-\mathrm{GaN}$ can remain stable at high temperature. Then we performed a comparative study to reveal how the physical properties vary with dimensionality. While 3D GaN is a direct-band-gap semiconductor, $g-\mathrm{GaN}$ in two dimensions has a relatively wider indirect band gap. Moreover, 2D $g-\mathrm{GaN}$ displays a higher Poisson ratio and slightly less charge transfer from cation to anion. In two dimensions, the optical-absorption spectra of 3D crystalline phases are modified dramatically, and their absorption onset energy is blueshifted. We also showed that the physical properties predicted for freestanding $g-\mathrm{GaN}$ are preserved when $g-\mathrm{GaN}$ is grown on metallic as well as semiconducting substrates. In particular, 3D layered blue phosphorus, being nearly lattice-matched to $g-\mathrm{GaN}$, is found to be an excellent substrate for growing $g-\mathrm{GaN}$. Bilayer, trilayer, and van der Waals crystals can be constructed by a special stacking sequence of $g-\mathrm{GaN}$, and they can display electronic and optical properties that can be controlled by the number of $g-\mathrm{GaN}$ layers. In particular, their fundamental band gap decreases and changes from indirect to direct with an increasing number of $g-\mathrm{GaN}$ layers.

• Received 2 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.085431