Metallicity of InN and GaN surfaces exposed to NH${}_3$

A systematic study of energies and structures of InN and GaN (0001) surfaces exposed to NH${}_3$ and its decomposition products was performed with first-principles methods. A phenomenological model including electron counting contributions is developed based on calculated DFT energies and is used to identify low-energy structures. These predictions are checked with additional DFT calculations. The equilibrium phase diagrams are found to contain structures that violate the electron counting rule. Densities of states for these structures indicate $n$-type conductivity, consistent with available experimental results.

Figure 1

(a) A schematic drawing of a (2 $\times$ 2) surface unit cell with different binding sites. The grey circles represent In (Ga) atoms and the white ones represent N. Differences in the binding energies between the structures predicted with the phenomenological model ($BE$${}_{\mathrm{model}}$) and calculated using DFT ($BE$${}_{\mathrm{DFT}}$) plotted against the predicted values for (b) GaN and (c) InN. Configurations used to fit the model parameters and some of those predicted by it are represented by full and empty squares, respectively.

Figure 2

The T $=$ 0 K formation energies of various configurations on the (a) GaN and (b) InN (0001) surface as a function of the In and Ga chemical potentials, respectively, at ${\mu }_{{\mathrm{NH}}_3}$ $=$ ${\mu }_{{\mathrm{NH}}_3}^{\mathrm{mol}}$. The energies are expressed in eV per ($1\times 1$) cell to include In(Ga) bilayers with a ($\sqrt{3}\times \sqrt{3}$) periodicity.[35] The labels describe the adsorbates and the corresponding binding sites (in parentheses).

Figure 3

The calculated phase diagrams of (a) GaN and (b) InN (0001) surfaces as a function of the Ga and In chemical potentials, respectively, and NH${}_3$. The labels describe the adsorbates and their corresponding binding sites (in parentheses). The axis on the right shows temperature corresponding to the NH${}_3$ chemical potential on the phase diagram and pressure of 1 bar. The dashed lines mark the values of enthalpy of formation at standard conditions.

Figure 4

Density of states plots for (a) bulk InN, (b) bare (relaxed) surface, (c) the NH${}_3$ $+$ 3NH${}_2$ configuration, and (d) the 2NH${}_3$ $+$ 2NH${}_2$ configuration, all using HSE functional. The insets show the regions close to the Fermi level (dashed lines) for each structure. The valence-band maxima are aligned at 0 eV.