Noncontact atomic force microscopy and density functional theory studies of the $\left(2\times 2\right)$ reconstructions of the polar AlN(0001) surface

Combined experimental and theoretical studies permit us to determine new protocols for growing by molecular beam epitaxy the technologically interesting N-rich aluminum nitride (AlN) surfaces. This is achieved by dosing the precursor gases at unusually low rates. With the help of calculated structures by using density functional theory and Boltzmann distribution of the reconstructed cells, we proposed to assign the measured surface obtained with a growth rate of 10 nm/h to a $\left(2\times 2\right)$ reconstructed surface involving one additional N atom per unit cell. These N-rich AlN surfaces could open new routes to dope AlN layers with important implications in high-power and temperature technological applications.

Figure 1

Top and side views along the [$1\overline{1}00$] axis of the atomic models of the three $\left(2\times 2\right)$ reconstructions, ${\mathrm{N}}_{\mathrm{ad}}$-H+Al-H, 3Al-H, and ${\mathrm{N}}_{\mathrm{ad}}$ obtained by DFT. The $\left(2\times 2\right)$ unit cell appears on the top views as a black lozenge. Al, N, and H atoms are represented as red, blue, and white balls, respectively.

Figure 2

NC-AFM topography image of AlN(0001) surface after growth of a 200-nm-thick sample at $T_{\mathrm{substrate}}=950{}^{\circ }\mathrm{C},{\mathrm{BEP}}_{{\mathrm{NH}}_3}={10}^{-5}$ Torr and a growth rate of 100 nm/h (a), and 5 nm thick at 10 nm/h (b). (c) Cross section along the dashed line in (b). NC-AFM parameters: (a) $A=5$ nm, $\mathrm{\Delta }f=-65$ Hz, $f_0=278.4$ kHz, $Q=35255,U_{\mathrm{sample}}=-4.7$ V; (b) $A=8$ nm, $\mathrm{\Delta }f=-25$ Hz, $f_0=274.8$ kHz, $Q=42780,U_{\mathrm{sample}}=-1$ V.

Figure 3

(a) Gibbs free energy of formation vs substrate temperature for the three reconstructions $\mathrm{IV}({\mathrm{N}}_{\mathrm{ad}}$-H+Al-H), V(3Al-H), and $\mathrm{VI}({\mathrm{N}}_{\mathrm{ad}}$) calculated with the experimental pressures $p_{{\mathrm{NH}}_3}=2\times {10}^{-6}$ Torr and $p_{\text{Al}}=3\times {10}^{-8}$ Torr, and $3\times {10}^{-9}$ Torr corresponding to the growth rate G1 and G2, respectively. (b) Occupation rate calculated with the Boltzmann distribution for the three reconstructions and the two sets of growth G1 and G2.

Figure 4

Phase diagrams with changing temperature: (a) $940{}^{\circ }\mathrm{C}$, (b) $990{}^{\circ }\mathrm{C}$, and (c) $1040{}^{\circ }\mathrm{C}$. The isoconcentration curves are blue, purple, and red for $c_i=0.5$, 0.7, and 0.9, respectively. The chemical potentials (${\mu }_{\mathrm{Al}},{\mu }_{\mathrm{H}}$) are plotted for three isopressures of $p_{\mathrm{Al}}$ (black dotted line) and $p_{{\mathrm{NH}}_3}$ (gray dashed line). The beginning and the end of the green arrows indicate the change in chemical potential when passing from G1 to G2 growth conditions.