Manganese 3$\times$3 and $\sqrt{3}\times \sqrt{3}$-$R{30}^{\circ }$ structures and structural phase transition on $w$-GaN(000$\overline{1}$) studied by scanning tunneling microscopy and first-principles theory

Manganese deposited on the N-polar face of wurtzite gallium nitride [GaN (000$\overline{1}$)] results in two unique surface reconstructions, depending on the deposition temperature. At lower temperature (less than 105${}^{\circ }$C), it is found that a metastable $3\times 3$ structure forms. Mild annealing of this Mn $3\times 3$ structure leads to an irreversible phase transition to a different, much more stable $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ structure which can withstand high-temperature annealing. Scanning tunneling microscopy (STM) and reflection high-energy electron diffraction data are compared with results from first-principles theoretical calculations. Theory finds a lowest-energy model for the $3\times 3$ structure consisting of Mn trimers bonded to the Ga adlayer atoms but not with N atoms. The lowest-energy model for the more stable $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ structure involves Mn atoms substituting for Ga within the Ga adlayer and thus bonding with N atoms. Tersoff-Hamman simulations of the resulting lowest-energy structural models are found to be in very good agreement with the experimental STM images.

Figure 1

RHEED patterns. (a) and (b) GaN after growth, annealing, and cooling to room temperature; (c) and (d) after Mn deposition at 90${}^{\circ }$C showing $3\times 3$ with 3$\times$ along both azimuths; (e) and (f) after annealing $3\times 3$ structure surface to 250${}^{\circ }$C showing $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ structure having 3$\times$ along [1$\overline{1}$00] but only 1$\times$ along [11$\overline{2}$0]; (g), (h) patterns for sample with more complete $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ coverage. Streak orders are labeled on the images.

Figure 2

STM image of Mn $3\times 3$ structure. Atomic rows are along $\langle$11$\overline{2}$0$\rangle$ ($V_s=-1.03$ V, $I_t=$ 63 pA). Inset: Zoom-in STM image taken from the same scan area but with a sharper tip, revealing a more complex structure ($V_s=-1.21$ V, $I_t=$ 63 pA).

Figure 3

High resolution STM image (shown in derivative mode) revealing clearly a trimer structure at each lattice site ($V_s=-1.21$ V, $I_t=$ 63 pA); a $3\times 3$ lattice is overlaid on top of the image, along with several envisioned trimer units.

Figure 4

Scan mode RHEED images as a function of time and temperature (increasing from top to bottom): (a) along [1$\overline{1}$00]; (b) along [11$\overline{2}$0]. Mn is deposited, and a $3\times 3$ pattern is formed; heating then begins, and the pattern begins to change towards $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$. Streak orders are labeled. Black dotted lines indicate no change in RHEED spacing during the entire process. Streak spacings along [1$\overline{1}$00] and [11$\overline{2}$0] have been set equal, but should be in the ratio $\sqrt{3}$:1.

Figure 5

(a) Large-area STM image of $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ surface. Terraces separated by a double-bilayer $w$-GaN(000$\overline{1}$) step; the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ structure is maintained across the step ($V_s=-2.10$ V, $I_t=$ 90 pA.). (b) Zoom-in STM image revealing atomic resolution, corresponding to the dashed-boxed region in part (a) ($V_s=-1.73$ V, $I_t=$ 96 pA.); a $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ lattice is overlaid on the image. Image is displayed with a local area background subtraction.

Figure 6

Tighter zoom-in with more atomic resolution detail for the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ surface; atomic rows on opposite sides of a phase-shift boundary (indicated by jagged black line) are shifted by one third the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ row spacing. Atomic sites on opposite sides of the boundary are indicated with yellow or green dots, interface sites indicated with blue. Inset shows detail of the reconstruction symmetry with $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ lattice sites indicated in green.

Figure 7

Scan mode RHEED image of $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ structure as a function of time and temperature (top to bottom). Only first-order and $\frac{2}{3}$-order streaks are visible; $\frac{1}{3}$-order streaks can hardly be seen here.

Figure 8

Theoretical models of the $3\times 3$ structure formed by low-temperature Mn deposition. (a) Model showing Ga $1\times 1$ adlayer structure without the Mn atoms; the spacing between Ga adatoms is $a=$ 3.189 Å; (b) the $3\times 3$ unit cell with atoms placed at 3$\times$ $a$ spacing. In (c)–(h), the models depicted on the left correspond to single or trimer Mn adatoms located at T4 sites, while the models on the right correspond to adatoms located at H3 sites. In particular, (c) and (d) correspond to single adatoms, (e) and (f) to trimer adatoms with one Ga atom at the center of the trimer, while (g) and (h) represent trimer models with a hollow site at the center.

Figure 9

Energy plots for the various $3\times 3$ models depicted in Fig. 8. The dashed lines correspond to the $3\times 3$ structure with single Mn adatoms. The solid colored lines correspond to the $3\times 3$ models with trimer Mn adatoms. In the trimer models, both T4 and H3 can have the trimer either with a central Ga atom or without it (hollow), as indicated in the legend. The reference structure is the T4 single Mn model.

Figure 10

The energetically stable model for the H3 Mn trimer $3\times 3$, after relaxation. (a) Top-view image, revealing the various lateral displacements of Ga atom positions due to the Mn trimer; (b) side-view image, showing the bond canting of Ga-N bonds away from the [000$\overline{1}$] surface normal direction, enabling Mn to settle into the surface. Mn atoms are bonded only with Ga atoms and not with N.

Figure 11

STM image (left) and T-H simulation (right) of the stable H3 Mn trimer-hollow structure. (a) Occupied-states STM image ($V_s=-1.21$ V, $I_t=$ 63 pA), with an overlay of the relaxed H3 trimer-hollow model. Bright protrusions correspond to Mn trimers; (b) occupied-states T-H simulated image with an overlay of the H3 trimer-hollow model. The Mn trimers correspond to the bright lobes. STM image in (a) shown in derivative mode, except for lower left two unit cells which are shown in topography mode (blue boxed region).

Figure 12

Structural models considered for the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$. (a) Ga $1\times 1$ adlayer structure without Mn atoms. (b), (c), and (e) depict structural models with Mn atoms in the substitutional, T4 adatom, and H3 adatom sites, respectively. (d) and (f) correspond to the substitutional $+$ T4 and substitutional $+$ H3 models, respectively.

Figure 13

Energy plots versus Ga chemical potential for the theoretical models considered for the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$ as shown in Fig 12. The substitutional $+$ T4 model is found to be lowest in energy over most of the range of Ga chemical potential considered, and it is chosen as the reference structure.

Figure 14

Top and side views of the final relaxed substitutional $+$ T4 model for the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$. The color coding of the atoms is the same as Fig. 10. (a) Top view of substitutional $+$ T4 structure, in which atomic displacement results in an effective 30${}^{\circ }$ rotation of the Ga adlayer sublattice; (b) side-view model revealing clearly the bonding between Mn and N as well as the Ga-N bonds tilting away from [000$\overline{1}$]. The Mn-N bonds are also tilted away from [000$\overline{1}$], but in the direction of [1$\overline{1}$00].

Figure 15

Comparison of occupied-states STM image ($V_s=-1.73$ V, $I_t=$ 96 pA.) with T-H occupied-states simulation for the $\sqrt{3}\times \sqrt{3}-R{30}^{\circ }$. The substitutional $+$ T4 model structure is overlaid onto both the STM image and the T-H simulation, showing clearly that Mn atoms correspond to depression sites in the image. Whereas, the protrusions seen in the occupied-states STM image correspond to the locations of the Ga adatoms.

Figure 16

Energy plots for structures with different periodicity and Mn coverage. For all cases, the T4 and H3 models are considered, but only the lowest-energy one is pictured. In the legend, the models are stated and the Mn coverage is indicated between parentheses. The reference structure is the T4 single Mn model.