**3. Experimental methodology**

a face‐centered cubic‐type *abc* stacking. Taking into account the periodic spacing of both the cation and anion layers, the structure repeats itself after six oxygen layers and six double layers of Al3+ cation (= 0.1299 nm) [28]. Therefore, the step height between the *A* and *B* oxygen stacking is equal to 0.217 nm as the monolayer step (**Figure 2(b)**). Moreover, no such opposing in‐plane rotational geometry can be deduced from the successive Al hexagon layers in contrast to that of the distorted oxygen hexagons, suggesting that the origin of SAGB comes

**Figure 2.** (a) Schematic of distorted oxygen hexagon layers in *A* and *B* stacking. (b) Side view of the *A* and *B* oxygen stacking showing the one monolayer step height. (c) Adaptation of the Thompson's notation to identify the rotation of the distorted oxygen hexagons. (d) Identification of rotation of distorted hexagons from *A* and *B* oxygen stacking layer.

To confirm this hypothesis, the AlN epilayer was grown directly on thermally cleaned sapphire substrate, which is having a monolayer step‐and‐terrace structure. The AlN growth temperature was 1285°C and the AlN thickness was about 0.9 μm. The atomic force micro‐ scopy (AFM) surface morphology of AlN (**Figure 3(a)**) indicates step‐and‐terrace structure which replicates the surface of thermally cleaned sapphire substrate. The x‐ray diffraction

**Figure 3.** (a) AFM surface morphology of AlN grown directly on thermally annealed sapphire substrate (*T*g = 1285°C). (b) (10‐12) XRD *φ*‐scan of AlN showing twin peaks which correspond to two AlN grains rotated in the in‐plane. The

(11‐23) phi‐scan of the sapphire substrate is also shown.

from the oxygen‐terminated surface of sapphire substrate.

46 Study of Grain Boundary Character

The AlN epilayers were grown on (0001) sapphire substrate by metal‐organic vapor phase epitaxy. Trimethylaluminum (TMA) and NH3 were used as source precursors for Al and N, respectively, while H2 was used as the carrier gas. The total reactor pressure was kept at ∼12 Torr. During the LT‐AlN BL growth, the NH3 and TMA flowrates were set to 1000 and 55 sccm, respectively; while, during HT‐AlN growth, the NH3 and TMA flowrates were set to 130 and 45 sccm, respectively. To study the influence of substrate's surface on the structural as well as optical quality of AlN, the temperature profiles depicted in **Figure 4** (*Profile a* and *Profile b*) were employed. For AlN growth under *Profile a*, the substrate thermal cleaning was introduced for 10 min under H2 ambient at the same optimized growth temperature for HT‐ AlN (*T*g =1285°C). Then the temperature was lowered to 1100°C for the growth of ∼15‐nm‐ thick LT‐AlN BL. The temperature was then increased to 1285°C for the growth of ∼1‐μm‐ thick HT‐AlN. For growth under *Profile b*, thermal cleaning was not introduced. Rather, the temperature was immediately brought to the desired BL *T*<sup>g</sup> (800‐1100°C) for the growth of ∼15‐nm‐thick LT‐AlN BL. Then the temperature was increased to *T*<sup>g</sup> = 1285°C for HT‐AlN growth. In the experiment, all temperature readings are from those indicated by the thermocouple placed near the substrate. Note that although both profiles incorporate LT‐AlN BL, the timing, hence, the substrate's surface structure at which the LT‐AlN BL is introduced is quite different, which is crucial forthe formation/elimination of small‐angle grain boundary. For analyses, atomic force microscopy (AFM) measurements were conducted to study the surface morphologies both of the substrate's surface and AlN epilayer, while XRD and transmission electron microscope (TEM) measurements were conducted to study the structural qualities and to assess the SAGB. CL measurements were conducted to study the optical properties of AlN.

**Figure 4.** Temperature profiles for two‐step growth of AlN on sapphire substrate. *Profile a* incorporates thermal clean‐ ing, while *Profile b* incorporates no thermal cleaning.
