Metastable atomic-ordered configurations for Al_1/2Ga_1/2N predicted by Monte-Carlo method based on first-principles calculations

Metastability of Aln/12Ga1-n/12N (n= 2-10: integer) with the 1-2 monolayer (ML) in-plane configuration towards the c [0001] direction has been demonstrated recently. To theoretically explain the existence of these metastable structures, relatively large calculation cells are needed. However, previous calculations were limited to the use of small calculation cell sizes to estimate the local potential depth (Delta sigma) of ordered Al1/2Ga1/2N models. In this work, we were able to evaluate large calculation cells based on the interaction energies between proximate Al atoms (delta EAl-Al) in AlGaN alloys. To do this, delta EAl-Al values were estimated by first-principles calculations (FPCs) using a (5a(1) x 5a(2) x 5c) cell. Next, a survey of the possible ordered configurations using various large calculation cell models was performed using the estimated delta EAl-Al values and the Monte-Carlo method. Then, various Delta sigma values were estimated by FPCs and compared with the configurations previously reported by other research groups. We found that the ordered configuration obtained from the (4a(1) x 2a(2) x 1c) calculation cell (C-42) has the lowest Delta sigma of -9.3 meV/cation and exhibited an in-plane configuration at the c(0001) plane having (-Al-Al-Ga-Ga-) and (-Al-Ga-) sequence arrangements observed along the m{1100} planes. Hence, we found consistencies between the morphology obtained from experiment and the shape of the primitive cell based on our numerical calculations.