B, Al, and Ga are trivalent cations with ionic radii in IV coordination of 0.11, 0.39, and 0.47 Angstrom, respectively. The presence of larger Al 3+ and Ga 3+ cations in the h-BN monolayers can be considered the origin of the observed out-of-plane protrusions. Consequently, doping in h-BN decreases the interlayer distance (see Table ). Moreover, B-N bond length in bulk h-BN (1.449 Å) is shorter than Al-N (Ga-N) bond of 1.857 Å (1.952 Å) in bulk h-AlN (bulk h-GaN). Table shows that bond length between Al/Ga and one of three N atoms in the h-BN plane is much shorter than the bond length along c-direction between Al/Ga and N of another h-BN layer. This suggests that in-plane Al/Ga-N bonds are stronger than out-of-plane Al/Ga-N bonds. To quantify the bond strength, we calculate the integrated crystal orbital Hamilton population (ICOHP), shown in Table . A more negative ICOHP means a stronger covalent bond. Indeed from the ICOHP, we find that the out-ofplane protrusion of the dopant facilitates a strong covalent bond between Al/Ga and N in the top layer. For example, ICOHP oop Al-N for protruded Al 0.125 B 0.875 N composition is -2.089 eV, which is much larger than that of flat structure, for which the computed ICOHP oop Al-N is -0.141 eV when Al is in the h-BN plane. As expected from the in-plane and out-of-plane bond length difference, the ICOHP for Al/Ga-N bonds in the plane are quite large (see Table ).