Direct evidence of 8:9 commensurate heterojunction formed between InN and AlN on c plane

We show that, despite a large difference in lattice constants, high-quality $\mathrm{In}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ heterostructures can be formed on Si(111) due to the existence of “magic” ratios between the lattice constants of comprising material pairs: 2:1 $(\mathrm{Si}∕{\mathrm{Si}}_3{\mathrm{N}}_4)$ , 5:4 $(\mathrm{Al}\mathrm{N}∕\mathrm{Si})$ , and 8:9 $(\mathrm{In}\mathrm{N}∕\mathrm{Al}\mathrm{N})$ . For InN growth on AlN with nitrogen polarity, by using reflection high-energy electron diffraction and cross-sectional transmission electron microscopy, we have found that the pseudomorphic to commensurate lattice transition occurs within the first monolayer of growth, resulting in an abrupt heterojunction at the atomic scale. This new route of lattice match allows the formation of commensurate and nearly strain-free interface with a common two-dimensional superlattice.