Asymmetric tilt boundaries and generalized heteroepitaxy

In conventional heteroepitaxy, lattice mismatch is accommodated through biaxial strain and interfacial misfit dislocations. In studies of the heterophase boundaries appearing in semicoherent α-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ precipitates grown in situ in a silicon matrix, we have found that part of the lattice mismatch can be accommodated by formation of low-energy asymmetric tilt boundaries, which accommodate the lattice mismatch without producing a long-range stress field. This result suggests that growth of misfit-dislocation–free lattice-mismatched tilted structures should be possible.