Strain Relaxation in Misfitting Transition Metal Dichalcogenide Monolayer Superlattices: Wrinkling vs Misfit Dislocation Formation

Two-dimensional (2D) superlattices composed of chemically heterogeneous transition-metal dichalcogenides (TMDs) have been proposed as key components in next-generation optoelectronic devices. For potential applications, coherent, defect-free compositional interfaces are usually required. In this paper, a combination of scaling theory and numerical analysis is employed to investigate strain relaxation mechanisms in misfitting, chemically heterogeneous TMDs. We demonstrate that, in free-standing superlattices, wrinkling of the monolayer is asymptotically preferred over misfit dislocation formation in both binary and ternary superlattices. For substrate-supported monolayers, however, misfit dislocation formation is thermodynamically favored above a critical superlattice width, implying the presence of an upper limit to the thermodynamic stability of coherent, misfitting 2D superlattices. Finally, it is shown numerically that the critical superlattice width is only weakly dependent on the misfit.