DFT study of elastic stiffening, frictional forces, and Raman spectroscopy*

Atomic-force microscopy (AFM) on 2D materials typically shows a reduction in frictional forces as the number of layers increases. This is because the forces are mostly due to out-of-plane surface deformation by the tip (i.e. puckering); adding more layers stiffens the surface and reduces puckering. However, Re-doped MoS₂ has an increase in friction with number of layers (see abstract of Baykara et al.; arXiv:2007.05805). We explain these observations by showing with DFT that Re dopants intercalated between MoS₂ layers significantly increase the out-of-plane elastic modulus, which decreases the puckering effect for a given number of layers. This stiffening effect is diluted as the number of layers increases, because when the Re concentration is low, most regions probed by the AFM have only one dopant. The experiments cannot be explained by a simpler picture involving just an unpuckered surface, because the friction actually decreases with number of layers (saturating after four). Experimental Raman spectra are more consistent with calculations for Re tetrahedrally intercalated as opposed to substituting for Mo (which leads to a much weaker stiffening effect). These results provide a framework for understanding the effects of chemical doping on the mechanics of 2D materials.