The study of the stacking stability of bilayer MoS2 is essential since a bilayer has exhibited advantages over single layer MoS2 in many aspects for nanoelectronic applications. We explored the relative stability, optimal sliding path between different stacking orders of bilayer MoS2, and （especially） the effect of inter-layer stress, by combining first-principles density functional total energy calculations and the climbing-image nudge-elastic-band （CI-NEB） method. Among five typical stacking orders, which can be categorized into two kinds （I： AA＇, AB and II： AA＇, AB＇, A＇B）, we found that stacking orders with Mo and S superposing from both layers, such as AA＇ and AB, is more stable than the others. With smaller computational efforts than potential energy profile searching, we can study the effect of inter-layer stress on the stacking stability. Under isobaric condition, the sliding barrier increases by a few eV/（uc.GPa） from AA＇ to ABt, compared to 0.1 eV/（uc.GPa） from AB to [AB]. Moreover, we found that interlayer compressive stress can help enhance the transport properties of AA＇. This study can help understand why inter-layer stress by dielectric gating materials can be an effective means to improving MoS2 on nanoelectronic applications.
