Over the past few years, Transition Metal Dichalgogenide (TMDC) materials have shown great potentials for next generation nanoelectronic applications. Both monolayers and van der Waals (vdW) heterostructures drawn from them have shown really interesting electronic and optoelectronic properties [1][2]. The electronic structure and properties of these materials can be significantly influenced by the number of material layers involved and van der Waals interaction between the layers of TMDC. Recent advancement in processing technology has allowed the controlled growth of vdW heterostructures by stacking and their successful integration in electronic device applications for low power electronics. Effects of intercalation of a 2D TMDC sheet in between two monolayers of MoS₂ have been shown in recent literature [1]. In this work, we have provided a detailed simulation study of the effects of biaxial strain on electronic properties like bandgap and carrier effective mass in the conduction band of vdW intercalated trilayers (MoS₂/MX₂/MoS₂ where, M=Mo/W and X=Se/S) from first principle simulation. We provide simulation results of three different stacking configurations: AAA, ABA and ACA as shown in fig. 1.

The simulation was carried out using PWSCF package of Quantum Espresso [3] simulation tool. After geometry optimization and relaxation of different stacking configurations, self-consistent field (SCF) calculation was done to determine electronic configuration for the relaxed atomic structure followed by bandstructure calculation using the same package. We used normconserving pseudopotenial functions in our simulation framework and 24x24x1 Monkhorst-Pack k-point grids for sampling in the brillouin zone. After extracted of geometrically relaxed structure, biaxial strain was applied to the lattice and the effects on band structure and carrier effective mass were observed. The carrier effective mass at the brillouin zone symmetry points was calculated by simple parabolic fitting to the extracted ab-initio band structure. At first, we performed structural geometry optimization for ABA and ACA stacking configurations. We extracted the optimized values of lattice constant and interlayer separation. Our extracted results showed good agreement with the values reported in [1].

Fig 2. Shows the effect of variation of electron effective mass at K point in the brillouin zone for the simulated lattice structure under strain. The figure reveals lowering of effective mass at K points in the brillouin zone as we move from compressive to tensile strain regime. It is also seen that, for stacking configuration AAA in all three lattice structures, the simulation reveals a slightly lower carrier effective mass at K point for high compressive strain. However, as we move towards tensile strain regime, the stacking configurations reveal almost similar effective masses at K point. The gradual lowering of carrier effective mass at K point in the Brillouin zone is consistent with the results reported in literature[4].

Fig.3 shows the effect of strain on bandgap of different stacking configurations of multilayer TMDC materials as extracted from simulation. In all three material structures used in this study, we see a gradual lowering of bandgap with strain and therefore a gradual shift from semiconducting to metallic properties which is consistent with the results reported in [5] for bilayer TMDC heterostructures. Of the three structures used in this study, MoS₂/WSe₂/MoS₂ shows the lowest bandgap and therefore the quickest transition to metallic state under tesile strain as seen from fig. 3(c). As observed from our simulation results, at unstrained condition, MoS₂/WSe₂/MoS₂ trilayer showed a direct bandgap for all three stacking configurations. On the other hand, unstrained MoS₂/MoSe₂/MoS₂ and MoS₂/WS₂/MoS2  trilayers showed indirect bandgap for all three stackings. The AAA stacking configuration is observed to be showing the lowest bandgap when compressive strain is being applied to the lattice.   

Some results extracted from our simulation for unstrained lattice configuration is listed below:

Lattice	Stacking	Lattice Constant(A0)	Bandgap, Eg(eV)	Effective mass,mK(m0)
	AAA	3.239	0.707	0.5035
MoS2/MoSe2/MoS2	ABA	3.24	0.729	0.5129
	ACA	3.238	0.752	0.5142
	AAA	3.186	1.293	0.5753
MoS2/WS2/MoS2	ABA	3.183	1.074	0.5886
	ACA	3.186	1.147	0.5877
	AAA	3.241	0.5035	0.5035
MoS2/WSe2/MoS2	ABA	3.237	0.542	0.5084
	ACA	3.243	0.562	0.5097

In this work, we have provided a detailed simulation results on the effects of intercalation on electronic properties of TMDC materials. The findings of this study would be helpful in modeilng electronic devices using these material structures.

References:

[1] Ning Lu, et al., Nanoscale 6.9 (2014): 4566-4571.

[2] Sheneve Z Butler., et al., ACS nano 7.4 (2013): 2898-2926.

[3] Paolo Giannozzi, et. al., Journal of Physics: Condensed Matter 21.39 (2009): 395502.

[4] Blanca Biel, et. al., Microelectronic Engineering 147 (2015): 302-305

[5] Ning Lu, et. al., Nanoscale 6.5 (2014): 2879-2886