Engineering 2D Material Properties
using Strain

Strain in a crystal changes the bond strengths between atoms and therefore modulates various properties arising from the periodic crystalline structures, such as electronic band structures, phonon band structures, and spin state splitting. Strain has been implemented into CMOS technology since the mid-2000s to enhance the performances of silicon FETs and continue the path of Moore's law. Strain engineering is so powerful that typical CMOS technology benefits 10s-of % performance enhancement from merely ≈1 % of strain. 

Unlike silicon or traditional semiconductors, 2D materials are composed of atomic layers weakly held together by van der Waals (vdW) force. The layered structure allows 2DMs to withstand an extreme (10+ %) level of mechanical strain without breaking covalent bonds, making them an optimal system for strain engineering. For instance, strain in the in-plane direction can easily modulate 100s-of meV of bandgap in monolayer transition metal dichalcogenides (TMDCs). Moreover, strains applied to 2D system in the out-of-plane direction modulate the vdW interaction between the 2DM and the substrate or between different 2D atomic layers. Since the vdW bond is orders of magnitude weaker than the in-plane covalent bonds, the out-of-plane strain is far more efficient in modulating the 2D materials and heterostructures' properties. 

Strain can be controllably applied to 2DMs using various approaches. In-plane strain is widely applied by bending or stretching a flexible substrate on which 2D materials are placed. Placing 2D materials on a topographically uneven substrate also produces spatially-predefined strain to the atomic layer. Although being less controllable, changing the temperature of 2D materials-substrate stacks results in in-plane strain due to the thermal expansion coefficient mismatch. Out-of-plane strain can be applied using a diamond anvil cell (DAC) apparatus, where two diamond anvils compress the sample in all directions (i.e., applying hydrostatic pressure). Optical measurements such as photoluminescence spectroscopy, Raman spectroscopy, and X-ray diffraction spectroscopy, as well as electrical conductivity measurements, can be carried out to characterize in situ strain-dependent material properties.

Electronic and optical bandgaps of 2D semiconductors can be engineered by 100s of meV by applying strain. Especially, out-of-plane compressive strain component is very effective in modulating physical properties, as the interlayer interaction can be greatly enhanced. A clear example of the enhanced interlayer interaction is the contrast in strain-dependent bandgap between multi-layer (bandgap decreases with strain) and monolayer (bandgap increases with strain) MoS2. 

Moreover, different 2D semiconductors with different elemental composition exhibit different strain-dependent bandgap modulation with strain. Not just the strain, but also the valence band maxima (VBM) and conduction band minima (CBM) show dissimilar behavior under strain. Such various band extrema evolution will allow for a novel device geometry where functionalities are modulated with strain--i.e., straintronics! 

In semiconductor 2D heterostructures, electrons and holes can be spatially separated into different layers but still be energetically bound to form quasiparticles, called inter-layer excitons (ILXs). The ILXs and other excitonic quasiparticles are expected to be applicable to excitonic computers, where information is transferred and processed in the form of excitons, instead of charges. Excitonic devices can be more power efficient and faster than conventional electron-based computers. 

The physical properties of ILXs are determined by the charge and energy transfers within the 2D heterostructures. By the use of compressive strain, we show that the interaction between monolayer MoS2 and WS2 has been greatly enhanced, resulting in non-monotonic, controllable modulation of charge and energy transfer. This is an innovative approach (i.e., mechanical) to modulate the 2D heterostructures' properties that can be adopted for not only excitonic devices, but also mechanical sensors and straintronics.