Strain manipulation is a critical technique for modifying the optoelectronic properties of lateral heterostructures, enabling precise control over band alignment, carrier mobility, and light-matter interactions. By applying mechanical strain, researchers can tailor material properties without altering chemical composition, offering a versatile approach for advanced device engineering. Among the various strain engineering methods, substrate bending stands out as a widely used technique due to its simplicity and effectiveness.

Substrate bending applies uniaxial or biaxial strain to heterostructures by mechanically deforming the underlying substrate. This method induces tensile or compressive strain depending on the bending direction. For example, convex bending generates tensile strain, while concave bending produces compressive strain. The magnitude of strain can be calculated using the relationship between substrate curvature and thickness. For a substrate of thickness *t* and radius of curvature *R*, the strain (*ε*) at the surface is given by *ε = t/(2R)*. Experiments have demonstrated that strain levels up to 1% can be achieved in 2D materials like transition metal dichalcogenides (TMDCs) using this approach, leading to significant shifts in photoluminescence (PL) peaks—often exceeding 50 meV for monolayer MoS₂ under biaxial strain.

Another strain manipulation technique involves the use of piezoelectric actuators, which provide dynamic and reversible strain control. By applying an electric field, these actuators induce precise displacements in the substrate, thereby transferring strain to the heterostructure. This method allows for real-time tuning of optoelectronic properties, making it suitable for adaptive photonic devices. Studies have shown that piezoelectric strain can modulate the bandgap of WS₂ monolayers by up to 2%, with corresponding changes in exciton binding energy.

Thermal mismatch strain is another effective approach, leveraging differences in thermal expansion coefficients between the heterostructure and substrate. Heating or cooling the system generates strain due to differential contraction or expansion. For instance, cooling a TMDC on a silicon substrate from growth temperature to room temperature introduces tensile strain due to silicon’s lower thermal expansion coefficient. This method has been used to achieve strain-induced bandgap narrowing in MoSe₂, enhancing its absorption in the visible spectrum.

Strain engineering also plays a crucial role in controlling crack propagation in lateral heterostructures. Cracks often initiate at defects or grain boundaries and propagate under applied stress, which can be detrimental to device performance. However, controlled cracking can be harnessed to create well-defined edges or patterned structures. The Griffith criterion describes the critical stress (*σ_c*) required for crack propagation in brittle materials: *σ_c = √(2Eγ/πa)*, where *E* is Young’s modulus, *γ* is surface energy, and *a* is crack length. By carefully managing strain distribution, researchers can guide crack paths and prevent uncontrolled fracture.

Strain mapping is essential for characterizing the spatial distribution of strain in heterostructures. Raman spectroscopy is a widely used technique, as shifts in phonon frequencies correlate directly with local strain. For example, the E₂g peak in MoS₂ shifts at a rate of approximately -4 cm⁻¹ per 1% tensile strain. High-resolution Raman mapping can resolve strain variations with sub-micron precision, enabling detailed analysis of strain gradients near interfaces or defects.

Microscopy-based techniques such as transmission electron microscopy (TEM) with geometric phase analysis (GPA) provide atomic-scale strain measurements. GPA quantifies lattice distortions by analyzing displacements in high-resolution TEM images, offering strain resolution better than 0.1%. This method has been employed to study strain relaxation in InGaAs/GaAs heterostructures, revealing localized strain pockets at misfit dislocations.

Digital image correlation (DIC) is another powerful tool for strain mapping, particularly in flexible substrates. By tracking the displacement of speckle patterns applied to the substrate surface, DIC constructs full-field strain maps with nanometer-scale sensitivity. This technique has been used to study strain transfer efficiency in graphene-polymer composites, demonstrating that only 30-50% of applied substrate strain is transferred to the 2D material due to interfacial slippage.

X-ray diffraction (XRD) provides non-destructive strain analysis with high statistical reliability. By measuring changes in lattice spacing, XRD can determine strain states averaged over large sample areas. For instance, XRD has quantified strain relaxation in GaN epitaxial layers, showing that misfit strain decreases exponentially with increasing layer thickness.

The integration of these strain manipulation and mapping techniques enables precise engineering of lateral heterostructures for optoelectronic applications. Strain-induced modifications of band structure enhance light absorption and emission efficiency, while controlled crack propagation can be leveraged for nanofabrication. Advanced strain mapping methods ensure accurate characterization, guiding the design of next-generation devices with tailored performance. The continued refinement of these approaches will further expand the possibilities for strain-engineered materials in photonics, electronics, and quantum technologies.