Piezoelectric effects in transition metal dichalcogenides (TMDCs) with odd-layer configurations have emerged as a significant area of research due to their unique non-centrosymmetric crystal structure, which is absent in even-layer counterparts. The broken inversion symmetry in odd-layer TMDCs allows for the generation of piezoelectric responses under mechanical deformation, making them promising candidates for energy harvesting, nanoscale sensors, and electromechanical systems. This article explores the theoretical foundations, experimental characterization via piezoresponse force microscopy (PFM), and potential applications in energy conversion technologies.

The piezoelectric effect in odd-layer TMDCs arises from their crystal symmetry. Monolayer TMDCs, such as MoS2, WS2, and WSe2, belong to the D3h point group, which lacks inversion symmetry. When stacked into odd numbers of layers, the overall structure retains non-centrosymmetry, while even-layer configurations restore inversion symmetry, nullifying the piezoelectric response. The piezoelectric coefficient (d11) quantifies the charge generation per unit mechanical stress and is a critical parameter for evaluating performance. Theoretical calculations based on density functional theory (DFT) predict d11 values for monolayer MoS2 in the range of 3.65 to 4.0 pm/V, while experimental measurements often align closely, confirming the robustness of these models. The coefficient decreases with increasing layer count but remains measurable in trilayer and other odd-layer systems.

First-principles calculations have been instrumental in understanding the piezoelectric behavior of odd-layer TMDCs. These models account for ionic and electronic contributions to the piezoelectric response, with the former dominating due to the relative displacement of positively charged transition metal atoms and negatively charged chalcogen atoms under strain. The electronic contribution, though smaller, becomes non-negligible in certain configurations. The directionality of the piezoelectric effect is also anisotropic, with the highest response observed along the armchair direction due to the alignment of dipoles. Theoretical studies further reveal that strain engineering can modulate the piezoelectric coefficients, though this aspect is distinct from intrinsic mechanical property discussions.

Experimental characterization of piezoelectricity in odd-layer TMDCs relies heavily on piezoresponse force microscopy (PFM), a technique capable of detecting electromechanical coupling at the nanoscale. PFM measures the deformation of a material in response to an applied electric field, providing both qualitative and quantitative insights. For monolayer MoS2, PFM studies have confirmed a piezoelectric coefficient of approximately 3.7 pm/V, consistent with theoretical predictions. The technique also maps the spatial distribution of piezoelectric activity, revealing uniform responses across defect-free regions but localized variations near edges or grain boundaries. In trilayer systems, the measured coefficients are typically reduced by 30-40% compared to monolayers, yet they remain sufficiently large for practical applications.

Beyond PFM, other techniques such as electrostatic force microscopy (EFM) and conductive atomic force microscopy (CAFM) have been employed to corroborate findings. These methods help distinguish between piezoelectric and electrostatic effects, ensuring accurate measurements. For instance, EFM can detect charge redistribution under strain, while CAFM measures current generation directly, providing complementary data to PFM. Combined, these techniques offer a comprehensive understanding of the electromechanical coupling in odd-layer TMDCs.

The applications of piezoelectric odd-layer TMDCs in energy harvesting are particularly compelling. Their atomic thickness and flexibility make them ideal for integration into wearable and portable devices where conventional piezoelectric materials like lead zirconate titanate (PZT) are unsuitable due to rigidity and toxicity. Theoretical estimates suggest that a monolayer MoS2-based energy harvester could generate power densities on the order of 10-100 μW/cm2 under realistic strain conditions, sufficient for low-power electronics. Experimental prototypes have demonstrated voltage outputs of 10-30 mV and currents in the nanoampere range under periodic mechanical deformation, validating their potential.

One promising application is self-powered nanodevices, where odd-layer TMDCs serve as active elements in piezoelectric nanogenerators (PENGs). These devices convert ambient mechanical energy, such as vibrations or human motion, into electrical energy without external power sources. Recent studies have shown that vertically stacked heterostructures of odd-layer TMDCs can enhance output by leveraging interfacial charge transfer effects. For example, a MoS2/WSe2 heterostructure exhibited a 20% increase in piezoelectric output compared to individual layers, highlighting the benefits of engineered interfaces.

Another application lies in strain sensors with built-in energy harvesting capabilities. Unlike conventional sensors that require external power, piezoelectric TMDC-based sensors can operate passively while generating signals proportional to mechanical stimuli. This dual functionality is advantageous for Internet of Things (IoT) devices, where energy efficiency and miniaturization are critical. Additionally, the biocompatibility of TMDCs opens avenues for implantable medical devices that harvest energy from physiological movements, such as heartbeats or muscle contractions.

The scalability of odd-layer TMDC production remains a challenge for large-scale applications. While chemical vapor deposition (CVD) can produce high-quality monolayers and few-layer films, achieving uniform odd-layer configurations over large areas is non-trivial. Advances in growth techniques, such as selective edge epitaxy or layer-by-layer transfer, are being explored to address this limitation. Furthermore, integrating TMDCs with flexible substrates like polyimide or polydimethylsiloxane (PDMS) requires careful optimization of interfacial adhesion to maintain performance under cyclic loading.

Future research directions include exploring alloyed TMDCs, such as MoS2(1-x)Se2x, to tailor piezoelectric properties through composition tuning. Preliminary studies indicate that selenium incorporation can enhance the piezoelectric coefficient due to increased polarizability, though systematic investigations are needed. Another avenue is the study of twisted bilayer systems, where controlled rotation angles between layers may introduce novel piezoelectric phenomena without restoring inversion symmetry.

In summary, odd-layer TMDCs exhibit well-defined piezoelectric effects governed by their non-centrosymmetric structure, with theoretical and experimental studies confirming their potential for energy harvesting and sensing applications. PFM has been indispensable in characterizing these materials, while prototype devices demonstrate feasibility for real-world use. Overcoming synthesis and integration challenges will be key to unlocking their full potential in next-generation electromechanical systems.