Thermoelectric materials convert heat into electricity and vice versa, offering potential applications in energy harvesting, cooling, and waste heat recovery. The efficiency of thermoelectric materials is quantified by the dimensionless figure of merit, ZT, defined as ZT = (S²σT)/κ, where S is the Seebeck coefficient, σ is electrical conductivity, T is absolute temperature, and κ is thermal conductivity. Enhancing ZT requires optimizing these interdependent parameters, a challenge that has driven research into nanostructured materials. Reduced dimensionality—quantum wells, nanowires, and quantum dots—offers unique advantages by decoupling electron and phonon transport, leading to improved thermoelectric performance.

Quantum wells, two-dimensional nanostructures, confine electrons in one dimension while allowing free movement in the other two. This confinement alters the electronic density of states, creating sharp features near the Fermi level that enhance the Seebeck coefficient without significantly reducing electrical conductivity. Additionally, phonon scattering at interfaces between the quantum well and barrier materials reduces lattice thermal conductivity. Experimental studies on superlattices, such as Bi₂Te₃/Sb₂Te₃, have demonstrated ZT values exceeding 2.0 at room temperature, a significant improvement over bulk counterparts. Theoretical models attribute this enhancement to selective carrier transport and increased phonon boundary scattering.

Nanowires, one-dimensional structures, further restrict phonon propagation due to their high surface-to-volume ratio. Phonons, which carry heat, are scattered at surfaces and defects, drastically reducing lattice thermal conductivity. At the same time, quantum confinement in nanowires can lead to electron filtering, where only high-energy electrons contribute to conduction, improving the Seebeck coefficient. Silicon nanowires, for example, exhibit thermal conductivities nearly two orders of magnitude lower than bulk silicon while maintaining reasonable electrical conductivity. This decoupling of electron and phonon transport has been experimentally verified in systems like PbTe and BiSbTe nanowires, with ZT values approaching 1.5.

Quantum dots, zero-dimensional nanostructures, provide the strongest quantum confinement, leading to discrete energy levels that can be engineered to enhance the Seebeck coefficient. By embedding quantum dots in a matrix, energy-dependent scattering filters low-energy electrons, increasing the average energy per carrier. Phonon scattering is also intensified due to the mismatch in vibrational modes between the dots and the matrix. Experimental work on PbSeTe quantum dot superlattices has shown ZT values above 1.8, with theoretical studies suggesting further improvements through optimized dot size and spacing.

The mechanisms of phonon blocking and electron filtering are central to the performance of nanostructured thermoelectrics. Phonon blocking arises from increased scattering at interfaces, grain boundaries, and defects, which disproportionately affects phonons due to their broader wavelength spectrum compared to electrons. In nanowires and quantum dots, boundary scattering dominates, reducing lattice thermal conductivity to near the amorphous limit. Electron filtering, on the other hand, relies on energy-selective transport. Quantum confinement creates sharp features in the density of states, while potential barriers at interfaces preferentially scatter low-energy carriers. This selective transport increases the Seebeck coefficient without severely degrading electrical conductivity.

Recent theoretical advances have provided deeper insights into these mechanisms. First-principles calculations and Boltzmann transport modeling reveal that interface roughness, alloy disorder, and strain fields play critical roles in phonon scattering. For electrons, the alignment of energy levels and tunneling probabilities between nanostructures determine the filtering efficiency. Computational studies predict that optimized quantum dot arrays could achieve ZT values exceeding 3.0 by precisely controlling carrier and phonon transport.

Despite these promising results, challenges remain in scalability and stability. Fabricating uniform nanostructures over large areas is difficult, and inhomogeneities can degrade performance. For example, variations in quantum dot size or nanowire diameter lead to inconsistent transport properties. Stability is another concern, particularly at high temperatures where diffusion and oxidation can alter nanostructure morphology. Encapsulation strategies and robust barrier materials are being explored to mitigate these issues, but long-term reliability remains unproven in many systems.

Integration into practical devices introduces additional hurdles. Electrical and thermal contact resistances at interfaces between nanostructured materials and electrodes can offset performance gains. Mechanical fragility is also a concern, especially for nanowire arrays subjected to thermal cycling. Advances in scalable assembly techniques, such as solution-based printing or template-assisted growth, are being pursued to address these challenges.

The potential applications of nanostructured thermoelectrics span multiple fields. In energy harvesting, they could convert waste heat from industrial processes or vehicle exhaust into usable electricity. For cooling, solid-state refrigerators based on these materials offer compact, reliable alternatives to conventional systems. However, economic viability depends on achieving high performance with cost-effective manufacturing, an area where further progress is needed.

In summary, nanostructured thermoelectric materials leverage reduced dimensionality to enhance ZT through phonon blocking and electron filtering. Quantum wells, nanowires, and quantum dots each offer unique advantages, with experimental and theoretical studies demonstrating significant improvements over bulk materials. However, scalability and stability challenges must be overcome to enable widespread adoption. Continued research into material design, fabrication techniques, and device integration will be critical to realizing the full potential of these advanced thermoelectrics.