Role of substrate strain to tune energy bands–Seebeck relationship in semiconductor heterostructures

In doped semiconductors and metals, the Seebeck coefficient or thermopower decreases monotonically with increasing carrier concentration in agreement with the Pisarenko relation. Here, we establish a fundamental mechanism to modulate and increase the thermopower of silicon (Si)/germanium (Ge) heterostructures beyond this relation, induced by the substrate strain. We illustrate the complex relationship between the lattice strain and the modulated thermopower by investigating the electronic structure and cross-plane transport properties of substrate strained [001] Si/Ge superlattices (SLs) with two independent theoretical modeling approaches: first-principles density functional theory and the analytical Kronig–Penny model in combination with the semi-classical Boltzmann transport equation. Our analysis shows that the SL bands, formed due to the cubic structural symmetry, combined with the potential perturbation and the intervalley mixing effects, are highly tunable with epitaxial substrate strain. The strain tuned energy band shifts lead to modulated thermopowers, with a peak approximately fivefold Seebeck enhancement in strained [001] Si/Ge SLs in the high-doping regime. As a consequence, the power factor of a 2.8% substrate strained SL shows a ≈ 1.8-fold improvement over bulk Si at high carrier concentrations, ≈ 12 × 10 20 cm − 3. It is expected that the fundamental understanding discussed here, regarding the complex effect of lattice strain to control energy bands of heterostructures, will help to exploit strain engineering strategies on a class of future technology-enabling materials, such as novel Si/Ge heterostructures as well as layered materials, including van der Waals heterostructures.