Power Factor Enhancement by Inhomogeneous Distribution of Dopants in Two-Phase Nanocrystalline Systems

In this work, we describe a novel idea that allows for high thermoelectric power factors in two-phase materials that are heavily doped with an inhomogeneous distribution of dopants. We show that a concurrent increase of the electrical conductivity and Seebeck coefficient and a consequent increase of the power factor can be achieved in such systems. To explain the concept, we employ a semiclassical one-dimensional model that considers both electron and phonon transport through a series connection of two-phases of the material. We discuss microscopic characteristics of the material and the formation of the two phases (grains and grain boundaries in our case) by the inhomogeneous distribution of dopants in the polycrystalline material. Our theoretical investigation reveals that: (1) the improvement in the Seebeck coefficient can be attributed to carrier filtering due to the energy barriers at the grain boundaries, and to the difference in the lattice thermal conductivity of the grains and grain boundaries, and (2) the improvement in the electrical conductivity is a result of a high Fermi level in the grains. This allows high energy carriers to contribute to transport, which increases the impurity scattering limited mean-free-path, and increases the conductivity in the grains and thus in the whole material. Such an unexpected concurrent in- crease of the electrical conductivity and the Seebeck coefficient was recently observed in heavily boron-doped polycrystalline silicon of grain sizes<100 nm in which a silicon-boride phase is formed around the grain boundaries. We provide a simple 1D model that explains the behavior of this system, indicating processes that can take place in heavily doped nanocrystalline materials.