A parameterized orthogonal tight-binding mathematical model of the quantum electronic structure of the bismuth telluride molecule has been devised for use in conjunction with a semiclassical transport model in predicting the thermoelectric properties of doped bismuth telluride. This model is expected to be useful in designing and analyzing Bi2Te3 thermoelectric devices, including ones that contain such nano-structures as quantum wells and wires. In addition, the understanding gained in the use of this model can be expected to lead to the development of better models that could be useful for developing other thermoelectric materials and devices having enhanced thermoelectric properties.
Bi2Te3 is one of the best bulk thermoelectric materials and is widely used in commercial thermoelectric devices. Most prior theoretical studies of the thermoelectric properties of Bi2Te3 have involved either continuum models or ab-initio models. Continuum models are computationally very efficient, but do not account for atomic-level effects. Ab-initio models are atomistic by definition, but do not scale well in that computation times increase excessively with increasing numbers of atoms. The present tight-binding model bridges the gap between the well-scalable but non-atomistic continuum models and the atomistic but poorly scalable ab-initio models: The present tight-binding model is atomistic, yet also computationally efficient because of the reduced (relative to an ab-initio model) number of basis orbitals and flexible parameterization of the Hamiltonian.
The present tight-binding model includes atomistic descriptions of the Hamiltonian with sp3d5s* basis orbitals, nearest-neighbor interactions, and spin-orbit coupling. For the purposes of the model, within each primitive cell of Bi2Te3, two of the Te atoms are denoted TeI and one is denoted TeII. The difference between TeI and TeII is that the nearest neighbors of TeI are three Te atoms and three Bi atoms, while those of TeII are six Bi atoms. To capture the difference, separate tight-binding parameters are assigned to TeI and TeII.
Altogether, the tight-binding model incorporates 71 independent parameters, which are determined by fitting the computed band structure to a first-principles band structure obtained by use of a submodel based on a screened-exchange local-density approximation. The first-principles band structure predicts the energy gap, the degeneracy of the edges of the conduction and valence bands, and the effective masses of these two bands, in good agreement with experimental results. In the fitting process, a higher priority is given to the highest valence and the lowest conduction bands than to the rest of the band structure, inasmuch as these two bands are mainly responsible for the thermoelectric properties of lightly doped Bi2Te3. Moreover, the locations, energies, and effective masses of the two band edges are emphasized, as they largely determine the accuracy of the thermoelectric properties predicted by use of this model.
The semiclassical transport model with which this tight-binding model is coupled is a solution of Boltzmann’s transport equation in the constant-relaxation-time approximation. The combination of models has been found to yield calculated values of thermoelectric properties within a few percent of experimentally determined values (for example, see figure).