Slater-Koster parameter

Slater-Koster parameters are a compact representation of atomic energies and inter-atomic hopping amplitudes. Since hopping amplitudes involve two atoms, they are define for each pair of atoms. Typically an explicit parametrization depends also on the reference crystal structure, but variations around the reference crystal structure is be accounted for by the general symmetry properties of atomic orbitals. Additionally, some Slater-Koster parameters also provide a correction the length-dependence scaling of the hopping amplitudes, which is otherwise taken to decay with the inverse distance squared.

The Device Builder currently comes with a small library of Slater-Koster parameters covering semi-conductors, such as Silicon and Gallium Arsenide. Moreover, it contains parameters for Silicon/Germanium random alloys, which provide hopping amplitudes for all combinations of bonds, Si-Si, Si-Ge, Ge-Si and Ge-Ge, while the Slater-Koster parameters for III-V semiconductors only provide hopping amplitudes between the anion and cation.

Furthermore, the Silicon/Germanium parameters implement a so-called "crystal field" corrections, lifting the degeneracy of the atomic energies based on its nearest neighbors, as outlined in the reference publication.

The SlaterKosterTuning model provided by the Device Builder can be used to tune the parameters of the Slater-Koster method. It contains the following properties:

• constituents: Defines the constituents of the device as a string containing atomic species separated by dashes, e.g., 'Si-Ge'. Only works for species, which are supported by the Device Builder. Supported constituents can be queried using the get_supported_slater_koster_parameters function of the Device Builder Python module.
• onsite_correction: Enables or disables the crystal field correction terms in the Slater-Koster model if present in the Slater-Koster parameters.
• length_dependent_hopping: Enables or disables the length-dependent hopping terms in the Slater-Koster model. If disabled, all bonds are taking at the equilibrium value, ignoring the actual distance implied by the periodic structure. This is useful for the description of random alloys, where the bond length implied by the periodic structure does not take into account the differences in bond length when relaxing the position of a concrete instance of a random alloy. Think of it as a "poor man's" relaxation of the atomic positions.
• bloch_vector: Sets the Bloch vector for the simulation, which by default is set to Γ (0, 0, 0). Has only an effect on lattice vector directions which are treated with periodic boundary conditions.
• distance_precision: Sets the precision for which two displacement vectors are considered equal.
• joint_probability_discretization: Sets the discretization for the joint probability distribution.
• enforce_complex_type: Enforces the use of complex wave functions.

NOTE: distance_precision and joint_probability_discretization control the decomposition of the Hamiltonian into "blocks", which affects the trade-off between efficiency and accurancy of the simulation.