Tight-Binding Calculation of Silicon Bands

In this work we implement a tight-binding calculation of the energy bands of silicon. This traditional method is still employed as a useful approximation for the electronic motion in solids. The tight-binding wavefunctions are taken as linear combinations of atomic orbitals located at each atom in the crystal, based on phase factors e(ik·R) (R are the position of such atoms) for coefficients. To address silicon, we implement a fcc lattice structure with 2 atoms per cell and four orbitals per atom, representing the atomic 3s and 3p. The method involves the diagonalization of an 8 × 8 matrix at each k-point in the Brillouin zone. We reconstruct the bands along a standard path through special k-points and we integrate the bands over the Brillouin zone to reconstruct the density of states of the system. Advisor: Dr. Nicola Manini Co-Advisor: Dr. Katalin Gaál-Nagy