($A_m$$B_n$${)}_x$ copolymers: A computational study of electronic and excitonic properties of quasi-one-dimensional superlattices

Periodic copolymers representing quasi-one-dimensional superlattices ($A_m$ $B_n$ ${)}_x$ have been studied within the tight-binding approximation. The linear-combination-of-atomic-orbitals (LCAO) approach was used to calculate the splitting into subbands, the widths of the subbands, and the number of subbands in the well as a function of segment lengths m and n (barrier and well width). The Stark shift of subbands and the perturbed Wannier functions for a ($A_{16}$ $B_{32}$ ${)}_x$ superlattice have been calculated for various electric field strengths using perturbation theory. Exciton resonances and the shift in exciton excitation energies due to an applied electric field have been computed by using a Pariser-Parr-Pople parameter for the electron-hole interaction. The parameters for the empirical tight-binding calculations were determined from fully self-consistent Hartree-Fock calculations and first-principles Green’s function calculations for the exciton energies for superlattices of shorter segment lengths. For the Stark shift of the exciton peak a red shift of ∼25 meV for 2×${10}^5$ V/cm is calculated, similar to the shifts calculated and observed in three-dimensional superlattices.