We develop a fully quantum-dynamical framework for modeling excitonic effects in group-IV semiconductor heterostructures based on a single-band (1s) tight-binding Hamiltonian. The model incorporates position-dependent band-edge potentials for electron and hole confinement, long-range Coulomb interaction, and external electric fields. Starting from the total Hamiltonian \(\hat{H}^{tb} = \hat{H}^{tb}_0 + \hat{H}^{tb}_{em} + \hat{H}^{tb}_C\) , we derive the equations of motion for the density matrix in superoperator form and solve them numerically using an adaptive Runge–Kutta scheme to ensure temporal accuracy for fast field-driven dynamics. This approach enables the calculation of stationary exciton states as well as time-resolved electronic and optical observables in realistic one-dimensional heterostructures, including single and multiple quantum wells. We systematically analyze how excitonic binding energies, absorption spectra, and carrier dynamics depend on Sn composition, quantum well geometry, and external driving fields. While multi-quantum well configurations can be engineered to modify the optical response, our results show that absorption enhancement critically depends on the spatial overlap and Coulomb coupling between confined electron and hole states. The presented framework provides microscopic insight into excitonic processes relevant for the design of Sn-based group-IV photonic materials operating in the mid-infrared regime.
