Theoretical Investigation of Excitons in Type-I and Type-II Si/Si 1−x Ge x Quantum Wires J. Costa e Silva, 1, ∗ Andrey Chaves, 1, † J. A. K. Freire, 1, ‡ V. N. Freire, 1, § and G. A. Farias 1, ¶ 1 Departamento de F´ ısica, Universidade Federal do Cear´ a, Caixa Postal 6030, Campus do Pici, 60455-900 Fortaleza, Cear´ a, Brazil (Dated: June 22, 2006) Abstract This work presents a theoretical study of the excitonic properties of Si 1−x Ge x cylindrical quan- tum wires surrounded by a Si matrix, considering two possibilities for the conduction band align- ment, type-I and type-II. The effect of non-abrupt interfaces between these materials on the exciton energies is investigated: an interfacial region of 15 ˚ A in a 50 ˚ A wide Si 0.85 Ge 0.15 (Si 0.7 Ge 0.3 ) type-I (type-II) QWR leads to an exciton energy blue shift of the order of 10 meV. The excitonic behavior under an applied magnetic field parallel to the wire axis is also studied: exciton energies in type-I wires are weakly affected, while for type-II wires, increasing the field causes the electron angular momentum to change almost periodically, giving rise to Aharonov-Bohm (AB) oscillations of the exciton ground state energy. PACS numbers: 78.67.Lt, 71.35.-y 1