Silicon Photonics: Fundamentals and Devices

6.3 Early Efforts: Zone Folding

Most textbooks on solid-state physics illustrate the formation of energy bands by employing a simple Kronig–Penney model, considering a one-dimensional (1D) chain of atoms separated by an interatomic distance d. The E–k relationship obtained from this model is periodic with gaps occurring at values of k = π/a. This variation is depicted in the reciprocal space within the first Brillouin zone bounded by in Figure 3.11 with reference to a superlattice.

The idea of zone folding in a 1D superlattice whose periodicity is of the order of a lattice constant was advanced long ago. The concept was revisited by People and Jackson 1 as well as by People 2, after the successful growth of a high-quality atomic layer (Si_mGe_n)_p superlattice, in which m and n are the number of monolayers of Si and Ge in each period and p is the number of periods. The larger period d in the superlattice gives rise to a minizone having boundaries at . It may be proved, assuming that the minimum in conduction band is at 0.8 k_max as in Figure 6.1, that if d ≈ 5a, where a is the lattice constant, then the E–k diagram is folded back in the new reduced minizone and the gap is converted into a direct one along the superlattice axis. The folding process and the resulting miniband structure ...