Inverse band design of SiGe superlattices with direct band-gaps*

Integrating optoelectronic functionalities directly into the mature Silicon-Germanium technology base would prove invaluable for many applications. Unfortunately, both Si and Ge display indirect band-gaps unsuitable for optical applications. It was previously shown (Zachai \textit{et al.} PRL \textbf{64} (1990)) that epitaxially grown [(Si)$_n$(Ge)$_m$]$_p$ (i.~e.~ a single repeat unit) grown on Si can form direc-gap heterostructures with weak optical transitions as a result of zone folding and quantum confinement. The much richer space of \emph{multiple-period} superlattices [(Si)$_{n_1}$(Ge)$_{n_2}$(Si)$_{n_3}$(Ge)$_{n_4}$\ldots$Ge_{n_N}$]$_p$ has not been considered. If $M=\sum n_i$ is the total number of monolayers, then there are, roughly, $2^M$ different possible superlattices. To explore this large space, we combine a (i) genetic algorithm for effective configurational search with (ii) empirical pseudopotential designed to accurately reproduce the inter-valley and spin-orbit splittings, as well as hydrostatic and biaxial strains. We will present multiple-period SiGe superlattices with large electric dipole moments and direct gaps at $\Gamma$ yielded by this search.