Photonic Band Gap and Light Routing in Self-Assembled Lattices of Epitaxial Ge -on- Si Microstructures

The emergence of a photonic band gap in $\\mathrm{Ge}$-on-$\\mathrm{Si}$ micropillars ordered in a two-dimensional square lattice is demonstrated by the finite-element method. Candidate architectures are fabricated through epitaxy and the opening of the photonic band gap experimentally proved by photoluminescence spectroscopy. When the direct-gap emission of $\\mathrm{Ge}$ is resonantly driven into the photonic gap, light propagation in the lattice plane is inhibited. Emission is eventually funneled out of plane, yielding a giant increase, i.e., about one order of magnitude, in the observed intensity. The demonstration of light routing in microcrystals' lattices opens interesting possibilities for $\\mathrm{Si}$ photonics. The epitaxial self-assembled microstructures introduced here can be monotonically integrated on $\\mathrm{Si}$ to improve the performances of group-IV lasers or engineered to optimize the working wavelength of future quantum photonic circuits.