Abstract: Silicene and germanene are the silicon and germanium counterparts of graphene, respectively. Recent experimental works have reported the growth of silicene on (1 1 1)Ag surfaces with different atomic configurations, depending on the growth temperature and surface coverage. We first theoretically study the structural and electronic properties of silicene on (1 1 1) Ag surfaces, focusing on the (4 x 4) silicene/Ag structure. Due to symmetry breaking in the silicene layer (nonequivalent number of top and bottom Si atoms), the corrugated silicene layer, with the Ag substrate removed, is predicted to be semiconducting, with a computed energy bandgap of about 0.3 eV. However, the hybridization between the Si 3p orbitals and the Ag 5s orbital in the silicene/(1 1 1)Ag slab model leads to an overall metallic system, with a distribution of local electronic density of states, which is related to the slightly disordered structure of the silicene layer on the (1 1 1)Ag surface. We next study the interaction of silicene and germanene with different hexagonal non-metallic substrates, namely ZnS and ZnSe. On reconstructed (0 0 0 1)ZnS or ZnSe surfaces, which should be more energetically stable for very thin layers, silicene and germanene are found to be semiconducting. Remarkably, the nature and magnitude of their energy bandgap can be controlled by an out-of-plane electric field, an important finding for the potential use of these materials in nanoelectronic devices. (C) 2013 Elsevier B. V. All rights reserved.