Ultrathin insulating films composed of a few atomic layers are being extensively used for controlling the electronic coupling of nanostructures deposited on a substrate. Ultrathin film, for example, a single layer of Cu 2N deposited on a Cu(100) surface (known as Cu2NCu(100) surface) has been used to determine the spectral properties of nanomagnets using scanning tunneling spectroscopy. However, recent experiments that measure spin relaxation times in a single atom suggest that the single layer of Cu 2N does not provide efficient electronic decoupling. In this work, we study the thermodynamic stability of a bi-layer of copper nitride on the Cu(100) surface. We calculate adsorption and co-adsorption energies of Cu and N as a function of their concentration on the Cu2NCu(100) surface using density functional theory. We find that the adsorption and co-adsorption energies of Cu and N on the Cu2NCu(100) surface are of the order of a few eV. This suggests that the bi-layer of copper nitride is thermodynamically stable on the Cu(100) surface. We also find that the work function of N-adsorbed Cu2NCu(100) increases with the N concentration, suggesting a better insulating character of the bi-layer of copper nitride on the Cu(100) surface. © 2011 American Institute of Physics.