\emph{Ab-initio} theory of nanoscale capacitors at finite bias

We present a novel technique for calculating the properties of an electric field applied to a periodic heterostructure with alternating metallic and insulating layers. This scheme allows us to investigate fully from first- principles the microscopic properties of a thin-film capacitor at finite bias potential. We demonstrate how the capacitance and local permittivity profiles can be readily obtained by performing calculations for the Ag(100)/MgO(100) and SrTiO$_3$(100)/SrRuO$_3$(100) systems. Applications range from the emerging field of electronic devices based on ferroelectric materials, to the {\em ab-initio} simulation of electrochemical cells.