Most conducting polymers used for light-emitting devices have a small electron affinity, creating a high barrier for electron injection resulting in low injection efficiency. To improve injection characteristics, we fabricated and investigated multi-layer contacts with a tunneltransparent dielectric layer of nanometer thickness. Polymer layers were prepared by spin coating, and dielectric and metallic contact layers subsequently grown by vacuum deposition. Samples with such multi-layer cathodes demonstrated a current-voltage characteristic with negative differential resistance. At larger applied voltage, electroluminescence was observed with an efficiency larger than for a simple cathode of the same metal. We have developed a model to describe double injection through multi-layer contacts which explains these salient observed features. The increase in injection efficiency is caused by the voltage drop at the dielectric layer, shifting the metal Fermi level relative to the polymer molecular orbitals responsible for carrier transport. The negative differential resistance is explained by the strong dependence of dielectric tunnel transparency on voltage, a dependence which is qualitatively different for electrons and holes. Further flexibility in the functional characteristics of the injecting contacts is achieved through the use of an additional thin metallic layer playing the role of a base electrode, similar to hot-electron transistors with metallic base.