High field tunneling as a limiting factor of maximum energy density in dielectric energy storage capacitors

In several low loss dielectric materials, it was observed that the energy loss remains very small under low and medium electric fields but dramatically increases at high field which is believed to be due to tunneling current. The increase of tunneling current at high field is due to the decrease of barrier width and height and is a universal phenomenon in all dielectric materials. Due to the requirement of high energy efficiency, high field conduction places a limit for the maximum operation field, which could be lower than the breakdown field and act as the limiting factor of energy density.