A cold-cathode electron source is formed that successfully achieves a high frequency and a high output. Embodiments include a cold-cathode electron source comprising emitters having a tip portion tapered at an aspect ratio R of not less than 4, thereby decreasing capacitance between the emitters and a gate electrode by a degree of declination from the gate electrode, such that the cold-cathode electron source is able to operate at a high frequency. Embodiments also include a cold-cathode electron source formed of a diamond with a high melting point and a high thermal conductivity, such that the emitters operate at a high current density and at a high output.