How hot is cold emission?

The temperature rise of nanocrystalline graphite coated silicon substrates and of gated p⁺ - silicon field emitter arrays fabricated on silicon was measured as a function of emission current. In both cases, the temperature rise is proportionate to I², indicating Joule´s heating. The temperature rise was calibrated using a substrate of similar size onto which a micromachined point heat source was fabricated. From these measurements, a spreading resistance can be deduced which is responsible for the I² heating. From the spreading resistance, a radius of the emission sites of run dimensions is obtained. This estimate agrees with Fowler-Nordheim analysis. For a 6460 silicon tip array, at a total emission current of 100 μA, the tip temperature is about 100°C