The numerical simulation of thermal effects in silicon field emitters

Thermal effects in silicon field emitters are simulated numerically using a model of the temperature-dependent electrical conductivity and thermal conductivity. Both the density variation and mobility variation of the carriers with temperature has been taken into account to derive the electrical conductivity in the model. Results of the simulation show that due to the influence of temperature, the states at the apex of a silicon emitter can be classified as three types corresponding to the three regions of the carriers’ excited states, namely the saturation region, the transition region and the intrinsic region. If the apex of an emitter operates in the state of the transition region, the electric potential at the apex may increase sharply with the emission current. This increment can weaken the electric field around the field emitter cathode and a saturation emission characteristic may appear.