Modeling of thermal effects in silicon field emitters

Thermal effects in silicon field emitters are analyzed and an attempt is made to identify "intrinsic" phenomena that can occur under normal operating conditions and that might trigger catastrophic breakdown. For this analysis an approximate quasi-equilibrium treatment is employed which is presumably most accurate at low current levels. Unlike for metal field emitters where Nottingham heating dominates, for silicon field emitters it is found that the heating is predominantly ohmic in origin except at very low currents. The temperatures produced by this heating are much larger than those in metals for a given current and geometry. And although the calculations indicate that for typical designs these temperatures are still small enough so as not to represent a direct reliability threat, their size coupled with their sensitivity to changes in current-ohmic heating increases as the square of the current-suggests caution both in design and in trusting the results of this relatively crude analysis. With respect to the former, designs for which the heat-sinking is weak, e.g., atomically-sharp tips or tips on high aspect-ratio poses, may be susceptible to thermal failure. Similarly, additional ohmic heating due to ac currents can push a design into thermal jeopardy. Finally, it is found that increasing the doping does not appear to lessen the ohmic heating significantly (because of band-bending and scattering effects) nor does the Nottingham effect, which under some circumstances seems to actually provide cooling, appear sufficient to offset the ohmic effects.