Electron overheating during field emission from carbon island films due to phonon bottleneck effect

The paper discusses a possible model of low-field electron emission that could be applicable to carbon island films on silicon. Such films were recently showed to have emission thresholds as low as 0.4–1.5 V/ $\mu$m. Discontinuity of the film – and not the presence of field-enhancing morphological features or low-workfunction spots - seems to be the necessary condition for good emission capability. We suggest a hot-electron emission model with emission center representing a single isolated nanosized island of $sp^2$ carbon having the properties of a quantum dot. Quantization of its electron energy spectrum determines electron/phonon decoupling (“phonon bottleneck” effect) and long electron relaxation times, which makes emission the dominating option for hot electrons of sufficient energy injected in the island. The consequences of this suggestion are quantitatively considered for typical experimental situation.