Frequency invariancy of space charge oscillations in electron emission microdiodes

Previous studies have revealed that space charge oscillations are influenced by the injected current density, which is crucial for the fabrication of electron emission devices, such as thermionic energy converters and virtual cathode oscillators. Although the oscillation frequency f_os as a key parameter has been investigated with long history, it is rather difficult to be estimated based on external parameters. In this work, based on particle-in-cell simulations the oscillation frequency is confirmed related to applied voltage V, gap distance d, injected current density J_inj, and initial velocity of emitted electrons v₀, i.e., f_os=f(V, d, J_inj, v₀). Two kinds of scale invariant similarity properties of different electron emission gaps are demonstrated. It is shown that the oscillation features follow the similarity theory, that is, the oscillation frequency scales proportionally with the gap size when the applied voltage is maintained, i.e., f_os/k=f(V, kd, J_inj/k², v₀), where k is a scaling factor of gap dimension. Further, we found that the oscillation frequency is kept unchanged when the gap size scales proportionally even though the scaling of applied voltage and injection current density, compared to the similarity law becomes different, i.e., f_os=f(k²V, kd, kJ_inj, kv₀). The discovery from this work enables the manipulation of the oscillation frequency by tuning the external macroscopic parameters which offers optimization strategies for the design of electron emission microdevices.