Absence of Space-Charge-Limited Current from Abnormal Field Emission in Collisional Diode

For field emission in a vacuum or solid diode, its current density is expected to be governed by the Child-Langmuir [1] or Mott-Gurney laws [2] law at sufficiently high voltage. Recently, we reported that for field emission not obeying the classical Fowler-Nordheim (FN) law [3] , the two-stage transition from source-limited field emission (FE) to space-charge-limited current (SCLC) is no longer valid [4] . Using a generalized FN scaling of ln(J/F k ) □ 1/F, where J is the current density and F is the applied field, we study the effects of different k to the current density-voltage (J-V) transition characteristic. For a vacuum diode, if the value of k is smaller than k crit =1.5, we will have pure FE with absolute absence of SCLC or 3-stage FE-to-SCLC-to-FE, depending on the size of the diode D. We extend the model to a solid diode (collisional transport), and the corresponding critical value becomes k crit =2. The transition behavior is more complicated, which depends not only on D, but also the electron mobility μ in the solid. Our findings provide a theoretical foundation for modelling unconventional field emission injection in both ballistic and collisional regimes, which is significant for various applications [5] in vacuum electronics, beam physics, gas-based diode, plasma, and dielectric.