Transit-time oscillations in nanoscale vacuum diode with a pure resistive load

Abstract

We examine the Ramo current in a nanoscale planar vacuum diode undergoing field emission in the presence of a DC voltage supply and an external resistor. We describe a simple mechanism for generating persistent current oscillations in the diode due to the voltage drop across the external resistor (beam loading) which reduces the total field and inhibits the emission. The amplitude and the frequency, which is in the THz domain, depend on the operating parameters of the diode. Molecular dynamics simulations are used to find the characteristics and physical basis of the mechanism, and a simple analytical model is presented, in good agreement with the simulation.

Figures (9)

• Figure 1: System schematic. Note that the planar diode is assumed to be infinite in extent, but the emitter area is finite.
• Figure 2: Evolution of the system with time. (a): Diode current. (b): Electrons in the vacuum gap. (c) The number of electrons emitted per time step, with red dots indicating electrons absorbed that originated from the immediately preceding emission event. (d): Applied potential (green) and anode potential (blue). $V_0{_m}$ = 1700 V, $D$ = 800 nm, $L$ = 1000 nm, $R$ = 240 k$\Omega$, $\phi$ = 2.0 eV, and $t_r$ = 0.8 ps. The orange curves show variations for a single period as obtained from the analytical model associated with Equations \ref{['eq:Diffeq']} and \ref{['eq:position']}.
• Figure 3: Map of existence of oscillation in $R - Z_0$ space. Green dots signify occurrence of persistent oscillations. Red crosses signify no persistent oscillations. $D$ = 1000 nm, $L$ = 1000 nm, $\phi$ = 2.0 eV. $R$ and $V_0{_m}$ are varied.
• Figure 4: Comparison of two different configurations with the same $Z_0$. Configuration A (red) has $\phi$ = 1.6 eV and $L$ = 395 nm. Configuration B (blue) has $\phi$ = 2.0 eV and $L$ = 1000 nm. Both configurations are for $V_0{_m}$ = 1700 V and $D$ = 1000 nm. Main graph shows current with (lower curves) and without (upper curves) 60 k$\Omega$ resistor and vanishing rise time for applied potential. Inset shows current for 60 k$\Omega$ resistor and 0.4 ps rise time.
• Figure S1: System behavior for increasing resistance values. Simulation parameters: $V_{0m} = 1700\,\mathrm{V}$, $D = 1000\,\mathrm{nm}$, $L = 1000\,\mathrm{nm}$, $\phi = 2.0\,\mathrm{eV}$, and $t_r = 0\,\mathrm{ps}$. A minimum resistance of approximately $60\,\mathrm{k}\Omega$ is required to sustain oscillations under these conditions.