Space-Charge Modulation in Vacuum Microdiodes at THz Frequencies

We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.

Figure 1

Schematic model of the system simulated. The variable parameters are the applied voltage $V$ and the gap width $d$. The resulting currents at the cathode (emitter), $j_C(t)$, and at the anode (absorber), $j_A(t)$, are measured.

Figure 2

Shape of the electron pulse when the externally applied voltage is varied. A fixed Gaussian photon profile is used. Only the highest voltage gives a 100% yield. Inset is earlier published experimental results, reproduced from Ref. 10. The experimentally obtained double-peaked shape was assigned to space-charge effects; this structure is recovered for the medium voltage.

Figure 3

Electron intensity as a function of time when a voltage of 1 V is applied over a $2\mu \mathrm{m}$ gap. A continuous photon beam transforms into a pulsed signal of electrons with a frequency of 720 GHz. An absorbed electron is attributed a Gaussian profile in time and for the black curve (gray curve) $\sigma =800\mathrm{fs}$ (400 fs). Note that the frequency remains unaffected of profile width and that the individual peaks are well separated.

Figure 4

Frequency as a function of applied electric field. The deviating behavior at small gap lengths (large electric fields) arises when the transit time of a charge sheet becomes comparable to the period of the density oscillation. Solid line is a linear fit to the obtained data. Dashed lines are from the proposed model given by Eq. (2).

Figure 5

Map of cathode showing regions open for emission, black, whereas gray and white regions are blocked. The circle marks the rim of the cathode. Left (1A), a blockade is formed as electrons are added. Middle (1B), the complete blockade has formed. Right (2), a reopening of the emitter occurs when the electron sheet exceeds a critical distance.