Energy Distribution Curves of Ultrafast Laser-Induced Field Emission and Their Implications for Electron Dynamics

Energy distribution curves of laser-induced electron pulses from a tungsten tip have been measured as a function of tip voltage and laser power. Electron emission via tunneling through and/or excitation over the surface barrier from photoexcited nonequilibrium electron distributions are clearly observed. The spectral shapes largely vary with the emission processes and are strongly affected by electron dynamics. Simulations successfully reproduce the spectra, thus allowing direct insight into the involved electron dynamics and revealing the temporal tunability of electron emission via the two experimental parameters. These results should be useful to optimize the pulse characteristics for many applications based on ultrafast laser-induced electron emission.

Figure 1

(a) a schematic diagram of the experimental setup (see text for further description). (b) a photograph of the experimental setup. The inset is the front view of the atomic structure of the tip apex based on a ball model.

Figure 2

(a) EDC of field emission from the tungsten tip together with a schematic diagram of field emission from a Fermi-Dirac distribution tunneling through a surface barrier. The transmission probability depends on the hatched area. The tip voltage $V_{\mathrm{tip}}$ was $-2300\mathrm{V}$. (b) schematic diagrams of nonequilibrium electron distributions just after laser absorption without (upper panel) and with (lower panel) electron-electron scattering. (c) and (d) show experimental EDCs and schematic diagrams of photoassisted field emission and photoemission, respectively. The magnified spectrum is also shown in (c). (c) $V_{\mathrm{tip}}=-2300\mathrm{V}$ and the laser power $P_L=50\mathrm{mW}$. (d) $V_{\mathrm{tip}}=-500\mathrm{V}$ and $P_L=50\mathrm{mW}$.

Figure 3

Measured and simulated EDCs for different tip voltages (dc fields $F_{\mathrm{dc}}$) and laser powers [excitation constant $C_{\mathrm{exc}}$, appears in Eq. (1)]. The work function $\Phi$ of 4.592 eV was used for the simulation. All the spectra are normalized at their maximum values. The measured EDCs are shown as dots, and the simulated EDCs as lines. Magnified spectra are also shown in the spectra at $V_{\mathrm{tip}}=-2300\mathrm{V}$ as circles for the experiments and lines for the simulations. The inset (bottom left) shows the measured laser power dependence of intensities for each excitation order ($V_{\mathrm{tip}}=-2300\mathrm{V}$). These intensities were obtained by integrating intensities over the respective energy regions: field emission (FE) is for $-1.2–0.3\mathrm{eV}$, photoassisted field emission and photoemission from 1PE for $0.3–1.85\mathrm{eV}$, 2PE for $1.85–3.4\mathrm{eV}$ and 3PE for $3.4–4.95\mathrm{eV}$. The lines are fitting curves with power functions; exponents are 1.3, 2.1, and 3.2 for 1PE, 2PE, and 3PE, respectively.

Figure 4

(a) Schematic diagrams and examples of simulations at three time steps. Transient electron distribution functions (upper) and EDCs (lower) are shown. The three EDCs are not drawn to scale. The following fitting parameters were used: $F_{\mathrm{dc}}=0.502\mathrm{V}/\mathrm{nm}$, $C_{\mathrm{exc}}=4.25\times {10}^{-5}$, $\Phi =4.592\mathrm{eV}$. (b) Fermi-Dirac and time-averaged transient electron distribution extracted from field emission and photoassisted field emission spectra at $V_{\mathrm{tip}}=-2300\mathrm{V}$ together with corresponding simulation curves (solid lines). The extracted data were normalized to be 0.5 at 0 eV and then multiplied by $(\mathrm{\text{laser-pulse cycle}})/(\mathrm{\text{simulation period}})$. The data points below 1 eV were cut to show only transient electron distribution. (c) Temporal line profile of the simulated electron pulse.