Triple electron emission from surfaces: Energy and angle relations

We discuss a proof-of-principle experiment in which we detect triple electron emission from a surface due to primary electron impact. The new aspect is the ability to record the energies and emission directions of the ejected electrons. We selected NiO films as a target, which have shown in previous electron pair emission studies to give an enhanced intensity compared to other materials. The triple sum energy spectrum displays a shape consistent with a self-convolution of the electronic density of states. We define two different emission geometries. While the energy distributions are essentially identical, the intensity levels differ by a factor of 2. Imposing a geometrical constraint on one of the emitted triples shows that the available energy is equally shared among the other two electrons. We discuss our findings within a simplified scattering model. We also present angular distributions. Prominent intensity minima for electron emission in the same direction are not observed in contrast to our previous electron pair emission studies.

Figure 1

The time-of-flight spectrometer consists of four channel-plate detectors with delay line anodes. The individual detectors are labeled LL, LC, RC, and RR. The excitation source is a pulsed electron gun. A triple coincidence circuit ensures the identification of an emitted electron triple.

Figure 2

Sketch of the two-step scattering mechanism leading to the emission of three electrons. We call this process (e,3e).

Figure 3

Single electron spectrum from a NiO film. The primary energy is $E_p=32$ eV. This spectrum is the sum of spectra from the individual detectors.

Figure 4

Triple sum energy spectra obtained with $E_p=29$ eV in panels (a) and (b). In (c), $E_p$ was set to 32 eV. The vertical dashed line marks the position of $E_{\text{sum}}^{\text{max}}$.

Figure 5

2D energy distribution of the triple intensity. The $y$ axis is the energy sum of two electrons while the $x$ axis is the energy of the third electron. The dashed red line marks the energetic position of $E_{\text{sum}}^{\text{max}}$. In panel (a), we present the data used in Fig. 4. Panel (b) is the result from our scattering model by assuming a 7-eV-wide valence band. The intensity in (a) are the accumulated counts, while in (b) it is the probability for triple emission within our model.

Figure 6

Triple intensity as a function of the energy of the third electron for the emission geometries depicted in the inset. The blue (black) data points originate from events in which two of the electrons hit on detector RR and LL (LC and RC), while the third electron hits either detector LC or RC (LL or RR). The intensity for the blue data points have been multiplied by a factor 2. The red curve is the result of our simulation.

Figure 7

2D energy distribution for two electrons under the constraint 3.4 $\mathrm{eV}\le E_3\le$ 6.4 eV. Panels (a) and (b) refer to the geometries introduced in the inset of Fig. 6. Panel (c) displays the result of the model. The red dashed diagonal line marks the energetic position $E_{\text{sum}}^{\text{max}}-E_3$. The intensity levels in (a) and (b) refer to the number of counts. For panel (c), we use the probability within our model.

Figure 8

Example of the angular emission analysis. We select the emission direction of the fixed electron which in the example is the complete detector LL. The free electrons arrive at detectors LC and RR, respectively. The emission angle with respect to the central emission of the fixed electron is given by the red arcs. The blue arc is a measure of angular separation of the free electrons.

Figure 9

Angular distribution of the triple intensity in which the fixed electrons is recorded on detector LL. Panels (a) and (b) refer to the geometries (a) and (b) introduced in the inset of Fig. 6. The black diagonal lines define the angle differences of ${\mathrm{\Delta }}_{\text{RR}-\text{LC}}$ and ${\mathrm{\Delta }}_{\text{RC}-\text{LC}}$. These values refer to the blue arc related to the free electrons, see Fig. 8.