«Laser-induced ultrafast electron emission from a field emission tip B Barwick1, C Corder, J Strohaber, N Chandler-Smith, C Uiterwaal and H Batelaan ...»
Laser-induced ultrafast electron emission from a field
B Barwick1, C Corder, J Strohaber, N Chandler-Smith,
C Uiterwaal and H Batelaan
Department of Physics and Astronomy, University of Nebraska—Lincoln,
116 Brace Laboratory, PO Box 880111, Lincoln, Nebraska 68588-0111, USA
Abstract. We show that a field emission tip electron source that is triggered
with a femtosecond laser pulse can generate electron pulses shorter than the
laser pulse duration (~100 fs). The emission process is sensitive to a power law of the laser intensity, which supports an emission mechanism based on multiphoton absorption followed by over-the-barrier emission. Observed continuous transitions between power laws of different orders are indicative of field emission processes. We show that the source can also be operated so that thermionic emission processes become significant. Understanding these different emission processes is relevant for the production of sub-cycle electron pulses.
PACS. Nr.: 07.78.+s, 32.80.Wr, 73.43.Jn, 81.07.-b Author to whom any correspondence should be addressed.
The temporal resolution of ultrafast electron diffraction (UED) [1, 2], ultrafast electron microscopy (UEM) [2-4] and ultrafast electron crystallography (UEC)  is limited to the duration of the electron pulse. The ultrafast electron source most commonly used in these applications is based on electron emission induced by focusing an amplified femtosecond laser pulse onto a surface [1, 5]. Due to the high particle density per pulse, space-charge broadens the pulse duration to ~500 fs . An interesting electron source implementing a Ti:sapphire oscillator has been used to generate 27-fs electron pulses  using impulsively excited surface plasmons. However, this method has a large kinetic energy spread ( ∆E ∼ 100 eV) in the emitted electrons, which would cause the pulse to expand temporally as it propagates. An electron gun has been proposed that could produce sub-fs electron pulses . This ~10 keV source would have an initial energy spread of ∆E ∼ 1 eV, but this spread would be reduced by injecting the electrons into an RF cavity to compensate for the different velocities, allowing the electron packet to arrive at a target in a sub-fs time window. A promising and experimentally realized source relies on the combination of a field emission tip with a low power femtosecond oscillator [8, 9]. The low laser powers required allow the production of few electrons per pulse with high repetition rates. This gives useful average electron count rates and overcomes spacecharge broadening. Field emission tip sources also have small energy spreads ( ∆E 1 eV) [10, 11], so their temporal expansion is suppressed. The electron pulses were experimentally shown to be shorter than 100 fs . Assuming that the emission process from the nanometer tip is due to optical field emission, the electrons bunches were claimed to be sub-cycle .
In this paper we focus on the nature of the emission process of electrons from a nanometer tip due to femtosecond laser pulses. Our pump-probe results support the claim that the electron pulses are shorter than 100 fs in agreement with Hommelhoff et al. . We investigate two possible mechanisms that could describe the emission process. The first is based on the instantaneous laser electric field lowering the potential barrier, thus allowing electrons to tunnel out of the tip (optical field emission). The second mechanism is multiphoton over-the-barrier emission . An analysis of our experimental data shows characteristics of both mechanisms. This is in accordance with the value of our Keldysh parameter [6, 13, 14]. The nature of the emission process is important for speculation on the electron pulse duration. In Refs.  and  the dominant process is identified as optical field emission, which leads to the prediction that this electron source could produce sub-cycle electron pulses . However, our results indicate a competing process that can be dominant, which stimulates a debate on the temporal characteristics and operating parameters of this source. Only direct experimental evidence, such as diffraction in time experiments [15-17], would unambiguously support the claim that the electron emission is sub-cycle.
To help determine the nature of the emission process we study the two mechanisms (Fig. 1). The optical field emission process is electron-tunneling through a barrier V that has been lowered by Ftot, the sum of a DC and laser field. Tunneling is most likely for electrons close to the Fermi level, EF. Multiphoton absorption can lead to over-the-barrier emission.
Upon absorption of four or more photons the gained electron energy exceeds the work function φ and direct emission can occur. An applied DC field reduces the workfunction to φeff (Schottky effect ) thus lowering the number of photons required for over-the-barrier emission. We also consider the possibility of photon absorption followed by tunneling. These models do not include any band structure , collision dynamics in the tip , or dynamic polarizability in the tip [20-24], and cannot be expected to describe the detailed dynamics of the emission process. However, our simple model agrees well with experiment. We now turn our attention to a more detailed description of the model.
For n-photon absorption the electron emission rate J abs,n is proportional to the (2n)-th power of the laser field (θ is the angle between the laser field polarization and the tip axis),
where the energy of the excited electron must exceed the effective potential barrier, n ω φeff. The Schottky effect is given by φeff = φ − e ⎡eFDC ( 4πε 0 ) ⎤ . Above-threshold ⎣ ⎦ photoemission ( n ≥ 5 ) could contribute to the total electron emission signal .
The polarization (θ ) dependence of the electron emission can be attributed to an increased probability of photon absorption when the electric field is perpendicular to a surface (parallel to the tip axis) . Other groups have attributed the polarization dependence to the motion of the conduction electrons in the metal tip [21-24]. This lightning effect treatment causes an enhancement of the field near the tip because the optical field could make conduction electrons bunch at the tip apex. There is considerable disagreement in both theoretical and experimental papers [21-24] to the amount of enhancement, but, fortunately, the lightning effect does not affect the power law behavior and is therefore not explicitly given in Eq. (1).
In our pump-probe experiments, the temporal dependence of the laser field is given by
where a and b are the complex beam parameters . This laser field is the superposition of two pulses, separated in time by a relative delay of x0 c which we introduce using an autocorrelator. We determine the magnitudes F0i of each of the two pulses separately by
measuring their average laser power Pavg :
in which frep is the repetition rate of the laser, d the full-width-half-maximum of the focal spot, and tlaser the laser pulse duration. We find the emission current as a function of the autocorrelator delay x0 / c by numerical integration over time. Equation (1) directly gives the electron emission as a function of polarization and laser power.
If the laser field causes electrons to tunnel, the current from the tip, J field, is given by the Fowler-Nordheim equation,
for a constant C0 , and the excited state populations are assumed to be proportional to a power of the laser intensity, an ∝ I n. The total electric field is the sum of the static and laser fields: Ftot = FDC + Flaser cos θ. The factor accounts for the field enhancement due to the lightning effect. The static electric field is given by FDC = V kr, where V is the voltage placed on the tip, r is the tip radius, and k (here equal to 5) accounts for details in the tip geometry . To describe tunneling preceded by absorption of n photons we lower the workfunction to φ − n ω. We find the emission current by numerical integration over time.
Such time averaging is only appropriate if the tunneling time of the electron from the metal tip () is shorter than the optical period of the laser light. In the field of an electromagnetic wave, the critical parameter identifying this regime is the Keldysh parameter γ. For γ 1 multiphoton absorption dominates, while tunneling dominates for γ 1 [13, 14].
For a metal surface the Keldysh parameter is given by γ = ω (2mφ )1/ 2 /(eFlaser ) . For a field emission tip the magnitudes of the DC field and laser field are of the same order and the emission process is strongly dependent on both fields. The Keldysh parameter should thus depend not only on Flaser but also on FDC. This dependence is present when the workfunction is replaced with the effective workfunction. Note that the Keldysh parameter is only meaningful when the photon energy is less than the workfunction.
We also consider the possibility of laser induced thermionic emission. It has been suggested that thermionic emission is most efficient when the laser polarization is perpendicular to the tip axis . On the other hand, in the investigated experimental regime thermionic emission is thought to be negligible [20, 28, 30].
A schematic of our experimental setup appears in Fig. 2. Laser pulses from a Ti:sapphire femtosecond oscillator (Spectra Physics Tsunami) are first compressed using a single-prism pulse compressor . A subsequent variable attenuator controls the delivered laser power. We use a Mach-Zehnder type autocorrelator to split the laser pulse into a pump and probe pulse and to provide a variable time delay between them. We let the recombined laser beam emanating from the autocorrelator pass through a half-wave plate to adjust the overall laser polarization. A frequency resolved optical gate (FROG) is used to measure the pulse characteristics just before the pulse enters the vacuum system. We measure a laser pulse width of 32 fs, with a time-bandwidth product of 0.5. The fused silica vacuum entrance window is 3 mm thick. To focus the laser beam onto the field emission tip we use a 90-degree off-axis gold-coated parabolic mirror placed in the vacuum system (parent focal length = 12.7 mm, P/N A8037-176 Janos Technology). We have connected the field emission tip to an XYZ translation stage through a flexible bellows to allow for optimization of the electron emission. The tungsten tip is etched with a lamella drop-off method .
Figure 2. Experimental setup.
A femtosecond laser oscillator produces radiation pulses at a rate of 75 MHz. An autocorrelator provides time adjustable pump and probe pulses. The laser pulses are focused on a field emission tip to extract electron pulses. (For a more detailed description see text.) The experiment is contained in an aluminum vacuum chamber that is evacuated with a turbomolecular pump and is operated at a pressure of ∼ 10−8 Torr. To estimate the tip radius the Fowler-Nordheim equation is fit  to the voltage-dependent electron emission yield, giving a value of ~40 nm. A metal plate with a 5-mm pinhole placed at 1 cm from the tip defines the ground potential. A channeltron (Sjuts KBL 520) is used to detect the electrons.
Once the laser pulses have left the vacuum system through a second optical window we measure the average beam power with a power meter. The electron pulse detection signals are sent through a constant fraction discriminating amplifier, and then fed into a multichannel scaling board. This board records electron emission autocorrelation spectra, which provides information on the femtosecond scale. The laser intensity autocorrelation trace (Fig. 3a) is measured simultaneously with the electron emission autocorrelation spectrum (Fig. 3b). In this way the laser intensity can be correlated to the electron emission. The oscillator delivers pulses at a repetition rate of 75 MHz, with a maximum average output power of ~500 mW corresponding to a pulse energy of ~10 nJ. This is enough to damage the tip so a variable attenuator is used. To avoid detector damage we limit the electron count rate to 106 /s (reached at ~25 mW depending on the applied DC voltage). We estimate the laser focus to have a full width at half maximum of ~ 4 µm.
When the two pulses emanating from the autocorrelator are delayed to the extent that they do not overlap, they act as a pump-probe pair. The first pulse influences the tip and the second pulse probes if the tip “remembers” the first pulse. Once the electron emission from the two laser pulses becomes additive, there is no memory of the first pulse anymore, so the electron emission process should be at least as fast as the delay for which this happens (Fig. 3c). The temporal resolution of this pump-probe experiment is limited to the duration of the laser pulse, because the two pulses are coherent with each other. As the delay between them is reduced below their temporal width, the two laser pulses start to interfere, creating an intensity modulation which is seen in the autocorrelation trace (Fig. 3a).
At delays greater than 100 femtosecond the sum of the electron signals with each laser pulse separately (blue and red), nearly equals the electron signal with both pulses present (black). As discussed above, this additive behavior indicates that the electron emission process is faster than 100 fs. In a very recent similar study  this additive behavior is also reported at 100 fs.
A duration of 100 fs is compatible with the mechanisms we consider, except for thermionic emission. For a field emission model one expects that the electron emission process is of sub-cycle duration . The time for multiphoton over-the-barrier emission for a tip is unknown to the authors and will depend on the detailed electron dynamics.