The photoelectric effect describes the ejection of an electron from a metal by a high-energy photon (photon energy > work function of the metal) ^{1, 2}. High intensity irradiation with low-energy photons can also result in electron emission by the multiphoton photoelectric effect^3-6.

Additionally, low-energy photons can generate hot electrons which are in thermal nonequilibrium with the host lattice^7-9. Electron-electron scattering leads to equilibration on a sub-picosecond time scale, which allows the application of the two-temperature model¹⁰. After the electron-phonon relaxation time, which is on the order of several picoseconds, electrons return to thermal equilibrium with the lattice by electron-phonon-scattering. Due to the comparatively low heat capacity of the electron gas, electron temperatures of the order of 10³ K to 10⁴ K are easily achieved while maintaining a cold lattice. These hot electrons can be thermally emitted into the environment as a current burst with a duration on the order of the electron-phonon relaxation time^11-13.

For a Gaussian beam, the absorbed volumetric energy density is

where E is the pulse energy, β is the fraction of absorbed radiation, w is the Gaussian beam radius, and μ = 142 nm is the effective absorption length of silver⁸. For low electron temperatures up to some 5000 K, the electron heat capacity of silver C_e is approximately C_e ≈ γ_eT_e¹⁴ where γ_e = 62.8 J m⁻³ K⁻² is the heat capacitance coefficient of silver¹⁴. Via C_e = dU/dT_e, the electron temperature T_e thus is

Figure 1 shows the electron temperature calculated according to Eq. (2).

A metal under irradiation in contact with an electrolyte emits electrons which undergo thermalization and solvation within a time span of 100 fs to 1 ps corresponding to the fast Debye relaxation time in water¹⁵. In an electron acceptor-free solution, solvated electrons may then diffuse back to the electrode and are reinjected. If, however, a sufficient number of electron acceptors (such as H₃O⁺, N₂O, or NO₃⁻) are present, the electrons can be scavenged¹⁶.

The work function from a metallic electrode into an electrolyte solution ϕ is the difference between the conduction band edge of the solution and the Fermi energy of the metal. ϕ depends on the electrode potential φ versus a reference potential and on the work function at that reference potential ϕ₀ so that

with the elementary charge q_e.

Thermionic electron emission from a heated electron gas in nonequilibrium with the host lattice has been calculated using a one-dimensional interface potential¹⁷. The emitted charge density q is mainly determined by the electron gas temperature T_e at the surface and the electrode potential contained in the work function¹⁷. At T_e < T_c (~ 1500 K¹¹) tunneling is predominant, whereas at T_e > T_c over the barrier emission prevails¹⁷. When T_e > T_c, the charge emitted from the electron gas into the electrolyte is

with the Richardson constant A₀ ≈ 120 A cm⁻² K⁻¹, the Boltzmann constant k_B, the duration of the current pulse which is equal to the electron-phonon relaxation time τ_e, and the work function in an electrolyte ϕ (Eq. (3)). Equation (4) describes the exponential dependence of q on the pulse energy E (Eqs. (1) and (2)) and the electrode potential φ (Eq. (3)). In the tunneling case, T_e < T_c, the emitted charge is negligible and cannot be measured experimentally¹⁷.

Due to the Gaussian laser beam shape, the electron temperature T_e and hence the emitted charge density q is radially nonconstant. Hence, the total emitted charge Q is

where r_e is the electrode radius.

At relatively high electrolyte concentrations, the electrochemical diffuse double-layer can be neglected. The latter represents the space charge in the electrolyte¹⁸.

There has been vivid interest in laser electrochemical phenomena and applications. Laser-induced electrochemical deposition of metals on metals relies possibly on thermal and defect generation effects¹⁹. When semiconductor substrates are chosen, locally photogenerated electrons can reduce metal ions resulting in metallic surface structures^20-22. Laser-induced electrochemical de- and repassivation investigations are of interest in in-situ corrosion research studies^23-25. The thermoemission of nonequilibrium electrons can be a unique technique for the generation of picosecond current pulses which cannot be realized by conventional instrumentation¹⁷. This allows short-lived intermediates of electrode reactions to be studied.

A block diagram of the laser-electrochemical system is depicted in Fig. 2. The electrochemical cell consists of a silver working microelectrode (μWE, r_e = 15 μm radius) and a macroscopic platinum wire (1 mm diameter, 15 mm length) as counter electrode (CE). The fabrication of the extremely small μWE with a diameter of only 30 µm required an elaborate procedure described in the Supplementary information. A saturated Hg/Hg₂SO₄ reference electrode (not shown in Fig. 2) was employed to monitor the steady-state electrochemical potential during laser irradiation and the impedance spectroscopy (see below) experiments. Argon purged 0.2 M aqueous K₂SO₄ was used as the electrolyte with a pH adjusted to 2.2 with concentrated H₂SO₄.

Via a large-valued resistor (R: 1 MΩ), the μWE was kept at the desired steady-state potential φ, controlled by a digital-to-analog converter (DAQ; DAQPad-6020E DAC, National Instruments). In order to facilitate measuring the small hot electron emission-induced signal Δφ(t) (order of millivolts) on the dc-bias background φ, a high pass amplifier (HPA) was employed. It provided an input impedance of 10¹² Ω, dc voltage suppression, an amplification of ~10², and a bandwidth of 1.5 MHz. The hot electron-induced transient potential change output Δφ(t) of the HPA was recorded by a digital storage oscilloscope (OSC; WaveRunner 64Xi, LeCroy).

A Ti:Sapphire Chirped Pulse Oscillator (fs-CPO; modified Femtosource XL, Femtolasers Produktions GmbH) delivered ultrashort pulses at a central wavelength of 800 nm ≙ 1.55 eV with a repetition rate of 11 MHz and pulse durations of either 55 fs or 213 fs. Pulses were picked with a Pockels cell at a rate of 50 Hz. The laser pulse energy E was adjusted using a half-wave plate/polarizer combination and delivered through a microscope objective (OBJ; EC Plan-NEOFLUAR 10×/0.3, Zeiss). The laser beam exiting the microscope objective was characterized with a custom knife edge beam profiler²⁶, yielding a beam waist radius of w₀ = (1.6 ± 0.1) µm and a Rayleigh length of z_R = (11.7 ± 0.4) µm. Using the method reported in ref.²⁷, the µWE was placed in front of the beam waist to achieve a beam radius of w = 10 µm.

The applied laser peak fluences F₀ were varied between 30 mJ cm⁻² and 70 mJ cm⁻², well below (factor of ~6) the multi-pulse damage threshold of silver immersed in the electrolyte, as determined by the A−ln(E) approach^28-30. φ was varied between −500 mV and +500 mV vs. the standard hydrogen electrode (SHE), which covers a potential region well within the polarizability range of the used silver microelectrode³¹ as confirmed by repeated cyclic voltammetry sweeps.

Owing to the comparatively large time constant of the electrochemical cell, the measurable quantity is the integral of the emission current, i.e., the emitted charge (Eq. (4)) which is observable as the transient voltage change Δφ(t) of the µWE. Figure 3 shows exemplary Δφ(t) transients triggered by a fs laser pulse irradiating the µWE. The extracted peak voltage change of Δφ₀ = (19.7 ± 0.1) mV is highlighted in the inset of Fig. 3(a).

The electrons emitted from the electrode into the electrolyte get solvated and quickly reduce the solvent, i.e., reduce the solvated H⁺ (hydronium ions). This leads to a recharging of the electrochemical double layer, characterized by its capacitance C_dl. That causes a transient change in the potential of the working electrode with amplitude Δφ₀. Thus, the emitted charge is Q = Δφ₀C_dl.

Impedance spectroscopy was employed for the determination of the double layer capacitanceC_dl(f, φ) as a function of frequency f and the dc bias potential φ. Figure 4 shows an exemplary impedance trace measured in situ prior to recording the Δφ(t) transient. Due to the large difference in surface area between the μWE and the CE (~10⁴), the electrolyte and counter electrode contributions to the overall impedance can be neglected. To account for slight deviations from the ideal capacitive 1/f behavior (which is commonly observed in electrode impedance measurements), a constant phase element model (CPE)^{32, 33} was applied to determine C_dl. In this specific example, a frequency dependent double layer capacitance of C_dl(f) = [(0.40 ± 0.02) (f/1 Hz)^{(−0.064 ± 0.003)}] nF was derived. For a frequency of 2.5 kHz, which approximates the inverse transient decay time of Δφ(t), this translates to a capacitance of (0.21 ± 0.01) nF. This particular example (τ = (55 ± 1) fs, F₀ = (64 ± 7) mJ cm⁻², φ = (−460 ± 40) mV vs. SHE) thus yields Q = (4.2 ± 0.2) pC.

Figure 5 shows the logarithmic plot of the emitted hot electron charge Q over the applied electrode bias φ and the peak laser fluence F₀ for two pulse durations, τ = (55 ± 1) fs and τ = (213 ± 1) fs. Despite the significant difference in terms of pulse duration (factor of ~4), emitted charges are largely unaffected. This also means that multiphoton excitation can be ruled out. The emitted charges range from 1 fC to 5 pC. This corresponds to 5×10³ to 3×10⁷ electrons emitted from the metal into the electrolyte solution. Thus, the external quantum efficiency is very low and ranges from 2×10⁻⁸ to 6×10⁻⁵. Considering the electron-phonon relaxation time (700 fs³⁴ for Ag) as the duration of the current pulse and the Gaussian beam area w²π as the emission surface, current densities exceeded 2×10⁶ A cm^{−211, 12, 35}.

A comparison with previous work shows that the maximum charge density below the damage threshold of Ag is comparable with the present results, i.e., ca. 1 µC cm^{−211, 12, 35}. However, the method of the Gaussian beam radius determination strongly deviated which affects the reported intensity scale. The previous studies relied on the simple evaluation of the diameter of the blackened area on a photographic paper. This is known to overestimate the actual Gaussian beam radius. In the present work, it was determined by the accurate knife edge method^{26, 36}.

The strongly superlinear, almost exponential, dependence of the emitted chargeQ, and thus current density, on the laser fluence F₀ is in accordance with the thermoemission model expressed by Eq. (5). The two employed pulse durations are significantly shorter than the electron-phonon relaxation time (~ 700 fs³⁴). With a weak temperature dependence of reflectivity and energy deposition depth, the local peak electron temperature T_e will depend only on the local fluence F(r) according to Eq. (2). The gray surface in Fig. 5 is calculated according to Eq. (5) using the following parameters. For silver, the work function in aqueous solution at the point of zero charge is 2.77 eV³⁷. The point of zero charge is −640 mV vs. SHE³⁸. With this, the work function is φ₀ = 3.41 eV at 0 V vs. SHE. The effective absorption length was reported as μ = 142 nm due to ballistic electron transport⁸. The electron heat capacity coefficient was reported to be γ_e = 62.8 J m⁻³ K⁻²¹⁴. For a moderately polished surface, a fraction of absorbed radiation of β = 0.15 can be assumed. On the other hand, the laser pulse durations had negligible impact on the emitted charge, which is incompatible with multiphoton emission.

The photonic excitation of the metallic Fermi sea leads to a broadened Fermi-Dirac distribution n(ε) in the metal electrode (Fig. 6). The scale of ε is opposite to the electrode potential scale φ. The electron transfer at the interface to the electrolyte takes place according to the Franck Condon principle at constant energy^{39, 40}. The Fermi level ε_F in the absence of irradiation, which is electrochemically controlled by the applied potential φ, is positioned such that electron transfer to the electron scavenger in the electrolyte is thermodynamically negligible. The Fermi sea, which is heated upon laser irradiation, can inject electrons at a higher energy level than the equilibrium state into the fluctuating states of the hydronium ions. This corresponds to a more negative electrode potential φ. The initial reduction product of this process is hydrogen in statu nascendi, atomic H⁰. According to the Franck Condon principle mentioned above, this extremely strong reducing agent can re-inject an electron into the metal. This became possible because the Fermi distribution returned to its equilibrium state after the electron-phonon relaxation.

Hot electrons in thermal nonequilibrium with the metal lattice were generated with low-energy photons from a femtosecond pulse laser. Two pulse durations, τ = (55 ± 1) fs and τ = (213 ± 1) fs significantly shorter than the electron-phonon relaxation time were employed with little effect on the emitted charge. A multiphoton emission scheme should depend strongly on intensity and thus pulse duration. This is however not observed, discouraging the interpretation of multiphoton photoemission. Electrons were emitted into an adjacent acidic K₂SO₄ electrolyte as giant current pulses with durations of the order of the electron-phonon relaxation time. Current densities reached 2×10⁶ A cm⁻². Emitted electrons reacted with the solvent by reducing the protons to hydrogen. The transient electrode potential change based on the recharging of the electrochemical double layer was registered. The strongly superlinear dependence of the emitted charge on the laser fluence is supported by the thermoemission model. The photonic excitation of the metallic Fermi sea leads to a broadened Fermi-Dirac distribution in the metal electrode. The former injects electrons at a higher energy level, i.e., at a more negative electrode potential, than the equilibrium value into the fluctuating states of the hydronium ions. The reduction products can re-inject electrons into the metal because the Fermi distribution has returned to its equilibrium state.