Time-dependent quantum tunneling and nonequilibrium heating model for the generalized Einstein photoelectric effect

Abstract

By combining the time-dependent Schrödinger equation with microscopic kinetic equations, a model for femtosecond-laser-induced electron emission from a metallic surface is developed to capture the physics of nonequilibrium heating and also the multiple-energy time-dependent tunneling. Using this model, we observe an enhanced electron emission due to the tranmission resonance at a particular energy level with a barrier height that produces a resonant frequency near to the laser frequency. Contrary to both pure optical tunneling and pure multiphoton emission models, the model provides better agreement with experiments. The generalized Einstein photoelectric effect is found to be inaccurate in this regime because of the nonequilibrium electron energy distribution, the resonant enhancement, and the ultrashort laser pulse width. The role of photons in the multiphoton electron emission regime is studied in detail. A smooth transition from the multiphoton regime to the optical tunneling regime is demonstrated.

Attosecond-controlled photoemission from metal nanowire tips in the few-electron regime

“…This could be attributed to the combined effect of the averaging over different emission sites and consequently different field strengths as discussed above, and different initial states as well as multiple electron emission. A number of recent studies [38][39][40][41] have focused on the excitations of electrons inside the metal and their influence on photoemission. For the low-repetition rate in our experiment, 38 the short laser pulse duration, 40 and the large tip volume compared to etched tips with the same radius, 41 we do not expect to observe a significant contribution of this effect.…”

“…A number of recent studies [38][39][40][41] have focused on the excitations of electrons inside the metal and their influence on photoemission. For the low-repetition rate in our experiment, 38 the short laser pulse duration, 40 and the large tip volume compared to etched tips with the same radius, 41 we do not expect to observe a significant contribution of this effect. The data do not provide clear signatures of thermionic emission; however, we expect future dedicated experimental and theoretical studies to shed some more light on this topic.…”

Delayed electron emission in strong-field driven tunnelling from a metallic nanotip in the multi-electron regime

“…For relatively weak laser fields, in combination with a strong DC voltage applied to the tip, electrons excited by multi-photon absorption tunnel through the surface barrier (DC tunnelling) or are emitted over the barrier as illustrated in Model A in Fig. 1(a)234567891011. These processes are insensitive to the laser phase and generate femtosecond electron pulses6789.…”

“…These processes are insensitive to the laser phase and generate femtosecond electron pulses6789. On the other hand, very strong laser fields largely modify the surface barrier and drive direct tunnelling emission through the barrier as shown in Model B (AC tunnelling), producing attosecond coherent electron waves91012131415161718192021. This laser-driven AC tunnelling emission - also termed optical field emission - has become the subject of intense research in ultrafast science.…”

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

“…12 There has been renewed interest in investigating whether an injection of time-varying current density can contribute to a larger current density that is transmittable across the diode space. [13][14][15][16][17][18][19][20][21] On the other hand, time-varying current emission through the diode anode arises naturally even when the injection current density is time-invariant, with the diode voltage being fixed. For example, a recent work based on the 1D charge sheet model investigated how the temporal interval becomes distorted due to the space-charge effect.…”