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

By combining the time-dependent Schrodinger 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.