Examining the Transition from Multiphoton to Optical-Field Photoemission From Silicon Nanostructures

We perform a detailed experimental and theoretical study of the transition from multiphoton to optical-field photoemission from n-doped, single-crystal silicon nanotips. Around this transition, we measure an enhanced emission rate as well as intensity-dependent structure in the photoelectron yield from the illuminated nanostructures. Numerically solving the time-dependent Schr\"odinger equation (TDSE), we demonstrate that the excess emission derives from the build-up of standing electronic wavepackets near the surface of the silicon, and the intensity dependent structure in this transition results from the increased ponderomotive potential and channel closing effects. By way of time-dependent perturbation theory (TDPT), we then show that the visibility of intensity dependent structure, the transition rate from multiphoton to optical-field emission, and scaling rate at high intensities are all consistent with a narrow band of ground-state energies near the conduction band dominating the emission process in silicon. These results highlight the importance of considering both coherent electron wavepacket dynamics at the emitter surface as well as the ground-state energy distribution when interpreting strong-field photoemission from solids.