High-harmonic generation in p-doped Si by band non-parabolicity, energy-dependent relaxation and dopant photo-ionization

We investigate ultrafast harmonic generation (HG) in Si:B, driven by intense 300-GHz pump pulses with fields up to 115 kV/cm, at $4 \sim \mathrm{K}$ and $300 \sim \mathrm{K}$. We report several novel findings: (i) Harmonics of order up to n=9 are observed at room temperature, while at low temperature we can resolve harmonics reaching even n=13. (ii) For T=300 K, simulations by multi-valence-band Monte-Carlo calculations combined with finite-difference time-domain propagation show that the HG process, upon increase of the radiation field, becomes more and more dominated by energy-dependent scattering rates over the contribution from band non-parabolicity. (iii) At T=4 K, we observe a drastic rise of the HG yield with the THz field strength, as one reaches the threshold for tunnel ionization at (internal) pump fields of 30 kV/cm. We disentangle the HG contributions in this case into contributions from the initial ‘generational’ and subsequent band-nonlinearities, and show that scattering severely degrades any coherent recollision during the subsequent oscillatory motion of the holes.