  We find that a donor-doped band-gap material can enhance the overall
high-order harmonic generation (HHG) efficiency by several orders of magnitude,
compared with undoped and acceptor-doped materials. This significant
enhancement, predicted by time-dependent density functional theory simulations,
originates from the highest-occupied impurity state which has an isolated
energy located within the band gap. The impurity-state HHG is rationalized by a
three-step model, taking into account that the impurity-state electron tunnels
into the conduction band and then moves according to its band structure until
recombination. In addition to the improvement of the HHG efficiency, the
donor-type doping results in a harmonic cutoff different from that in the
undoped and acceptor-doped cases, explained by semiclassical analysis for the
impurity-state HHG.
