Higher-harmonic generation in boron-doped silicon from band carriers and bound-dopant photoionization

TL;DR

This study explores ultrafast harmonic generation in boron-doped silicon at different temperatures, revealing high-order harmonics, temperature-dependent nonlinear responses, and the effects of ionization and scattering on harmonic yields.

Contribution

It demonstrates high-order harmonic generation up to n=13 in Si:B and analyzes the temperature-dependent nonlinear charge carrier dynamics with combined experimental and theoretical methods.

Findings

Harmonics up to n=13 observed at low temperature.

Susceptibility per charge carrier comparable to graphene.

High fields cause saturation due to optical-phonon emission.

Abstract

We investigate ultrafast harmonic generation (HG) in Si:B, driven by intense pump pulses with fields reaching ~100 kV/cm and a carrier frequency of 300 GHz, at 4 K and 300 K, both experimentally and theoretically. We report several novel findings concerning the nonlinear charge carrier dynamics in intense sub-THz fields. (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. The susceptibility per charge carrier at moderate field strength is as high as for charge carriers in graphene, considered to be one of the materials with the strongest sub-THz nonlinear response. (ii) For T=300 K, where the charge carriers bound to acceptors are fully thermally ionized into the valence subbands, the susceptibility values decrease with increasing field strength. Simulations incorporating multi-valence-band Monte-Carlo and finite-difference-time-domain (FDTD) propagation show that here, the HG process becomes increasingly dominated by energy-dependent scattering rates over the contribution from band non-parabolicity, due to the onset of optical-phonon emission, which ultimately leads to the saturation at high fields. (iii) At T=4 K, where the majority of charges are bound to acceptors, we observe a drastic rise of the HG yields for internal pump fields of 30 kV/cm, as one reaches the threshold for tunnel ionization. We disentangle the HG contributions in this case into contributions from the initial 'generational'- and subsequent band-nonlinearities, and show that scattering seriously degrades any coherent recollision during the subsequent oscillation of the holes.