Giant enhancement of attosecond tunnel ionization competes with disorder-driven decoherence in silicon

TL;DR

High-harmonic generation in solids is highly sensitive to attosecond tunnel ionization and coherent electron-hole transport. This study shows that amorphization of Si by Ga+ Focused Ion Beam dramatically enhances tunnel ionization (>$250$×) and reshapes the HHG spectrum, boosting lower harmonics while suppressing higher ones due to disorder-induced decoherence over a length scale of $\Delta_0 \approx 6a_0$. The dynamics are captured with real-space semiconductor Wannier equations incorporating a distance-dependent dephasing $\Gamma_{RS}(|\Delta_{nm}|)$, linking the observed spectral roll-off to medium-range order. Dose-controlled mapping reveals a critical amorphization threshold with remnant crystalline order in HHG, and non-resonant laser annealing demonstrates in situ healing of amorphous islands. Overall, the work establishes HHG spectroscopy as a nanoscale probe of structural disorder and points to CMOS-compatible routes for patterning silicon for lightwave nanoelectronics.

Abstract

High-harmonic generation (HHG) is a strong-field phenomenon that is sensitive to the attosecond dynamics of tunnel ionization and coherent transport of electron-hole pairs in solids. While the foundations of solid HHG have been established, a deep understanding into the nature of decoherence on sub-cycle timescales remains elusive. Furthermore, there is a growing need for tools to control ionization at the nanoscale. Here, we study HHG in silicon along a crystalline-to-amorphous (c-Si to a-Si) structural phase transition and observe a dramatic reshaping of the spectrum, with enhanced lower-order harmonic yield accompanied by quenching of the higher-order harmonics. Modelling the real-space quantum dynamics links our observations to a giant enhancement (>250 times) of tunnel ionization yield in the amorphous phase and a disorder-induced decoherence that damps the electron-hole polarization over approximately six lattice sites. HHG spectroscopy also reveals remnant order that was not apparent with conventional probes. Finally, we observe a rapid and targeted non-resonant laser annealing of amorphous silicon islands. Our results offer a unique insight into attosecond decoherence in strong-field phenomena, establish HHG spectroscopy as a probe of structural disorder, and pave the way for new opportunities in lightwave nanoelectronics.

Figures (17)

• Figure 1: HHG in a-Si vs c-Si.a, TEM micrograph showing the cross-section of an amorphized region of the Si surface. Numbers indicate the 1: c-Si substrate, 2: a-Si film, 3-4: protective carbon layers deposited prior to lamella milling. Log-scaled colormap of the CBED patterns with the electron beam focused on b, the amorphized silicon layer and c, the crystalline silicon substrate. Illustrations of d, the amorphous and e, crystalline structures at the atomic scale. The green bond lines illustrate the residual medium-range order aligned with the original cubic structure. f, Raman spectra measured in reflection mode with a 633 nm excitation wavelength for an unexposed (purple) and an amorphized (green) region of the silicon wafer. g, Schematic layout of the experimental apparatus for measuring HHG radiation. Relative to a, the laser is incident from left to right on layer 2 and harmonics are collected in reflection. h, Experimentally measured HHG signal for the crystalline (purple) and amorphized (green, $\mathrm{5\times 10^{15}\,cm^{-2}}$ ion dose) regions of the Si surface at a peak laser intensity of $\mathrm{360\,GW\cdot cm^{-2}}$. i-l, Polarization-dependent HHG yield for harmonics h5-h11, respectively, for c-Si (purple) and a-Si (green).
• Figure 1: a-g, Yield of harmonics h5-h17, respectively, as a function of peak laser intensity for samples with Ga dose ranging from 3.5-120$\mathrm{\times 10^{13}\,cm^{-2}}$. h, Continuum/noise background as a function of laser intensity. Black dashed lines: noise level.
• Figure 1: a, Illustration of the Raman backscatter geometry and the penetration depth, $\delta$, for the two different lasers. The schematics indicate the crystalline and amorphous regions of the sample. The a-Si film thickness is approximately 65 nm. Raman spectra of c-Si (black) and a-Si measured with b, a 514 nm excitation wavelength. and c, a 633 nm excitation wavelength.
• Figure 2: Role of disorder in attosecond quantum dynamics. Schematic illustration of the tunneling barrier in a strong electric field for a, c-Si and b, a-Si. c, Trajectory picture of HHG in a disordered crystal, where longer trajectories explore more of the inhomogeneous energy landscape, which randomizes their return time and energy. d, Parameterizations of the real-space dephasing (colored/shaded areas) used in g and semiclassical estimate of the the peak electric field required for the electron-hole excursion to reach $\Delta_{e-h}$ (black curve). The black arrows indicate the point where the dephasing rate reaches a third of a cycle, i.e., $\Delta_0$. e, Electric field and f, the corresponding population density calculated for a-Si (green) and c-Si (purple). g, Spectra calculated from the SWEs using a 1D model with a 1.75 eV band gap with real-space dephasing rates given by the curves in d. h, Spectra calculated with the same model as in g, but comparing c-Si (purple, gap 3.5 eV and $\Delta_0=16a_0$) and a-Si (green, gap 3.5 eV and $\Delta_0=6a_0$). The peak intensity was $340 \,\mathrm{GW\cdot cm^{-2}}$ in each calculation.
• Figure 2: a, Large-scale TEM cross section of a lamella extracted from a sample with Ga ion dose $\mathrm{4\times 10^{16}\, cm^{-2}}$, highlighting the Kikuchi patterns in the c-Si substrate. b, Zoomed in image of the sample in a, focused on the region with the correct orientation for electron diffraction. The 6 blue circles indicate the regions where CBED was performed. 1-6, Log-scaled image of the CBED patterns for the regions circled in a.