Mechanisms of high-regularity periodic structuring of silicon surface by sub-MHz repetition rate ultrashort laser pulses

Laser-induced periodic surface structures (LIPSS), also referred to as ripples, were observed by Birnbaum in 1965 on a silicon surface irradiated with a ruby laser.¹ Since that, the formation of laser-induced periodic surface structures has been produced for a broad range of wavelengths and pulse durations on metals,^2–4 semiconductors,^5–11 dielectrics,^12,13 and polymers¹⁴ and their importance was demonstrated for various scientific, biomedical, and industrial applications (see detailed reviews in Refs. 15–17). One of the frequently cited mechanisms of LIPSS formation is attributed to mild ablation that produces ripples by etching an unperturbed surface at laser fluence very close to ablation threshold.^2–6 Majority of previous publications report the mild-ablation LIPSS on metals, semiconductors, dielectrics, and polymers, but their periodic ripples suffer from irregularity due to multiple branching points where several ripples merge together. Those bifurcations of the LIPSS are characteristic of that approach because the process of ripple formation is distorted by localized perturbations of either laser fluence around the ablation threshold (e.g., due to scattering at surface roughness) or material response. Also, attempts to cover large areas with LIPSS by scanning techniques have faced the fundamental challenge of low speed of surface processing by the ablation at fluence about ablation threshold.

Although the use of femtosecond lasers has brought the possibility to produce finer structures by high spatial frequency LIPSS (or HSFL),^4,7,15 nanostructuring large areas with a high-quality bifurcation-free LIPSS remains a challenge due to a highly reduced throughput. A relatively low speed of the ablation-LIPSS generation (estimated as ∼30 mm²/min for the irradiation conditions of Ref. 18) strongly limits the transfer of LIPSS direct-writing methods from laboratories to industry. Recently, a thermochemical mechanism of LIPSS formation was proposed¹⁹ that delivers a more regular ripple structure over large areas^19–21 by forming oxide layers on the top of original surface.^19,20 De la Cruz et al.²² have demonstrated an optimized LIPSS generation by utilizing a galvanometric scanner to cover 9 cm² area of chromium surface with regular LIPSS in less than 6 min. Although a record-high speed of the surface nanostructuring has been reported for the thermochemically produced LIPSS (1.0–1.5 m/s, Ref. 20), the limited speed of the oxidation processes involved in that method puts several fundamental limitations on the range of applications of this approach. In particular, it is advantageous for metal surfaces while nanostructuring of non-metal materials with the thermochemical LIPSS is not feasible at a high speed.

Here, we report the production of highly regular LIPSS at laser fluence significantly above the ablation threshold to nanostructure large areas of non-metal surfaces, e.g., silicon (Figure 1) at a rate that significantly exceeds the speed of the thermochemical nanostructuring. The ablation ripples show bifurcation-free structure on large areas of the surface evenly treated at the rate acceptable for industrial use. The specific regime of the LIPSS formation by fast scanning of Si surface with high-power (well above the ablation threshold) laser pulses at a repetition rate of the order of 10²kHz calls for a substantial revision of existing concepts of LIPSS formation. For such a regime of strong ablation, evolution of a laser-excited surface toward imprinting of highly reproducible ripple structures by single²³ or very few overlapping pulses should involve several competing and complementary processes. Below we analyze conditions of the LIPSS formation at a high speed of scanning and propose a plausible scenario of the physical processes responsible for the rapid LIPSS formation.

A sketch of the experimental setup is shown in Figure 2. Optical pulses (central wavelength 1030 nm, pulse width 213 fs (FWHM), repetition rate 600 kHz) were delivered by Yb:KGW chirped-pulse application laser system (model PHAROS 20 W from Light Conversions Ltd.) and were forwarded to a galvanometric scanning head (Cambridge Technology). Alignment of linearly polarized laser light was controlled by a half-wave plate. The surface treatment was done in air at room temperature by scanning laser beam across sample surface. To control the average power of the laser pulses at sample surface, a motorized attenuator was utilized to transmit about 2.5% of incident power of the laser system. Average power hitting the focusing lens was 0.5 W. The laser beam was focused by an F-theta lens with a focal length 55 mm that produced an approximate diameter of the irradiation spot of 7.34 μm (1/e of peak intensity) on the sample. Transmittance of the focusing system was measured independently prior to the experiments and was found to be 80% at the laser wavelength. With those data, we estimated the peak fluence as ∼1.58 J/cm² on the surface. For the scanning approach, 10 mm long lines were formed in Y-direction by moving the laser spot with the galvanoscanner while switching from line to line was done in X-direction by moving the sample with a motorized stage so as to provide approximately 4 μm interline spacing.

For this work, the sample was a single crystalline undoped Si ⟨111⟩ wafer, of 4 Ω·cm resistivity and thickness of 300 μm. The treated-surface morphology was characterized with both secondary electron microscopy (SEM) imaging and custom modes using a FEI Nova NanoSEM 450 equipped with X-EDS, model Bruker QUANTAX-200. The cross sections of the laser-treated samples and the corresponding images were obtained by means of a FEI Strata 235 M dual beam system. The system combines a Focused Ion Beam (FIB) equipped with a Ga Liquid Metal Ion Source (LMIS) and a SEM column equipped with a Schottky field-emission gun in a single apparatus. A cross section of silicon surfaces was obtained using FIB (E-beam = 30 keV) for milling, setting 1 nA as the ion beam current for milling and 300 pA for the final polishing.

The typical speed of linear scanning of the laser spot along the sample surface was about 10²cm/s. The SEM images (Figures 3(a) and 3(b)) uncover highly regular and homogeneous linear ripples with no bifurcations over entire treated surface except small areas (∼10 μm wide) next to the edges of the treated surface. Nanoparticles observed on the ripples indicate possible back-deposition of the ablation products on the LIPSS. The energy dispersive X-ray (EDX) map clearly shows almost pure silicon in the “valleys,” whereas “peaks” of the nanostructures have slightly increased (approximately by 2%) content of oxygen, while carbon can be attributed to polishing-induced contamination (Figure 3(d)). Contrary to the thermochemical LIPSS,^19–21 the ablation LIPSS do not show a remarkable increase of oxygen. The FIB images (Figure 3(c)) reveal a highly regular structure of LIPSS cross-section with the depth of the ripples (h) of ∼340 nm (from top to bottom) and the period (a) of ∼900 nm. Due to the ablation mechanism of the nanostructuring, peaks of the ripples are below the initial surface.

Exceptional reproducibility of LIPSS over large area implies that the LIPSS formation is mainly driven by highly deterministic microscopic processes that are totally controlled by laser parameters rather than by stochastic processes in the laser-excited material. Majority of the reported methods of the LIPSS formation utilize overlapping of many pulses at either sub-ablation-threshold⁸ or slightly above the ablation-threshold fluence that results in accumulation of the action of many pulses. Those conditions are favourable for the thermochemical mechanisms of LIPSS formation^19–21 or mild-ablation LIPSS.^2–6 By contrast, the high-speed nanostructuring reported here considers no more than 3–4 partially overlapping pulses at high fluence that implies a strong ablation regime. Based on the presented experimental data, we propose the following scenario of the high-speed HR-LIPSS formation on silicon.

Interference of incident laser beam with a scattered surface wave (Figure 4(a-i)) leads to a periodic distribution of absorbed energy of light across a laser spot on the surface in accordance with the Sipe-Drude mechanism.^6,24 One of dominating contributions to the absorption is provided by electron excitation from valence to conduction band (Figure 4(b)) paralleled with heating of conduction electrons.²⁵ Energy of a single laser photon (about 1.2 eV) supports several channels of the inter-band electron transitions: direct three-photon, indirect one-photon, and indirect two-photon (Figure 4(b)). The indirect processes involve electron-phonon collisions with a characteristic frequency about 10¹²–10¹³ 1/s.²⁶ Therefore, rates of those processes make a negligible contribution to the total process of electron excitation within a single laser pulse at the specific fluence. The direct inter-band three-photon transitions involve the states near the Γ-point of the Brillouin zone (Figure 4(b)): $Γ8+→Γ6−$ (band gap E′₀ = 3.28–3.5 eV); $Γ8+→Γ8−$ (band gap E′₀ + Δ′₀= 3.29–3.57 eV); and $Γ7+→Γ8−$ (band gap E′₀ + Δ′₀ + Δ₀= 3.36 eV). Since the Keldysh adiabatic parameter²⁷ is about 0.9 for the direct transitions in silicon, the rates of these transitions are evaluated from the Keldysh formula²⁷ with proper values of direct energy gaps and effective masses.²⁶ The total rate of the three-photon transitions is in the range of 10¹⁸–10¹⁹ fs⁻¹cm⁻³ at intensity 3.5 TW/cm² utilized in the experiments. Therefore, the three-photon transitions make a dominating contribution to the nonlinear energy absorption in silicon and increase of conduction-electron density at the beginning stage. Due to a strong nonlinear dependence on laser intensity, the three-photon absorption is more favourable for stronger confinement and localization of energy deposition from each individual laser pulse and makes the process of electron-hole plasma formation substantially deterministic and efficient at the local sites of the enhanced absorption as shown in Figure 4(a-ii).

Increase of conduction-electron density due to the nonlinear absorption and parallel heating of the electron-hole plasma stimulates photoemission (J_MP) and thermionic emission (J_TH) of electrons (tunnelling mechanism is banned by the parallel alignment of the electric field and the surface).²⁸ Their rates are given by the following equations:²⁸ 

where σ_N – the coefficient of multiphoton photoemission evaluated from the Keldysh formula²⁷ for interband transition between two parabolic bands; N is the minimum number of laser photons required to bridge the electron affinity W; ω is the laser frequency; h and ℏ are the Plank and Dirac constants; k is the Boltzmann constant; T and m are the electron temperature and mass respectively. The parametric dependence of the emission rates suggests that the photoemission dominates at the early stage of the laser-surface interaction. It involves the conduction electrons of the X-valley (the corresponding electron affinity is 4.05 eV)²⁶ and the non-equilibrium electrons appearing around the Γ-point of the conduction band due to the direct interband excitation (the corresponding energy gap W is about 1.89 eV). Electron transport from the Γ-point states to the X-valley states requires significant variations of electron momentum that can be provided only by inter-valley phonons (both optical and acoustic).²⁶ Low electron-phonon collision rate (10¹¹–10¹² 1/s)²⁶ suggests that the inter-valley electron transport can be neglected compared to significantly faster processes of the nonlinear absorption and electron emission. Therefore, the contributions to photoemission are independently made by 4-photon and 2-photon excitations of the two groups of conduction electrons. The thermionic emission is delayed and dominates at the tail part of laser pulse because it requires heating of the conduction electrons by 2–4 eV via electron-photon-phonon collisions. For the given laser parameters, the total emission yield from the two mechanisms is about 10¹⁹ 1/cm³ per pulse that supports formation of sub-micrometer domains of silicon surface with a reduced electron density and a transient localized positive charge.²⁵ An interference-induced modulation of the electromagnetic field intensity within the laser spot²⁹ should inevitably lead to a modulation of the positive-charge density across the surface. The partial positive charge may not be high enough to eject ions,²⁵ but being combined with the high rate of the interband electron excitation, it can support a periodically modulated bond softening that facilitates ablation from an electrostatically unstable surface sites.³⁰ Followed by non-thermal ablation from solid phase,³¹ the electrostatic instability of the silicon surface can be the main mechanism of LIPSS formation at laser fluence close to the ablation threshold.³² Note that thermionic emission does not require a direct action of electric field and can continue contributing after the laser-pulse termination,²⁵ further facilitating surface instability.

For the specified above irradiation regimes, massive ablation should occur at picosecond timescale after electron-lattice thermalization and melting of a surface layer. As shown in Ref. 29, a periodic temperature modulation on molten silicon surface, if generated, can preserve for as long time as ∼100 ps. At ultrashort laser pulses, ablation of molten phase occurs mainly through the phase explosion mechanism³³ with creation of periodic surface relief (Figure 4(a-iii)). Note that, in silicon whose melting proceeds with material compaction by ∼9%, mechanical expulsion of melt due to lateral stress generation³⁴ cannot noticeably contribute to ablation because the relatively low expansion coefficients of solid and liquid silicon do not sufficiently counterbalance compaction upon melting. However, a recoil pressure of the ablation plume can push remaining melt to the colder (lower absorption) sites as shown schematically by arrows in Figure 4(a-iii), thus helping to form a more pronounced periodic relief.

It has been proven that crack formation is one of the fundamental constituents of laser-induced nanograting formation inside fused silica and a number of other transparent crystals and glasses.³⁵ Similarly, cracking can play an important role in deepening of the LIPSS and making them more pronounced after the strong ablation phase. Upon solidification and further cooling, formation of cracks can be expected along the formed tranches due to tensile stress applied to “weak,” laser-scribes sites (Figure 4(a-iv)). The process of crack formation can be facilitated by rapid solidification of melt remains which occurs far from thermodynamic equilibrium.^36,37 For the most of materials which experience compaction upon solidification, the rapid solidification can lead to the formation of cavitation voids and bubbles in the LIPSS valleys due to rapid drop in pressure. For silicon whose behaviour upon solidification is opposite, the pressure in the LIPSS valleys can swiftly increase, thus leading to dislocations which in their turn will facilitate crack formation. Subsequent laser pulses are better absorbed in the LIPSS valleys, thus exacerbating the process of crack-assisted LIPSS trenches' deepening. However, non-equilibrium thermodynamics aspects of LIPSS formation call for further studies.

The incident laser fluence is, at the first glance, incompatible with LIPSS formation. However, LIPSS formation is driven by effective absorbed fluence that is significantly affected by the increase of silicon reflectivity produced by electron-hole plasma density generated during the laser pulse action. For femtosecond IR laser pulses, the reflection coefficient of silicon can increase up to 70%–80% at laser fluences four times above the melting threshold.³⁸ Hence, the effective absorbed fluence can be as low as ∼0.5 J/cm² in the irradiation spot center that is comparable to that of single IR laser pulses creating ripples on steel²³ whose reflectivity is ∼60%–65% at wavelengths ∼1 μm. However, according to simulations which are under progress, such level of absorbed fluence brings the external layer of material to a supercritical fluid state³⁹ that culminates in strong ablation of several dozens of nanometers. Also note that, according to the heat flow estimations for the repetition rate exploited in this work, heat accumulation has no pronounced effect. Those effects can become important for silicon at repetition rates of several MHz and higher and/or at reduced scanning rate favorable for increase of the number of laser pulses coupling to the same irradiation spot.

In conclusion, the exceptionally regular LIPSS have been produced on large area of silicon surface by infrared femtosecond laser pulses with sub-MHz repetition rate at extremely high processing speed. Covering 1 cm² by HR-LIPSS requires less than a minute that makes this technique appropriate for industrial applications. Theoretical analysis of the physical processes involved into formation of the HR-LIPSS suggests that the electrostatically assisted bond softening may noticeably contribute to initializing the ablation process.

N.M.B. and T.M. acknowledge the support from the state budget of the Czech Republic (project HiLASE: Superlasers for the real world: LO1602). V.G. acknowledges support from the U.S. National Science Foundation (Award No. CBET # 1336111). I.G. and L.O. would like to thank Alberto Rota and Enrico Gualtieri (Centro Intermech-MO.RE. - University of Modena and Reggio Emilia) for the FIB characterization.