The TNT layers of thicknesses of ∼1 μm and ∼20 µm with the nanotube diameter of ∼80 nm and ∼110 nm respectively were prepared by electrochemical anodization of Ti foils as described in the previous papers (Das et al., 2016; Zazpe et al., 2016). In brief, Ti foils (0.127-mm thick, Sigma-Aldrich, 99.7% purity) were degreased by sonication in isopropanol and acetone and dried in air. Afterwards, the Ti foils were anodized at room temperature in an electrochemical cell using a 2-electrode configuration with the Ti foil serving as anode and a Pt foil as a cathode. A high-voltage potentiostat (PGU-200, Elektroniklabor GmbH) was employed as a voltage source. ∼1 µm thick TNT layers were produced in a glycerol-based electrolyte containing 50 vol% H₂O and 270 mM NH₄F (Sigma-Aldrich, reagent grade) at 20 V for 100 min (Das et al., 2016). ∼20 µm thick TNT layers were produced in an ethylene glycol-based electrolyte containing 1.5 vol% H₂O and 170 mM NH₄F at 60 V for 4 h (Zazpe et al., 2016). The anodized area of each foil was 1 cm². After anodization, the TNT layers were rinsed, sonicated in isopropanol, and dried in air.

The morphology of the TNT layers was characterized by a field-emission Scanning Electron Microscope (FE-SEM JEOL JSM 7500F) and by a High-Resolution Transmission Electron Microscope (FEI Titan Themis 60–300) operated at 300 keV and equipped with a Cs (spherical aberration) image corrector. Raman spectra were recorded by LabRAM HR (Horiba Jobin Yvon) and acquired in a continuous scanning mode under a laser excitation wavelength of 532 nm. The composition of the TNT layers was monitored by X-ray Photoelectron Spectroscopy (XPS) (ESCA2SR, Scienta-Omicron) using a monochromatic Al Ka (1,486.7 eV) X-ray source. A typical image of an as-prepared ∼20 µm thick TNT layer used in the laser annealing experiments, a magnified view of the nanotubes from the top of the layer, and its cross-sectional view are shown in Figure 1.

The band gap of the main crystalline phases of TiO₂ is somewhat larger than 3 eV (Scanlon et al., 2013). Hence, for efficient absorption of laser light with a nanosecond pulse duration, a UV spectral range is appropriate (Wawrzyniak et al., 2020a; Wawrzyniak et al., 2020b; Siuzdak et al., 2023). However, the absorption depth for UV light is rather short, of the order of few dozens of nanometers. To evaluate the absorption depth, we have applied the Maxwell-Garnett effective medium framework (Heavens, 1960). The effective medium theory allows evaluating the optical properties of composite and porous materials via taking into account the dielectric function of each component. The Maxwell-Garnet expression for the TiO₂ nanotubes under air surrounding can be written as ε e f f − ε m ε e f f − 2 ε m = f ε T i O 2 − ε m ε T i O 2 − 2 ε m where ε eff , ε m , and ε T i O 2 are the effective dielectric function of the TNT layer and the dialectic functions of the external medium (air) and TiO₂ respectively; f is the volume fraction of TiO₂ in the layer. The above expression yields the following formula ε e f f = ε m 1 + 3 f β 1 − f β  with  β = ε T i O 2 − ε m ε T i O 2 − 2 ε m .

The results of calculations of the absorption depth and the reflection coefficient based on the above formulas are shown in Figure 2 for a 260 nm wavelength and similar results are obtained for wavelengths of 193 nm (ArF laser) and 355 nm (Siuzdak et al., 2023). For ∼40% volume fraction of TiO₂ in TNT layers, absorption is mostly localized in a ∼100-nm top layer. Hence, in the UV spectral range, light absorption takes place on the tops of TNT layers, leading to local heating and melting, while the heat extraction along nanotubes is relatively slow. Indeed, from the heat flux equation, one can easily extract an evaluating expression ∆ x ∼ √ λ h Δ t / c p ρ where λ _h , c _p and ρ are the thermal conductivity, heat capacity, and density respectively. This expression gives that, in titania during time interval ∆ t ∼ 1 µs, the heat front propagates only to approx. 1.3 µm. This is the origin of strongly distorted nanotube tops reported in the literature which however can lead to the conversion of amorphous TNTs into the anatase phase (Siuzdak et al., 2023).

To explore the possibilities of laser annealing of the TNT layers with minimal damage to their morphology, we have used different lasers, which are outlined in Table 1 and their applications are analyzed in the next sections.

We anticipate that, at optimal conditions of ultrashort laser annealing, we observe an effect of the pressure-induced solid-phase crystallization, often called explosive crystallization. The pressure-induced crystallization represents a transition from the low density amorphous to a higher density (pressurized) amorphous phase, followed by crystallization (Pandey et al., 2011). Ultrashort laser heating of a top layer of a sample may yield a strong unloading stress/shock wave propagating toward the sample depth (Zhigilei et al., 2009; Karim et al., 2016), which can trigger such phase transformation. Let us evaluate the possibility of a shock/compression wave under our irradiation condition in the stress-confinement regime.

The absorbed laser energy at the top of the nanotube can be evaluated as E ab = 1 − R F / d where R is the reflection coefficient, F is the incident laser fluence, and d is the absorption depth. Using the thermodynamic relation c p Δ T = E ab and the data from Figure 2, one can estimate that, at the optimal laser fluence of 1 mJ/cm², the temperature increase is confined within the absorption depth of ∼100 nm and it is only of ΔT ∼ 125 K, well below the melting point. For a hollow cylinder, the stress corresponding to such heating can be estimated as σ z = E α T 0 − T max / 1 − μ with E , α , and µ to be Young’s modulus, the coefficient of linear expansion, and the Poisson ratio respectively (Kingery, 1955). This yield for a single shot σ z ∼ −560 MPa. This is a noticeable stress formed in only 2-ps time that should generate a stress (or shock) wave propagating along each nanotube as shown in Figure 8A. Note that the initial stress is lower than the compressive strength of TiO₂ (680 MPa) and hence the nanotubes are not damaged mechanically. Important is that the stress wave propagates in a one-dimensional manner and hence its dissipation is rather small. If such a wave ignites crystallization in some nanotube sites, the heat of ∼22.6 kJ/mol is released upon crystallization that can result in a self-propagating wave of crystallization (Rogachev et al., 2017) along the nanotubes.

The activation energy ΔE _act for amorphous-to-anatase transformation is 69 kJ/mol, lower than that for anatase-to-rutile transformation (129 kJ/mol), that is in favor of anatase formation at relatively mild stresses (Figure 8B). We also note that, according to Ostwald’s rule (Ostwald, 1897), phase transformation proceeds first not to the most stable phase (rutile in the case of TiO₂) but to a less stable polymorph which is closest in energy to the original state (anatase for TiO₂ although it is a metastable phase). On the release path of the shock wave, the sequence of observed phase transitions depends on whether the pressure is reduced slowly or rapidly or, in other words, if the new crystalline phase is frozen or can further transform into a more stable phase.

Summarizing, the laser-induced crystallization of the amorphous TNT layers into anatase with the HiLASE PERLA-C laser is a fast and clean process, avoiding oxidation of underlying titanium substrate and enabling to produce a patterned crystallization in localized areas. Such a solid-phase crystallization can be performed by other ultrashort laser systems, provided that the energy of their harmonics in the UV spectral range is sufficient for triggering crystallization. As soon as the absorbed laser energy exceeds the threshold for TiO₂ melting, either in a single pulse or upon heat accumulation at multipulse irradiation, the TNTs are melted and can be distorted. However, we found that, at ultrashort laser irradiation, the distortion is considerably lower than for nanosecond laser pulses. In the next sections we will discuss the mechanism of another solid phase crystallization effect upon laser annealing of stacks of amorphous Ge/Si nanolayers.

The samples for laser annealing represented stacks of hydrogenated amorphous germanium (a-Ge) and amorphous silicon (a-Si) alternating nanolayers with thicknesses 15 nm and 40 nm respectively deposited on a Si(100) substrate by Plasma-Enhanced Chemical Vapor Deposition (PECVD) with a-Si as the top layer (Figure 9). The substrate temperature during deposition was 225°C. The precursor was germane (GeH₄) or silane (SiH₄) diluted with argon, leading to hydrogen being present in the amorphous germanium and silicon alternating nanolayers. Growth conditions are described in more detail in (Volodin et al., 2023).

Two laser systems were used to anneal the multilayered samples, a picosecond laser (HiLASE PERLA-B, λ = 1,030 nm, pulse duration 1.4 ps, pulse energy up to 10 mJ) and a femtosecond laser (Astrella, Coherent) in combination with an optical parametric amplifier (TOPAS, Light Conversion). The latter enables tuning the laser wavelength in the range from 1,160 nm to 15 µm. In this work, we will focus on the results obtained at λ = 1,500 nm with a pulse duration of 70 fs and pulse energy up to 0.4 mJ, which provided the best results of annealing, presumably without melting. All the results which will be discussed below were obtained at single-pulse irradiation. More experimental details can be found in (Volodin et al., 2023).

Figure 10 presents Raman spectra of the sample sites annealed by femtosecond pulses at different peak laser fluences. The Raman spectrum of the original sample is also presented, showing that both Si and Ge are purely amorphous (a-Si and a-Ge). The sample modification threshold fluence was measured to be ∼50 mJ/cm². Starting from this fluence, a peak of crystalline Ge begins to appear in the Raman signal. At a fluence of 64 mJ/cm², the crystalline Ge peak is distinct while Si does not show any modification and there are no signs of Si-Ge intermixing (red dashed line in Figure 10). The percentage of crystallization (fraction of Ge nanocrystals in the a-Ge matrix) is evaluated as ∼30%. The evaluation is based on the following expression (Hao et al., 2020) ρ c = I c I c + γ I a where ρ c is the crystalline volume fraction, I c and I a are the experimentally measured integrated Raman scattering intensities for crystalline and amorphous phases respectively, and γ = Σ c / Σ a is the ratio of the integrated Raman cross sections for crystalline to amorphous phase. It was found (Hao et al., 2020) that the parameter γ for germanium has the following dependence on the size of nanocrystallites: γ L = 1 + 3 exp − L 0 L − 1.5   n m 2

Here the parameter L 0 is 2.8 nm and L is the average diameter of germanium nanocrystals. The average size of nanocrystals can be estimated, using the phonon confinement model (Volodin et al., 2014 and references therein), by the shift of the Raman peak toward lower frequencies relative to monocrystalline Ge (the position of the peak is 301.5 cm^-1). For 64 mJ/cm², the observed shift is ∼5.5 cm^-1 that corresponds to the average size of nanocrystallites of ∼3 nm. We call the regime of irradiation in the range from 50 mJ/cm² to ca. 65 mJ/cm² as Regime I which is the most important for applications due to preserving the semiconductor layers from intermixing which affects the sample properties (Lee et al., 2019). Regime I enables annealing the multilayer films while preserving sharp interfaces between nanolayers are of high demand for efficient low-power devices (Ding et al., 2021).

With increasing laser fluence, signs of melting or at least an increased mobility of atoms are observed at the interfaces between the films, resulting in Ge-Si intermixing, that are out of the scope of this paper. We shortly outline such regimes as follows. In Regime II, the Si layers as a whole stay still intact but a Ge-Si intermixing peak appears in the Raman spectra as shown for the fluence of 70 mJ/cm² in Figure 10 by green dotted line. In this regime, the mass fraction of crystalline Ge reaches about 75%. In Regime III, the Ge layers are 100% crystallized and the peak of crystalline Si becomes visible in the Raman spectra (103 mJ/cm² in Figure 10, blue dash-dotted line). In Regime IV, the Si layers exhibit substantial crystallization and a strong intermixing between Ge and Si layers occurs (148 mJ/cm² in Figure 10, light-blue dot-dot-dashed line) that culminates in the formation of GeSi alloy across the sample. However, this regime is not suitable for applications because of a strong material ablation during annealing (Volodin et al., 2023). Here we will focus on Regime I where we assume mechanisms of non-thermal solid-solid annealing to be involved resulting in the formation of layers of nanocrystalline Ge surrounded by amorphous Si nanolayers. We note that other film thicknesses down to few nm of Ge demonstrate similar results (to be published).

A well-known and widely used technique of solid-solid crystallization is metal-induced crystallization (Kryshtal et al., 2022), which proceeds through the formation of a eutectic couple leading to a decrease of the temperature of the phase transformation to levels below 100°C depending on a metal used. However, this technique can result in metal contamination of crystallized semiconductors that affects their properties. Thermal annealing under a controllable temperature is a long process which often assumes melting and solidification that is not suitable for nanostructured semiconductor materials. In this work, we show that ultrashort laser annealing using IR laser sources can be a fast efficient technique for crystallizing amorphous semiconductors into a desired phase as was shown above for amorphous TNT layers.

In our previous work (Volodin et al., 2023), we attributed the crystallization of Ge layers without intermixing with Si to the mechanism of explosive crystallization. If an external heat source such as a laser or a particle beam acts to an amorphous (metastable) semiconductor, it can trigger locally an appearance of crystalline seeds. Upon their formation, the crystallization heat is released and propagates to the adjacent amorphous regions, leading to a chain process: crystallization leads to heat release which activates crystallization in adjacent regions followed by heat release, etc. This provides a “crystallization wave” propagating in the material, a process known as explosive “crystallization” (Sharma et al., 1984; Césari et al., 1985; Volodin et al., 2011). It is often believed that this process, although extremely fast (with the speed of crystallization front up to 20 m/s), proceeds via local melting in the crystallization front that is still under debate (Nikolova et al., 2014; Deringer et al., 2021). Another trigger of explosive crystallization is related to stress. Upon annealing, a film of amorphous semiconductor experiences tensile stresses due to a mismatch of the thermal expansion coefficients with the substrate or with adjacent films in multilayer stacks as in our case (Park et al., 2009).

Comparing the crystallization regimes of TNT layers and Ge in a-Ge/a-Si multilayer stacks (Regime I), we conclude that in both cases we deal with explosive solid-solid crystallization triggered by laser-induced stress. In both cases, the estimations show that materials are heated well below the melting point, ΔT of ∼125 K for TNTs (see above) and ∼250–400 K for Ge (Volodin et al., 2023). The estimated stresses for the two cases are not dramatically different, ∼560 MPa for TNTs and a maximum 970 MPa for Ge, thus, both are at a sub-GPA level. However, in the case of Ge films confined by two adjacent cold layers of amorphous Si, the release of the stress is suppressed. If in each individual TiO₂ nanotube, a mild unloading stress wave propagates toward the Ti substrate while the thermal expansion of the top layer leads to some release of stress, Ge in nanolayers tends to expand laterally, experiencing a strong mismatch at the interfaces with the Si layers (note that the coefficient of linear thermal expansion of germanium is more than 10 times larger than that of silicon, Volodin et al., 2023). The strong confinement regime together with the interface mismatch and a higher stress level provide conditions for a-Ge crystallizations already at single-pulse exposure while the crystallization of TiO₂ nanotube proceeds in an accumulative manner, pulse by pulse, seed by seed for crystal growth. These aspects of the stress-induced crystallization still require further studies and understanding as the described laser annealing technique may be a powerful tool for highly selective laser annealing of semiconductor materials into desired phases on desired areas which can be localized on a few micrometers scale.

Finally, it is necessary to touch another fundamental effect, which can manifest itself during the annealing of Ge films by femtosecond laser pulses, the mechanism of ultrafast non-thermal phase transition (in other words, non-thermal melting). When a significant fraction (∼10–15%) of the valence electrons are excited to the conduction band of a semiconductor, the interatomic bonds experience softening and a sharp reduction of the average bonding-antibonding splitting. It is followed by lattice destabilization and disordering that looks like melting although at a cold lattice yet. Such so called non-thermal melting is observed already on a sub-ps time scale (Van Vechten et al., 1976; Stampfli and Bennemann, 1990; Sokolowski-Tinten et al., 1995; Rousse et al., 2001; Sundaram and Mazur, 2002; Tkachenko et al., 2021). The evaluation of the electron number density indicates that, already in Regime I, the density of the ionized atoms in the amorphous Ge nanolayers approaches the criterion of non-thermal phase transition (Volodin et al., 2023). Hence, one can anticipate that the metastable amorphous lattice of a semiconductor material, being destabilized by strong electronic excitation and experiencing significant stress, can transform into a more energetically stable and denser crystalline form. This fundamental aspect calls for further studies.