# The Role of Crystalline Orientation in the Formation of Surface Patterns on Solids Irradiated with Femtosecond Laser Double Pulses

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## Abstract

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## Abstract

_{2}of (001) and (100) surface orientation with femtosecond (fs) double pulsed lasers was performed in ablation conditions, for which, apart from mass removal, phase transformation and surface modification of the heated solid were induced. A parametric study was followed to correlate the transient carrier density and the produced lattice temperature with the laser fluence, pulse separation and the induced damage. The simulations showed that both temporal separation and crystal orientation influence the surface pattern, while both the carrier density and temperature drop gradually to a minimum value at temporal separation equal to twice the pulse separation that remain constant at long delays. Carrier dynamics, interference of the laser beam with the excited surface waves, thermal response and fluid transport at various pulse delays explained the formation of either subwavelength or suprawavelength structures. The significant role of the crystalline anisotropy is illustrated through the presentation of representative experimental results correlated with the theoretical predictions.

## 1. Introduction

_{2}and more specifically for materials with different crystal orientations. In particular, in a previous report, a parametric study of the laser conditions and the induced structures revealed that there is a difference in the response of the material if crystals with orientation (001) and (100) are irradiated [46,47,48]. In that study, it was emphasised that a key difference between the two crystal orientations is the effective electron mass (apart from the fact that interactions between atoms, thermomechanical response and melting are strongly affected by the interatomic distance which varies with the crystal orientation [49]); the discrepancy of the optical mass (measured or calculated in precious reports [47,48,50,51,52,53,54]) affects optical parameters of the material, amount of the absorbed energy and, eventually, thermal response of the system that is also projected on the type of LIPSS that are formed [46]. Nevertheless, despite these early results and conclusions, a more elaborated approach is required to evaluate more explicitly the impact of crystal orientation in the energy absorption; it is noted that TiO

_{2}is a uniaxial birefringent material with optical axis parallel to direction (001). Therefore, in the case of an irradiation under normal incidence of the face (001), the electromagnetic wave of laser propagates according to the normal refractive index $\left({n}_{\perp},{k}_{\perp}\right)$. On the other hand, in the case of irradiation under normal incidence of the face (100) or (110), the optical axis lies in the plane of the surface. Thus, there are waves propagating according to refractive indexes $\left({n}_{\perp},{k}_{\perp}\right)$ and $\left({n}_{\parallel},{k}_{\parallel}\right)$ respectively. Furthermore, although, the difference in the optical response of the system induced by the distinct crystal orientation for irradiation with femtosecond pulses has been investigated [46], no previous study has been conducted to explore the impact of the shape of the laser pulse and more specifically of temporarily separated pulses. In previous reports, the effect of the irradiation of various types of materials with temporarily separated pulses has been investigated which revealed a significant variation in the ultrafast dynamics, thermal response of the material and finally, changes in the LIPSS frequencies [29,36,55]. Therefore, and given the role of the crystal orientation, a detailed description of the ultrafast dynamics resulting from irradiating semiconductors with different crystal orientation with double pulses of variable temporal separation would provide significant information. More specifically, elucidation of this issue is of paramount importance, firstly, to elucidate the underlying multiscale physical mechanisms of laser-matter interaction and secondly to associate the resulting thermal effects with the induced surface patterns.

_{2}[22,26,30,56,57,58], to account firstly, for excitation and electron-phonon relaxation upon irradiation of TiO

_{2}in two crystal orientations with periodic ultrashort laser double-pulses separated by a temporal delay from zero to tens of picoseconds (Section 2). The details of an experimental protocol that has been developed is described in Section 3, while a thorough analysis of results and validation of the theoretical model are presented in Section 4 by discussing the ultrafast dynamics, thermal response and induced surface modification predictions. Concluding remarks follow in Section 5.

## 2. Theoretical Model

#### 2.1. Ultrafast Dynamics

_{2}with (001) and (100) surface orientation was considered through a laser beam of wavelength λ

_{L}= 248 nm that corresponds to photon energies equal to ~5 eV which is higher than the band gap of the material (~3.0 eV, at 300 K); thus, it is assumed that predominantly one- and (secondly and with a substantially smaller probability) two-photon absorption mechanisms contribute to excitation of the charge carriers in the valence and conduction bands, while higher order photon processes are less likely to occur. Furthermore, linear free carrier photon absorption on the intraband transitions are possibly increase the carrier energy (but not the carrier density), while Auger recombination and impact ionization processes lead to a decrease and increase, respectively, of the number of carriers in the conduction band.

_{c}, carrier temperature T

_{c}and lattice temperature T

_{L}:

_{c}(C

_{L}) is the carrier (lattice) specific heat, K

_{L}corresponds to the lattice heat conductivity, $\hslash {\omega}_{L}$ stands for the photon energy and ${\alpha}_{SPA}$ and ${\beta}_{TPA}$ correspond to the single and two-photon absorption coefficients, respectively. C

_{c}is provided by the expression ${C}_{c}=3{N}_{c}{k}_{B}$, where ${k}_{B}$ stands for the Boltzmann constant. The lattice specific heat and heat conductivity for TiO

_{2}are C

_{L}= 690 J Kgr

^{−1}K

^{−1}[59] and K

_{L}= 13 Wm

^{−1}K

^{−1}[60], respectively. At λ

_{L}= 248 nm, ${\alpha}_{SPA}\sim {10}^{6}\times \mathrm{exp}\left({T}_{L}/300\right)$ cm

^{−1}[61] while ${\beta}_{TPA}\sim $37 cm/GW [46,62]. In Equation (1), τ

_{c-l}is the carrier-phonon energy scattering time which is derived from $1/{\tau}_{c-l}\simeq {10}^{4}{N}_{c}^{1/3}$ s

^{−1}[50]. Finally, γ is the coefficient for Auger recombination (γ~10

^{−32}cm

^{6}/s [63]) and θ is the impact ionization rate coefficient. In this work, an intensity dependent expression is used for the impact ionization parameter θ [33,64] (unlike an approximating formula used for other semiconductors and at higher laser wavelengths, i.e., $~{e}^{-{E}_{g}/{k}_{B}{T}_{c}}$ s

^{−1}, for Silicon at 800 nm [22,57].

_{0}stands for the vacuum permittivity, m

_{r}(i.e., m

_{r}= 0.5m

_{e}) is the reduced electron mass and n is the refractive index of the material, while I is the peak intensity of the laser beam, and τ

_{c}is the electron collision time. Based on previous reports [50], scattering rates for electron-hole and electron-electron collisions scale as ${N}_{c}$ and ${N}_{c}^{1/3}$, respectively, yielding approximate value τ

_{c}~1 fs for TiO

_{2}regardless of the orientation. This is the value that was used in this work. ${E}_{g}$ stands for the energy band gap of rutile TiO

_{2}(~3 eV) [46]. The ‘source term’ that appears in the first equation in Equation (1) [22,56,57] is given by

_{p}is the total fluence of the laser beam and τ

_{p}is the pulse duration (i.e., full width at half maximum), R

_{0}is the irradiation spot-radius (distance from the centre at which the intensity drops to 1/e

^{2}of the maximum intensity, and R is the reflectivity while irradiation under normal incidence was assumed. The value of 3τ

_{p}in the exponent in Equation (5) has been chosen to ensure that the intensity switches off at t = 0. The objective of the current work is to illustrate the impact of temporarily separated pulses, therefore, Equation (5) provides the total intensity of a double pulse of pulse delay equal to t

_{delay}. In Equation (5), Cartesian coordinates have been used.

_{v}stands for the valence band carrier density (~5 × 10

^{23}cm

^{−3}for TiO

_{2}) and ε

_{un}is the dielectric parameter of the unexcited material at λ

_{L}= 248 nm. In previous reports, the values of ε

_{un}[67,68,69,70,71,72] and the optical mass ${m}_{opt}^{*}$ [47,48,50,51,52,53,54] were measured and estimated for both (001) and (100), respectively. As noted above, the dielectric parameter is expected to affect the energy absorption and therefore precise parameter values for ${m}_{opt}^{*}$ and ε

_{un}are required. Based on the aforementioned works, the values ${\epsilon}_{un}^{\left(100\right)}=1.3+7.61i$, ${\epsilon}_{un}^{\left(001\right)}=3.09+6.95i$, ${m}_{opt}^{*\left(100\right)}=6{m}_{e}$, ${m}_{opt}^{*\left(001\right)}=2{m}_{e}$ were used in the current study. For a flat surface, the reflectivity and free carrier absorption coefficients are computed through the following expressions

_{ext}is the extinction coefficient of the material that is calculated from ${\epsilon}^{\prime}$.

#### 2.2. LSFL Formation

_{d}= 1) for a flat surface (number of pulses, NP = 1). Therefore, a requirement for a semiconductor to obey the above relation and conditions [22,82] is that $Re\left({\epsilon}^{\prime}\right)<-1$ and the computed SPP wavelength Λ

_{SPP}is given by

^{22}cm

^{−3}(for (100)) are capable to lead to the excitation of SPP (Figure 1a) for nearly flat profiles. Although, Equation (8) can be used to calculate the SPP for nearly flat surfaces, there exists a discrepancy between the experimentally measured ripple periodicities and predictions due to the above expression. This is due to the fact that in order to observe periodic profiles experimentally, a sufficient number of pulses are required. On the other hand, repetitive irradiation is accompanied with a continuously varying depth of the periodic profile which results from a shift of the SPP wavelength to smaller values [21,78,83,84] that leads to SPP frequencies that deviate from the value resulting from Equation (8).

_{2}for (001 and (100), a larger range of Λ

_{SPP}values for (100) is predicted (~205 nm) compared to the computed value (~232 nm) for (100). The minimum values of Λ

_{SPP}occur for ~27 × 10

^{22}cm

^{−3}(001) and ~44 × 10

^{22}cm

^{−3}(100), respectively.

_{c}with the formation of laser-induced surface structures, the inhomogeneous energy deposition into the irradiated material is computed through the computation of the product $\eta \left(\stackrel{\rightharpoonup}{K},\overrightarrow{{k}_{i}}\right)\times \left|b\left(\stackrel{\rightharpoonup}{K}\right)\right|$ [40]. In this expression, $\eta $ stands for the efficacy with which a surface roughness at the wave vector $\stackrel{\rightharpoonup}{K}$ (i.e., $\left|\stackrel{\rightharpoonup}{K}\right|$ = ${\lambda}_{L}/\mathsf{\Lambda}$, where $\mathsf{\Lambda}$ is the predicted structural periodicity along the direction in which the periodic structures are formed) induces inhomogeneous radiation absorption, $\overrightarrow{{k}_{i}}$ stands for the component of the wave vector of the incident laser beam on the material’s surface plane and b is a measure of the amplitude of the surface roughness at $\stackrel{\rightharpoonup}{K}$. In principle, surface roughness is represented by spherically shaped islands and standard values from Sipe’s theory for the ‘shape’ (s = 0.4) and the ‘filling’ (f = 0.1) factors [25,40,85] are considered. In the current work, linearly p-polarised laser beams are used and based on Sipe’s theory, LIPSS are formed where $\eta $-maps show sharp features. The position of maximum value of $\eta $ along K

_{x}(Figure 1b,c) for 27 × 10

^{22}cm

^{−3}(001) and ~44 × 10

^{22}cm

^{−3}(100) yields $\mathsf{\Lambda}=$233 nm and $\mathsf{\Lambda}=$206 nm, respectively, which are close to the one derived from Equation (8). According to Figure 1b,c, the produced structures are oriented perpendicularly to the polarisation vector of the incident beam.

#### 2.3. Fluid Transport. Ripples and Grooves

_{2}upon irradiation of material with repetitive pulses, the laser fluence is assumed to be sufficiently high that results in a phase transformation. The melting temperature of the material (${T}_{melting}$ = 2110 K [86]) is considered as the threshold at which phase transformation occurs. Following a slow resolidification process, a non-flat relief is induced on the material. Moreover, the fluence values used for the simulations and experiments in the current work are sufficiently high to cause ablation. To simulate mass ablation, it is assumed that it occurs if the material is heated above a critical temperature (~${T}_{L}$>${T}_{L}^{boiling}$ where ${T}_{L}^{boiling}$ ~3245 K for TiO

_{2}). It is noted that the choice of the critical temperature T

_{critical}above which mass removal occurs has been investigated in previous studies. According to the discussion in reference [87], a typical value of T

_{critical}is 1–2 times higher than the boiling temperature. In other studies, it was noted that a solid material which is heated with ultrashort pulsed lasers at sufficiently high fluences undergoes a phase transition to a superheated liquid whose temperature reaches values ~$0.90\times {T}_{cr}$ (${T}_{cr}$ stands for the thermodynamic critical point [88]) and evaporation due to dynamics of the Knudsen layer (adjacent to the liquid-vapor interface [22,88]). To argue the choice of the ablation temperature threshold, it would be useful to know an estimate of ${T}_{cr}$, however, to the best of our knowledge, a relevant value for ${T}_{cr}$ for TiO

_{2}does not exist in the literature (except from a very high value for Ti (~15,500 K [89])). Based on the above discussion, for the sake of simplicity, the boiling temperature was selected to represent the threshold for mass removal.

^{3}) [90] and $\mu $ stand for the density and viscosity of molten TiO

_{2}, while P and $\overrightarrow{u}$ stand for the pressure and velocity of the fluid, respectively. On the other hand, σ corresponds to the surface tension of the material (see [9], for a more detailed description of the fluid dynamics module; similarly, temperature dependent values for μ, σ are used [91]). It is noted that in this work, Cartesian coordinates are used and (x,y,z) converts to (X,Y,Z) assuming a profile change with increasing NP. In Equation (9), superscript T denotes the transpose of the vector $\overrightarrow{\nabla}\overrightarrow{u}$.

_{c}, T

_{L}, N

_{c}, and P are computed at the centre of each element; on the other hand, the time derivatives of the displacements and first-order spatial derivative terms are evaluated at locations midway between consecutive grid points. A common technique to solve the NSE is the projection method and the velocity and pressure fields are calculated on a staggered grid using fully implicit formulations [92,93]. On the other hand, the horizontal and vertical velocities are defined in the centres of the horizontal and vertical cells faces, respectively. It is noted that a multiple pulse irradiation scheme is required to derive the formation of a periodic relief [9]. More specifically, LIPSS are formed in the following steps:

- The first pulse irradiates a flat surface which leads to the formation of a crater and small protrusions (humps) at the edges on the surface of the heated zone due to mass displacement [22,33]. Moreover, due to the high fluence value, some ablation also occurs. The first pulse irradiates a flat surface with no corrugations, therefore the formation of periodic structures is not expected to happen. It is noted that due to the axial symmetry of a Gaussian beam, for NP = 1, Equations (1)–(9) can be solved in 2D.
- The second pulse, then, irradiates the attained pattern and therefore the spatial symmetry breaks; as a result, 2D modelling can no longer be used. The coupling of the electric field of the incident beam with the induced surface-scattered wave produces a nonuniform, periodic distribution of the absorbed energy. The periodic variation of the absorbed energy, in turn, leads to a periodic excited electron density distribution [9]. It is noted, however, that the computation of the amount of the absorbed energy at each position requires the evaluation of the energy deposition on a curved surface (i.e., Equation (7) for reflectivity is valid for flat profiles). Therefore, appropriate computational schemes are used to compute the absorbed energy on each point of the curved surface [9]. The calculated spatially modulated electron energy distribution is transferred to the lattice system (through the second equation of Equation (1)) and subsequently, upon phase transition fluid transport and resolidification processes, LIPSS are formed.
- The above methodology is used to describe the formation of LIPSS for N$P\ge $2 (including a correction to the surface plasmon wavelength shift to smaller values with increasing depth of the profile following an increase in dose [13,32,39]); however, there is a resonance at which further excitation of surface plasmons stops being the driving force behind the induced surface profile and suprawavelength structures are produced. In a previous report, it was shown that if the surface profile becomes sufficiently deep (at large NP) normal thermocapillary waves which lead to regular LIPSS are not produced [8,23]. By contrast, another solution of NSE dominates, namely, hydrothermal waves that propagate between the wells of the ripples in a perpendicular direction to the laser beam polarisation [8]. Another important feature of these solutions is that, only, waves of a certain periodicity (i.e., larger than the laser wavelength) lead to stable structures upon solidification, which are orientated perpendicularly to the beam polarisation and they are termed grooves.

## 3. Experimental Protocol

_{2}single crystals (Crystal-GmbH), maintained at room temperature, were irradiated by a hybrid distributed feedback dye laser/KrF excimer system delivering linear polarised 450 fs pulses at 248 nm at repetition rate varied of 10 Hz. The double-pulse irradiation was performed with a temporal delay between pulses varying between 0.5 and 450 ps using a Michelson-type interferometer. After appropriate spatial filtering and focusing, the laser beam on the sample was of quasi-Gaussian of size 19 μm measured at 1/e

^{2}of the maximum intensity. The surface morphology after the irradiation was examined by Jeol Scanning Microscope JSM 7000F, which employs a Schottky type field-emission (T-FE) gun for the electron source operating at pressure 10

^{−8}Pa, with a function for high-resolution image observation. The spatial resolution achieved was 1.2 nm at 30 kV (max accelerating voltage).

## 4. Discussion

_{c}(t = 0) = T

_{L}(t = 0) = 300 K, and N

_{c}= 10

^{12}cm

^{−3}at t = 0. On the other hand, for NSE (Equation (9)), it is assumed that the velocities of the fluid at t = 0 are zero. The values of the laser beam used in the simulation are: the (peak) fluence of ${E}_{p}\left(\equiv \sqrt{\pi}{\tau}_{p}{I}_{0}/\left(2\sqrt{ln2}\right)\right)$, where I

_{0}stands for the peak value of the intensity while R

_{0}in Equation (5) is taken to be equal to 20 μm and τ

_{p}= 450 fs. Double pulses of equal constituent pulses are used with temporal separation in the range [0 ps, 20 ps]. The ultrafast dynamics and the thermal response of the heated material are investigated to take into consideration the role of fluence, pulse separation, and crystal orientation.

#### 4.1. Single Pulse Excitation (t_{delay} = 0)

_{delay}= 0) with no interference effect are considered and the ultrafast dynamics are investigated. Two sets of the equal laser pulses with E

_{p}= 50 mJ/cm

^{2}and E

_{p}= 125 mJ/cm

^{2}, respectively, lead to a total pulse fluence on the solid sample of 100 mJ/cm

^{2}and 250 mJ/cm

^{2}, respectively. The evolution of the carrier density, carrier temperature and the lattice temperatures on the surface of the material (at the centre of the Gaussian pulse where the energy absorption is maximal) are illustrated in Figure 2a–c, respectively, for the aforementioned fluences and (100) and (001) crystal orientation. Results illustrate that the maximum carrier densities are higher for (100) than for (001) which highlights the important role of the value of the optical mass. A similar monotonicity is followed by the maximum carrier temperature and simulations show that the maximum value is acquired shortly after the time the carrier density reaches the peak value which agrees with results in previous reports for other semiconductors [26,56,57,94,95]. We note there is an initial rise of the carrier temperature (Figure 2b) during the first moments of irradiation due to the significantly large heat capacity of the carrier system with respect to that of the lattice.

_{c}rises rapidly with an increase in the pulse energy. The initial increase can be explained through the examination of the contribution of the competing mechanisms indicated by the various components in the “source term” (see an enlarged region in Figure A1 in Appendix A). Similarly, this behaviour is followed by a small decrease. At large fluences, larger amounts of carriers are produced and (given the fact that one-photon absorption and Auger recombination are the two predominant factors that alter carrier density) Auger recombination becomes significant because it varies as ${N}_{c}^{3}$. Hence, the enhanced Auger recombination [94] converts carrier ionization energy into kinetic energy that results in an increase in the carrier temperature. It is noted that T

_{c}attains very high values and this could potentially influence the energy band-gap response. Certainly, a more rigorous approach (e.g., based on first principles [96]) should also be considered to estimate a possible E

_{g}variation for large T

_{c}. Nevertheless, without loss of generality, it is assumed that substantial qualitative and quantitative changes (that yields different morphological changes) do not occur if E

_{g}is considered constant. Results indicate that differences of the maximum values of T

_{c}and N

_{c}for (001) and (100) at E

_{p}= 125 mJ/cm

^{2}are not very distinct compared to those at lower fluences due to the fact that this energy value rapidly yields maximum value of N

_{c}close to N

_{v}(thus, the upper value of available carriers for excitation is nearly reached). Furthermore, it is noted that although longer wavelengths and other semiconductors both impact ionization and two-photon absorption play an important role in the carrier dynamics and lattice response, for TiO

_{2}and Λ

_{L}= 248 nm (that yield energies well above E

_{g}) the latter processes appear to yield insignificant changes in N

_{c}and T

_{c}(see Appendix B). Nevertheless, for the sake of completeness and aiming to present a general theoretical framework that describes processes that also take place in other semiconductors, even at higher photon energies, a full model is considered assuming a nonzero ${\beta}_{TPA}$ and θ (Equation (3)).

_{L}evolution rises faster for (001) and therefore, the crystal orientation plays an important role (Figure 2c). To avoid confusion, it is noted that the maximum value of T

_{L}(~3245 K) occurs at different depths of the irradiated material because ablation is more intense at higher fluences and therefore a larger volume is ablated. More specifically, the size of the ablated volume should be larger at higher fluences as the absorbed energy is distributed at larger depths. Nevertheless, the approach followed in the current analysis takes into account the fact that the temperatures attained are high enough to induce evaporation of the material and therefore, to avoid an overestimation of the material surface temperature in the calculations, a correction to the simulation scheme is required. Hence, becausethe boiling temperature is assumed to be the condition for evaporation, in the simulations, all points which exceed that temperature are removed. Thus, the region which is simulated at each timepoint varies dynamically and upon removal of all points with ${T}_{L}>{T}_{L}^{boiling}$, the depth of the induced morphology increases. It is noted that the constant temperature (${T}_{L}={T}_{L}^{boiling}$) in Figure 1c is due to the fact that energy relaxation between the lattice and carrier subsystems is not been reached for some picoseconds; this indicates that until the moment of equilibration between ${T}_{L}$ and ${T}_{c}$, the carrier subsystem will continue to give energy to the lattice system which might rise above the ${T}_{L}^{boiling}$ even if the surface points dynamically change. Hence, the surface continues to reach the boiling temperature and it evaporates leading to ablation while this elevating high temperature remains constant until relaxation processes start to become stronger. By contrast, a cutoff in the temporal decay of the carrier density or the reflectivity is not observed in the simulations. This results from the fact that the carrier density drops slowly after the end of the pulse due to an Auger recombination. Other processes that influence the variation of carrier density (see third equation in Equation (1)) such as the single photon absorption process that is dependent on the lattice temperature has ended before the lattice reaches ${T}_{L}^{boiling}$. Similarly, for the same E

_{p}, the enhanced T

_{c}for (001) yields a larger T

_{L}which, in turn, implies a larger ablation compared to the mass removal for (100).

_{2}(Figure 2d)

_{.}Notably, although the shape of the reflectivity curves is similar for both crystal orientations, the different value of the initial reflectivity for (100) and (001) causes variation in the energy absorption. On the other hand, for the same crystal orientation, irradiation with higher fluences increases the metallisation process of the material. This leads to a rapidly enhanced carrier density followed by a larger peak value of the reflectivity of the excited material. The latter is attributed the generation of an increased number of carriers at higher fluences (Figure 2a).

#### 4.2. Double Pulse Excitation (t_{delay} ≠ 0)

_{delay}= 0.5 ps, 0.9 ps, and 1.5 ps for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}and both crystal orientations. Results are shown for a temporal delay between pulses smaller than 2τ

_{p}(0.9 ps) where the two pulses overlap as well as for pulses with a larger separation (1.5 ps). According to simulations (Figure 6b,c), the maximum surface carrier density and temperature decrease gradually for short delays (t

_{delay}< 2τ

_{p}), reaching a minimum value that remains unchanged even at longer t

_{delay}. To explain this behaviour, it is important to note that the first of the constituent pulses leads to ablation; hence, the enhanced surface lattice temperature (~${T}_{L}^{boiling}$) of the material yields similar ${\alpha}_{SPA}$ (i.e., $\sim {10}^{6}\times \mathrm{exp}\left({T}_{L}^{boiling}/300\right)$ cm

^{−1}) before the second pulse irradiates the material for t

_{delay}> ~2τ

_{p}. Figure 6a, illustrates that ${T}_{L}~{T}_{L}^{boiling}$ at, approximately, t

_{delay}= 1 ps which justifies the appearance of the minimum ${T}_{L}$ at t

_{delay}> 2τ

_{p}. This behaviour is different from the one exhibited in other laser conditions (i.e., nonablation conditions at Λ

_{L}= 800 nm) for which the second pulse leads to higher carrier densities and temperatures [36,97]. Due to the substantially larger contribution of one-photon based excitation at low wavelengths and the negligent contribution of impact ionization and two-photon ionization, the fact that ${\alpha}_{SPA}$ remains constant at t

_{delay}> ~2τ

_{p}leads to unchanged values for T

_{c}and N

_{c}.

_{c}, T

_{L}and N

_{c}can provide a detailed description of the laser energy distribution and thermal effects on the affected layer of the material, exploration of dynamics through analysis of the thermal changes on the surface (in ablation conditions at E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}) is hindered by the fact that the material remains at the isothermal ${T}_{L}={T}_{L}^{boiling}$ for a long time and therefore, important details of the thermal effects below the surface of the material are not easily manifested. It is evident that one way to illustrate how pulse separation influences the energy absorption and thermal effects at larger depths in ablation conditions is by presenting the affected zone characteristics (i.e., temperature distribution, volume of affected zone, position of surface after ablation). By contrast, to show the impact of the laser parameters on the induced thermal effects below the ablated region (and at depths characterized by lower energy distribution), an alternative investigation is performed; more specifically, simulations are conducted assuming excitation of the material at lower fluences (i.e., that do not cause ablation; this is equivalent to exploration of dynamical effects in places where material is excited but is not removed). To emphasise on the significant role of the one-photon excitation and at conditions that do not induce ablation (i.e., ${T}_{L}<{T}_{L}^{boiling}$) before the second pulse irradiates the material, simulations have been performed for irradiation with E

_{p}= 10 mJ/cm

^{2}for t

_{delay}= 0.7 ps, 1.5 ps, 4 ps and 10 ps (Figure 7). Interestingly, the carrier density is higher for (001) than for (100) (Figure 7a–d) unlike the behaviour for ablation conditions. This can be attributed to the almost insignificant variation of reflectivity at low fluences and the fact that energy absorption (due to lower reflectivity) is higher for (001) than for (100) at low carrier densities (Figure 4). Results for the carrier density and lattice temperature will help to understand the thermal response of the material at larger depths when high temperatures (but not equal to the boiling point are generally reached). Another interesting issue that is revealed by comparing the carrier density evolution in the two regimes (i.e., ablative and nonablative regimes) is the drop of N

_{c}as a function of time. In contrast to the pronounced smoother gradual decrease in the carrier density value at lower fluences (part of the curve in Figure 7b–d due to the first pulse) for which the maximum attained value for N

_{c}is low, there is a substantially steeper decrease when a substantially peak value of N

_{c}has been reached (Figure 2a, Figure 3 and Figure 7a–d (after exposure to the second pulse)). It is noted that the smooth decrease in N

_{c}for small carrier densities has also been reported in previous works [26,56,57,94,95].

_{L}has not started to increase), any change in the carrier density is predominantly caused from the contribution of I and secondly to the Auger recombination. At low fluences (~10 mJ/cm

^{2}), no sharp increase in the carrier density is computed because it occurs at higher fluences (Figure 2a and Figure 3). By contrast, when the second constituent pulse irradiates the material, the energy of the lattice system is sufficiently high (Figure 7e–h) to lead to high levels of excitation as ${\alpha}_{SPA}$ increases rapidly. Thus, a large number of excited carriers is produced.

_{L}increases as the temporal delay becomes larger. This can be attributed to the enhanced one-photon absorption (${\alpha}_{SPA}$ attains large values during the first pulse, but it is about two orders higher when the second pulse irradiates the material due to its T

_{L}dependence (Figure 7e–h)) and free carrier absorption while the influence of impact ionisation appears to be minimal. According to Figure 7, the second pulse irradiates an already hot material (at increasing T

_{L}) that further increases the single photon absorption that leads to a higher carrier density which affects eventually T

_{L}through electron-phonon scattering. This is also manifested at a higher t

_{delay}where ablation starts to occur (Figure 7h). It is noted that the t

_{delay}value (Figure 7h) for which the temperature reaches ablation conditions, there is large jump of the carrier density to the increase in the energy absorption and production of a large number of energetic carriers. It is noted that at these fluences, reflectivity variation during the pulse is insignificant and it does not induce changes in energy absorption. To summarise, Figure 7 illustrates that in subablation conditions, an increase in the maximum values of T

_{L}occurs and due to heat diffusion and heat transfer it is more enhanced at higher depths inside the material volume as t

_{delay}increases. These results indicate that in regions where the energy deposition is not high enough to induce material removal (at higher depths inside the material) a larger volume of the material will be affected with increasing t

_{delay}. This conclusion is of paramount importance to interpret the distinct surface patterning at longer delays (i.e., ripples and grooves).

#### 4.3. LIPSS Formation

_{2}of different crystal orientation with ultrashort double laser pulses.

_{2}(001) and (100) influences the surface morphological features (i.e., types of structures and periodicities). The images in Figure 8 show the TiO

_{2}(001) surface after irradiation with two pulses of (peak) fluence (for each pulse) E

_{exp}= 125 mJ/cm

^{2}and different temporal delays between laser pulses. According to results in a previous report [46], this fluence corresponds to the LSFL domain of morphological surface maps (MSM). In agreement, ripples were formed at a small delay of t

_{delay}≤ 4 ps (Figure 8a,b). However, at a longer delay of ~10 ps (Figure 8c), suprawavelength grooves were formed; they coarsened at even longer delay of ~30 ps (Figure 8d) and disappeared at ~60 ps, being replaced by spike-like columns (not shown).

_{p}= 125 mJ/cm

^{2}for (100) and (001) TiO

_{2}, respectively (t

_{delay}= 4 ps). As mentioned in the previous section, the decrease in SPP wavelength with the increase in the irradiation dose NP is related to the expected shift of SPP wavelength to smaller values as the profile becomes deeper [21,78]. Furthermore, according to Figure 7a–h, the larger carrier densities (and thermal response) produced for the orientation (001) lead to a more rapidly attained deeper profile with respect to that for (100). Hence, the curve that shows the decrease in the ripple periodicity as a function of NP should be steeper for (001) while SPP wavelengths also are expected to expand to a larger range of values (Figure 9). Furthermore, simulation results predict a substantially smaller SPP wavelength for (001) orientation which should be also projected on the periodicity of the induced ripples.

_{delay}= 4 ps), and NP, it is also very important to evaluate potential morphological variations for different pulse separation. In Figure 10, simulations and experimental results are shown after a double pulse of E

_{p}= 125 mJ/cm

^{2}irradiated (001) TiO

_{2}for two delays, t

_{delay}= 4 ps and t

_{delay}= 10 ps. An interesting point regarding the two values of the pulse separation is that they are situated before and past an optimum pulse separation value (t

_{delay}~6 ps) for which the depth is critical to lead to a transition of structures from ripples (i.e., subwavelength structures oriented perpendicularly to the laser polarization direction) to grooves (i.e., suprawavelength structures that are aligned with laser polarization direction); therefore it is important to evaluate the impact of small and large pulse separation. Due to the fact that for a smaller pulse separation (t

_{delay}= 4 ps), damage related temperatures will be developed into smaller regions, a shallower profile will be produced compared to that for t

_{delay}= 10 ps. Hence, the condition for promoting the production of grooves will be satisfied more easily at longer delays. Simulation results show rippled structures (Figure 10a) for NP = 80 for the above conditions at t

_{delay}= 4 ps of periodicity ~220 nm and grooves (Figure 10b) for NP = 80 at t

_{delay}= 10 ps of periodicity ~1.8 μm. Experimental results on (001) TiO

_{2}rutile surface that validate the simulations are illustrated in Figure 8b,c, which show the production of ripples and grooves, respectively, for NP = 100. Interestingly, irradiation of (100) rutile TiO

_{2}surface does not lead to the formation of grooves [46]. Instead of grooves, a featureless flat area replaces the ripples when the delay between laser pluses increases (see Appendix C). The formation of this unusual structure is not yet explained by simulations. This emphasises that crystalline orientation of the irradiated surfaces is a key parameter in the formation processes of suprawavelength periodic structures under femtosecond laser irradiation.

_{2}while a transition from ripples to grooves was also derived. It is evident that more accurate conclusions will be drawn if more appropriately developed experimental (for example time-resolved) protocols are also introduced to evaluate ultrafast dynamics and relevant parameter valuessuch as electron-electron and electron-hole scattering frequencies, electron-phonon relaxation times, and reflectivity changes. It is noted that although the theoretical predictions appear to agree with the evolution of the surface structures, simulation results manifested a significant ablation that takes place for the fluence values used in the experiment which to some extent deviates from experimental observations. This can also be attributed to the choice of various parameters such as the electron effective mass that affects the dielectric constant and eventually the optical properties of the material and energy absorption; this is a critical issue to both the induced carrier density and thermal response of the material. Values for ${m}_{opt}^{*}$ used in the current work and at low wavelengths might need to be revised appropriately through a more rigorous theoretical approach and suitable experimental protocols. Similarly, in extreme laser conditions that induce severe ablation, it is very important to estimate more accurately the role of evaporation and employ more advanced theoretical schemes such as FDTD algorithms to evaluate electrodynamical effects that are related to the underlying mechanisms of surface modification [24]. Nevertheless, the predominant aim of the study focused on the exploration of the underlying physical mechanisms that correlate laser parameters with the material’s crystal orientation and the induced ultrafast dynamics and produced surface patterns. The qualitative and quantitative results presented in the current investigation were aimed to provide a first insight into the patterning techniques of rutile TiO

_{2}with femtosecond pulses in ablation conditions and highlight the significant role of the material characteristics of the material related to the crystal orientation in the response of the solid. The detailed analysis emphasized the role of the different direction dependence of the electron effective masses for the two crystal orientations as the distinct two cases lead to different excitation processes, energy absorption and anisotropic laser surface patterning.

## 5. Conclusions

_{2}of different crystal orientations with ultrashort double laser pulses in ablation conditions. Results manifest that the crystal orientations and interpulse delays play an important role in the onset of surface pattern formation because they influence both the carrier dynamics and thermal response of the irradiated structure. Simulations showed that although both the maximum carrier temperature and density drop with increasing pulse separation, these parameters reach a minimum value at about t

_{delay}> 2τ

_{p}after which no variation occurs. Interestingly, irradiation of TiO

_{2}with (100) orientation lead to higher T

_{c}and N

_{c}values than for (001) which are well explained by the underlying physical processes and the excitation conditions. To illustrate the response of the material deeper in the surface of the irradiated solid, simulations indicated an increase in the maximum values of T

_{L}due to heat diffusion and heat transfer that is more enhanced at higher depths inside the material volume as t

_{delay}increases. These results are very important because they are also associated with the induced surface patterning. Furthermore, surface modification is greatly affected by the pulse separation and both simulation results and experimental observations explain the occurrence of grooves on (001) compared to the formation of subwavelength structures at smaller delays. For values of the pulse separation past an threshold value (~ 6 ps), the depth of the surface pattern allow the formation of grooves instead of ripples, which indicates that the modulation of the frequencies of the induced LIPSS on the surfaces of solids can be tailored by a control of t

_{delay}and the number of pulses. Furthermore, simulation results indicate that the crystal orientation influences the periodicity of the LSFL structures, leading to patterns of lower periodicity for (001) TiO

_{2}.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

_{c}. It is evident that the carrier energy increases even when the laser energy is very low and, in principle, the linear processes such as single photon absorption and free carrier absorption account for this increase. As shown in Figure A1, the carrier temperature attains the maximum value shortly after the laser pulse reaches its maximum.

**Figure A1.**Evolution of values of carrier for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation at x = y = 0 and on the surface of the material.

## Appendix B

_{c}as a result of the single photon absorption and Auger recombination.

**Figure A2.**Simulation results of maximum carrier density (

**a**) and carrier temperature (

**b**) for t

_{delay}= 0 ps, E

_{p}= 50 mJ/cm

^{2}for (100) TiO

_{2}.

## Appendix C

**Figure A3.**SEM images of surface structures on (100) rutile TiO

_{2}obtained after laser irradiation (248 nm, 450 ps, NP = 100) with total measured fluence of 300 mJ/cm² and delay between pulses of 4 ps (

**a**) and 10 ps (

**b**). The double-headed arrow indicates the direction of laser polarization.

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**Figure 1.**(

**a**) Surface plasmon wavelength as a function of the excited carrier densities for (001) and (100) crystal orientation. Prediction of structure periodicity based on Sipe’s theory for (

**b**) 44 × 10

^{22}cm

^{−3}(100) and (

**c**) 27 × 10

^{22}cm

^{−3}(001). Inset shows the profile of the efficacy factor along K

_{x}(white dashed line). The black double headed arrow indicates the direction of the polarisation vector.

**Figure 2.**Evolution of values of carrier density (

**a**), carrier temperature (

**b**), lattice temperature (

**c**) and reflectivity (

**d**) for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation at x = y = 0 and on the surface of the material.

**Figure 3.**Evolution of carrier densities for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation at t

_{delay}= 0.5 ps (

**a**), 0.9 ps (

**b**), and 1.5 ps (

**c**).

**Figure 4.**Evolution of reflectivity for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation at t

_{delay}= 0.5 ps (

**a**), 0.9 ps (

**b**), and 1.5 ps (

**c**).

**Figure 5.**Evolution of carrier temperature for E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation at t

_{delay}= 0.5 ps (

**a**), 0.9 ps (

**b**), and 1.5 ps (

**c**).

**Figure 6.**(

**a**) Lattice temperature at t

_{delay}= 0.9 ps. (

**b**) Maximum carrier density and (

**c**) maximum carrier temperature for t

_{delay}in the range [0–10 ps] (E

_{p}= 50 mJ/cm

^{2}and 125 mJ/cm

^{2}for (001) and (100) crystal orientation.

**Figure 7.**Evolution of maximum carrier density (first row) lattice temperature (second row)) for t

_{delay}= 0.7 ps (

**a**,

**e**), 1.5 ps (

**b**,

**f**), 4 ps (

**c**,

**g**) and 10 ps (

**d**,

**h**), respectively. (E

_{p}= 10 mJ/cm

^{2}) for (001) and (100) crystal orientation.

**Figure 8.**Surface structures on (001) rutile TiO

_{2}obtained after laser irradiation (248 nm, 450 ps, NP = 100) with total measured fluence of 250 mJ/cm² and delay between pulses of 0 ps (

**a**), 4 ps (

**b**), 10 ps (

**c**) and 30 ps (

**d**). Doubled–ended arrow indicates laser polarisation direction.

**Figure 9.**SPP wavelength vs. NP. (t

_{delay}= 4 ps, E

_{p}= 125 mJ/cm

^{2}for (100) and (001) TiO

_{2}).

**Figure 10.**Simulation results of periodic surface profiles for t

_{delay}= 4 ps (

**a**) and t

_{delay}= 10 ps (

**b**). Results are illustrated in a quadrant. Results are for (001) TiO

_{2}. Double–ended arrow indicates laser polarisation direction.

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**MDPI and ACS Style**

Tsibidis, G.D.; Museur, L.; Kanaev, A.
The Role of Crystalline Orientation in the Formation of Surface Patterns on Solids Irradiated with Femtosecond Laser Double Pulses. *Appl. Sci.* **2020**, *10*, 8811.
https://doi.org/10.3390/app10248811

**AMA Style**

Tsibidis GD, Museur L, Kanaev A.
The Role of Crystalline Orientation in the Formation of Surface Patterns on Solids Irradiated with Femtosecond Laser Double Pulses. *Applied Sciences*. 2020; 10(24):8811.
https://doi.org/10.3390/app10248811

**Chicago/Turabian Style**

Tsibidis, George D., Luc Museur, and Andrei Kanaev.
2020. "The Role of Crystalline Orientation in the Formation of Surface Patterns on Solids Irradiated with Femtosecond Laser Double Pulses" *Applied Sciences* 10, no. 24: 8811.
https://doi.org/10.3390/app10248811