Origin of femtosecond laser induced periodic nanostructure on diamond

We study the evolution of periodic nanostructures formed on the surface of diamond by femtosecond laser irradiation delivering 230 fs pulses at 1030 nm and 515 nm wavelengths with a repetition rate of 250 kHz. Using scanning electron microscopy, we observe a change in the periodicity of the nanostructures by varying the number of pulses overlapping in the laser focal volume. We simulate the evolution of the period of the high spatial frequency laser induced periodic surface structures at the two wavelengths as a function of number of pulses, accounting for the change in the optical properties of diamond via a generalized plasmonic model. We propose a hypothesis that describes the origin of the nanostructures and the principal role of plasmonic excitation in their formation during multipulse femtosecond laser irradiation.


I. INTRODUCTION
Laser-induced periodic surface structures (LIPSS) have attracted considerable attention by researchers, as indicated by the growth in the number of papers published on the topic in recent years. 1 LIPSS can enhance the absorption 2-5 at the surface of materials and can therefore open new avenues for technological applications such as micro-solar cells devices. LIPSS formation is a universal phenomenon and has been observed in dielectrics, semiconductors, metals and polymers. 1,6 Generally, two types of ripples can be observed during the irradiation by multipulse femtosecond laser, low spatial frequency LIPSS (LSFL) and high spatial frequency LIPSS (HSFL).
Derrien et al. 10 used an above ablation threshold fluence where the critical density of plasmonic excitation is achieved with the first femtosecond laser pulse. They observed ablation in the middle of the laser spot surrounded by LSFL and at the edge where the fluence is low, they found the HSFL. So we suggest that this repartition of the two kinds of LIPSS observed within the same volume spot laser are the result of different physical mechanisms.
LSFL formation for the majority of materials is well explained by the interference between the incident laser wave and the surface plasmon-polariton (SPP) excitation, 1,7,8 which involves a periodic spatial modulation of the energy deposited on the irradiated surface. 9,10 This interaction leads to the formation of nanostructures with periods close to or less than the laser wavelength λ L . There is still some controversy in the literature regarding the physical mechanisms underlying the formation of HSFL. The physical models proposed include interference, 10,11 second harmonic generation (SHG) 12,13 and surface plasmon polariton excitation. 14  The interference model depends necessarily on the angle of the incident laser, but it has been shown that the incident angle has no effect in the case of HSFL formation. 8,12 The SHG model is based on the formula: Λ = λ L 2n and so the nanostructure period depends strictly on the wavelength. In contrast, there are several experimental works where a change in the period of the HSFL has been observed by varying the pulse number at the same wavelength (Tab. I).
Miyazaki et al. 15 and Miyaji et al. 14,16,17 proposed a model for HSFL formation where they consider the effect of the number of pulses. They proved experimentally that the formation of nanostructures was due to a non-thermal process, where the random nanoablation is initiated by the disorder (non-thermal melting) during the multipulse femtosecond laser irradiation, followed by plasmonic excitation. In this model, a large number of laser pulses at low energy are necessary to generate HSFL type. 13,15 Forster et al. 19 showed a 50 nm period obtained due to a phase transition from crystalline diamond to a graphitic phase, along with 200 nm nanostructures consisting of crystalline diamond (see Tab. I). Clearly, a more sophisticated model is needed to provide insight into the formation of HSFL.
In this paper, we investigate the change in diamond surface morphology induced by ultrafast laser pulses when varying the scanning speed (i.e. number of pulses per spot size diameter) and the laser power (fluence) at 1030 nm and 515 nm wavelength. We illustrate the advantage of using plasmonic excitation in modeling the HSFL formation. We propose a general plasmonic model to follow the evolution of LIPSS formation and the changing diamond optical properties as a function of the electron-holes plasma excitation. Our model demonstrates the importance of plasmonic excitation in the dynamic change of non-thermal melting as an origin of HSFL formation.

II. EXPERIMENTAL SETUP
The samples used in this work were polished single crystal CVD diamond 7.5 mm × 7.5 mm × 0.5 mm. Their optical properties are discussed later in the theoretical model. To irradiate the diamond we used a Light Conversion Pharos amplified femtosecond laser delivering 230 fs pulses at 1030 nm and 515 nm wavelengths with a repetition rate of 250 kHz. The laser was incident normal to the target surface and focused with a 0.42 NA (50×) microscope objective, with a spot size of approximately 1.6 µm and 0.8 µm at 1030 nm and 515 nm wavelengths, respectively. To investigate the creation of surface nanostructures we varied the pulse number by changing the scanning speed, , through the relationship: N = 2ω 0 R r where R r is the repetition rate, 2ω 0 is the spot size and N the number of pulses delivered per spot diameter. 20 The laser polarization was parallel to the scanning direction, and all the experiments were carried out in air. After the irradiation, we analyzed the change in morphology of diamond surfaces using a scanning electron microscope (SEM).

III. THEORETICAL MODEL
We propose a generalized plasmonic model to study the development of periodical nanostructures on diamond surface during the irradiation with multipulse femtosecond laser at wavelengths of 1030 nm and 515 nm. We consider air as the dielectric environment. The plasmonic model has shown its validity in the case of metals. 35 Applying this model to semiconductors and dielectrics such as diamond is justified by the fact that a thin layer which has metallic character is induced during multipulse femtosecond laser irradiation. 27 In this paper, we call it "pseudo-metal layer". For this reason, the surface plasmon polariton SPP excitation is used to calculate and explain the formation of periodic nanostructures in diamond. The SPP dispersion relation is: 21 where ε pm is the dielectric function of pseudo-metal layer and k sp = k sp1 + ik sp2 is the plasmon propagation number with k sp1 = k sp = 2π λ sp = π Λ (Ref. 18) where λ sp is the plasmon wavelength and Λ is the period of nanostructures and ε d is the dielectric function of the material surrounding the pseudo-metal layer. This dielectric function is approximated as ε d = mε di + (1 m)ε air where m represents the factor of mixed state depending implicitly on the pulse number and it varies from 0 and 1, ε air = 1 and ε di = 5.72 and 5.90 at 1030 nm and 515 nm wavelengths, respectively, according to the relationship n 2 = 1 + 0.3306λ 2 . The dielectric function of the pseudo-metal layer is given by the Drude model: 23 ( with where n 0 is the electron concentration in the valence band (we consider a value of 10 23 cm 3 ), τ ee the electron-electron collision time (1 fs), ω is laser frequency and ω p = n eh e 2 ε 0 m * opt m e is plasma frequency, with ε 0 = 8.85 × 10 −12 F.m and the optical effective mass m * opt estimated via the relationship 23 18 determined the groove period of Si after constructing the numerical formulas for k sp1 and k sp2 using the critical density of plasmon excitation n cr for the purpose to simplify the calculations, such as k sp1 (n cr ) = 0. In our case is n cr = 2.32 × 10 21 cm −3 and 7.58 × 10 21 cm −3 at λ L = 1030 nm, 515 nm, respectively, but their formulas become valid only for the properties of Si and the wavelength used. In this paper, without employing the critical density n cr , we will build the general formulas of k sp1 and k sp2 adapted for all semiconductor and dielectric materials and for all wavelengths.
According to Eq. (1) And 1 We set: Which implies: We also have: Replacing Eq. (13) in Eq. (11), we obtain: The solution of Eq. (14) is: Therefore, from Eq. (12) we obtain: This model was simulated using MATLAB software.

IV. RESULTS AND DISCUSSION
Diamond surface excitation by femtosecond laser pulses builds up a thin pseudo-metal layer 27 due to the non-thermal melting (disorder) which takes place at sub-vibrational time scale, since the pulse duration of the femtosecond laser is lower than the electron-phonon relaxation time. [27][28][29][30][31] This change of states affects optical properties of diamond such as reflectivity R, as shown in Fig. 1, with R = (n−1) 2 +k 2 (n+1) 2 +k 2 , where n = 1 1 2 is the real part of the refractive index and k = ε pm2 2n is the absorption coefficient. 32 We observe an increase of the reflectivity as a function of the excited electron-hole plasma density n eh during the multipulse femtosecond laser interaction, where the reflectivity R is calculated for normal incident radiation. This indicates that the diamond surface takes a metallic character with high free electron density. We can remark that the reflectivity at 515 nm is higher than 1030 nm due to the difference in electron density excited (note that x-axis is different for each plot because n cr 1030 nm n cr (515 nm )). Under our experimental conditions, we have observed morphological changes of the femtosecond laser irradiated diamond surface with the variation of the scanning speed (i.e. number of pulses N) at a fixed fluence F, always keeping the laser polarization parallel to the translation direction of the sample. Figure 2 shows SEM images taken on the irradiated diamond surface for the two selected wavelengths. According to these images, the femtosecond laser is inducing nanostructures with sub-wavelength period (HSFL) perpendicular to the polarization of the laser beam. Previous results suggest that random nanoablation would result from the lattice disorder and intense near-field. 14,16 However, we have observed in experiment an ordered nanostructure and therefore we suggest that a periodic process is responsible for the ordering of the nanoablation. Moreover, we observed in Fig. 2 that the period of the nanostructure decreases when the number of pulse increases. With each incident femtosecond laser pulse, the density of excited electrons increases, resulting in a decrease of the real part of dielectric function of the irradiated layer, allowing for plasmonic excitation. Therefore, we suggest that the formation of HSFL can be attributed initially to the excitation of SPP in the surface layer. From our simulations, we show the importance of the plasmonic excitation on the formation of the HSFL, and also shed insight into other physical processes involved. It can also be observed in Fig. 2 that there is ablation of the material at the center of the micro-grooves, where the peak fluence of the Gaussian beam is highest. This effect is more noticeable for lower scan speeds, as heat accumulation is more pronounced for a greater number of pulses interacting within the focal volume in the pseudo-metal layer. 20 Despite the ablation at the center of the tracks, nanostructures can be observed at the sides of the micro-grooves, indicating that the periodic nanostructures are produced at fluences slightly below the ablation threshold. 11  during the interaction with the femtosecond laser, which is attributed to the incubation of nano-ripples when greater energy density is delivered to the lattice. Figure 4 shows a recapitulation of the effect of fluence (power) and speed (number of pulses) on the nanostructure period for 515 nm (a) and 1030 nm (b) wavelengths. The period of the nanostructures increases with scan speed for both wavelengths. The minimum period is 110 nm and 190 nm for 515 nm and 1030 nm wavelengths, respectively, for the lowest speed (3 mm/s). From this, we deduce that the formation of nano-ripples has a strong dependence on the wavelength, with the period increasing with wavelength.
One can also observe, according to Fig. 4, that the nanostructures are not obtained for all values of fluence or speeds, due to the large band gap of diamond (5.5 eV), where the electrons can be excited by one photon if it has enough energy, or by a multiphoton absorption if the photon energy is below the gap. 33 To observe nanostructures for powers lower than 4 mW (F = 6.36 J/cm 2 ) at 515 nm writing wavelength Fig. 4(a), we need to increase the number of pulses by decreasing the scan speed. However at the green wavelength, we found a narrower energy window between ablation and no modification, making it more difficult to observe the formation of nanostructures.
Next we simulate the evolution of the periodicity of nanostructure HSFL type via the generalized plasmonic model proposed above. When the pulse number increases, the excited electron density n eh increases until the condition ε pm = ε air (m = 0) is reached. At this point, the First Ordered Nanostructure (FON) can be observed, with a period of Λ FON = 250 nm at λ L = 515 nm ( Fig. 5(a)), and a period of Λ FON = 510 nm at λ L = 1030 nm ( Fig. 5(b)). This corresponds to the minimum Plasmon Resonance RP min . This RP min is caused when the plasmons tend to coherently couple with the incident laser wave at the pseudo-metal/air interface as if the original material (diamond) did not exist.
The smallest nanostructure or the Last Ordered Nanostructure (LON) can be observed when ε pm = ε di (m = 1) with period of Λ LON = 83 nm and 197 nm at wavelength 515 and 1030 nm, respectively (Fig. 5). This corresponds to the maximum Plasmon Resonance RP max . In the data shown in Fig effect of the penetration of plasmonic evanescent wave at both interfaces of the pseudo-metal layer on the periodicity of the nanostructures with the increase of the number of incident laser pulses. Fig.  6 shows the penetration depth of the irradiated wave as a function of electron-hole plasma excitation, d = c 2ωk (Ref. 18) where all the parameters were previously defined. d is the penetration depth of laser during the irradiation. When the number of pulses increases, the density of excited electrons and the absorption coefficient k increase, then the penetration depth decreases. Based on (Fig. 6), the depth of the pseudo-metal layer is tens of nanometers. Therefore, the pseudo metal layer remains a mix state (from the point of view of the dielectric function) between air and bulk diamond when ε pm decrease from ε air to ε di . Therefore, we can assume that there is a transverse migration of the SPP from the pseudo-metal/air interface to the diamond/pseudo-metal as the number of femtosecond laser pulses increases, where the nanostructure period decreases from Λ FON to Λ LON . So we deduce that the ordered nanostructures (HSFL type) can be observed only inside the range [RP min , RP max ]. It is important to note that this model is valid in a specific carrier density corresponding to the plasmonic excitation. Our experimental results are in agreement with these calculations, where the measured periods ( Fig. 4) are included in the plasmonic range calculated for the both wavelengths (Fig. 5). The period Λ LON is also called saturation period as it is the minimum pitch of the nanostructures. 34 We have highlighted in Fig. 6 the case corresponding to RP min and RP max . So based on our reasoning above the d max which corresponds to RP max is the smallest depth possible, taking on values d max = 61 nm, 32 nm at λ L = 1030 nm, 515 nm respectively, therefore, all the absorbed energy at the pseudo-metal layer with depth d max to be reserved to the SPP excitation, and this is why the period Λ LON can enhance the surface absorption. 4,5 Thus, it is important to find this period if the aim is to obtain high efficiency micro-solar cells with femtosecond laser pulses, to avoid energy dissipation inside the material. It has been confirmed experimentally that with only LIPSS the absorption can be enhanced to more than 90% via plasmonic excitation, 2-5 because the plasmons wave oscillateds at a scale of λ sp which is less than λ L . Therefore, the plasmons are able to efficiently absorb the incident light, i.e. they are able to respond together at the same point of time and space to the incident radiation.
Our model for the formation of HSFL in diamond during the interaction with femtosecond laser pulses can also be applied in general to dielectrics and semiconductors, taking into account the effect of plasmonic excitation in non-thermal melting dynamics. Experimental results show that the period of the nanostructures decreases when the number of laser pulses increases. On the other hand, during the analysis of the LIPSS period versus the electron-hole plasma excitation, we see that the period Λ decreases when the factor of mixed states m decreases until reaching the saturation at the maximum Plasmonic Resonance RP max . This implies that the pseudo-metal layer transitions from crystalline diamond to a graphitic phase occurs progressively when the period decreases from Λ FON to Λ LON . As this transition is due to non-thermal melting (disorder), 19 we can conclude that the ordered nanostructures are formed by a combination of two processes: the random nanoablation due to the near field induced during irradiation, and the plasmonic excitation, that plays a complementary and simultaneous role to order the nanoablation because of its specific wave periodicity (frequency).
Finally, as the random nanostructures are generated by random disorder, it can be called ordinary disorder, while as HSFL are due to disorder forced by the plasmon wave, it can be called plasmonic disorder. The overview of this description is presented in Fig. 7, which also helps to summarize the physical processes involved in the formation of the HSFL during the irradiation with femtosecond laser pulses. It is shown that the origin of random nanostructures is related to one process (disorder), in contrast to order nanostructures of HSFL type that are related to a combination of two processes (disorder + plasmonic excitation).

V. CONCLUSION
In this paper, we have studied the origin of the formation of periodic nanostructures (HSFL) by femtosecond laser pulses on the surface of diamond. The experimental results have shown that the periodicity observed depends on the pulse number for both wavelengths used (1030 nm and 515 nm). We suggest that the non-thermal melting (disorder) and plasmonic excitation have a very important role in the dynamic process. We propose a generalized plasmonic model that can be used directly to simulate the evolution of periodic nanostructure HSFL for dielectric or semiconductor materials at any wavelength. Using this model for the particular case of diamond allows us to calculate the period of nanostructures formed on the surface, and we have confirmed with the experimental results that the period decreases when the number of pulses increases via the variation of both carrier density and the mixed state factor. We conclude that the periodic nanostructures can only be observed in the range of plasmonic excitation bounded by a minimum and maximum plasmon resonance [RP min , RP max ], whereas random nanostructures can be formed below RP min . Finally, we propose a physical description that shows the importance of plasmonic excitation in the formation of sub-wavelength nanostructures, where the plasmonic excitation effect for non-thermal melting dynamics (disorder) can be considered as a fundamental process for the periodic nanoablation as origin of HSFL nanostructures.