Graphene nano-sieves by femtosecond laser irradiation

The formation of nano-pores in graphene crystal structure is alternative way to engineer its electronic properties, chemical reactivity, and surface interactions, enabling applications in technological fields such as sensing, energy and separation. The past few years, nano-perforation of graphene sheets has been accomplished by a variety of different methods suffering mainly from poor scalability and cost efficiency issues. In this work, we introduce an experimental protocol to engineer nanometer scale pores in CVD graphene membranes under ambient conditions, using low power ultra-short laser pulses and overcoming the drawbacks of other perforation techniques. Using Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM) we visualized and quantified the nanopore network while Raman spectroscopy is utilized to correlate the nano-perforated area with the nanotopographic imaging. We suggest that Raman imaging provides the identification of nanoporous area and, in combination with AFM, we provide solid evidence for the reproducibility of the method, since under these experimental conditions, nanopores of a certain size distribution are formed.


Introduction
Since 2004, when graphene was first reported [1], new exciting prospects in molecular separation technologies have been opened [2]. Due to its atomic thickness, graphene is the thinnest known barrier [3] and along with the ability to sustain pores of nanometer size in its structure [4], can serve as an ideal atomically thin perforated membrane. The formation of nano-pores with controllable size and density in graphene crystal structure is crucial to examine its potential for controlling mass transport at the nanoscale, pointing towards a variety of membrane applications such as water desalination [5] and gas [6] or water [7] purification. Interestingly, the size and spatial density of nanopores play a significant role in engineering of electronic properties [8], chemical reactivity [9] and surface interactions [10] of perforated atomically thin graphene membranes enabling applications in the fields of sensing [11][12][13][14], energy storage [15][16][17], supercapacitors [18][19][20], separation [4][5][6][21][22][23] and DNA sequencing [24].
Femtosecond (fs) lasers have become an advanced tool in the field of micromachining due to their extensive use for the processing of advanced materials [50,51]. Their ultra-short light pulses combined with high peak powers offer unique advantages such as sub-micrometer spatial resolution, repeatability, non-contact processing and non-thermal heating of the affected area [52]. In this context, femtosecond laser illumination for patterning or engineering defects on graphene can be utilized for the fabrication of graphene-based devices. In 2001, before single layer graphene was experimentally discovered, Jeschke et al [53] identified by means of molecular dynamics simulations a new ablation mechanism of thin graphite films at fluences below the threshold for the damage of graphite planes (∼170 mJ cm −2 ). The last decade much work has been done [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] for the optimization of fs laser patterning processes in graphene by investigating the dependence of ablation process on the fs laser exposure parameters (e.g. fluence, pulse energy, pulse duration, repetition rate, exposure time and scanning speed). A summary of the recent literature is presented in table S1, where the irradiation energy, power or fluence are presented along with other crucial laser parameters and the effect (damage) caused in graphene by ultrashort laser pulses. It is worth noting in table S1 that several patterning protocols have been used for graphene while a variety of laser sources with pulse durations ranging from ps to fs at various wavelengths have been utilized (see table S1).
Most research efforts have been focused on patterning the graphene structure above the ablation threshold, while few works [54,55,69] conducted at laser fluences distinctly below the ablation damage threshold as done in this work (see table S1). In the latter case, graphene (suspended or supported onto Si/SiO 2 ) is subjected to laser-induced chemical functionalization under ambient conditions, whereas, preserving its long-range structural integrity [70][71][72]. Koivistoinen et al [70] studied the photo-oxidation of graphene and concluded that the oxidation is initiated in small independent seeds which progressively grow and finally coalesce in such a way that form a random nanomesh consisting of oxidized islands and graphene nanoribbons. Johansson et al [71] revealed that the chemical composition of two-photon oxidized graphene is mainly composed of epoxide and hydroxyl groups with a small percentage of carboxylic groups. Besides, Mendoza et al [72] studied the laser-induced two-photon oxidation on a free standing single layer graphene, where the irradiation effect was categorized into three distinct regimes, exhibiting progressively enhanced structural disorder and nanopore formation. Recently, Johansson et al [73] studied the effect of fs laser irradiation on graphene with low energy pulses under both inert and ambient conditions. They found that the pulsed laser beam induces local expansion on the graphene lattice due to laser induced defects resulting in forging. Under inert atmosphere and on the absence of oxygen, the forging of graphene lattice is more homogeneous and intense. Following up the forging effect under inert atmosphere and by adjusting the exposure parameters, the graphene lattice can be blistered into various shapes when irradiated with fluences below its ablation threshold [73][74][75]. It can thus be concluded that nanopore formation in single layer graphene (suspended or supported) is possible under ambient conditions and under moderate laser fluences well below the graphene ablation threshold. However, to the best of our knowledge no prior attempts have been made to visualize and correlate the nanopore network characteristics (size and porosity) with Raman imaging and the fs laser irradiation parameters.
In this work we have managed to perforate CVD graphene on Si/SiO 2 at ambient conditions by femtosecond laser irradiation, below the ablation threshold. Evidence of nanopore formation by femtosecond laser irradiation in the graphene literature can only be found in reference [72] but in suspended graphene. We have visualized and explored the nanopores and nanopore network using AFM. Also, the porosity and the size of nanopores as a function of femtosecond irradiation parameters have been quantified. Utilizing Raman imaging we managed to directly correlate the nanoperforated area vis-a-vis AFM topography imaging. Based on these results, Raman imaging provides a direct identification of the porous areas, assisting the establishment of a specific protocol for nano-perforation of CVD graphene on Si/SiO 2 substrates and enhancing the scalability and repeatability of the method.

Sample fabrication
CVD grown graphene samples on polycrystalline copper foils were supplied by Aixtron (UK) and transferred onto 90 nm thick Si/SiO 2 wafers. The transferring procedure involves the following steps: (a) samples are spin-coated with poly(methyl methacrylate) (PMMA) at a rotation speed of 1000 rpm, (b) the Cu/graphene/PMMA stacks are then placed in 1M NaOH solution for copper etching, and (c) after washing with deionized water, PMMA/graphene stacks were transferred onto 90 nm thick Si/SiO 2 substrates. The samples left to dry overnight into nitrogen atmosphere.

Femtosecond laser irradiation
Irradiation of the graphene samples performed at standard ambient temperature and pressure with a 820 nm Ti:Sapphire femtosecond laser oscillator, generating 80 fs pulses with 80 MHz repetition rate. The laser beam passed through a x5 expanding telescope and was then focused onto the samples by means of a x100 air objective lens (NA = 0.90). The irradiation power was controlled by a λ/2 plate and a polarizer placed on a motorized rotating holder. An electronic shutter of 3 ms rise time was used to control the irradiation time. The samples were placed on a x-y-z motorized translational stage with 5 cm travel range and 0.1 μm spatial resolution.

Raman spectroscopy
Raman measurements were carried out using an InVia2000 Raman spectrometer equipped with a 1200 grooves mm −1 grating, providing ∼2 cm −1 spectral resolution and ∼0.1 cm −1 spectral accuracy. For excitation the 514 nm laser line was focused on the sample by means of a x100 objective (NA = 0.90), yielding a laser spot size of about 600 nm [76]. The laser power was kept below 200 μW to eliminate laser heating effects. Raman maps took place in rectangular areas ranging from 20 × 20 to 5 × 5 μm, using a high speed optically encoded motorized sample stage (Renishaw, UK) with a step of 200 nm. The spectral line shape parameters were extracted by fitting Lorentzian functions to the experimental peaks after background subtraction. The Raman fingerprints of the pristine CVD grown graphene samples indicate high structural quality, while there were no significant variations in the Raman spectral features between different samples and sample areas (see supplementary sections 2 and 3 for more details).

SEM and AFM characterization
The morphology of the fabricated structures was characterized by Scanning Electron Microscopy using a LEO SUPRA 35VP microscope. Atomic Force Microscopy (AFM) measurements were performed with a Dimension Icon microscope (Bruker) operating in contact mode. Images were collected using ScanAsyst-Air probes (silicon tips on silicon nitride cantilever, Bruker) with 2 nm tip radius and 0.4 N m −1 nominal spring constant of the cantilever. All AFM scans (trace, retrace) have been performed with 1024 lines and sampling was 1024 points per line corresponding to 1024 × 1024 pixels per image. The authenticity of the pore structures was validated through several cantilevers. To quantify the created nanopores in the laser irradiated areas, AFM images were processed and analyzed using the free SPM data analysis software Gwyddion v2.59.

Results and discussion
In our experiments we illuminated monolayer CVD grown graphene samples deposited onto SiO 2 substrates, with low energy femtosecond laser pulses, corresponding to fluences well below the ablation threshold of graphite [53] . It was found that fluence of 1.6 mJ cm −2 is not sufficient to initiate the formation of nanopores on graphene lattice. The lowest laser fluence for nanopore initiation was found to be 4.8 mJ cm −2 , while at fluences higher than 19.1 mJ cm −2 up to 50.9 mJ cm −2 graphene was almost ablated. Therefore, the available fluence window in our experiments ranges from 1.6 to 19.1 mJ cm −2 . In this frame, laser treatment was accomplished at well-ordered spots on a graphene grid pattern using the following protocols: (a) constant exposure time of Δτ = 20 s (for higher exposure times the observed structural modifications were of minor importance) under irradiation fluences in the range of 1.6-19.1 mJ cm −2 (irradiation dose 3.2 × 10 10 -3.8 × 10 11 pJ·s cm −2 ), and (b) constant laser fluence irradiation of 4.8 mJ cm −2 , Δτ was varied from 1 up to 500 s (4.8 × 10 9 -2.4 × 10 12 pJ·s cm −2 ).  8 mJ cm −2 (Δτ = 20 s) recorded from the same sample area. The laser treated area is clearly visible in both images, consisting of three morphologically distinct regions as delineated by the two concentric dashed line circles. The outer region (Area I) is the non-irradiated area of no damage, the middle region (Area II) appears brighter than Area I (high contrast white area) in SEM image (figure 1(b)) and the third region (Area III) at the center of the exposed area corresponds to the nanopore formation area and can clearly be identified from the AFM image (figure 1(a)). Figure 1(c) illustrates representative Raman spectra of the treated monolayer CVD graphene in the range 1200-3000 cm −1 , recorded at different locations within the aforementioned areas ( figure 1(b)). Raman spectrum 1 from Area I is typical of high-quality CVD grown graphene. However, in spectra 2 and 3 from Area II the intensity of D and D΄ bands rise considerably, the 2D band intensity falls off and the D + D΄ peak starts to emerge (vide infra). In Area III (spectra 4, 5) the intensity of D and D΄ bands increase relative to the G band. The 2D band intensity is reduced further becoming comparable to that of the D + D΄ band. In addition, the corresponding Raman spectra shows a twofold and fourfold reduction of the overall spectral intensity as compared to those recorded at Areas I and II. Therefore, Raman spectroscopy is a powerful tool to distinguish the Areas I-III and, as will be shown below, specific Raman features can be utilized to quickly identify the structural state of graphene in the irradiated area. It is worth noting here that by increasing considerably the laser fluence up to 38.2 mJ cm −2 , the morphology of the Area III changes significantly, as shown in the SEM image in figure S3(a) (supplementary section S4). This is also prominent by the extremely low intensity of the Raman signal recorded at Area III ( figure S3(b)). This Raman spectrum originates most probably from the remaining nanocrystalline graphene fragments indicating almost complete removal of graphene in this area. Figure 2 illustrates a comparison of SEM imaging vis-àvis AFM topography from areas irradiated with 1.6 mJ cm −2 (3.2 × 10 10 pJ·s cm −2 ) and 4.8 mJ cm −2 (9.6 × 10 10 pJ·s cm −2 ) at Δτ = 20 s. At least 10 different spots from the graphene sample at each fluence level were produced and characterized. In the SEM image of figure 2(a), the treated area can be identified by the bright (higher contrast) circular area, while the various grey lines correspond to wrinkles of the graphene sample which are unavoidably formed during transferring. It is evident that there is no Area III formation in the irradiated area, meaning that for fluence of 1.6 mJ cm −2 nanopore formation is inhibited. On the contrary, upon increasing the fluence to 4.8 mJ cm −2 Area III is clearly formed (figure 2(d)), denoting the minimum fluence for nanopore formation for our set-up at Δτ = 20s. In figures 2(b) and (e) the AFM topography images of the areas enclosed in the dashed rectangles of the SEM images (figures 2(a) and (d)), show the differences between the treated areas with fluences 1.6 mJ cm −2 and 4.8 mJ cm −2 , respectively. The formation of an extensive nanopore network, resembling a sieve at the nanoscale (Area III), is apparent in figure 2(e). Regarding the wrinkling network formed during CVD graphene transferring, the AFM topography (figure 2(e)) shows that it remains unaltered in Areas I and II. Similarly, in figure 2(b) the wrinkling network does not change in the treated area (bright area). However, within Area III (figure 2(e)) the emergence of wrinkles is obscured due to severe structural modifications caused by the interaction of the wrinkle with the laser pulses while the nanoporous material in Area III prevent the emergence of wrinkles.

Nanopore imaging and structural characterization
To analyze further the topography of the laser treated area, the height profiles along the dashed lines shown in figures 2(c) and (e) are considered. Regarding the height profile of figure 2(c) caused by the lowest fluence (1.6 mJ cm −2 ) it is evident that graphene is detached from the underlying Si/SiO 2 substrate, bulging out-of-plane by about 1 nm. Therefore, the bright area in the corresponding SEM image (figure 2(a)) resembles a dome with diameter of about 600 nm and height 1 nm.
Regarding the height profile of figure 2(f) caused after tripling the laser fluence (4.8 mJ cm −2 ), the dome is disappeared and a crater shaped graphene depression with a smooth central area (Area III) is created (figure 2(f)). The crater rim corresponds to Area II and is formed by detached graphene having height of 1 nm. Careful inspection of the AFM height profile shows that the wrinkles reach a certain maximum height of 2.5 nm. Similarly, in the SEM image of figure 2(a), the bright area (white contrast) corresponds to the crater rim denoting the bulging of the graphene membrane. It is important to note here that the bright graphene bulging Areas II (white contrast areas) in SEM images originate from variation of the signal intensity of the collected secondary electrons due to the nanometer roughness of graphene in this region [77].
In the area irradiated with 1.6 mJ cm −2 , the observed ∼1 nm graphene inflation is in excellent agreement with the data report in [73], collected under ambient conditions and using similar irradiation fluences. The swelling of graphene lattice as a result of the interaction with the laser pulses, has been attributed to the formation of Stone-Wales (SW) defects that gradually transform to Haeckelite structures generated by a periodic arrangement of pentagons, hexagons and heptagons [73]. It is well known that in SW defects the rotated C-C bond is compressed and the carbon atoms move out of plane in order to relief the strain, dragging the neighboring atoms out of plane [78]. Besides, Rublack et al [79] reported the formation of blisters on 100 nm thick SiO 2 which transform to annular bulges with increasing fluence, due to melting and evaporation of the underlying Si layer, forcing the SiO 2 to form such shapes in fluences below ablation threshold. However, the range of fluences used in this work is not sufficient to provoke this kind of behavior on Si/SiO 2 substrate (∼20 to 30 times smaller fluences used in our experiments). Also, careful examination of the characteristic Raman mode of silicon at 520 cm −1 , shows that its crystal quality is unaffected in the irradiated areas (see supplementary section S5).
In supplementary section S6 the corresponding figures for irradiation fluences of 8 mJ cm −2 (1.6 × 10 11 pJ·s cm −2 ), 14.3 mJ cm −2 (2.9 × 10 11 pJ·s cm −2 ) and 19.1 mJ cm −2 (3.8 × 10 11 pJ·s cm −2 ) are shown. In all these cases the two distinct regions, Area II and Area III, delineated by the concentric circles with increasing diameters, are identified. In figure S5(j) the mean diameter of the treated areas and the formed Area III as a function of the fluence with values in the nanopore formation window (1.6-19.1 mJ cm −2 ) is illustrated. The diameter of the treated area grows linearly with the fluence. The mean diameter of Area III is measured between 1.1 and 2.5 μm, while the mean diameter of the irradiated Areas II and III is in the range of 1.2-4 μm. For the lowest fluence value of 1.6 mJ cm −2 , Area III was not formed as explained above. Corresponding three-dimensional (3D) topography AFM images are, also, presented in figure S6.

Raman imaging of laser treated areas
As mentioned previously ( figure 1(c)) Raman scattering by phonons can be used to identify the Areas I, II and III generated at the focal spot due to the interaction of CVD graphene in air with the ultrashort laser pulses. These data raise the question, which is not systematically addressed despite the efforts so far [80][81][82][83], which characteristic features of the Raman spectra from the defected areas can be exploited as metrics for discriminating Areas II and III with high spatial resolution. Apparently, the answer of this question will be based on recent experimental work in graphene [80,81] which has been dedicated to correlate the lattice structural disorder, originated from different defect types, with spectral features of specific Raman bands. In addition to SEM imaging and AFM topography of the irradiated areas presented in figure 2  The circular morphology of the treated areas in all Raman images is in complete analogy with SEM images and AFM topography in figures 2 and S5 as described in the previous section. In addition, the heat map representation of Raman images of figure 3 reveals the discrimination of the Areas I, II and III. In particular, for fluences higher than 4.8 mJ cm −2 , the deep blue/green and yellow/red contours correspond to Area II and III, respectively. The purple areas representing the lowest values in the I(D)/I(G) and FWHM(G) heat maps delineate the Area I. The associated graphs (bottom panels in figures 3(a)-(c)) show the corresponding 'height' profiles along the dashed line in figure 3(b). The spectral characteristics of the most prominent Raman bands D, G and 2D for the Areas I, II and III are summarized in table 1. Each tabulated value is the average from a certain number of the spectra associated with Areas I, II and III. The values of the spectral characteristics of the Raman bands from Area I resulted after averaging out 927 Raman spectra recorded during mapping and from this point on, they are considered as reference (table 1).
For fluence 4.8 mJ cm −2 a blue shift of ∼2.5 cm −1 of the mean Pos(G) occurs in Area II, while in Area III a significant shift to higher frequencies of ∼8 cm −1 is evident, relative to the corresponding values of Area I ( figure S7(a)). Similarly, a broadening of FWHM(G) of ∼4 and ∼20 cm −1 for Areas II and III, respectively, is measured ( figure S7(b)). By increasing the laser fluence, the FWHM(G) is found almost constant ( figure S7(b)), while the Pos(G) significantly increases to ∼4 and ∼11 cm −1 for Areas II and III, respectively, and remains unchanged for fluences higher than 8 mJ cm −2 ( figure S7(a)). The changes of the Pos(2D) and FWHM(2D) exhibit similar but not so pronounced behavior as a function of the laser fluence, as depicted in table 1 and figures S7(c) and (d). Pos (2D) shifts to higher frequencies in both Areas II and III by ∼2 and 4 cm −1 , respectively, for fluence of 4.8 mJ cm −2 and remains roughly constant within the experimental error in both Areas II and III at ∼5 and 10 cm −1 for higher fluences (table 1 and figure S7(c)). Similarly, the variation of FWHM (2D) follows the same trend, namely, increases by ∼2 cm −1 (Area II) and 5 cm −1 (Areas III) for 4.8 mJ cm −2 being almost constant for higher fluences by about 4 and 17 cm −1 (table 1 and figure S7(d)).
According to the three-stage classification of disorder in reference [84], the evolution of the spectral characteristics of D, G and 2D bands from Area I to Area II (table 1) shows that the laser induced structural disorder of Area II corresponds to a transformation from graphene to nanocrystalline graphene (Stage 1). The steep increase of FWHM(G) and FWHM(2D) provides clear evidence of the high structural disorder that happens in Area III (vide infra). Overall, in the range of fluence values where the nanoporous Area III is visible (4.8-19.1 mJ cm −2 ) the spectral parameters of the G and 2D bands within the Areas I-III show a noteworthy stability, indicating that the density of point-like defects (Areas I and II) and nanopores (Area III) is essentially independent on the laser fluence (table 1, figures 3 and S7).
The I(D)/I(G) ratio correlates to the sp 2 /sp 3 carbon ratio and it constitutes a reliable indicator of structural disorder in graphitic-like films [82,85]. The mean ratio I(D)/I(G) for Area I is ∼0.12 ± 0.09, implying low defect concentration and quite good structural quality of graphene in the nonirradiated areas (table 1). This value is very similar to the one recorded for the pristine graphene (see supplementary section S2 and table S2), justifying the assignment of Area I as the reference area. In Area II, the mean value of the I(D)/I(G) increases significantly ranging between 0.77 ± 0.20 and 0.85 ± 0.32, within the used fluence window. Similarly, in Area III the ratio ranging between 1.66 ± 0.07 and 1.82 ± 0.15, being significantly higher that the ratios of both Areas I and II and essentially independent of the laser fluence. Figure S8 illustrates additional spatially resolved Raman images for Pos(G), I(D)/I(G) and FWHM(G) of spots irradiated with various fluences (1.6-19.1 mJ cm −2 ) for Δτ = 20 s, verifying the exceptional repeatability of the results. From the above analysis it is evident that Raman spectroscopy can be used to distinguish and give insights (vide infra) into the different areas formed by the low power femtosecond laser irradiation of graphene structure, providing unique and complementary information compared to SEM and AFM.
Raman imaging is also utilized to further analyze the type and density of defects in Areas II and III by correlating I(D)/I(G) with FWHM(G) [80][81][82]. Such a correlation at a particular wavelength allows the discrimination of low and high disorder regimes in graphene lattice [86]. The graph of figure 4 illustrates the aforementioned correlation extracted from the Areas (I, II and III) as revealed in figure 3. Each data point of the graph corresponds to a spectrum recorded from a spot on the graphene flake under laser fluence within the used window (1.6-19.1 mJ cm −2 ). A clear clustering of the data points in three distinct domains corresponding to Areas I, II and III is evident in the graph of Finally, with the Raman imaging we exploited the high sensitivity of D and D΄ peaks to capture the amount and type of point-like defects [80]. It has been found that when the intensity ratio I(D)/I(D΄) ≈ 13, 7, 3.5 the point-like defects type is sp 3 hybridization, vacancy defects and boundary defects, respectively [80,81]. The nanopore Area III is excluded from our analysis because the measured I(D)/I(D΄) ratio values cannot be attributed to point-like defects. In Area II, however, the rise of the D΄ peak can provide information about the nature of defects. By plotting the I(D)/I(D΄) ratio as a function of fluence (inset of figure 4) we found that the values lie in the range of 4-9, indicating the coexistence of several types of defects in this area [80]. In this context, it should be noted that according to theoretical prediction [87] a ratio of I(D)/I(D΄) ∼10.5 is estimated, for hopping defects such as SW which may be responsible for the swelling of graphene in Area II [73]. The calculations, however, consider an ideal configuration of these defects in which they are isolated. In reality, SW defects most likely coexist with other defect types (such as vacancy and sp 3 defects) created by the spatial variation of the degree of functionalization, within the laser intensity Gaussian profile. Indeed, functionalization of Area II is milder than Area III. This is in accordance with the findings of Koivistoinen et al [70], Johanson et al [71] and Mendoza et al [72], where an enhancement of the I(D)/I(G) ratio is attributed directly to the photo-oxidation of graphene. Functionalization moieties in graphene structure caused by photo-oxidation is the main reason for the creation of defective sites and the concomitant creation of pores at higher defect densities. According to the proposed mechanism [70,71], photo-oxidation initiates at sites where oxygen absorbed on graphene and probably assisted by water molecules from the transferring process. This results in a nonuniform oxidation where initially functionalized sites are most likely to grow more than the less functionalized ones. This leads to the formation of heavily oxidized islands which coalesce together forming districts of more oxidized and less oxidized areas. According to their results, the photo-oxidized graphene lattice contains mostly hydroxyl (C-OH) and epoxide (C-O-C) functional groups and a few percent of carboxyl (COOH) groups. Additionally, Hong et al [88] claimed that apart from the above mentioned functional groups, ether and carbonyl (C=O) moieties are also formed in the oxidized graphene.
Focusing on the low defect density Area II we can use the I(D)/I(G) ratio to estimate the mean inter-defect distance,

Number of spectra
where E L is the excitation energy and E F is the shift of the Fermi energy level. This relation is valid for L D 10 nm, E F <E L /2 and applied to Raman active defects [89]. For the samples prior to laser irradiation or the Area I, E F is about 150 meV and L D ranging between 24 and 28 nm, corresponding to defect density of 3.4-4.3 × 10 11 cm −2 (table S2). For the experiment shown in figure 3, L D in Area II is reduced considerably down to ∼11 nm, being almost independent of the laser fluence.

Nanopore characterization and porosity
As mentioned in the introduction, Mendoza et al [72] first identified using TEM the formation of nanopores in free standing single layer graphene and attributed to the effect of two-photon oxidation which takes place under illumination with fs laser pulses at ambient conditions. In particular, they showed that the oxygen to carbon (O/C) ratio increases up to ∼1 where it saturates at high irradiation doses, most likely due to the decreased number of unoxidized carbon atoms. In addition, this saturation of O/C ratio is observed at an irradiation dose value which constitutes the threshold for the generation of pores. The creation of pores could be a result of C-C bonds breakage due to formation of reactive oxygen species such as hydroxyl radicals which reduce the energy barrier of C-C bond. Indeed, photo-oxidized areas are non-uniform constituting from heavily and less oxidized districts [70,71]. Thus, even though the exact mechanism of photo-oxidation seems to remain unclear, the breakage of C-C bonds is most likely to occur selectively in the heavily oxidized districts leading to the formation of pores.
In our experiments the AFM topography images shown in figures 5(a)-(d) were used to analyze the size distribution of the nanopores (black spots) and the porosity of the Area III (green area). The AFM images were analyzed using the available tools in Gwyddion 2.59 [90]. It should be stressed that pore shapes and sizes larger than 10 nm (equivalent radius) as measured with AFM (see below) are not affected significantly by the tip radius and geometry. As mentioned in the Experimental section, the tip which was used throughout the work has a radius of 2 nm, which limits the ability of the measurement to resolve pore size lower than 4 nm in diameter. The possibility for the tip apex getting blunt with continuous usage has been mitigated using new cantilevers. Finally, pore sidewalls of graphene are steep with depth ∼1 nm and can be easily resolved by the tip apex of the selected AFM tip (15°-front angle, 25°-back angle and 17.5°-side angle).
The porosity was measured as the ratio of the area of the nanopore to the total area of the Area III. The linear nanochannels not highlighted in green (figure 5) are formed on wrinkle locations and have been excluded from the calculation of the total area covered by Area III. For the used fluence values (4.8-19.1 mJ cm −2 ), porosity is found to be in the range of 30%-40%. This rather broad range of porosity values could be attributed to the presence of wrinkles inside the irradiated areas which slightly alters the real dimensions of the Area III. By assuming that the nanopores are circular, we measured their distribution of equivalent radius for each particular fluence as shown in the bar graphs of figures 5 (a 1 )-(d 1 ). It can be deduced that for fluences greater than 4.8 mJ cm −2 , the majority of the nanopores (80%-90%) have radius ranging from 11 to 40 nm. For all fluences, pore equivalent radius are clustered as follows: ∼30%-50% of the total pores within 11-20 nm, ∼20%-30% within 21-30 nm and ∼15%-20% within 31-40 nm. This clustering is better visualized in the bar chart of figure 5(e) where the percentage equivalent pore radius distribution is presented for various fluences. Therefore, from the above results it is clear that although the total surface area of Area III grows linearly with fluence as already explained above (see figure S5(j)), the nanopore size distribution is unaltered, within the range 4.8-19.1 mJ cm −2 .

Nanoporosity as a function of the exposure time
To examine the effect of irradiation time, Δτ , in the formation of nanopores we irradiated CVD graphene for Δτ of 1, 5, 100 and 500 s at constant laser fluence of 4.8 mJ cm −2 , corresponding to irradiation doses of 4.8 × 10 9 , 2.4 × 10 10 , 4.8 × 10 11 , 2.4 × 10 12 pJ·s cm −2 , respectively. The treated graphene was microscopically imaged by AFM and SEM and indicative images are presented in figures S9 (a)-(l). As expected, in each image the irradiated spot resembles a crater with an increasing rim height and width with Δτ, a behavior analogous with the crater like blisters of varying shape with irradiation time at low fluence, created under inert atmosphere in [74,75]. Alternatively, this shape change of crater rims can be observed in figure S10 where a 3D view of the AFM  Raman imaging on the spots of the treated areas as represented by the heat maps of Pos(G), I(D)/I(G) and FWHM(G) of figure S11, reveals the circular morphology of the spots in complete analogy with SEM images and AFM topography in figures S9 and S10. The associated graphs (bottom panels in figures S11(a)-(c)) show the corresponding 'height' profiles along the dashed line in figure S11(b). The spectral characteristics of the most prominent Raman bands D, G and 2D for the Areas I, II and III are summarized in table S3. Each tabulated value is the average from a certain number of the spectra associated with Areas I, II and III. The values of the spectral characteristics of the Raman bands from Area I resulted after averaging out 198 Raman spectra recorded during mapping and from this point on, they are considered as reference (table S3).
The change, Δ, of Raman spectral parameters in Areas II and III with respect to Area I (reference) appear to have similar dependence on the exposure time, Δτ as shown in the graphs of figure S12 where table S3 has been visualized. In particular, Pos(G) and Pos(2D) of area II blueshift by about 2.5 cm −1 and 1 cm −1 versus Δτ, respectively (figures S12(a) and (c)). At Area III Pos(G) and Pos(2D) blueshift by about 8 and 6 cm −1 , respectively, with slight variation with Δτ. However, for Δτ = 500 s, it seems that Pos(G) and Pos(2D) of Area III tend to be higher due to likely the nanoscale roughness of the irradiated area presented in figures S9(k) and S10(d). It is worth noting here that ΔFWHM(G) and ΔFWHM(2D) in Area III show substantial variation with Δτ (figures S12(b) and (d)) and is associated with the two-photon oxidation of graphene and the subsequent nanopore network formation.
Nanoporosity analysis and the pore diameter distribution as a function of Δτ are presented in figure S13. The extracted nanoporosity varies in the range of 25%-32% with no clear dependence on Δτ. As explained previously in the nanoporosity analysis of figure 5, this variation is attributed to the presence of wrinkles inside Areas III which slightly alter the percentage of porosity by creating linear channels instead of nanopores. Residues (white dots in AFM images of figure S13) from the transferring procedure can also affect the nanoporous area III. Regarding the distribution of the nanopore equivalent radius, it was found that about 80% of the formed nanopores for all Δτ were in the range of 11-40 nm (figure S13(e)). The basic difference between the several irradiation times is the total area of the formed pores.
Finally, we used the AFM images in figures S9(b), (e), (h) and (k) to evaluate the diameter, D, of Area III as a function of Δτ. The measurements are presented in figure S13 (f) where D increases exponentially as a function of Δτ, with a time constant of about 20 s. In the same graph the diameter of the whole crater (Area II + III) is also presented exhibiting similar behavior as D with Δτ.

Conclusions
We have studied by SEM, AFM and Raman spectroscopy the effect of laser irradiation with ultra-short laser pulses of monolayer CVD graphene on top of Si/SiO 2 substrate, at ambient conditions, using various exposure times and fluences below the ablation threshold. We have explored and quantify the nanopores and nanopore network of Area III, lying at the center of the laser treated spot, using AFM. Within the nanopore formation window, the obtained porosity is almost independent of laser fluence, lying in the range of 30%-40%, while the ∼80% of the nanopores have an equivalent radius ranging between 11 and 40 nm. Experiments under different exposure times (1-500 s) at 4.8 mJ cm −2 revealed that nanopores formulate their final shape and size during the first second of irradiation. The total area covered by these pores is slightly growing as the irradiation time rises to 100 s and then remains constant for longer exposure times.
Using Raman imaging and by collecting and analyzing thousands of spectra we managed to spectroscopically identify the Areas II and III without the requirement for AFM or SEM techniques. The evolution of the spectral parameters of the main Raman peaks showed that laser induced structural disorder from graphene to nanocrystalline graphene takes place in Area II. A significant reduction of the inter-defect distance, L D , of pristine samples (24-28 nm) compared to irradiated ones (∼11 nm) is determined. The extracted I(D)/I(D΄) ratio in Area II indicates the coexistence of sp 3 , vacancy type and other point-like defects such as SW induced by the laser pulses. Also, the population of pores exhibit a linear dependence with the fluence in the range between 4.8 and 19.1 mJ cm −2 .
In this study, we introduce an experimental protocol to engineer nanometer scale pores in CVD graphene membranes with the above characteristics using ultra-short laser pulses (duration of 80 fs with wavelength 820 nm), low irradiation fluence (5-20 mJ cm −2 ) and exposure time at least 1 s. The proposed methodology offers many advantages such as reproducibility, scalability, and cost efficiency, opening new prospects in membrane technology.