Confocal Raman spectromicroscopy of graphene

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Introduction
Since the discovery of the important electronic properties of graphene and related materials [1], its characterisation has been the subject of many investigations as outlined through numerous important reviews [2,3].As a rapid, versatile, and easy to implement technique, Raman spectroscopy is often used to characterise graphene layer thickness, and can be used as a method to assess and control parameters in CVD graphene growth and monitor film quality [4].
Graphene-like materials are extensively characterised through Raman spectral signatures relating to the G (~1580 cm − 1 ), D (~1350 cm − 1 ), D′ (~1620 cm − 1 ), and 2D bands (~2700 cm − 1 ) [2].Here, spectral peak shifts, peak shape and the intensity ratios of spectral features, which can be excitation wavelength dependant, are often used to characterise the materials.However, significant variations in the intensity ratios of various features have been reported throughout the literature.Specifically, ratios of the 2D to G peak intensities have been reported with values between 2 and 5.4 for single layer graphene (SLG) [5][6][7][8], 1.8-2.4 for bilayer graphene (BLG) [7] and ~0.3-0.8 for multilayer graphene samples [9,10] (see also [11,12] for variations in the Raman spectra relating to graphene layer number).As such there is significant potential for graphene mischaracterisation, making the largescale analysis of synthetic nanocarbons difficult [13].It is therefore unsurprising that the quality of graphene products varies markedly across the increasing number of companies claiming to produce graphene products [14,15].
In analysing Raman spectra, peak intensities are favoured over peak areas because of the problems with deconvoluting the G and D′ peaks that are closely lying in energy [16].Other ratios, such as the I D /I G and I D * /I G , I 2D /I D+G I 2D /I D+D ʹ [17][18][19] reflect the disorder or defect sites within the graphene layers [20], and chemical functionalisation.These parameters have therefore become particularly important when characterising chemically modified carbon materials, such as graphene oxide and graphene layers prepared through the reduction of graphene oxide [21][22][23][24].Other ratios reflect the type of defects, such as the I D /I D ʹ [25].
Another and complementary method for nanomaterial characterisation is atomic force microscopy (AFM).While AFM is a powerful method for characterising the dimensionality of nano structured materials, it provides no chemical information about the observed materials.Combining AFM with Raman imaging through a confocal microscopy setup, has emerged as an effective method for chemically and topographically characterising mechanically exfoliated graphene flakes [11].Unfortunately, sample preparation requirements and measurement time restricts the ability to perform extensive AFM within a large-scale production environment.Also, for single layer graphene AFM has been shown to provide a range of values (0.4-1.7 nm) due to several factors including, for example, buffer layers between the graphene and substrate and operational parameters.This is still an ongoing area of research and has implications for using AFM as an analysis tool for all 2D materials.Raman spectroscopy, with an appropriate choice of laser power, is largely regarded as an accurate and non-destructive analysis method for graphene samples from 1 to 5 layers regardless of substrate.Confocal Raman microscopy is therefore a favoured analysis technique for rapid prototyping and analysis owing to its ease of use and speed.
In our Raman spectral characterisation of exfoliated 2D materials from graphite we have often seen puzzling observations as exemplified in Fig. 1, in that the 2D/G ratio of carbon materials varies with instrumental settings such as the confocal stage height.This observation is somewhat peculiar owing to the 2D and G Raman signals of graphene both originating from an atomically thin single layer having a thickness of 0.34 nm as determined through the interplane spacing [35].We therefore sought to understand the origin of this behaviour, as it may contribute to the variability in data reported in the characterisation of single and multilayer graphene materials.This behaviour has implications for confocal microscopy depth profiling [36], with single layer graphene emerging as a tool for determining the resolution in confocal depth profiling [37].This variability may also influence investigations into transport phenomena through Raman intensities [38].This has broader consequences in the context of nanometrology, where it may be necessary for increase data sampling of powders for accurate characterisation [39] and high quality control standards are required for improved quality control [40].Here specifically, these applications will require robust instrumental protocols and analysis techniques to produce accurate and highly reproducible data.
In regards to confocal microscopy, Ferrari and Basko [2] have stated that objective numerical aperture should be taken into account when comparing theory and experiment without going into any significant details.In this work, we illustrate how experimental aspects of confocal Raman microscopy influence the Raman spectra of graphene samples.From this study, we explain the origin of the variations observed, and provide protocols for the characterisation of these and other 2D materials to account for such effects.These techniques therefore provide a robust method of materials characterisation.Here we stress the importance in overcoming these issues in analysis to ensure that materials are accurately quantified so they can be readily used in devices.

Methods and materials
Single layer CVD grown Graphene on 285 nm thickness SiO 2 /silicon (p-doped) was purchased from Graphene Supermarket (https://www.graphene-supermarket.com) and used without further modification.Additional mechanically exfoliated graphene was prepared from a HOPG sample.
Raman spectroscopy was performed using a Witec alpha 3000R Confocal Raman Microscope with Nikon Plan Fluor ELWD ×40/0.60 and Nikon E Plan ×100/0.90objective lenses.Here a 532 nm laser was used for the Raman spectromicroscopy.In this microscope system, the 50 μm internal diameter of an optical fibre acts as the confocal pinhole.Here spectra were typically recorded using a 600 g/mm grating and CCD camera.
Samples were also analysed by a Horiba XploRA Plus using a 638 nm excitation laser with an Olympus MPlan N ×100/0.90objective lens.A 100 μm confocal pinhole was used.Again, spectra were recorded using a 600 g/mm grating and CCD camera.
Samples were analysed by recording Raman spectra at various zheights along the microscope optical axis, with the sample z-position controlled through the microscope stage.Using a conventional diffraction grating CCD camera approach, the Raman scattering CCD counts are binned according to detected wavelength.We therefore correct spectra using a Jacobian factor during conversion from wavelength to wavenumber [41].We suspect that the inclusion or neglect of this Jacobian factor can also be a source of intensity variation among Raman scattering features.The spectra and data were then analysed using non-linear fitting procedures to determine peak intensities, areas, positions, and widths.Here we employed Voight or Gaussian line shapes for Raman features to account for the natural and instrumental spectral profile.We also removed a base level fluorescence/CCD dark count background from the true Raman spectral contribution through fitting a linear or higher order polynomial background to the Raman Spectra or spectral region of interest.Atomic force microscopy (AFM) data was acquired using a Bruker Dimension ICON AFM with a Nanoscope V controller.Images were obtained using tapping mode in ambient atmosphere, with all parameters including setpoint, scan rate and feedback gains adjusted to optimize image quality.The AFM probe used was a Mikromasch HQ: NSC15 Si probes with a nominal spring constant of 40 Nm − 1 and a nominal tip radius of 8 nm.The scanner was calibrated in x, y and z directions using a silicon calibration grid (Bruker model number VGRP: 10 μm pitch, 180 nm depth PG: 1 μm pitch, 110 nm depth, Mikromasch model TGZ01: 3 μm pitch, 18 nm depth).Graphene thickness was determined using the depth analysis function of the Nanoscope analysis software Version 2 which allows for the accurate determination of heights across a selected area of an AFM image.

Results and discussion
To assess confocal Raman microscopy in the characterisation of graphene and other 2D materials, we have performed Raman spectral line scans of a commercial CVD-grown single layer graphene sample on silicon as it moves along the microscope optical axis (z-axis line scan).The Raman spectra at each confocal z-height is then analysed to observe the peak intensity of specific Raman features, as shown in Fig. 2.These profiles are measured at two distinct sample locations (Regions 1 and 2) where we have pristine and disordered spectral behaviours.By undertaking the measurements at multiple sample locations, each with unique physical characteristics, we mitigate any influence associated with local heterogeneity within the sample.
Here we observe that the peak maxima of the CVD-grown graphene features vary with the sample distance from the confocal microscope plane, as summarised in Table 1.In the case of graphene, this causes a problem in interpreting the graphene layer number, as the 2D/G intensity ratio varies significantly with the sample height used to undertake the measurement, as illustrated in Fig. 3 for both the ×100 and ×40 objective lenses.Here the 2D/G ratio was found to vary between 1.2 -4.5 and 0.9-3.0 for the pristine and disordered graphene regions.
Respectively (see Table 2).We believe that this span of variation must be contributing to the variability in the reported 2D/G ratio of graphene and related materials throughout the literature and makes the characterisation and comparison of materials challenging.We expect this to be particularly problematic for uneven samples, where the sample height may vary across a region.
This result raises serious questions about how graphene and other 2D materials can be accurately characterised, and the best protocols for their characterisation.It also brings into question what is the origin of Fig. 2. Peak intensities vs confocal z-height for Raman scattering features of single layer CVD graphene on silicon using (a-e) a ×100 and (f-j) a ×40 objective lens.See legends and text for further details.this ratio variation, is it a feature of Raman scattering from graphene or is it an instrumental artefact, and if so, how can we correct for it?
We postulate that the origin of this variation is a chromatic aberration of the Raman confocal microscope lens system.Chromatic aberrations may not be anticipated as modern microscope objectives typically "compensate and correct" for such chromatic effects.However, such chromatic aberrations have been observed in confocal spectromicroscopy of microbial spores [42] and polymers [43], and have been discussed in the context of depth profiling measurements [36].The presence of chromatic aberrations in the microscope lenses can alter the confocal volume that is sampled at each detected wavelength.These may be more pronounced in high numerical aperture systems with short working distances.For normal wavelength dispersion, where the refractive index increases with the decrease in wavelength, we expect that the confocal length increases with increasing detected wavelength (Stokes scattering) [36].
Lasch et al. [42] have proposed a correction for axial chromatic aberrations in confocal Raman microscopy for imaging spore morphology.This method corrects the confocal height at each detected wavelength, through a calibration of the wavelength dependent peak maximum for the imaged spore.While this resolves the influence of chromatic aberrations on imaging position, it is not sufficient in spectroscopy as the overlap of the incident and collected wavelength volumes are no longer confocally matched.Note that it is only in the absence of dispersion that the confocal volumes become independent of the detected wavelengths.Here any variation in the intensity of features at different Raman shifts will influence the observed ratio of spectral features.Thus, all 2D material characterization methods reliant on a ratio of spectral features are susceptible to effects of chromatic aberrations in a confocal Raman microscopy setup.This sensitivity to the confocal volume detected has been studied in the context of Raman and photoluminescence measurements for thin slabs of ion implanted surfaces [36].Atomically-thin single layer graphene (SLG) provides an ideal substrate for developing and refining such models as it gives an impulse response to the specific overlap of the excitation laser and detected wavelength.This is reflected by SLG being recently used to estimate axial spatial resolution in confocal depth profiling [37].
We have therefore developed a model to account for the overlap of confocal excitation and aberrated detected wavelength, which has broad applicability to confocal Raman and photoluminescence systems.We start from the confocal optics model developed by Koppel et al. [44], that has been subsequently employed in particle analysis [45].Here the confocal aperture diameter, s, defines the object size (s 0 ) after considering the magnification (M), This defines the depth of focus in the object space, where α is the collection half angle of the objective.Here α relates the numerical aperture, NA, of the objective and the refractive index, n, of the imaging medium between the objective and sample through: Under this setup, assuming a Gaussian beam profile, the diffractionlimited laser spot for a wavelength, λ Ex , has a 1/e 2 beam waist radius, ω 0 , given by: This creates a laser excitation beam profile dependent on the distance from the optical axis, r, and the distance along the optical axis, z, given by: where I 0 is the optical power of the beam and the z-dependent beam radius is given by: Here z is referenced to the working distance at the excitation wavelength, and we use the convention of positive z being away from the objective lens.It is then possible to define an approximate radial point source collection efficiency function relating to light with wavelength, λ, emitted (fluorescence) or scattered (Raman) from a sample plane located a distance z ʹ from the objective working plane, through [44]: .
Under this model, there is an implicit assumption that there is no chromatic aberration of the objective imaging system, as some chromatic aberrations are somewhat compensated for in sophisticated lens design.In the case a slight chromatic aberration, we may expect that the objective working distance (WD) for the incident laser wavelength, λ Ex , shifts by a distance Δ λ for a fluorescence emission or Raman scattering wavelength, λ, to produce the confocal image.In this model, the distance Δ λ , can be experimentally inferred from the location of a peak maxima in a confocal z-line scan.Once determined, the level of chromatic aberration for the imaging system is in principle then known.
Under these conditions, the collection half-angle (α) then determines the maximum radial distance, r max , accepted through the object lens and imaged onto the confocal pinhole through: This differs from that at the emitted beam's working plane, where the half-angle (α λ ), is governed through: Note that this adjustment influences the depth of focus, l λ , for the detected emitted or scattered beam.
For a particular wavelength of scattered/emitted light, the overall detection efficiency along the z-axis resulting from a single plane is then, .
To obtain the confocal detector response function, we must then convolute the detection efficiency response with a Lorentzian function, L (z), to account for the z-positioning of the confocal aperture, Here we approximate the full width at half maximum of the Lorentzian function as the depth of focus (l 0 ) in object space.
An implementation of this model for our ×100 objective configuration is shown in Fig. 4, where we illustrate the incident beam profile, the chromatic-shifted collection function, and the resultant product.The convoluted profiles are also shown in Fig. 4(h), where we can observe that the peak of the collection function shifts to higher confocal distances because of the chromatic shift.Note that this is a general model of a confocal system and doesn't account for the specific Raman response of the sample at the excitation wavelength.To illustrate the general nature of this phenomena, in that the behaviour relates to chromatic aberrations and is not specific to a particular confocal instrument/setup, we performed additional experiments on a CVD graphene sample using a different confocal Raman microscope that employed a λ Ex = 638 nm excitation source.All confocal microscope setups were then modelled and compare to the experimental results in Fig. 5.Here we obtain the spectral response function from the model for each spectral feature such that the maximum of the instrumental response occurs at the z-height where we experimentally observed the maximum peak intensity.To account for the intensity variation of the 2D and G scattering behaviour, we then use a non-linear least squares fitting algorithm to determine the 2D and G intensity that give the best ratios with respect to the confocal response.Here the model reproduces the gross features in the intensity variation observed across all confocal systems.From this model we therefore demonstrate that the likely origin of the variation in 2D/D ratio is chromatic aberrations in the objective imaging system.
One may argue that we can correct for the confocal displacement of each feature in determining the 2D/G ratio, as has been undertaken in Lasch et al. [42].Here however, the model indicates that the confocal response with chromatic aberrations have different profiles, such that a confocal distance is not sufficient to correct the variation in an intensity ratio.We illustrate this is not routinely possible in Fig. 6, where we would expect the ratio to be constant if this correction procedure of Lasch et al. [42] was applicable.
The question of what is the correct confocal 2D/G ratio still remains, as it appears to be system specific with the instrumental response difficult to fully characterise.It therefore seems pragmatic to implement an instrument calibration using a high-quality commercial CVD-grown graphene sample as a reference calibration standard.Alternatively, a SLG flake that has been mechanically exfoliated from highly ordered pyrolytic graphite (HOPG) and confirmed to be single layer through AFM may also be an appropriate reference standard.Any measurements of chemically or mechanically exfoliated samples can then be compared to the ratio of the calibration standard measured on the same instrument, under identical measurement conditions.Here we note that in performing this comparison, the same confocal z-height of the measurement must also be achieved.Examples of equivalent confocal heights that could be used are the substrate (Si) plane, or the confocal plane of the G-peak maxima.Here we favour the substrate plane as it is usually easily determined via quick z-scan while recording the silicon Raman spectrum, and should be consistent across a sample.
Importantly, we have illustrated that it is challenging, if not impossible, to accurately determine the 2D/G intensity ratio from a single Raman spectrum owing to chromatic aberrations within the lenses of the confocal setup.To obtain this information, multiple spectra must be acquired to determine the instrumental influence on the measurements.In particular, spectral z-line scans are ideally required to reliably determine the reference spectral plane where measurements can then be compared to a calibration reference sample.
We therefore propose the following protocol for ensuring measurement repeatability and quantitative sample comparison.
1.All measurements should be conducted in a common confocal plane, such as the substrate plane (z = 0).This plane can be determined from a substrate peak maximum in a confocal depth scan.2. Measurement of spectra are only directly comparable to reference material obtained under identical measurement conditions (and not literature reported values).This should be a relevant internal lab calibration standard for the sample, such as CVD-grown or mechanically exfoliated SLG from highly ordered pyrolytic graphite (HOPG) for graphene.This could also be a control sample/starting material in assessing chemically modified materials.3. Measured sample values should be reported together with values obtained for the internal lab calibration samples to enable instrument-to-instrument or lab-to-lab comparisons.
Note that by establishing an analysis protocol in this way, the confocal volume of all samples analysed becomes fixed at a specific Raman shift, so that heterogeneity over the sample, such as doping area on the micrometer scale that may alter local peak intensities [46], are always sampled in a consistent way.Variation in obtained spectra are therefore likely to be representative of physical or chemical differences in the sample, instead of instrumental effects.This protocol is also sufficiently general and implementable that it can be applied to solution-processed graphene nanosheets for large-scale applications.With this protocol it becomes feasible for processed solutions to be appropriately diluted (if necessary) and cast onto suitable substrates for large area confocal mapping in the substrate plane.Such analysis would then provide representative Raman spectromicroscopy that could characterise the produced sheet size distribution and synthesised product quality.
To explicitly demonstrate this, we prepared a mechanically exfoliated graphene flake from highly ordered pyrolytic graphite (HOPG).The flake was characterised using atomic force microscopy (AFM), as shown in Fig. 7(a), to identify and confirm single and multiple layer graphene regions of the sample from the thickness of the flake.Note that the independent assessment of the graphene flake through AFM is required to ensure that we can obtain a reference spectrum for ME-HOPG SLG, and that the spectra will be directly comparable to that for the CVD-grown SLG.Here ~1 nm is consistent with the thickness of SLG on silicon.
Which has been measured from 0.4 to 1.7 nm when determined under tapping mode in air [35].Likewise, the thickness of 1.8 nm indicates multilayer graphene (MLG).Raman mapping of the 2D region [Fig.7 (b)] enabled us to locate this flake and identify the single and multilayer sample regions, where we performed confocal depth scans  with different objective lenses to locate the substrate plane (z = 0).The Raman spectra for the single and multi-layer graphene regions in the substrate plane are shown in Fig. 7(c and d).Here we observed 2D/G intensity ratios of 1.45 and 2.21 for the ×100 and ×40 objective lenses, respectively.These ratios are of comparable magnitude to that obtained for the defect-free regions of the CVD grown graphene at 1.22 and 1.54, respectively.Most importantly, we can be confident in comparing the 2D/G ratios obtained for these two different samples as they have been measured under comparable experimental conditions.Here we may expect some variation between the graphene mechanically exfoliated (ME) from bulk HOPG and that grown through CVD methods, as domain boundaries and edge effects may influence the G and 2D peak intensities [47].This observation indicates a potential issue in using a CVD grown sample as a reference standard, as the presence of domain boundaries can create ambiguity in the standard ratio.This may make it preferential to use ME HOPG single layer graphene flakes as the calibration standard, or identifying CVD growth conditions and commercial suppliers that are able to reliably create large-area SLG domains that can appropriately  serve as the "gold standard" for confocal microscope calibration of graphene.
As demonstrated through our measurements, in the absence of an ideal calibration sample, the 2D/G intensity ratio from a single layer CVD-grown graphene sample measured in the substrate image plane under a specific instrumental condition may also serve as a de facto calibration standard and reference for a specific instrument.Here we note that care must be taking in understanding the quality of the calibration standard, and how comparable it is to that which is being measured.This may restrict the broad utility of CVD graphene to serve as a calibration standard.
Finally, the sensitivity of the intensity ratio to the instrumental parameters suggests that comparing results with previously reported values is insufficient for characterising graphene materials, and that the comparisons must be made with reference to a standard calibration sample where measurements are performed under the same instrumental conditions.Ideally such calibration standards could be shared across many spectroscopic characterisation facilities, as has been implemented for AFM cantilever calibration [48].This will allow different laboratories to check and verify their data acquisition methodology and ultimately improve the quality of data generated through confocal spectromicroscopy.
We further note that this methodology of comparing to a reference standard also implicitly accounts for the spectral sensitivity of the CCD sensors used to detect the emitted or Raman scattered light [49], as this can also be difficult to accurately calibrate without appropriate spectral light sources.

Conclusions
In this study, we have illustrated that the 2D/G intensity ratio of SLG is sensitivity to the spectral confocal volume and focal imaging plane used in obtaining the Raman spectrum.As this sensitivity can influence the characterisation of carbon materials, we have developed and proposed a protocol for performing confocal Raman microscopy investigations.These protocols require determining the substrate plane and performing all surface analysis in this reference imaging plane.Note that this may differ from other approaches which maximise the Raman signal of interest.We further propose that an internal calibrated single layer graphene standard sample is used to help with reproducibility in the Raman analysis of carbon materials.With this information and related protocols, the analysis of the quality of graphene films and exfoliated graphene's can become more quantitative.It is hoped that through more robust characterisation protocols, the quality and reproducibility of graphene-derived products may be improved.We also note that the observed behaviour of graphene spectral responses within a confocal microscope setting may be further exploited for improving spatial resolution in confocal depth profiling.

Fig. 1 .
Fig. 1.Raman spectra of single layer CVD graphene on silicon at different confocal z-heights obtained using (a) a ×100 objective on a defect free region and (b) a ×40 objective lens on a disordered region.Spectra are Jacobian and baseline corrected, with the spectra above 730 cm − 1 rescaled by a factor of 10.See text for further details.
D.B. Jones et al.

Fig. 3 .
Fig. 3. Ratio of different graphene peak intensities for different confocal z-heights at different sample regions using (a) ×100 and (b) ×40 confocal objective lens.

Fig. 4 .
Fig. 4. Model of our ×100 confocal microscope setup accounting for chromatic aberrations.(a) The Gaussian beam intensity distribution of the excitation laser, λ Ex = 532 nm.(b-d) The confocal collection efficiency and (e-g) the effective signal for aberration shifted confocal planes, Δ λ = 0, 0.55 μm (graphene G band), and 0.95 μm (graphene 2D band), respectively.(h) The computed detector intensity distribution arising from different Δ λ values.All distributions are with respect to the confocal plane of the excitation wavelength (z = 0 μm) and radial distance from the optical axis of the microscope, r.See text for further details.
D.B. Jones et al.

Fig. 5 .
Fig. 5. Experimental I 2D /I G ratio for graphene peaks at different sample regions and results from our model of a confocal Raman system using (a) ×100, (b) ×40, objectives with λ Ex = 532 nm excitation wavelength and (c) a ×100 confocal objective lens with a λ Ex = 638 nm excitation wavelength.See text and figure for further details.
D.B. Jones et al.

Fig. 6 .
Fig. 6.Experimental I 2D /I G ratio for graphene peaks with a chromatic z-height correction to the confocal distance based on the detected wavelength for the (a) ×100, (b) ×40, objectives with λ Ex = 532 nm excitation wavelength and (c) a ×100 confocal objective lens with a λ Ex = 638 nm excitation wavelength.See text and figure for further details.

Fig. 7 .
Fig. 7. Spectromicroscopic characterisation of a graphene flake, mechanically exfoliated from HOPG.(a) Atomic force microscopy (AFM) image, with cross section insets of the single (SLG, lilac) and multilayer graphene regions (MLG, green).Overlayed lines indicate the approximate locations where the cross sections were obtained.(b) Raman map of the 2D-band region intensity.Also shown are the approximate locations where Raman spectra of SLG (red) and MLG (blue) were obtained using (c) ×100 and (d) ×40 objective lenses where the measurements are observed in the silicon confocal plane.See text and figure for further details.

Table 1
Confocal z-height of single layer graphene (SLG) peak maximum using different confocal settings and for different sample regions.Here the confocal z-height is referenced to the peak maximum of the Si band (~522 cm − 1 ) at z-height of 0 μm.

Table 2
Range of I 2D /I G ratio for different confocal z-heights where the measured ratio has an uncertainty of less than 10 % for different confocal settings and different single layer graphene regions for λ Ex = 532 nm.D.B. Jones et al.