摘要：二維層狀材料（石墨烯、二維過渡金屬硫族化合物等）因具有獨特的物理性質(zhì)，引起了研究學(xué)者們的廣泛關(guān)注，極大促進(jìn)了化學(xué)、材料科學(xué)和凝聚態(tài)物理學(xué)的發(fā)展。開發(fā)能夠探究層狀材料中層數(shù)依賴的光學(xué)、電學(xué)、力學(xué)和熱學(xué)特性的新技術(shù)一直是二維材料領(lǐng)域最活躍的研究方向之一。光熱顯微鏡利用光激發(fā)后非輻射躍遷產(chǎn)生的熱效應(yīng)，可實現(xiàn)在單個顆?；騿畏肿铀缴铣上衽c檢測，并實時捕捉微觀尺度熱弛豫和熱傳輸過程。本文對比研究了石墨烯薄片在不同光熱介質(zhì)（空氣、甘油）中隨厚度變化的光熱特性，發(fā)現(xiàn)了在兩種介質(zhì)中光熱信號強度與樣品厚度之間均存在非線性依賴關(guān)系。相比于空氣介質(zhì)，甘油介質(zhì)中光熱信號強度具有更高的對比度，且隨著厚度增加表現(xiàn)出非單調(diào)變化。該研究提供了不同介質(zhì)環(huán)境中不同層數(shù)石墨烯光吸收和熱弛豫特征的細(xì)節(jié)信息，相關(guān)研究結(jié)論將為層狀材料及其異質(zhì)結(jié)的熱學(xué)性質(zhì)研究提供依據(jù)。

關(guān)鍵詞：石墨烯；光熱顯微成像；層數(shù)依賴；光吸收；非輻射弛豫

中圖分類號：O642

Photothermal Microscopy of Graphene Flakes with Different Thicknesses

Abstract： Two-dimensional （2D） layered materials have attracted widespreadresearch interest and have significantly promoted the development of chemistry，material science， and condensed matter physics. Since the emergence ofgraphene， 2D materials with unique mechanical， thermal， optical， and electricalproperties have been developed. In the case of graphene， its extraordinarymechanical strength， carrier mobility， thermal conductivity， and light-absorptionover the whole spectral range in UV-Vis and near infrared guarantee a wide rangeof prospective applications. The electronic structure and properties of grapheneflakes are dominated by their thickness， twist angle， and dielectric environment.Tailoring the interlayer interactions of graphene layers can provide additionalopportunities for developing optical and electrical nanodevices， resulting inpioneering outcomes， such as the magic-angle graphene. Over the past decade，one of the most active research directions in the field of 2D materials has been the development of novel techniques thatcan probe the thickness-dependent physical properties of layered materials. In contrast with the intensively studiedmechanical， electrical， and optical properties， microscopic investigations of the thermal characteristics of graphene flakesremain to be explored. Photothermal （PT） microscopy is a new all-optical microscopic imaging technique that has gainedsubstantial attention and undergone long-term development in recent years， especially in the fields of nanomaterials andlife sciences. The fundamental principle of PT microscopy is to heat the target sample based on the absorption of a heatingbeam and use a probe beam to indirectly capture information on microscale heat generation and transport. Inspired byseveral pioneering studies， we conducted a comparative study of the thickness-dependent PT properties of mechanicallyexfoliated graphene flakes in two different PT media， i.e.， air and glycerol. Whereas a nonlinear relationship between thePT intensity and sample thickness was observed in both media， the PT intensities from the two media were distinct. A highcontrastand non-monotonic PT response was observed in glycerol. The PT intensity of monolayer graphene was higherthan that of bilayer graphene， and the PT intensities of graphene flakes with 2–4 layers exhibited a good linear relationshipwith the thickness. We also analyzed the relationship between the PT intensity and heating or probe power， demonstratingthat the PT intensity as well as the absorption cross-section of graphene derived from the PT signal vary linearly with thepower of both laser beams. Our study provides insights into light absorption and thermal relaxation features of grapheneflakes of different thicknesses， which can guide future studies on the thermal properties of layered materials and theirheterostructures.

Key Words： Graphene; Photothermal microscopy; Thickness-dependence; Optical absorption;Nonradiative relaxation

1 Introduction

The rise of graphene 1 and other monolayer materials 2–6 hasopened up a new 2D world for exploring thickness-dependentphysical phenomena on the atomic scale 7，8. Taking graphite asan example， the variations in the number of layers affect theelectronic structure and its optical and thermal properties 9. Tobe consistent with most literature， here we use graphene flakesto represent monolayer to few-layer graphene flakes. Monolayergraphene has an amazing energy band structure with zero gap，and one of its most important properties is that its charge carriersbehave as massless relativistic particles or Dirac fermions 10. Forbilayer graphene， the band gap can be modulated by applying avertical electric field 11，12. Meanwhile， bilayer graphene ortwisted bilayer graphene exhibits abundant exotic strongcorrelation and topological effects， such as superconductivity，correlated insulating states， and quantum anomalous Hall effect，etc.， which significantly contribute to the development ofcondensed matter physics 13–17. In addition， multilayer grapheneoffers unique opportunities whose importance has grown rapidlyin the past few years 18–20. On the other hand， transition metaldichalcogenides （TMDs） from bulk material to monolayer yieldan indirect-to-direct band gap evolution， which opens upabundant research interest in optoelectronics and valleytronics 21–24.

The above examples show layer-dependent electrical andoptical properties of layered materials， and some exoticcharacteristics at the 2D limit are now being seriously consideredfor applications in optoelectronic devices. After photonabsorption， there are multiple relaxation pathways for anexcited-state electron to go back to the ground state， typical processes including fluorescence/phosphorescence emission andnonradiative pathways， such as thermal relaxation 25， carriertransport 26， graphene plasmonics 27，28， photo-acousticgeneration 29， and photochemical processes 30. Among all theabove pathways， thermal relaxation is the most basic one whichexists in almost all cases. Thus， understanding and control ofthermal relaxation is essential in a wide range of optoelectronicapplications including sensing， energy harvesting， and lighting.Recently， there are also pioneering progresses on the thermalproperties of layered materials 31，32 and their heterostructures 33.Kim’s work reported that by stacking atomically thin layers ofMoS2 randomly， the heat transfer capacity of layered materialswould vary greatly in different directions 31. Zhang et al.achieved electrical and thermal rectification simultaneously in aMoSe2/WS2 lateral heterojunction 33. However， a systematicstudy on the layer-dependent thermal relaxation properties oflayered materials is still lacking. In this regard， a technique forprecisely capturing and imaging the layer-number-dependentthermal properties of nanomaterials is essential for acceleratingthe study and exploration of graphene and related materials 34，35.

Photothermal （PT） microscopy is a new optical microscopicimaging technique that has gained extensive attention and longtermdevelopment in recent years， especially in nanomaterialsand life sciences 36，37. The principle of PT microscopy is basedon the thermal lens effect 36，38， which detects the small additionaldivergence of the probe beam by heating-induced thermal lenses，i.e.， the refractive index gradient around the heated analytes（Fig. 1， right inset）. Thus， PT imaging is actually an indirectdetection of absorption， thermal relaxation， and transport for materials with neglectable fluorescence quantum yield. In thiswork， we utilized PT microscopy to gain substantial insights intothe thickness-dependent thermal properties of mechanicallyexfoliated graphene flakes. Effects on different PT media， andexcitation power have been investigated and discussed. The PTintensity shows a monotonically increasing but nonlinearrelationship with thickness in the air media， while in the glycerolmedia we found a non-monotonic PT response. This study offersinsights into the thermal relaxation characteristics of grapheneflakes with different thicknesses. Moreover， since opticalemission and thermal relaxation are two competing processes，our work will also benefit future research related to absorption，emission， and thermal generation in layered materials and theirheterostructures.

2 Experimental

2.1 Sample preparation

Kish graphite crystals were purchased from CovalentMaterials Corp， Japan. We prepared mono- and multi-layergraphene flakes on glass coverslips （Fisherbrand） by a PDMSassisted（Titan） dry transfer method after mechanical exfoliation1，39，40. The coverslips were cleaned with Milli-Q water （type 1），special wash solution in turn for 40 min， blown with nitrogen （≥99.999%）， and exposed to plasma for 2 min not only for highercleanliness but also for higher transferability from PDMS to thecoverslip.

2.2 Micro-area Raman and transmittance spectroscopy

Raman spectra and absorption spectra were measured by aconfocal micro-Raman spectrometer （HORIBA Scientific，Horiba HR Evolution， Japan）. To collect the Raman spectra ofmono- and multi-layer graphene flakes， a 633 nm continuous wave laser was used as the excitation source （～5 mW whenarriving at the sample）， and a 600 lines per millimeter gratingwas used to get a suitable resolution （～1 cm?1）. For theabsorption spectra， we measured the micro-area transmittance ofthe sample. A 50× objective （Olympus， NA = 0.5） was appliedto excite the sample， and a 100× objective （Olympus， NA = 0.9）was used to collect the signal. We used a near-infrared light（Thorlabs， SLS201L （/M）， the United States） ranging from 360nm to 2600 nm as the excitation source and a 100 lines permillimeter grating was used to obtain sufficient intensity. Thetransmittance spectra of a sample （T） and coverslip substrate （T0）were collected， and then the final micro-area transmittancespectra were obtained according to T/T0. All spectra wereprocessed in Labspec6 software.

2.3 Optical contrast analysis

To identify the number of layers of graphene flakes， wemeasured the greyscale values of the samples. Color opticalimages （RGB format） of few-layer graphene were converted togreyscale images. Then， we measured the greyscale values ofdifferent domains in the graphene flakes. Above data processingwas completed with ImageJ.

2.4 Photothermal microscopy

A schematic diagram of the optical setup and workingmechanism is shown in Fig. 1， similar to the previous work 41，42.Briefly， the PT signal arises from a slight change in the refractiveindex of the PT medium （air or glycerol） due to the thermalrelaxation after absorption of the heating beam. The refractiveindex change is measured with another probe beam with adifferent wavelength. In this work， a 532 nm laser was used asthe excitation source （heating beam）， and a 1064 nm laser wasused as the probe beam. The heating beam was modulated usingan AOM （AA Opto Electronic， MT80-A1，5-VIS， France） at a repetition frequency of 5 kHz. The probe beam overlapped withthe heating beam on the sample through a high NA objective（UPlanFLN， NA = 0.6–1.3， Japan）. Then， the backscattered lightof the probe beam was collected by the same objective lens anddetected by a photodiode （PD） （Femto， OE-300-IN-01-FC，Germany）. The PT signal was extracted from the modulation ofthe scattered light by a lock-in amplifier at the same frequencyas the heating beam. Optical transmission images can becollected by an optical camera （Mshot， MS23）. PT imagescovering a whole sample area can be obtained by scanning thesample with a motorized positioning stage （TANGO 2 Desktop，Germany）.

3 Results and discussion

To systematically study the layer-dependent PT properties ofgraphite， graphene flakes with different thicknesses wereprepared using the mechanical exfoliation method 1. Fig. 2ashows the optical image of the few-layer graphene flakes on aglass slide substrate， where the opacity increases with increasingthickness. To confirm the number of layers of graphene， we alsoconducted a contrast profile analysis. Two greyscale valueprofiles of cross-section over the sample are shown in Fig. 2b.The substrate shows a greyscale value of ～207， the first step ismonolayer graphene， and the greyscale values exhibit a linearincrease as the number of layers increases 43. In addition， wecharacterized graphene flakes by both Raman and transmissionspectroscopy （Fig. 2c，d）. Fig. 2c shows typical Raman spectra ofgraphene with 1–4 layers acquired under the same conditions.Two main peaks at ～1580 and ～2690 cm?1 are the G-band and2D-band， respectively. As we used high-quality Kish graphitecrystal for mechanical exfoliation， no D-band is observed. Theintensity of the G-band increases with the increase of graphenethickness. Meanwhile， the full width at half maximum of the 2Dpeaks gradually increases and the peak-center blue shifts as thenumber of graphene layers increases， which is in goodagreement with the Raman spectra of few-layer graphenereported in the literature 44–46. According to the transmissionspectra （Fig. 2d）， the absorbance of the monolayer graphene is～2.0%， and the absorbance of graphene flake increases almostlinearly with the number of layers exhibiting the typical featuresof graphite with different thicknesses 47，48. All of the aboveresults accurately confirm the number of layers of our samples.

Fig. 3a shows an optical microscopic image of the grapheneflake on a glass slide substrate with a weak optical contrast. Fig.3b shows a PT image of graphene in the air with a scanning areaof 40 μm × 40 μm. The PT signal has a uniform distributionwithin sample areas with the same thickness. It should be notedthat the graphene has absorption at 1064 nm which may affectthe results. To exclude the effect of the probe beam， weperformed the PT measurement without excitation of the heatingbeam and no PT signal was observed （Fig. S1， SupportingInformation）. A statistical analysis of the PT intensity formonolayer， bilayer and trilayer graphene is shown in Fig. 3c. ThePT intensity is about 0.018 mV for monolayer， 0.028 mV forbilayer and 0.029 mV for trilayer， indicating a nonlinearrelationship between PT intensity and thickness differing from the absorption of graphene 49. This may be due to the limitedcapability of air as a PT medium to induce temporal and spatiallyvarying refractive index changes and hence prevent theidentification of small differences in the bilayer and trilayersamples 50.

In this technique， a frequency-modulated heating beamexcites the absorber， which releases heat to the surroundingmedium via nonradiative relaxation pathways 51. The heat bringsabout a temperature increase in the region around the absorber，which induces a temporally and spatially modulated refractiveindex change. To enhance PT sensitivity， we further choseglycerol as the medium to conduct PT measurements. Fig. 4adisplays a PT image of the few-layer graphene flakes in theglycerol. The statistics of the PT intensity for 1–4 layers ofgraphene flakes are shown in Fig. 4b. The PT intensity is about2.2 × 10?3 mV for the monolayer， 7.6 × 10?4 mV for the bilayer，8.5 × 10?3 mV for the trilayer and 1.7 × 10?2 mV for the fourlayer.The signal to noise ratio （SNR） of graphene in differentPT media was calculated to be 8.1， 13.5， 13.9 and 14.9 for 1–4layers graphene in the air and 9.2， 3.2， 36.4 and 74.2 in theglycerol， respectively. Except for the bilayer graphene， the SNRin the glycerol is significantly higher than that in the air.Comparatively， the PT intensity in the glycerol has a nonlinearand non-monotonic relationship with thickness. If we comparethese values with the PT intensity of monolayer graphene， wecan see that the PT intensity of monolayer graphene is higherthan that of bilayer graphene. In addition， the PT intensity of 2–4 layers shows a good linear relationship with thickness. Thereason for the unusually high PT intensity of monolayergraphene could be the extremely high thermal conductivity 52，53，which eases the delivery of heat to glycerol and causes a higherPT signal as compared to bilayer graphene. In contrast， the PTintensity of bilayer graphene is lower than expected， although itshows a good linear relationship with the trilayer and four-layergraphene. It is known that the thermal conductivity can bemodulated by varying the geometric structures or foldingprocess， and the thermal conductivity of folded graphene can besignificantly decreased of its counterpart due to the phononUmklapp and normal scattering enhancement 54，55. Thus， wealso investigated the effects of folding on the PT intensity ofgraphene both in the air and glycerol （Fig. S2）. Similar to fewlayergraphene flakes， the PT intensity of the folded plane regionin the air is two times that of the monolayer graphene， while theintensity of folded plane region in the glycerol is about half thatof monolayer graphene， which is consistent with the bilayergraphene.

Then， we comprehensively analyzed the relationship betweenthe PT intensity and heating or probe power. Graphene andgraphite absorb light in a wide wavelength range， but in ourplatform， the PT response is a differential signal between theheating light on and off， so it can be assumed that the PT signalmainly originates from the absorption of the heating beam by thesample. To avoid damaging the sample， we controlled the powerof the heating and probe light within 200 and 3000 μW，respectively. The PT intensity as a function of the powers of thetwo laser beams is shown in Fig. 4c，d. The PT intensity showeda good linear power dependence for both laser beams. In detail，the slopes of the PT intensity of monolayer， bilayer， trilayer andfour-layer to the heating power are 1.1 × 10?5， 3.7 × 10?6， 4.9 ×10?5， and 10.3 × 10?5 mV?μW?1， and to the probe power are 4.5× 10?7， 2.9 × 10?7， 2.9 × 10?6 and 6.3 × 10?6 mV?μW?1，respectively.

The PT signal comes from the heat generated by theabsorption of light. Due to the extremely low fluorescencequantum yield of graphene， almost all the absorbed light isconverted to heat. Thus the absorption cross-section can becalculated directly from the PT intensity because PT intensity isproportional to the absorption cross-section as discussed in thesupporting information. Here we used 20 nm gold nanoparticles（Zhongkeleiming Daojin Technology Co.， Ltd.） as referenceswhich also have extremely low fluorescence quantum yield. Theabsorption cross-section of graphene at 532 nm is calculated tobe σabs （532 nm） ≈ 1.6 × 10?18 cm2 per C atom， as described inthe Supporting Information. This result is very close to the valueof 5 × 10?18 cm2 per C atom calculated based on the 2.3%absorption of graphene.

4 Conclusions

In conclusion， we have systematically investigated thethermal properties of graphene flakes with different thicknesses.We found a nonlinear relationship between PT intensity andthickness in both air and glycerol as PT media. The PT intensityof the monolayer graphene in both air and glycerol is significantly different from that of few-layer graphene flakes. Amuch clearer PT contrast and a non-monotonic PT response wereobserved in the glycerol medium. Then， we analyzed therelationship between the PT intensity and heating or probepower， demonstrating that the PT intensity exhibits a good linearrelationship with the power of both laser beams. In addition， wealso calculated the absorption cross-section of graphene by thePT signal. This study provides insights into the light absorptionand thermal relaxation features of graphene flakes with differentthicknesses， and provides a possible method to recognize thethickness by PT signals. Thanks to the various unique propertiesand new applications of few-layer graphene and moirésuperlattices， PT microscopy will provide broader informationfor both future fundamental research and practical applications.

Author Contributions： Conceptualization， Y.T.， W.X. andZ.W.; Sample Preparation， D.Z.; Methodology， W.Y. and Z.W.;Formal Analysis， Z.W.， A.D.， Y.W.， Q.S.， L.L. and Y.W.; DataCuration， A.D.， Z.W. and Y.W.; Data Curation andVisualization， A.D.， Y.W. and Z.W.; Writing – Original DraftPreparation， A.D.， Y.W. and Z.W.; Writing – Review amp; Editing，A.D.， Y.W.， Z.W.， Q.S. and L. Z.; Visualization andSupervision， Y.T.， W.X. and Z.W.

Supporting Information： available free of charge via theinternet at http：//www.whxb.pku.edu.cn.

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國家自然科學(xué)基金（22073046， 22173044， 62011530133）， 國家重點研發(fā)計劃（2020YFA0406104）， 中央高校基本科研業(yè)務(wù)費專項資金（020514380256，020514380278）， 生命科學(xué)分析化學(xué)國家重點實驗室（SKLACL2217）， 江蘇省自然科學(xué)基金（BK20220121）及江蘇省研究生科研與實踐創(chuàng)新計劃（KYCX22_0096）資助項目