Since its discovery in 2004, graphene has triggered enthusiasm in the world’s scientific community due to its outstanding properties [1,2]. In particular, near-ballistic transport at room temperature and high carrier mobilities [3-4]make it a potentially attractive material for nanoelectronics.

However, as in all materials, realistic graphene structures always contain defects [5]. One generally refers to defects in graphene as anything that breaks the symmetry of the ideal infinite carbon honeycomb lattice. Thus, different types of defects can be defined such as edges, grain boundaries, vacancies, implanted atoms, dopants, and defects associated to a change of carbon-hybridization, for example, from sp2into sp3. The amount and nature of defects strongly depend on the production method and may change from sample to sample. Both the amount and the nature of defects can have a strong influence on the properties of graphene samples [6]. For example, resonant scatterers, atomic-sized defects that introduce midgap states close to the Dirac point, have been identified as the major limitation of electron mobility for graphene deposited on substrates [7].On the other side, the control of the location of defects and their arrangement into ordered and extended structures allows making preparation of new graphene-based materials with novel properties. Extended line defects could be used to guide charge as well as spin, atoms, and molecules [8].Defects also have strong influence on the chemical reactivity [9], thus making defective graphene a prospective catalyst.Therefore, it is of fundamental importance to be able to probe defects in graphene and to establish accurately the precise nature of disorder.

Raman spectroscopy is a well-established technique for investigating the structure of graphene-based materials [10]. Lowest-order Raman processes correspond to the scattering with a zero-momentum phonon (q=0). The Raman G line in graphene and graphite (1582 cm-1) is a lowest-order process associated with the E2g phonon at Gamma 

Raman spectra (left) for samples of defective graphene (as modelled on the right).

 

Graphene and graphite present other lines, due to higher-order processes, which are usually interpreted in terms of the so-called double-resonance (DR) mechanism. The DR mechanism is used to interpret two distinct kinds of phenomena. The first is the excitation of a phonon with momentum q0 due to the presence of defects in the sample. This process, called defect induced, is not allowed in a purely crystalline sample (without defects) because of momentum conservation [11]. 

In graphene and graphite, it gives rise to the well studied D line at 1350 cm-1and also to less intense lines such as the D’ (1600 cm-1) and the D’’(1100 cm-1 – not shown). The second process corresponds to the excitation of two phonons with opposite momenta q and −q. This process, called two phonon, can be observed in purely crystalline samples since the momentum is conserved and gives rise to the very intense 2D line at 2700 cm-1(which is an overtone of the D line) and, for instance, to the D + D’’ and 2D’lines at 2450 cm-1and 3200 cm-1. The lines related to DR defect-induced and two-phonon processes have a remarkable property: they are dispersive, i.e., their positions change with excitation energy.

The Raman spectroscopy technique is thus not only able to identify graphene from graphite and few-layers graphene (modification of the 2D line in shape, width and postion), but is also extremely sensitive to defects, excess charge (doping), strain and to the atomic arrangement of the edges [12].Graphene is the ideal material to study defects because its two-dimensional nature makes it easy to add, remove or move carbon atoms, that is, to introduce only a specific type of defect, in contrast to graphite or carbon nanotubes. In graphene, the D and D' defect-peaks are associated to zone border phonons and are activated by the elastic scattering that breaks the translational symmetry of the perfect graphene lattice. The intensity of these peaks in the Raman spectra is correlated with the amount of defects present in the sample. However, the intensity of the D peak and the exact amount and type of defects remains unknown [13]. Graphene is thus the perfect target to investigate the sensitivity of the Raman spectrum on the nature of defects in order to finally build up a complete theory linking the Raman peak intensities to the number and type of defects which is the goal of the present scientific proposal.

More specifically, the role of the FunMat PhD student will be to investigate resonnant Raman spectroscopy in defective graphene (including « realistic » structural defects) using various tight-binding models enriched by first-principles calculations or even fully ab initio. Up to now, most theoretical studies on graphene have been performed using tight-binding (TB) approaches based on very simple parametrization, and full calculation of Raman matrix elements to obtain frequencies, intensities and linewidths of Raman bands has not been performed [14]. The developpement of a fully ab initio theoretical tool to compute Raman spectra is therefore higly desirable and particularly relevant for realistic graphene systems where a simple TB parametrization of the electronic structure is not accurate enough and the electron-phonon interaction is currently not available. The UCL team has a clear scientific expertise in this field since the study of defects in graphene, and most specifically, their specific effects on the transport properties, has been a major research direction during the last few years [15-27]. The PhD student will mainly rely on the ABINIT software application for the first-principles simulations envisioned in the present project. ABINIT is a free software (GNU General Public Licence), that can be downloaded straightforwardly from the Web (www.abinit.org) and whose development is coordinated in our group at UCL.

The incorporation of these models of realistic defects in graphene and the prediction of their corresponding Raman signatures will be performed in close collaboration with Prof. Francesco Mauri (University Pierre et Marie Curie) who has recently proposed a new approach to calculate these Raman spectra using conventional ab initio techniques [14]. Indeed, frequencies, intensities, and linewidths of all DR Raman bands may be determined by the calculation of the Raman cross section that can be estimated either fully ab initio or using TB models enriched by first-principles simulations (when the corresponding defective graphene system contains too many atoms to allow a fully ab initio treatment). Within such a new framework, the many different approximations frequently used in the literature (e.g. constant electron-phonon matrix elements, resonant phonons are assumed to be on some high-symmetry line, in some cases the electronic dispersion is conic, the electronic lifetime is a parameter, etc.) will be avoided. Consequently, the role of the FunMat PhD student will be to predict theoretically the shape, the intensity and the position of defect-activated (D, D’, D”) and 2-phonon (D+D”, 2D, 2D’) resonant Raman peaks for these specific defective graphene models. In addition, the detailed description of the Raman process will allow the identification of the most relevant phonons, scattering events, and defect types involved in each Raman peak.

In summary, the goal of the present research PhD project consists in identifying theoretically a specific Raman signature for various structural defects (isolated point defects or line of defects – edges or grain boundaries) embedded in graphene in order to predict their presence (and possibly their quantitative amount) in real samples. During the PhD thesis, the FunMat student will have the opportunity to compare his/her first-principles calculations of Raman spectra to resonant Raman measurements performed at MIT (collaboration with Prof. M.S. Dresselhaus under the MIT-UCL Seed Fund framework) in order to suggest the presence of dominant « realistic » defects which act as scattering centers in their corresponding graphene samples.

References

[1] K.S. Novoselov, Rev. Mod. Phys. 83, 837 (2011).

[2] A.K. Geim, Rev. Mod. Phys. 83, 851 (2011).

[3] S.V. Morozov, et al. Phys. Rev. Lett. 100, 016602 (2008).

[4] K.I. Bolotin, et al. Phys. Rev. Lett. 101, 096802 (2008).

[5] M.H. Gaas, et al. Nat. Nanotechnol. 3, 676 (2008).

[6] F. Banhart, et al. ACS Nano 5, 26 (2011).

[7] J.-H. Chen, et al. Phys. Rev. Lett. 102, 236805 (2009).

[8] J. Lahiri, et al. Nat. Nanotechnol. 5, 326 (2010).

[9] D. Boukhvalov, et al. Nano Lett. 8, 4373 (2008).

[10] A.C. Ferrari, et al. Phys. Rev. Lett. 97, 187401 (2006).

[11] M.S. Dresselhaus, et al. Nano Lett. 10, 751 (2010).

[12] A.C. Ferrari, et al. Nat. Nanotechnol. 8, 235 (2013).

[13] A. Eckmann, et al. Nano Lett. 12, 3925 (2012).

[14] P. Venezuela, M. Lazzeri, and F. Mauri, Phys. Rev. B 84, 035433 (2011).

[15] S.M.-M. Dubois, A. Lopez-Bezanilla, A. Cresti, F. Triozon, J.-C. Charlier, and S. Roche, ACS Nano 4, 1971 (2010).

[16] N. Leconte, J. Moser, P. Ordejon, H. Tao, A. Lherbier, A. Bachtold, F. Alsina, C.M. Sotomayor Torres, J.-C. Charlier,

 and S. Roche, ACS Nano 4, 4033 (2010).

[17] A. Lherbier, S.M.M. Dubois, X. Declerck, S. Roche, Y.-M. Niquet, and J.-C. Charlier, Phys. Rev. Lett. 106, 046803 (2011).

[18] N. Leconte, D. Soriano, S. Roche, J.­C. Charlier, and J.-J. Palacios, ACS Nano 5, 3987 (2011).

[19] D. Soriano, N. Leconte, P. Ordejon, J.­C. Charlier, J.-J. Palacios, and S. Roche, Phys. Rev. Lett. 107, 016602 (2011).

[20] A.R. Botello-Méndez, X. Declerck, M. Terrones, H. Terrones, and J.-C. Charlier, Nanoscale 3, 2868 (2011).

[21] A.R. Botello-Méndez, E. Cruz-Silva, J.M. Romo-Herrera, F. López­Urías, M. Terrones, B.G. Sumpter, H. Terrones,

J.­C. Charlier, and V. Meunier, Nano Lett. 84, 235420 (2011).

[22] N. Leconte, A. Lherbier, F. Varchon, P. Ordejon, S. Roche, and J.­C. Charlier, Phys. Rev. B 107, 016602 (2011).

[23] A. Lherbier, S.M.M. Dubois, X. Declerck, Y.-M. Niquet, S. Roche, and J.-C. Charlier, Phys. Rev. B 86, 075402 (2012).

[24] R. Lv, Q. Li, A.R. Botello-Mendez, T. Hayashi, B. Wang, A. Berkdemir, Q. Hao, A.-L. Elias, R. Cruz-Silva, H.R. Gutiérrez, Y.A. Kim, H. Muramatsu, J. Zhu, M. Endo, H. Terrones, J.-C. Charlier, M. Pan, and M. Terrones,

Nature - Scientific Reports 2, 586 (2012).

[25] A. Lherbier, S. Roche, O.A. Restrepo, Y.-M. Niquet , A. Delcorte, and J.-C. Charlier, Nano Research 6, 326 (2013).

[26] A. Lherbier, A.R. Botello-Méndez, and J.-C. Charlier, Nano Lett. 13, 1446 (2013).

[27] A. Berkdemir, H.R. Gutiérrez, A.R. Botello-Méndez, N. Perea-Lopez, A.L. Elias, C.-I. Chia, B. Wang, V.H. Crespi,

 F. Lopez-Urias, J.-C. Charlier, H. Terrones and M. Terrones, Nature - Scientific Reports 3, 1755 (2013).

Project Partners

The Louvain node has a recognized expertise in modeling quantum transport in graphene and graphene nanoribbons using first-principles techniques [1-5]. The Paris node has a strong experience in ab initio simulation of Raman spectroscopy data in graphitic materials [6-8].The industrial partner, Imec performs world-leading research in nano-electronics and leverages its scientific knowledge with the innovative power of its global partnerships in ICT, healthcare and energy. It delivers industry-relevant technology solutions in a unique high-tech environment. The institute is headquartered in Leuven, Belgium, and has offices in Belgium, the Netherlands, Taiwan, US, China and Japan. Its staff of more than 1,750 people includes over 550 industrial residents and guest researchers. In 2010, the revenue of the research center (P&L) was 275 millions €.

Successful applicant will have the opportunity to work in the laboratories of Professor Francesco Mauri (University of Pierre et Marie Curie, Paris, France) and Professor Jean-Christophe Charlier (University of Louvain, Belgium). In addition, she/he will also work in close collaboration with the IMEC research center (Leuven, Belgium - Dr. Geoffrey Pourtois). Indeed, this project is of considerable importance for the activities performed in the research center imec, which are driven by the growing industrial interest to graphene. Although this is a very fundamental problem, the identification of the major source of the defects present in graphene and its coupling to the Raman signature has some practical consequences into the characterization of the quality of the graphene layers grown in imec. Imec will support this initiative by organizing regular meeting between the Ph.D. candidate and the nanotechnology team of imec so that all partners could mutually benefit from the generated knowledge.

Related Publications

[1]          Electronic properties and quantum transport in graphene-based nanostructures

              S.M.-M. Dubois, Z. Zanolli, X. Declerck, and J.-C. Charlier

              European Physical Journal B 72, 1-24 (2009)

[2]          Electron-hole transport asymmetry and conduction gaps in edge-defected graphene nanoribbons.

              S.M.-M. Dubois, A. Lopez-Bezanilla, A. Cresti, F. Triozon, J.-C. Charlier, and S. Roche

              ACS Nano 4, 1971-1976 (2010).

[3]          Damaging graphene with ozone treatment : a chemically tunable metal-insulator transition

              N. Leconte, J. Moser, P. Ordejon, H. Tao, A. Lherbier, A. Bachtold, F. Alsina,

              C.M. Sotomayor Torres, J.-C. Charlier, and S. Roche

              ACS Nano 4, 4033-4038 (2010).

 [4]          Two-dimensional Graphene with structural defects: elastic mean free path,

              minimum conductivity and Anderson transition

              A. Lherbier, S.M.-M. Dubois, X. Declerck, S. Roche, Y.M. Niquet, and J.-C. Charlier

              Physical Review Letters 106, 046803 (2011).

 [5]          Quantum transport in graphene nanonetworks

              A.R. Botello-Méndez, E. Cruz-Silva, J.M. Romo-Herrera, F. López­Urías,

              M. Terrones, B.G. Sumpter, H. Terrones, J.­C. Charlier, and V. Meunier

              Nano Letters 11, 3058-3064 (2011).

 [6]          Raman spectrum of graphene and graphene layers

              A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi M. Lazzeri, F. Mauri,

              S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, and A.K. Geim

              Phsical Review Letters 97, 187401 (2006).

 [7]          Structure, stability and edge states, and aormaticity of graphene ribbons

              T. Wassmann, A.P. Seitsonen, A.M. Saitta, M. Lazzeri, and F. Mauri

              Phsical Review Letters 101, 096402 (2008).

 [8]          Transport properties of graphene in the high-current limit

              A. Barreiro, M. Lazzeri, J. Moser, F. Mauri, and A. Bachtold

              Phsical Review Letters 103, 076601 (2009).