# Effects of substrate and graphene surface roughness on graphene sheet plasmons

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2014)

- Volume: 3, Issue: 1
- ISSN: 2299-3290

## Access Full Article

top## Abstract

top## How to cite

topKeenan Lyon, and Z.L. Miškovic. "Effects of substrate and graphene surface roughness on graphene sheet plasmons." Nanoscale Systems: Mathematical Modeling, Theory and Applications 3.1 (2014): null. <http://eudml.org/doc/269738>.

@article{KeenanLyon2014,

abstract = {We study the effects of roughness in a graphene layer that lies on a substrate with rough surface on the dynamic response of such a structure. Using an analytical expression for the dielectric function of flat graphene in the optical limit allows us to tackle the effects of roughness on the sheet plasmon in graphene. We first formulate a stochastic eigenvalue problem for the plasmon dispersion in terms of the roughness parameters that include both the auto– and the cross–correlation functions of graphene and the substrate surfaces. Using the projection operator methodwe reduce this problem to an integral equation for an effective dielectric function of graphene,which implies the existence of plasmon damping due to the roughness effects.},

author = {Keenan Lyon, Z.L. Miškovic},

journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},

keywords = {graphene; plasmon; surface roughness},

language = {eng},

number = {1},

pages = {null},

title = {Effects of substrate and graphene surface roughness on graphene sheet plasmons},

url = {http://eudml.org/doc/269738},

volume = {3},

year = {2014},

}

TY - JOUR

AU - Keenan Lyon

AU - Z.L. Miškovic

TI - Effects of substrate and graphene surface roughness on graphene sheet plasmons

JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications

PY - 2014

VL - 3

IS - 1

SP - null

AB - We study the effects of roughness in a graphene layer that lies on a substrate with rough surface on the dynamic response of such a structure. Using an analytical expression for the dielectric function of flat graphene in the optical limit allows us to tackle the effects of roughness on the sheet plasmon in graphene. We first formulate a stochastic eigenvalue problem for the plasmon dispersion in terms of the roughness parameters that include both the auto– and the cross–correlation functions of graphene and the substrate surfaces. Using the projection operator methodwe reduce this problem to an integral equation for an effective dielectric function of graphene,which implies the existence of plasmon damping due to the roughness effects.

LA - eng

KW - graphene; plasmon; surface roughness

UR - http://eudml.org/doc/269738

ER -

## References

top- [1] P. Avouris and F. Xia, Graphene applications in electronics and photonics, MRS Bulletin 37, 1225 (2012). [WoS]
- [2] A. H. Castro Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
- [3] S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, Density-dependent electrical conductivity in suspended graphene: Approaching the Dirac point in transport, Rev. Mod. Phys. 83, 407 (2011).
- [4] T. O. Wehling, M. I. Katsnelson, and A. I. Lichtenstein, Adsorbates on graphene: Impurity states and electron scattering, Chem. Phys. Lett. 476, 125 (2009).
- [5] M. Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams, Atomic structure of graphene on SiO2, Nano Lett. 7, 1643 (2007).
- [6] S. Adam, E. H. Hwang, V. M. Galitskii, and S. Das Sarma, A self-consistent theory for graphene transport, Proc. Natl. Acad. USA 104, 18392 (2007).
- [7] M. Gibertini, A. Tomadin, F. Guinea, M. I. Katsnelson, and M. Polini, Electron-hole puddles in the absence of charged impurities, Phys. Rev. B 85, 201405(R) (2012). [WoS]
- [8] H. E. Romero, N. Shen, P. Joshi, H. R. Gutierrez, S. A. Tadigadapa, J. O. Sofo, and P. C. Eklund, n-type behavior of graphene supported on Si/SiO2 substrates, ACS Nano 2, 2037 (2008). [WoS][PubMed][Crossref]
- [9] B.Wunsch, T. Stauber, F. Sols, and F. Guinea, Dynamical polarization of graphene at finite doping, New J. Phys. 8, 318 (2006).
- [10] E. H. Hwang and S. Das Sarma, Dielectric function, screening, and plasmons in two-dimensional graphene, Phys. Rev. B 75, 205418 (2007).
- [11] K. F. Allison, D. Borka, I. Radovic, Lj. Hadzievski, and Z. L. Miskovic, Dynamic polarization of graphene by moving external charges: Random phase approximation, Phys. Rev. B 80, 195405 (2009).
- [12] T. S. Rahman and A. A. Maradudin, Effect of surface roughness on the image potential, Phys. Rev. B 21, 2137 (1980).
- [13] G. A. Farias and A. A. Maradudin, Surface plasmons on a randomly rough surface, Phys. Rev. B 28, 5675 (1983).
- [14] W. G. Cullen, M. Yamamoto, K. M. Burson, J. H. Chen, C. Jang, L. Li, M. S. Fuhrer, and E. D.Williams, High-Fidelity Conformation of Graphene to SiO2 Topographic Features, Phys. Rev. Lett. 105, 215504 (2010). [WoS]
- [15] R. R. Netz, Buckling and nonlocal elasticity of charged membranes, Phys. Rev. B 64, 051401 (2001).
- [16] P.S. Swain and D. Andelman, The Influence of Substrate Structure on Membrane Adhesion, Langmuir 15, 8902 (1996).
- [17] E. A. Kim and A. H. Castro Neto, Graphene as an electronic membrane, EPL 84, 57007 (2008). [WoS]
- [18] I. Abril, R. Garcia-Molina, C. D. Denton, F. J. Pérez-Pérez, and N. R. Arista, Dielectric description of wakes and stopping powers in solids, Phys. Rev. A 58, 357 (1998).