0
Research Papers: Micro/Nanoscale Heat Transfer

Simulation of Electron–Phonon Coupling and Heating Dynamics in Suspended Monolayer Graphene Including All the Phonon Branches

[+] Author and Article Information
Marco Coco

Department of Mathematics
and Computer Science,
Università degli Studi di Catania,
viale Andrea Doria 6,
Catania 95125, Italy;
Research Group GNFM at INDAM,
Piazzale A. Moro 5,
Roma 00185, Italy
e-mail: mcoco@dmi.unict.it

Vittorio Romano

Department of Mathematics
and Computer Science,
Università degli Studi di Catania,
viale Andrea Doria 6,
Catania 95125, Italy;
Research Group GNFM at INDAM,
Piazzale A. Moro 5,
Roma 00185, Italy
e-mail: romano@dmi.unict.it

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 12, 2017; final manuscript received April 17, 2018; published online May 25, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(9), 092404 (May 25, 2018) (10 pages) Paper No: HT-17-1272; doi: 10.1115/1.4040082 History: Received May 12, 2017; Revised April 17, 2018

Thermal effects in monolayer graphene due to an electron flow are investigated with a direct simulation Monte Carlo (DSMC) analysis. The crystal heating is described by simulating the phonon dynamics of the several relevant branches, acoustic, optical, K and Z phonons. The contribution of each type of phonon is highlighted. In particular, it is shown that the Z phonons, although they do not enter the scattering with electrons, play a non-negligible role in the determination of the crystal temperature. The phonon distributions are evaluated by counting the emission and absorption processes during the MC simulation. The crystal temperature raise is obtained for several applied electric fields and for several positive Fermi energies. The latter produces the effect of a kind of n-doping in the graphene layer. Critical temperatures can be reached in a few tens of picoseconds posing remarkable issues regarding the cooling system in view of a possible application of graphene in semiconductor devices. Moreover, a significant influence of the lattice temperature on the characteristic curves is observed only for long times, confirming graphene rather robust as regards the electrical performance.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Castro Neto, A. H. , Guinea, F. , Peres, N. M. R. , Novoselov, K. S. , and Geim, A. K. , 2009, “ The Electronic Properties of Graphene,” Rev. Mod. Phys., 81(1), pp. 109–162. [CrossRef]
Ferry, D. K. , and Shishir, R. S. , 2009, “ Velocity Saturation in Intrinsic Graphene,” J. Phys.: Condens. Matter, 21(34), p. 344201. [CrossRef] [PubMed]
Li, X. , Barry, E. A. , Zavada, J. M. , Buongiorno Nardelli, M. , and Kim, K. W. , 2010, “ Surface Polar Phonon Dominated Electron Transport in Graphene,” Appl. Phys. Lett., 97(23), p. 232105. [CrossRef]
Romano, V. , Majorana, A. , and Coco, M. , 2015, “ DSMC Method Consistent With the Pauli Exclusion Principle and Comparison With Deterministic Solutions for Charge Transport in Graphene,” J. Comput. Phys., 302, pp. 267–284. [CrossRef]
Camiola, V. D. , and Romano, V. , 2014, “ Hydrodynamical Model for Charge Transport in Graphene,” J. Stat. Phys., 157(6), pp. 1114–1137. [CrossRef]
Morandi, O. , and Schürrer, F. , 2011, “ Wigner Model for Quantum Transport in Graphene,” J. Phys. A: Math. Theor., 44(26), p. 265301. [CrossRef]
Barletti, L. , 2014, “ Hydrodynamic Equations for Electrons in Graphene Obtained From the Maximum Entropy Principle,” J. Math. Phys., 55(8), p. 083303. [CrossRef]
Coco, M. , Mascali, G. , and Romano, V. , 2016, “ Monte Carlo Analysis of Thermal Effects in Monolayer Graphene,” J. Comput. Theor. Transp., 45(7), pp. 540–553. [CrossRef]
Coco, M. , Majorana, A. , and Romano, V. , 2016, “ Cross Validation of Discontinuous Galerkin Method and Monte Carlo Simulations of Charge Transport in Graphene on Substrate,” Ricerche Math., 66(1), pp. 201–220. [CrossRef]
Borowik, P. , Thobel, J.-L. , and Adamowicz, L. , 2007, “ Modified Monte Carlo Method for Study of Electron Transport in Degenerate Electron Gas in the Presence of Electron-Electron Interactions, Application to Graphene,” J. Comput. Phys., 341, pp. 397–405. [CrossRef]
Morandi, O. , 2014, “ Charge Transport and Hot-Phonon Activation in Graphene,” J. Comput. Theor. Transp., 43(1–7), pp. 162–182. [CrossRef]
Lichtenberger, P. , Morandi, O. , and Schürrer, F. , 2011, “ High-Field Transport and Optical Phonon Scattering in Graphene,” Phys. Rev. B, 84(4), p. 045406. [CrossRef]
Das Sarma, S. , Adam, S. , Hwang, E. H. , and Rossi, E. , 2011, “ Electronic Transport in Two-Dimensional Graphene,” Rev. Mod. Phys., 83(2), pp. 407–407. [CrossRef]
Borysenko, K. M. , Mullen, J. T. , Barry, E. A. , Paul, S. , Semenov, Y. G. , Zavada, J. M. , Buongiorno Nardelli, M. , and Kim, K. W. , 2010, “ First-Principles Analysis of Electron-Phonon Interactions in Graphene,” Phys. Rev. B, 81(12), p. 121412(R). [CrossRef]
Mascali, G. , and Romano, V. , 2014, “ A Comprehensive Hydrodynamical Model for Charge Transport in Graphene,” International Workshop on Computational Electronics (IWCE), Paris, France, June 3–6.
Alì, G. , Mascali, G. , Romano, V. , and Torcasio, C. R. , 2012, “ A Hydrodynamic Model for Covalent Semiconductors, With Applications to GaN and SiC,” Acta Appl. Math., 122(1), pp. 335–348.
Camiola, V. D. , Mascali, G. , and Romano, V. , 2012, “ Numerical Simulation of a Double-Gate Mosfet With a Subband Model for Semiconductors Based on the Maximum Entropy Principle,” Continuum Mech. Therm., 24(4–6), p. 417. [CrossRef]
Mounet, N. , and Marzari, N. , 2005, “ First-Principles Determination of the Structural, Vibrational, and Thermodynamical Properties of Diamond, Graphite, and Derivatives,” Phys. Rev. B, 71(20), p. 205214. [CrossRef]
Nika, D. L. , and Balandin, A. A. , 2012, “ Two-Dimensional Phonon Transport in Graphene,” J. Phys.: Condens. Matter, 24(23), p. 233203. [CrossRef] [PubMed]
Pop, E. , Varshney, V. , and Roy, A. K. , 2012, “ Thermal Properties of Graphene: Fundamentals and Applications,” MRS Bull., 37(12), p. 1273. [CrossRef]
Mascali, G. , 2015, “ A Hydrodynamic Model for Silicon Semiconductors Including Crystal Heating,” Eur. J. Appl. Math., 26(4), pp. 447–496. [CrossRef]
Hao, Q. , Chen, G. , and Jend, M.-S. , 2009, “ Frequency-Dependent Monte Carlo Simulations of Phonon Transport in Two-Dimensional Porous Silicon With Aligned Pores,” J. Appl. Phys., 106(11), p. 114321. [CrossRef]
Péraud, J.-P. M. , and Hadjiconstantonou, N. G. , 2011, “ Efficient Simulation of Multidimensional Phonon Transport Using Energy-Based Variance-Reduced Monte Carlo Formulations,” Phys. Rev. B, 84(20), p. 205331. [CrossRef]
Vallabhaneni, A. K. , Singh, D. , Bao, H. , Murthy, J. , and XiuRuan, X. , 2016, “ Reliability of Raman Measurements of Thermal Conductivity of Single-Layer Graphene Due to Selective Electron-Phonon Coupling: A First-Principles Study,” Phys. Rev B, 93, p. 125432. [CrossRef]
Landon, C. D. , and Hadjiconstantonou, N. G. , 2014, “ Deviational Simulation of Phonon Transport in Graphene Ribbons With Ab Initio Scattering,” J. Appl. Phys., 116(16), p. 163502. [CrossRef]
Seo, J. H. , Jo, I. , Moore, A. L. , Lindsay, L. , Aitken, Z. H. , Pettes, M. T. , Li, X. , Yao, Z. , Huang, R. , Broido, D. , Mingo, N. , Ruoff, R. S. , and Shi, L. , 2010, “ Two-Dimensional Phonon Transport in Supported Graphene,” Science, 328(5975), pp. 213–216. [CrossRef] [PubMed]
Lugli, P. , and Ferry, D. K. , 1985, “ Degeneracy in the Ensemble Monte Carlo Method for High-Field Transport in Semiconductors,” IEEE Trans. Electron Devices, 32(11), pp. 2431–2437. [CrossRef]
Pop, E. , Sinha, S. , and Goodson, K. E. , 2006, “ Heat Generation and Transport in Nanometer-Scale Transistors,” Proc. IEEE, 94(8), pp. 1587–1601. [CrossRef]
Muscato, O. , Di Stefano, V. , and Wagner, W. , 2013, “ A Variance-Reduced Electrothermal Monte Carlo Method for Semiconductor Device Simulation,” Comput. Math. Appl., 65(3), pp. 520–527. [CrossRef]
Dorgan, V. E. , Bae, M. H. , and Pop, E. , 2010, “ Mobility and Saturation Velocity in Graphene on SiO2,” Appl. Phys. Lett., 97(8), p. 082112. [CrossRef]
Gierz, I. , Riedl, C. , Starke, U. , and Ast, C. R. , 2008, “ Atomic Hole Doping of Graphene,” Nano Lett., 8(12), pp. 4603–4607. [CrossRef] [PubMed]
Freitag, M. , Steiner, M. , Martin, Y. , Perebeinos, V. , Chen, Z. , Tsang, J. C. , and Avouris, P. , 2009, “ Energy Dissipation in Graphene Field-Effect Transistor,” Nano Lett., 9(5), pp. 1883–1888. [CrossRef] [PubMed]
Sullivan, S. , Vallabhaneni, A. , Kholmanov, I. , Ruan, X. , Murthy, J. , and Shi, L. , 2017, “ Optical Generation and Detection of Local Nonequilibrium Phonons in Suspended Graphene,” Nano Lett., 17(3), pp. 2049–2056. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 2

TO distribution after 10 ps in the case εF = 0.6 eV and E = 20 kV/cm

Grahic Jump Location
Fig. 3

Phonon branches temperatures versus time in the case εF = 0.4 eV when E = 5 kV/cm

Grahic Jump Location
Fig. 4

Phonon branches temperatures versus time in the case εF = 0.4 eV when E = 20 kV/cm

Grahic Jump Location
Fig. 5

Phonon branches temperatures versus time in the case εF = 0.6 eV when E = 5 kV/cm

Grahic Jump Location
Fig. 1

LO distribution after 10 ps in the case εF = 0.6 eV and E = 20 kV/cm

Grahic Jump Location
Fig. 6

Phonon branches temperatures versus time in the case εF = 0.6 eV when E = 20 kV/cm

Grahic Jump Location
Fig. 7

Local equilibrium temperature TLE versus time in the case εF = 0.4 eV (on the left), and in the case εF = 0.6 eV (on the right), with different values of the applied electric field

Grahic Jump Location
Fig. 8

Comparison of average velocity versus time without and with thermal effects in the case εF = 0.6 eV when E = 20 kV/cm (on the left) and E = 50 kV/cm (on the right)

Grahic Jump Location
Fig. 9

Comparison of local equilibrium temperature versus time with and without the inclusion of Z phonons for εF = 0.4 at different values of the electric field

Grahic Jump Location
Fig. 10

Comparison of local equilibrium temperature versus time with and without the inclusion of Z phonons for εF = 0.6 at different values of the electric field

Grahic Jump Location
Fig. 11

Effect of the inclusion of Z phonons on the phonon branches temperatures, for εF = 0.6 and E = 20 kV/cm

Grahic Jump Location
Fig. 12

Effect of the inclusion of Z phonons on the average velocity versus time, for εF = 0.6 at E = 5 kV/cm (on the left) and E = 20 kV/cm (on the right)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In