Simulation of Graphene Piezoresistivity Based on Density Functional Calculations


The piezoresistive effect in graphene ribbon has been simulated based on the first-principles electronic-state calculation for the development of novel piezoresistive materials with special performances such as high flexibility and low fabrication cost. We modified theoretical approach for piezoresistivity simulation from our original method for semiconductor systems to improved procedure applicable to conductor systems. The variations of carrier conductivity due to strain along with the graphene ribbon models (armchair model and zigzag model) have been calculated using band carrier densities and their corresponding effective masses derived from the one-dimensional electronic band diagram. We found that the armchair-type graphene nano-ribbon models have low conductivity with heavy effective mass. This is a totally different conductivity from two-dimensional graphene sheet. The variation of band energy diagrams of the zigzag-type graphene nano-ribbon models due to strain is much more sensitive than that of the armchair models. As a result, the longitudinal and transverse gauge factors are high in our calculation, and in particular, the zigzag-type graphene ribbon has an enormous potential material with high piezoresistivity. So, it will be one of the most important candidates that can be used as a high-performance piezoresistive material for fabricating a new high sensitive strain gauge sensor.

Share and Cite:

M. Gamil, K. Nakamura, A. Fath El-Bab, O. Tabata and A. El-Moneim, "Simulation of Graphene Piezoresistivity Based on Density Functional Calculations," Modeling and Numerical Simulation of Material Science, Vol. 3 No. 4, 2013, pp. 117-123. doi: 10.4236/mnsms.2013.34016.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva and A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science, Vol. 306, No. 5696, 2004, pp. 666-669.
[2] W. Thomson, “On the Electro-Dynamic Qualities of Metals: Effects of Magnetization on the Electric Conductivity of Nickel and of Iron,” Proceedings of the Royal Society of London, Vol. 8, 1856, pp. 546-550.
[3] Y. Lee, S. Bae, H. Jang, S. Jang, S.-E. Zhu, S. H. Sim, Y. I. Song, B. H. Hong and J.-H. Ahn, “Wafer-Scale Synthesis and Transfer of Graphene Films,” Nano Letters, Vol. 10, No. 2, 2010, pp. 490-493.
[4] X. Chen, X. Zheng, J.-K. Kim, X. Li and D.-W. Lee, “Investigation of Graphene piezoresistors for Use as Strain Gauge Sensors,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 29, No. 6, 2011, Article ID: 06FE01.
[5] H. Hosseinzadegan, C. Todd, A. Lal, M. Pandey, M. Levendorf and J. Park, “Graphene Has Ultra-High Piezoresistive Gauge Factor,” IEEE 25th International Conference of Micro Electro Mechanical Systems (MEMS), Paris, 29 January-2 February 2012, pp. 611-614.
[6] Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng and Z. X. Shen, “Uniaxial Strain on Graphene: Raman Spectroscopy Study and Band-Gap Opening,” ACS Nano, Vol. 2, No. 11, 2008, pp. 2301-2305.
[7] A. C. Neto, F. Guinea, N. Peres, K. Novoselov and A. Geim, “The Electronic Properties of Graphene,” Reviews of Modern Physics, Vol. 81, No. 1, 2009, p. 109.
[8] K. Nakamura, Y. Isono, and T. Toriyama, “First-Principles Study on Piezoresistance Effect in Silicon Nanowires,” Japanese Journal of Applied Physics, Vol. 47, No. 6, 2008, pp. 5132-5138.
[9] K. Nakamura, Y. Isono, T. Toriyama and S. Sugiyama, “First-Principles Simulation on Orientation Dependence of Piezoresistance Properties in Silicon Nanowires,” Japanese Journal of Applied Physics, Vol. 48, No. 6, 2009, Article ID: 06FG09.
[10] K. Nakamura, Y. Isono, T. Toriyama and S. Sugiyama, “Simulation of Piezoresistivity in n-Type Single-Crystal Silicon on the Basis of the First-Principles Band Structure,” Physical Review B, Vol. 80, No. 4, 2009, Article ID: 045205.
[11] K. Nakamura, T. Toriyama and S. Sugiyama, “First-Principles Simulation on Piezoresistive Properties in Doped Silicon Nanosheets,” IEEJ Transactions on Electrical and Electronic Engineering, Vol. 5, No. 2, 2010, pp. 157-163.
[12] K. Nakamura, T. Toriyama and S. Sugiyama, “First-Principles Simulation on Thickness Dependence of Piezoresistance Effect in Silicon Nanosheets,” Japanese Journal of Applied Physics, Vol. 49, No. 6, 2010, Article ID: 06GH01.
[13] K. Nakamura, T. Toriyama and S. Sugiyama, “First-Principles Simulation on Piezoresistivity in Alpha and Beta Silicon Carbide Nanosheets,” Japanese Journal of Applied Physics, Vol. 50, No. 6, 2011, Article ID: 06GE05.
[14] M. Bockstedte, A. Kley, J. Neugebauer and M. Scheffler, “Density-Functional Theory Calculations for Poly-Atomic Systems: Electronic Structure, Static and Elastic Properties and ab Initio Molecular Dynamics,” Computer Physics Communications, Vol. 107, No. 1, 1997, pp. 187-222.
[15] P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Physical Review, Vol. 136, No. 3B, 1964, pp. B864- B871.
[16] J. P. Perdew, K. Burke and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters, Vol. 77, No. 18, 1996, pp. 3865-3868.
[17] D. Hamann, “Generalized Norm-Conserving Pseudopotentials,” Physical Review B, Vol. 40, No. 5, 1989, pp. 2980-2987.
[18] R. Heyrovska, “Atomic Structures of Graphene, Benzene and Methane with Bond Lengths as Sums of the Single, Double and Resonance Bond Radii of Carbon,” General Physics, 2008.
[19] J. P. Lu, “Elastic Properties of Carbon Nanotubes and Nanoropes,” Physical Review Letters, Vol. 79, No. 7, 1997, pp. 1297-1300.
[20] M. Treacy, T. Ebbesen and J. Gibson, “Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes,” Nature, Vol. 381, 1996, pp. 678-680.
[21] A. Krishnan, E. Dujardin, T. Ebbesen, P. Yianilos and M. Treacy, “Young’s Modulus of Single-Walled Nanotubes,” Physical Review B, Vol. 58, No. 20, 1998, pp. 14013- 14019.
[22] D. Sánchez-Portal, E. Artacho, J. M. Soler, A. Rubio and P. Ordejón, “Ab Initio Structural, Elastic, and Vibrational Properties of Carbon Nanotubes,” Physical Review B, Vol. 59, No. 19, 1999, pp. 12678-12688.
[23] K. Shintani and T. Narita, “Atomistic Study of Strain Dependence of Poisson’s Ratio of Single-Walled Carbon Nanotubes,” Surface Science, Vol. 532-535, 2003, pp. 862- 868.
[24] T. Chang and H. Gao, “Size-Dependent Elastic Properties of a Single-Walled Carbon Nanotube via a Molecular Mechanics Model,” Journal of the Mechanics and Physics of Solids, Vol. 51, No. 6, 2003, pp. 1059-1074.
[25] C. Kittel, “Introduction to Solid State Physics,” 8th Edition, Wiley, New York, 2005.
[26] J. M. Ziman, “Principles of the Theory of Solids,” 2nd Edition, Cambridge University Press, New York, 1972.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.