Abstract
We present a simplified theoretical analysis of diffusive thermoelectric power (TEP) in a highly asymmetric bilayer graphene nanoribbon (BGN) within the framework of the tight binding formalism. BGN possesses two sets of subbands, the upper and the lower. We have shown that, for a highly asymmetric BGN (Δ = γ, where Δ and γ are the gap and interlayer coupling constant, respectively), the density of states in the lower set of subbands increases compared with the upper. The effect of ribbon width on the TEP under the aforementioned phonon scattering regime has also been quantitatively shown. The TEP exhibits an oscillatory dependence on ribbon width. Reflection coefficients of the carriers in both the upper and lower subbands have been treated in detail. Results of the ballistic formalism have been obtained as a special case in the present analyses under certain limiting conditions, forming an indirect validation of our theoretical formulations.
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References
A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009).
A. Naeemi and J.D. Meindl, IEEE Trans. Electron. Dev. 56, 1822 (2009).
E.V. Castro, K.S. Novoselov, S.V. Morozov, N.M.R. Peres, J.M.B. Lopes dos Santos, J. Nilsson, F. Guinea, A.K. Geim, and A.H. Castro, Phys. Rev. Lett. 99, 216802 (2007).
T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Science 313, 951 (2006).
E. McCann, Phys. Rev. B 74, 161403 (2006).
R. Ma, L.J. Zhu, L. Sheng, M. Liu, and D.N. Sheng, Europhys. Lett. 87, 17009 (2009).
E. McCann and V.I. Falko, Phys. Rev. Lett. 96, 086805 (2006).
E.A. Henriksen, Z. Jiang, L.-C. Tung, M.E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, and H.L. Stormer, Phys. Rev. Lett. 100, 087403 (2008).
E.H. Hwang and S. Das Sarma, Phys. Rev. B 77, 115449 (2008).
S.S. Kubakaddi, Phys. Rev. B 79, 075417 (2008).
M. Barbier, P. Vasilopoulos, F.M. Peeters, and J.M. Pereira Jr, Phys. Rev. B 79, 155402 (2009).
M. Koshino and T. Ando, Phys. Rev. B 73, 245403 (2006).
B. Sahu, H. Min, A.H. MacDonald, and S.K. Banerjee, Phys. Rev. B 78, 045404 (2008).
B.R. Nag, Electron Transport in Compound Semiconductors (Berlin: Springer, 1980).
D.K. Ferry, Semiconductor Transport (London: Taylor and Francis, 2000).
M.W. Lundstrom, Fundamentals of Carrier Transport (Cambridge: Cambridge University Press, 2000).
Y.B. Zhang, Y.W. Tan, H.L. Stormer, and P. Kim, Nature 438, 201204 (2005).
C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, and W.A. de Heer, J. Phys. Chem. B 108, 1991219916 (2004).
B.E. Feldman, J. Martin, and A. Yacoby, Nat. Phys. Lett. 5, 889 (2009).
L.A. Falkovsky, Phys. Lett. A 372, 51895192 (2008).
P.J. Price, J. Appl. Phys. 53, 6863 (1982).
R. Kimand and M. Lundstrom, IEEE Trans. Electron. Dev. 56, 132 (2009).
J.P. McKelvey, R.L. Longini, and T.P. Brody, Phys. Rev. 123, 5157 (1961).
J.S. Blakemore, Semiconductors Statistics (New York: Dover, 1987).
N.F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (New York: Dover, 1958).
A. Das, B. Chakraborty, S. Piscanec, S. Pisana, A.K. Sood, and A.C. Ferrari, Phys. Rev. B 79, 155417 (2009).
Y. Ouyang, P. Campbell, and J. Guo, Appl. Phys. Lett. 92, 063120 (2008).
S. Bhattacharya and S. Mahapatra, Phys. Lett. A 374, 2850 (2010).
N. Harada, M. Ohfuti, and Y. Awano, Appl. Phys. Exp. 1, 024002 (2008).
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Bhattacharya, S., Mallik, R.C. Diffusive Thermoelectric Power in Highly Asymmetric Bilayer Graphene Nanoribbons. J. Electron. Mater. 40, 1181–1189 (2011). https://doi.org/10.1007/s11664-011-1585-1
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DOI: https://doi.org/10.1007/s11664-011-1585-1