Energy Structure of Two-Dimensional Graphene-Semiconductor Quantum Dot

Jin Tong Wang, Guang-Lin Zhao, Diola Bagayoko, Dong-Sheng Guo, Jincan Chen, Zhiwei Sun

Department of Physics, Southern University and A&M College, Baton Rouge, USA.
Institute of Mechanics, Chinese Academy of Sciences, Beijing, China.
Xiamen University, Xiamen, China.

DOI: 10.4236/wjcmp.2013.33023                

Abstract

Graphene is a newly discovered material that possesses unique electronic properties. It is a two-dimensional singlelayered sheet in which the electrons are free and quasi-relativistic. These properties may open a door for many new electronic applications. In this paper we proposed a flat 2-dimensional circular graphene-semiconductor quantum dot. We have carried out theoretical studies including deriving the Dirac equation for the electrons inside the graphene-semiconductor quantum dot and solving the equation. We have established the energy structure as a function of the rotational quantum number and the size (radius) of the dot. The energy gap between the energy levels can be tuned with the radius of the quantum dot. It could be useful for quantum computation and single electron device application.

Keywords

Graphene; Quantum Dot; Dirac Equation; Semiconductor; Energy Levels

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	“Quantum Dots—Background Briefing”. http://www.nanocotechnologies.com
[2]	L. E. Brus, “Chemistry and Physics of Semiconductor Nanocrystals,” 2007. http://www.columbia.edu/cu/chemistry/fac-bios/brus/group/pdf files/semi_nano_website_2007.pdf
[3]	D. J. Norris, “Measurement and Assignment of the SizeDependent Optical Spectrum in Cadmium Selenide (CdSe) Quantum Dots,” Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 1995.
[4]	C. B. Murray, C. R. Kagan and M. G. Bawendi, “Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies,” Annual Review of Materials Research, Vol. 30, No. 1, 2000, pp. 545-610.
[5]	A. I. Ekimov and A. A. Onushchenko, “Quantum Size Effect in Three-Dimensional Microscopic Semiconductor Crystals,” Jounal of Experimental and Theoretical Physics Letters, Vol. 34, 1981, pp. 345-349.
[6]	C. X. Guo, H. B. Yang, Z. M. Sheng, Z. S. Lu, Q. L. Song and C. M. Li, “Layered Graphene/Quantum Dots for Photovoltaic Devices,” Angewandte Chemie International Edition, Vol. 49, No. 17, 2010, pp. 3014-3017.
[7]	W. X. Zhang, J. C. Cui, C. A. Tao, Y. G. Wu, Z. P. Li, L. Ma, Y. Q. Wen and G. T. Li, “A Strategy for Producing Pure Single-Layer Graphene Sheets Based on a Confined Self-Assembly Approach,” Angewandte Chemie International Edition, Vol. 48, No. 32, 2009, pp. 5864-5868. doi:10.1002/anie.200902365
[8]	D. Li, M. B. Muller, S. Gilje, R. B. Kaner and G. G. Wallace, “Processable Aqueous Dispersions of Graphene Nanosheets,” Nature Nanotechnology, Vol. 3, 2008, pp. 101-105. doi:10.1038/nnano.2007.451
[9]	X. Wang, L. J. Zhi, N. Tsao, Z. Tomovic, J. L. Li and K. Mullen, “Transparent Carbon Films as Electrodes in Organic Solar Cells,” Angewandte Chemie International Edition, Vol. 47, No. 16, 2008, pp. 2990-2992. doi:10.1002/anie.200704909
[10]	X. Wang, L. J. Zhi and K. Mullen, “Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells,” Nano Letters, Vol. 8, No. 1, 2008, pp. 323-327. doi:10.1021/nl072838r
[11]	L. P. An, T. B. Wang and N. H. Liu, “Inter-Well Coupling and Resonant Tunneling Modes of Multiple Graphene Quantum Wells,” Communications in Theoretical Physics, Vol. 56, No. 2, 2011, pp. 367-372. doi:10.1088/0253-6102/56/2/29
[12]	J. M. Pereira Jr., V. Mlinar and F. M. Peeters, “Confined States and Direction-Dependent Transmission in Graphene Quantum Wells,” 2006.
[13]	P. R. Wallace, “The Band Theory of Graphite,” Physical Review, Vol. 71, No. 9, 1947, pp. 622-634. doi:10.1103/PhysRev.71.622
[14]	M. Wilson, “Electrons in Atomically Thin Carbon Sheets Behave Like Massless Particles,” Physics Today, Vol. 59, No. 1, 2006, p. 21. doi:10.1063/1.2180163
[15]	G. W. Semenoff, “Condensed-Matter Simulation of a Three-Dimensional Anomaly,” Physical Review Letters, Vol. 53, No. 26, 1984, pp. 2449-2452. doi:10.1103/PhysRevLett.53.2449
[16]	I. A. Luk’yanchuk and Y. Kopelevich, “Phase Analysis of Quantum Oscillations in Graphite,” Physical Review Letters, Vol. 93, No. 16, 2004, Article ID: 166402. doi:10.1103/PhysRevLett.93.166402
[17]	L. A. ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov and A. K. Geim, “Chaotic Dirac Billiard in Graphene Quantum Dots,” Science, Vol. 320, No. 5874, 2008, pp. 356-358.
[18]	T. Ando, “Theory of Electronic States and Transport in Carbon Nanotubes,” Journal of Physical Society of Japan, Vol. 74, No. 3, 2005, pp. 777-817. doi:10.1143/JPSJ.74.777
[19]	P. V. Ratnikov and A. P. Silin, “Quantum Well Based on Graphene and narrow-Gap Semiconductors,” Bulletin of the Lebedev Physics Institute, Vol. 36, No. 2, 2009, pp. 34-43. doi:10.3103/S106833560902002X
[20]	K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and A. A. Firsov, “Two-Dimensional Gas of Massless Dirac Fermions in Graphene,” Nature, Vol. 438, No. 7065, 2005, pp. 197-200. doi:10.1038/nature04233
[21]	Y. Zhang, Y.-W. Tan, H. L. Stormer and P. Kim, “Experimental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene,” Nature, Vol. 438, No. 7065, 2005, pp. 201-204. doi:10.1038/nature04235
[22]	L. Brey and H. A. Fertig, “Electronic States of Graphene Nanoribbons,” Physical Review B, Vol. 73, No. 23, 2006, Article ID: 235411. doi:10.1103/PhysRevB.73.235411
[23]	L. Brey and H. A. Fertig, “Elementary Electronic Excitations in Graphene Nanoribbons,” Physical Review B, Vol. 75, No. 12, 2007, Article ID: 125434. doi:10.1103/PhysRevB.75.125434
[24]	Y.-W. Son, M.L. Cohen, S.G. Louie, “Energy Gaps in Graphene Nanoribbons,” Physical Review Letters, Vol. 97, No. 21, 2006, Article ID: 216803. doi:10.1103/PhysRevLett.97.216803
[25]	E. Mccann and V. I. Fal’ko, “Symmetry of Boundary Conditions of the Dirac Equation for Electrons in Carbon Nanotubes,” Journal of Physics: Condensed Matter, Vol. 16, No. 13, 2004, pp. 2371-2379. doi:10.1088/0953-8984/16/13/016
[26]	X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo and H. Dai, “Room-Temperature All-Semiconducting Sub-10-nm Graphene Nanoribbon Field-Effect Transistors,” Physical Review Letters, Vol. 100, No. 20, 2008, Article ID: 206803. doi:10.1103/PhysRevLett.100.206803
[27]	R. Saito, G. Dresselhaus and M. S. Dresselhaus, “Physical Properties of Carbon Nanotubes,” Imperial College Press, London, 1998. doi:10.1142/p080
[28]	J. T. Wang, D. S. Guo, G. L Zhao, J. C. Chen, Z. W. Sun and A. Ignatiev, “Graphene-Semiconductor Quantum Well with Asymmetric Energy Gaps,” World Journal of Condensed Matter Physics, Vol. 3, No. 1, 2013, pp. 67-72. doi:10.4236/wjcmp.2013.31012