electronic properties of graphene

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  1. 1. (..765) : . . , 2012
  2. 2. 1 , (tight binding approximation), , , (zone folding). , , Brillouin . Fermi t s . , Brillouin. , * . zigzag (=0) 23% . , 0.178 / %gdE eV d Fermi 6 0.025 10 / ( %)Fdv m s d 5%. . .
  3. 3. 2 Abstract In the present thesis, the tight binding approximation is used to investigate the electronic properties of graphene, which comprises a two dimentional (2D) form of carbon, discovered in 2004. The effect of uniaxial strain on the electronic structure of graphene has been studied along with the electronic structure of carbon nanotubes, which is closely related to that of graphene (zone folding approach). More scecifically, in the case of graphene, we have constructed the recripocal lattice and the first Brillouin zone and we obtained the energy dispersion relations for the electrons of the carbon atoms which are relevant for the electron transport and other solid state properties. We also calculated the Fermi velocity and compared the derived graphene energy dispersion for different values of the tight binding parameters. Comparing our results with recent ab initio calculations, tight binding approximation gives a satisfactory description of graphenes electronic energy dispersion near the high symmetry points and . By applying the elasticity theory for graphene, we studied the change of and * energy bands according to uniaxial strain magnitude and direction. We show that an energy gap is opened for strain about 23% along the zigzag direction (=0). Calculations also show that the energy gap increases with a rate of 0.178 / % gdE eV d and the Fermi velocity decreases with a rate of 6 0.025 10 / ( %)Fdv m s d , for strain up to 5%. In the last chapter we studied the structure and electronic properties of selected metallic and semiconducting carbon nanotubes.
  4. 4. 3 1: 1.1 ............................................................................................5 1.2 ...........................................................................................................5 1.3 ....................................................................................................................... 6 1.4 ........................................................................................7 1.5 ..............................................................................................10 1.6 ...........................................................11 1.7 ................................................................................................11 1.8 (CVD)..............................................................................12 2: 2.1 .......15 2.2 ...17 2.3 Brillouin .....17 2.4 ....19 2.5 ......21 2.6 ...24 2.7 ......29 2.8 ............................30 2.9 Fermi ...35 2.10 ....37 2.11 ab initio .....38 3: 3.1 ......40 3.2 ...41 3.3 .......44 3.4 ......45 3.5 .46 3.6 47 3.7 48
  5. 5. 4 3.8 ..49 3.9 ...........................................49 3.10 ...........................................................................................................................51 3.11 ...............................................55 3.12 ..............56 3.13 ab initio .........................................................................63 3.14 ...........................................................................................................64 4: 4.1 ......................................................................65 4.2 ................................................65 4.3 ............................................................................67 4.4 ................................................................................................67 4.5 ............................................................................................69 4.6 .............................................................70 4.7 Brillouin ................................70 4.8 ........................................73 4.9 armchair .............................................75 4.10 zigzag ..............................................80 4.11 .......................................................................................................82 .......................................................................................................84 1 .................................87 2 Fermi Dirac..................................89 3 .................................................................90 4 ....................................................................91 5 ..................................................................................................................92 6 ......................93 7 ..................94
  6. 6. 5 1: 1.1 (2D) [1]. , , . , , . , Hall [2],[3]. [4] zp (0,344nm). , [5],[6], Oscar Klein [7]. , . H . . Andre K. Geim Kostantin S. Novoselov Manchester, 2010 Nobel , [1]. 1.2 O . DNA . O , . , . , , . , (Fullerenes) [8]. 60 ( 60C ) . 20 12 . Nobel 1996. - , , 1993 [9].
  7. 7. 6 . , . , . 2004 , . Geim, K. Novoselov [1], . . 1.1. , [11]. 1960 [10] . , , , . , . Geim Novoselov. 1.3 , 0.142 nm.
  8. 8. 7 (Boron-Nitride) 2MoS (Molybdenum-disulphide) 2004 [12]. , . Fermi , 2.8. , Fermi, . , , : 2 /e h . Fermi, , ( p) ( n) . To , . ( 6 1 1 0.96 10 cm ), ( 6 1 1 0.60 10 cm ). Fermi, . , , . , Dirac . , , Dirac. 1 eV, -. , Hall . . , 2.3 % . , , ( 1/137 ). (2D) , . , . 1.4 , 1947 P. R. Wallace [13]. Wallace .
  9. 9. 8 1956 J.W. McClure Dirac G.W. Semenoff 1984 [14]. 2004, . A. Geim K. Novoselov Manchester () Chernogolovka (), . 2004 Science [1], , . ( Scotch tape). R. Ruoff [15] . H , . 1.2, , . 1.2. TEM . , . , 500nm [52]. , 1.3. . , . 9k . , , Manchester, ,
  10. 10. 9 [2],[3]. Hall . 1.3. all . Hall ( ) () [2]. , , Walter de Heer Georgia Tech. SiC (Silicon Carbide) 0 1300 C . , [10]. de Heer, 2004, Geim Novoselov, [16]. , de Heer , . , P. Kim Columbia . (AFM) . , 10 . , - , Hall. To Geim, Novoselov
  11. 11. 10 Kim. 2005, . , [18]. Hall [18]. , , [19]. Dirac, Klein [7]. . , . 2009 Young Kim [6]. 1.5 , . , . , (200.000 2 1 1 cm V s ) [21], Terahertz [22]. , , . , 70 cm, . , , ITO (Indium-Tin-Oxide) [23]. . , 2NO 3NH . , [26]. , Hall , [24]. , [24].
  12. 12. 11 1.6 , , [27]. , . , . , . 1. (Bottom-up) . 2. (Top-down) . 1 , , . (CVD) . . .. . . 1.7 , , [1],[34]. 100 m, . , : [34] [1] . [35],[36] Manchester 20 100 . ,
  13. 13. 12 (flakes). , , , . A. Geim K. Novoselov, [1],[34]. 2SiO . , . , . , . , Raman [37] . 1.4. ..Geim Manchester Scotch-tape, (SEM) [38]. 1.8 (CVD) , . , . , Li CVD cm [38].
  14. 14. 13 . , . . , . , . 3 [40],[41],[42]. , . 0.1 4 2 82 NH S O [43]. , . 1.5. . , [45]. [44],[45]. , . 1.1 .
  15. 15. 1.1. [27] 10 m [28] nm [29] m Si SiC [30] >50 m (CVD) [31] >100 m ( ) Solvothermal synthesis [32] m [33] - 4 m
  16. 16. 2: 2.1 , . . , Bravais , ( 2.1). 1a 2a 0 60 ( 0 120 ).

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