Electronic structure calculations for a carbon nanotube capacitor with a dielectric medium

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 23, 2009, Pages

  Uchida, Kazuyuki ^a,b   Oshiyama, Atsushi ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68949112248     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.235444     Document Type: Article

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23. When the finite input charge ±Q is accommodated in the electrode CNTs, we definitely obtain the Fermi levels F (8,0) and F (26,0) as the outputs. We then calculate the bias voltage as μ= F (8,0) - F (26,0). When Q=0 and μ is in the range of 0≤μ≤ Eg, with F (8,0) and F (26,0) located somewhere in the band gap of the TWCNT. In this case, exact positions of F (8,0) and F (26,0) are not well defined. We thus define that F (8,0) = F (26,0) is located at the center of the energy gap when μ=0 and F (8,0) [F (26,0)] moves to the bottom (top) of the conduction (valence) band when μ increases to Eg. The results presented in this paper are unaffected by the way of defining the Fermi levels in the case of Q=0. We restrict ourselves to the case of μ0 in this paper.
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28. The slight difference between the potential shift Vsh (=0.084eV) and the increase in the band gap Eg′ - Eg (=0.08eV) is ascribed to small modifications of the band structures in each CNT.
29. In Fig. 6, the energy bands of (a) the TWCNT and (b) the constituent CNTs are first aligned with the common vacuum level. Then, the energy bands of the (8,0) and (17,0) CNTs are shifted upward by 0.084 and 0.031 eV, respectively.
30. As we use the ultrasoft pseudopotential method in the present paper, Eq. 1 is slightly modified according to the treatments shown in Ref. to compensate for the deficit charge.