Semiconducting graphene

Shin, K.-S., et al., High quality graphene-semiconducting oxide heterostructure for inverted organicphotovoltaics. Journal of Materials Chemistry, 2012. 22(26) p. 13032-13038. 

The ID electronic energy bands for carbon nanotubes [170, 171, 172, 173, 174] are related to bands calculated for the 2D graphene honeycomb sheet used to form the nanotube. These calculations show that about 1/3 of the nanotubes are metallic and 2/3 are semiconducting, depending on the nanotube diameter di and chiral angle 6. It can be shown that metallic conduction in a (n, m) carbon nanotube is achieved when... 

Closely related to the ID dispersion relations for the carbon nanotubes is the ID density of states shown in Fig. 20 for (a) a semiconducting (10,0) zigzag carbon nanotube, and (b) a metallic (9,0) zigzag carbon nanotube. The results show that the metallic nanotubes have a small, but non-vanishing 1D density of states, whereas for a 2D graphene sheet (dashed curve) the density of states... 

Fig. 20. Electronic 1D density of states per unit cell of a 2D graphene sheet for two (n, 0) zigzag nanotubes (a) the (10,0) nanotube which has semiconducting behavior, (b) the (9, 0) nanotube which has metallic behavior. Also shown in the figure is the density of states for the 2D graphene sheet (dotted line) [178].

Fig. 3. The 2D graphene sheet is shown along with the vector which specifies the chiral nanotube. The pairs of integers ( , ) in the figure specify chiral vectors Cy, (see Table I) for carbon nanotubes, including zigzag, armchair, and chiral tubules. Below each pair of integers (n,m) is listed the number of distinct caps that can be joined continuously to the cylindrical carbon tubule denoted by (n,wi)[6]. The circled dots denote metallic tubules and the small dots are for semiconducting tubules.

Figure 3.2 Nearest-neighbor tight-binding calculation of the density of electronic states (DOS) as a function of energy for a graphene sheet (black), a metallic (9,0) SWNT (blue), and a semiconducting (10,0) SWNT (red).

When an anode contains an appropriate amount of metals (or metal oxide), novel carbon materials such as SWNTs, metallofuJlerenes, filled nanocapsules, bam-boo -shaped tubes (23), nanochains (10), and MWNTs filled with metal carbides (24,25) are formed. Especially SWNTs are now attracting a great deal of interest from researchers in physics and materials science, because exotic electronic properties that vary between semiconducting and metallic states depending on how a graphene sheet is rolled (i.e., diameter and helical pitch of a tube) are predicted theoretically (26-28) and because unique quantum effects are revealed experimentally (29,30). 

Let us recall that nanotubes can be considered as graphene sheets rolled up in different ways. If we consider the so-called chiral vectors c = nai + na2, in which a and a2 are the basis vectors of a 2D graphite lattice, depending on the value of the integers n and m, one can define three families of tubes armchair tubes (n = m), zig-zag tubes (n or m = 0), and chiral tubes (n m 0). Band structure calculations have demonstrated that tubes are either metallic compounds, or zero-gap semiconductors, or semiconductors [6,7]. More commonly, they are divided into metallic tubes (when n-m is a multiple of 3) or semiconducting ones. 

These factors, in turn, are dependent on the diameter and helicity. It has been found that metallicity occurs whenever (2n + m) or (2 + 2m) is an integer multiple of three. Hence, the armchair nanotube is metallic. Metallicity can only be exactly reached in the armchair nanotube. The zigzag nanombes can be semimetallic or semiconducting with a narrow band gap that is approximately inversely proportional to the tube radius, typically between 0.5 -1.0 eV. As the diameter of the nanombe increases, the band gap tends to zero, as in graphene. It should be pointed out that, theoretically, if sufficiently short nanotubes electrons are predicted to be confined to a discrete set of energy levels along all three orthogonal directions. Such nanotubes could be classified as zero-dimensional quantum dots. 

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