Band structure semiconduction

The existence of carbon nanotubes with diameters small compared to the de Broglie wavelength has been described by Iijima[l,2,3] and others[4,5]. The energy band structures for carbon nanotubes have been calculated by a number of authors and the results are summarized in this issue by M.S. Dresselhaus, G. Dres-selhaus, and R. Saito. In short, the tubules can be either metallic or semiconducting, depending on the tubule diameter and chirality[6,7,8]. The calculated density of states[8] shows singularities... 

In addition to the stoichiometry of the anodic oxide the knowledge about electronic and band structure properties is of importance for the understanding of electrochemical reactions and in situ optical data. As has been described above, valence band spectroscopy, preferably performed using UPS, provides information about the distribution of the density of electronic states close to the Fermi level and about the position of the valence band with respect to the Fermi level in the case of semiconductors. The UPS data for an anodic oxide film on a gold electrode in Fig. 17 clearly proves the semiconducting properties of the oxide with a band gap of roughly 1.6 eV (assuming n-type behaviour). 

CNTs can exhibit singular electronic band structures and can show metallic and semiconducting behavior. As a general rule, n.m tubes with n-m being an integer multiple of 3 are metallic, while the remaining tubes are semiconducting. 

Figure 6.40 Proposed band structure for an oxidized p-type semiconducting polymer. Reprinted, by permission, from J. M. G. Cowie, Polymers Chemistry Physics of Modern Materials, 2nd ed., p. 419. Copyright 1991 by J. M. G. Cowie.

While many of the standard electroanalytical techniques utilized with metal electrodes can be employed to characterize the semiconductor-electrolyte interface, one must be careful not to interpret the semiconductor response in terms of the standard diagnostics employed with metal electrodes. Fundamental to our understanding of the metal-electrolyte interface is the assumption that all potential applied to the back side of a metal electrode will appear at the metal electrode surface. That is, in the case of a metal electrode, a potential drop only appears on the solution side of the interface (i.e., via the electrode double layer and the bulk electrolyte resistance). This is not the case when a semiconductor is employed. If the semiconductor responds in an ideal manner, the potential applied to the back side of the electrode will be dropped across the internal electrode-electrolyte interface. This has two implications (1) the potential applied to a semiconducting electrode does not control the electrochemistry, and (2) in most cases there exists a built-in barrier to charge transfer at the semiconductor-electrolyte interface, so that, electrochemical reversible behavior can never exist. In order to understand the radically different response of a semiconductor to an applied external potential, one must explore the solid-state band structure of the semiconductor. This topic is treated at an introductory level in References 1 and 2. A more complete discussion can be found in References 3, 4, 5, and 6, along with a detailed review of the photoelectrochemical response of a wide variety of inorganic semiconducting materials. 

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. 

Although the overall semiconducting nature remains unchanged upon orientational ordering, the details of the band dispersion show an interesting change. In Fig. 4, the band structure of the orientationally ordered sc solid C60 and that... 

The LDA electronic band structure of the ACB-stacking rhombohedral polymer was reported to be semiconducting with an indirect fundamental gap. The... 

Fig. 2.8 Schematic electron energy band structures for (a) a metallic crystal and (b) a semiconducting or insulating crystal.

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