Bandgaps

Aspnes D E 1985 Above-bandgap optical anisotropies in cubic semiconductors a visible-near ultraviolet probe of surfaces J. Vao. Sc/. Teohnoi. B 3 1498-506... 

Figure Bl.19.5. Tunnelling/-Fcurves acquired across a defect on Si(lOO). Away from the defect a bandgap can be seen. Over the defect itself, the bandgap disappears, suggesting that it possesses metallic character.

A more effective carrier confinement is offered by a double heterostructure in which a thin layer of a low-gap material is sandwiched between larger-gap layers. The physical junction between two materials of different gaps is called a heterointerface. A schematic representation of the band diagram of such a stmcture is shown in figure C2.l6.l0. The electrons, injected under forward bias across the p-n junction into the lower-bandgap material, encounter a potential barrier AE at the p-p junction which inliibits their motion away from the junction. The holes see a potential barrier of... 

AE at the n-p heterointerface which prevents their injection into the n region. The result is that the injected minority carriers are confined to the thin narrow-bandgap region. If this region is thinner than the average diffusion... 

Gillis H P, Choutov D A and Martin K P 1996 The dry etching of Group Ill-Nitride wide bandgap semiconductors J. Mater. 48 50-5... 

Fig. 2. Schematic diagram of active layer stmctures employed in LEDs under forward bias showing the conduction band (CB) and valence band (VB). The simplest devices employ (a) a homostmcture active layer wherein the bandgap is constant throughout the device. More advanced stmctures consist of (b) single and (c) double heterostmctures. Heterostmctures faciUtate the confinement and injection of carriers in the active region where the carriers may...

As an example, PL can be used to precisely measure the alloy composition xof a number of direct-gap III-V semiconductor compounds such as Alj Gai j, Inj Gai jfAs, and GaAsjfPj j(, since the band gap is directly related to x. This is possible in extremely thin layers that would be difficult to measure by other techniques. A calibration curve of composition versus band gap is used for quantification. Cooling the sample to cryogenic temperatures can narrow the peaks and enhance the precision. A precision of 1 meV in bandgap peak position corresponds to a value of 0.001 for xin AljfGai j, which may be usefiil for comparative purposes even if it exceeds the accuracy of the x-versus-bandgap calibration. 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

The high electrical resistivity and the magnitude of the optical bandgap of Cfio can be reduced by the application of high pressure, with decreases in resistivity of about one order of magnitude observed per 10 GPa pressure [117]. However, at a pressure of 20 GPa, an irreversible phase transition to a more insulating phase has been reported [117]. 

As the nanotube diameter increases, more wave vectors become allowed for the circumferential direction, the nanotubes become more two-dimensional and the semiconducting band gap disappears, as is illustrated in Fig. 19 which shows the semiconducting band gap to be proportional to the reciprocal diameter l/dt. At a nanotube diameter of dt 3 nm (Fig. 19), the bandgap becomes comparable to thermal energies at room temperature, showing that small diameter nanotubes are needed to observe these quantum effects. Calculation of the electronic structure for two concentric nanotubes shows that pairs of concentric metal-semiconductor or semiconductor-metal nanotubes are stable [178]. 

Although it is required to refine the above condition I in actuality, this rather simple but impressive prediction seems to have much stimulated the experiments on the electrical-conductivity measurement and the related solid-state properties in spite of technological difficulties in purification of the CNT sample and in direct measurement of its electrical conductivity (see Chap. 10). For instance, for MWCNT, a direct conductivity measurement has proved the existence of metallic sample [7]. The electron spin resonance (ESR) (see Chap. 8) [8] and the C nuclear magnetic resonance (NMR) [9] measurements have also proved that MWCNT can show metallic property based on the Pauli susceptibility and Korringa-like relation, respectively. On the other hand, existence of semiconductive MWCNT sample has also been shown by the ESR measurement [ 10], For SWCNT, a combination of direct electrical conductivity and the ESR measurements has confirmed the metallic property of the sample employed therein [11]. More recently, bandgap values of several SWCNT... 

Changes in the bandgap values depending on these patterns are summarised in Table 1 [16], where it is shown that only armchair-type CNT can have zero bandgap at a certain bond-alternation pattern even if they have not isodistant bond patterns. It should be emphasised that actual bond pattern is decided only by the viewpoints of energetical stabilisation, which cannot be predicted by the Hiickel-type tight-binding calculation. 

Table 1. The bandgap values of CNTs satisfying 2a + b = 3N with various bond-alternation patterns.

Synthetic principles for bandgap control in tt-conjugated systems of poly-(thiophene) and related systems with fused thiophene rings 97CRV173. 

The electrical current of a coplanar interdigilal gold/LPPP/gold device is space charge limited due to p-type charge earner traps localized in the bandgap [28]. This can be inferred from the field dependence of the dark current at room temperature. The thermally stimulated current spectrum exhibits two peaks, corresponding to two distinct trap levels ,1 and ,", which can be calculated from the rise in current, /, below the peak temperature ... 

The photoinduced absorption and the electrical characteristics of the conjugated LPPP show that the optoelectrical properties are strongly dependent on charge carrier traps in the bandgap. From aromatic molecular crystals it is known that impurities and structural imperfections form localized states [34]. LPPP forms homogeneous and dense films with a mean interchain distance of about 20 A and ncgligi-... 

Figure 9-22. Energy diagram ol a metal/ scmiconductor/meta Schottky barrier (0... workfunction, x,. electron affinity, /,... ionization potential, . ..bandgap, W... depletion width).

---