Quantum bandgap

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]. 

Vogel R, Hoyer P, WeUer H (1994) Quantum-sized PbS, CdS, AgiS, SbiSs, and BiiSs particles as sensitizers for various nanoporous wide-bandgap semiconductors. J Phys Chem 98 ... 

Bandgap Structure and Photoluminescence of CdSe Quantum Dots... 

Interestingly, it has been argued that nanoparticulate formation might be considered as a possibility for obtaining new silicon films [379]. The nanoparticles can be crystalline, and this fact prompted a new line of research [380-383], If the particles that are suspended in the plasma are irradiated with, e.g., an Ar laser (488 nm), photoluminescence is observed when they are crystalline [384]. The broad spectrum shifts to the red, due to quantum confinement. Quantum confinement enhances the bandgap of material when the size of the material becomes smaller than the radius of the Bohr exciton [385, 386]. The broad PL spectrum shows that a size distribution of nanocrystals exists, with sizes lower than 10 nm. 

A very crude model to calculate the increase in bandgap energy is the effective-mass particle-in-a-box approximation. Assuming parabolic bands and infinitely high barriers the lowest conduction band (CB) level of a quantum wire with a square cross-section of side length w is shifted by AEC compared to the value Ec of the bulk crystal [Lei, Ho3] ... 

The question of whether the bandgap of the quantum structures is direct or indirect has been discussed by several authors. However, it has been pointed out that the electron and hole wave functions are spread in k space, breaking the... 

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