Hole dispersion relation

Fig. 1.1 Parabolic electron and hole dispersion relations showing vertical electron—hole recombination and photon emission.

On the other hand, molecular crystals are characterized by the existence of strongly bound (Frenkel type) excitons, and it has been shown that the lower-energy part of the absorption spectrum (say, the first 2 eV) is completely dominated by these excitons [168], even to the extent that the absorption corresponding to electron-hole pair generation is completely hidden in the exciton spectrum [128] and is revealed only by such methods as modulated electrorefletance [169]. The only states in the exciton bands that are accessible by photon absorption are those at the center of the Brillouin zone, so the absorption is not a continuous band as for semiconductors, but a sharp line. The existence of this sharp line therefore does not mean that the exciton band is narrow (i.e., that its dispersion relation in the Brillouin zone is flat). On the contrary, since that dispersion is caused by dipolar interactions, exciton bandwidths can be several eV [168,170] the total bandwidth is four times the coupling term. This will be particularly... 

The energy bands are no longer described by the -k dispersion relations, but instead by a density-of-states distribution N E), illustrated in Fig. 1.6. Also the electron and hole effective masses must be redefined as they are usually expressed as the ciu-vature of (k). 

Shin H., Catrysse P. B., and Fan S. (2005). Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes. Plys. Rev. B 72 085436. 

In the case of solids, the band dispersion describes a complicated dependence of energy on momentum, that usually cannot be described analytically. However, in the case of a semiconductor, the dispersion relations at the top of the valence band (TVB) and at the bottom of the conduction band (BCB), can often be described approximately as parabolic. Therefore, near the band edges, the delocalized electrons or holes, follow a quadratic equation of the form... 

To calculate the dispersion relation of the hybrid excitons we approximate the WE energy by a parabola with the in-plane effective mass mw = me + rrih, being the electron (hole) mass, and neglect the FE dispersion since the typical masses are (5-100) mq ... 

Electron-hole recombination is illustrated in Fig. 1.1. Electrons in the conduction band and holes in the valence band are assumed to have the parabolic dispersion relations... 

Using the requirement that electron and hole momenta are the same, the photon energy can be written as the joint dispersion relation... 

Figure 2.8 Free charge carriers in a solid have a parabolic dispersion relation ( (k) oc k ). In a semiconductor, the energy bands for free electrons and holes are separated by an energy gap g. In a bulk semiconductor, the states are quasi-continuous, and each point in the energy bands represents an individual state. In a quantum dot (QD), the charges are confined to a small volume. This situation can be described...

The parametrization procedure that we have opted for in the most recent works is as follows (1) Compute the intermolecular dynamic correlation energy for the ground state with a second-order Mpller-Plesset (MP2) expression that only contains the intermolecular part and which uses monomer orbitals. Fit the dispersion parameters to this potential. To aid in the distribution of the parameters, a version of the exchange-hole method by Becke and Johnson is sometimes used [154,155], Becke and Johnson show that the molecular dispersion coefficient can be obtained fairly well by a relation that involves the static polarizability and the exchange-hole dipole moment ... 

Since sparger hole diameter in some sense relates to bubble diameter, this correlation suggests mixing increases with increased bubble diameter. These workers also suggest that dispersion coefficient for the coalescent bubble-slug flow conditions follows ... 

---