Dispersive electronic excitation transport

Extrinsic semiconductors ate those in which the carrier concentration, either holes or electrons, are controlled by intentionally added impurities called dopants. The dopants are termed shallow impurities because their energy levels lie within the band gap close to one or other of the bands. Because of thermal excitation, -type dopants (donors) are able to donate electrons to the conduction band and p-type dopants (acceptors) can accept electrons from the valence band, the result of which is equivalent to the introduction of holes in the valence band. Band gap widening/narrowingmay occur if the doping changes the band dispersion. At low temperamres, a special type of electrical transport known as impurity conduction proceeds. This topic is discussed in Section 7.3. 

In order to obtain the energy band dispersion from UPS experiments, we need to use the momentum conservation role as well as the energy conservation role upon photoelectron emission. A three-step model is generally adopted for the photoelectron spectroscopy process, which consists of an optical dipole excitation in the solid, followed by transport to the surface and emission to the vacuum [37, 38]. General assumptions are as follows (i) both the energy and momentum of the electrons are conserved during the optical transition, (ii) the momentum component parallel to the surface is conserved while the electron escapes through the surface, and (iii) the final continuum state in the solid is a parabolic free-electron-like band in a constant inner potential Vq,... 

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