Electronic states amorphous semiconductors

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

Fig. 2-33. Electron energy and state density in amorphous semiconductors A and C = diffuse band tail states B = gap states, cmc = mobility edge level for electrons MV = mobility edge level for holes ...

The difference between amorphous and crystalline solids shows up more clearly in phonon excitations than in electronic excitations. Contributions from the entire phonon density of states appear in the first-order Raman and infrared spectra of amorphous solids. All modes in elemental amorphous semiconductors are active in the infrared. 

Direct measurements of the change in the number of states caused by doping with oxygen have only been made by a few groups. Of particular interest are electronic states that are in the band gap, but whose concentrations are too small to be observed using conventional optical transmission measurements. Photothermal deflection spectroscopy (PDS) is capable of revealing sub-gap states and has been used extensively on amorphous inorganic semiconductors [52]. PDS has been... 

The disorder of the atomic structure is the main feature which distinguishes amorphous from crystalline materials. It is of particular significance in semiconductors, because the periodicity of the atomic structure is central to the theory of crystalline semiconductors. Bloch s theorem is a direct consequence of the periodicity and describes the electrons and holes by wavefunctions which are extended in space with quantum states defined by the momentum. The theory of lattice vibrations has a similar basis in the lattice symmetry. The absence of an ordered atomic structure in amorphous semiconductors necessitates a different theoretical approach. The description of these materials is developed instead from the chemical bonding between the atom, with emphasis on the short range bonding interactions rather than the long range order. 

The critical value of VJB for complete localization is about three. Since the band widths are of order 5 eV, a very large disorder potential is needed to localize all the electronic states. It was apparent from early studies of amorphous semiconductors that the Anderson criterion for localization is not met. Amorphous semiconductors have a smaller disorder potential because the short range order restricts the distortions of the bonds. However, even when the disorder of an amorphous semiconductor is insufficient to meet the Anderson criterion, some of the states are localized and these lie at the band edges. The center of the band comprises extended states at which there is strong scattering and... 

The electronic structure is illustrated in Fig. 1.9. The energy of the mobiUty edge within the band depends on the degree of disorder and is typically 0.1-0.5 eV from the band edge in all amorphous semiconductors. The properties of states near the mobility edge are actually more complicated than in this simple model of an abrupt mobiUty edge and are described in more detail in Chapter 7. Nevertheless, the model of Fig. 1.9 provides a good description of amorphous semiconductors. 

Crystals exhibit excitonic effects near the band edges, in which the Coulomb interaction between an electron and a valence band hole results in absorption which does not follow the one-particle joint density of states in Eq. (3.25). Excitons produce an absorption peak just below the band gap energy and modify the absorption at higher energies. There is no exciton absorption peak observable in any amorphous semiconductor, because it is broadened out by the disorder. The Coulomb interaction is present in a-Si H, but its significance in the optical absorption is unclear. 

The Coulomb interaction between the electron and the donor core is, of course, present in an amorphous semiconductor and binds an electron in much the same way, so the shallow donor state is preserved. The effective mass theory for dopants cannot be applied directly to amorphous semiconductors, because it is formulated in terms of the momentum-space wavefunctions of the crystal. It is not immediately obvious that the effective mass has any meaning in an amorphous... 

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