Extended states conduction

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... 

Electronic conduction in crystalline semiconductors (except for the case of extremely high doping levels or very low temperatures) invariably involves motion in extended states. However, because of the high densities of defect centers, the possibility exists for transport by direct tunneling between localized states. 

Fig. 36 Schematic drawing of a DNA molecular wire in contact with a dissipative environment. The central chain (extended states) with N sites is connected to semiinfinite left (L) and right (R) electronic reservoirs. The bath only interacts with the side chain sites (c), which we call for simplicity backbone sites, but which collectively stay for non-conducting, localized electronic states. The Hamiltonian associated with this model is given by Eqs. (443), (444), and (445) in the main text.

So far no amorphous semiconductors have been made with a Fermi energy in the extended states beyond the mobility edge. The Fermi energy of doped a-Si H moves into the band tails, but is never closer than about 0.1 eV from the mobility edge. There is no metallic conduction, but instead there are several other possible conduction mechanisms, which are illustrated in Fig. 1.11. 

The central problem in studying the conductivity is to find the energy and temperature dependence of ct( ) and the related p( ) and to understand the physical processes involved in the transport. The motion of the carriers at non-zero temperatures may be either in extended states or by hopping in localized states and the magnitude of the conductivity is determined by the elastic and inelastic scattering mechanisms. In addition, when there is any local inhomogeneity of the... 

The idea of a lower limit on the scattering length leads to the concept of a minimum metallic conductivity o , = o( c)- Conduction below this value was thought to be impossible in extended states. In this model the conductivity drops discontinuously at T = 0 K because there is no conduction in the localized states below <, We shall see shortly that more recent ideas have changed this conclusion. 

Examples of the low temperature luminescence spectra are shown in Fig. 8.12. The luminescence intensity is highest in samples with the lowest defect density and so we concentrate on this material. The role of the defects is discussed in Section 8.4. The luminescence spectrum is featureless and broad, with a peak at 1.3-1.4 eV and a half width of 0.25-0.3 eV. It is generally accepted that the transition is between conduction and valence band tail states, with three main reasons for the assignment. First, the energy is in the correct range for the band tails, as the spectrum lies at the foot of the Urbach tail (Fig. 8.12(6)). Second, the luminescence intensity is highest when the defect density is lowest, so that the luminescence cannot be a transition to a defect. Third, the long recombination decay time indicates that the carriers are in localized rather than extended states (see Section 8.3.3). 

There have been several studies of plasma-polymerized acrylonitrile (Hirai and Nakada, 1968 Munro and Grunwald, 1985 Bhuiyan et al., 1988 Bhuiyan and Bhoraskar, 1988 Tyczkowski and Sielski, 1990). Tyczkowski and Sielski have reported that both electrons and holes are mobile with comparable mobilities. The mobilities increase with increasing conductivity. For very high conductivities, a transition from hopping to extended-state transport was reported. 

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