Charge Transport in Disordered Materials
This chapter surveys general theoretical concepts developed to qualitatively understand and to quantitatively describe the electrical conduction properties of disordered organic and inorganic materials. In particular, these concepts are applied to describ
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This chapter surveys general theoretical concepts developed to qualitatively understand and to quantitatively describe the electrical conduction properties of disordered organic and inorganic materials. In particular, these concepts are applied to describe charge transport in amorphous and microcrystalline semiconductors and in conjugated and molecularly doped polymers. Electrical conduction in such systems is achieved through incoherent transitions of charge carriers between spatially localized states. Basic theoretical ideas developed to describe this type of electrical conduction are considered in detail. Particular attention is given to the way the kinetic coefficients depend on temperature, the concentration of localized states, the strength of the applied electric field, and the charge carrier localization length. Charge transport via delocalized states in disordered systems and the relationships between kinetic coefficients under the nonequilibrium conditions are also briefly reviewed.
Many characteristics of charge transport in disordered materials differ markedly from those in perfect crystalline systems. The term “disordered materials” usually refers to noncrystalline solid materials without perfect order in the spatial arrangement of atoms. One should distinguish between disordered materials with ionic conduction and those with electronic conduction. Disordered materials with ionic conduction include various glasses consisting of a “network-formers” such as SiO2 , B2 O3 and Al2 O3 , and of “network-modifiers” such as Na2 O, K2 O and Li2 O. When an external voltage is applied, ions can drift by hopping over potential barriers in the glass matrix, contributing to the electrical conduction of the material. Several fascinating effects have been observed for this kind of electrical conduction. One is the extremely nonlinear dependence of the conductivity on the concentration of ions in the material. Another beautiful phenomenon is the so-called “mixed alkali effect”: mixing two different modifiers in one glass leads to an enormous drop in the conductivity in comparison to that
9.1
General Remarks on Charge Transport in Disordered Materials ........................ 163
9.2
Charge Transport in Disordered Materials via Extended States ............................. 167
9.3
Hopping Charge Transport in Disordered Materials via Localized States ............... 9.3.1 Nearest-Neighbor Hopping......... 9.3.2 Variable-Range Hopping ............ 9.3.3 Description of Charge-Carrier Energy Relaxation and Hopping Conduction in Inorganic Noncrystalline Materials............. 9.3.4 Description of Charge Carrier Energy Relaxation and Hopping Conduction in Organic Noncrystalline Materials.............
9.4
169 170 172
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180
Concluding Remarks ............................ 184
References .................................................. 185
of a single modifier with the same total concentration of ions. A comprehensive description of these effects can be found in the review article of Bunde et al. [9.1]. Although
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