Transport processes in bulk solids
Thinking of semiconductors as being composed of a bulk and interface （e.g., contact and grain boundary） portion allows us to address transport systematically in these regions. We undertake the modeling of bulk-region conduction band and valence band transport in this book using the concepts of drift and diffusion. The assumptions behind, and the development of, this drift-diffusion formalism are presented in detail in Appendix D. The key transport equations that come out of the drift-diffusion approach of Appendix D are summarized here for convenience. These equations are rigorously valid for single-crystal solids. In cases of multicrystalline and microcrystalline inorganic solids, the drift-diffusion model is strictly valid within crystals so long as the scattering length is less than the characteristic dimension of the crystal. In polycrystalline materials, intragrain drift-diffusion transport may be in series with injection, recombination, or tunneling processes at grain boundaries. For nanocrystalline materials, a drift-diffusion model can suffice by using an effective mobility, which depends on grain size. The drift-diffusion approach also works well for amorphous inorganic and amorphous and crystalline organic materials. In the case of amorphous materials, there can also be transport via the gap states in parallel with conduction band and valence band transport. For organic materials, transport between molecules controlled by tunneling mechanisms can dominate in some cases. For nanoparticles, transport is expected to be interface dominated and also to depend on the matrix in which the particles are imbedded. In the latter two situations, carriers may have to percolate through a solid as they search for optimum interface tunneling paths.