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The problem of impurity conduction at moderate compensation has been treated using the concept of multi-electron single-phonon transitions. The problem was treated in the region of density, temperature and compensation where two- (or many- ) electron transitions begin to be important. A compensation of 0.5 is used with a temperature range of 1 K to 5 K and an average majority impurity separation of 200 to 600 in germanium. The problem is treated by comparing the transition rates of one- and multielectron transitions of the localized electron system where the one-electron transition defines the critical impedance in a percolation path at low densities and high temperatures. It is found that two and three electron effects may account for the lowering of the 'activation energy' seen experimentally as the density of impurities is raised. Comparison to currently available experimental data is made.
First-generation semiconductors could not be properly termed "doped- they were simply very impure. Uncontrolled impurities hindered the discovery of physical laws, baffling researchers and evoking pessimism and derision in advocates of the burgeoning "pure" physical disciplines. The eventual banish ment of the "dirt" heralded a new era in semiconductor physics, an era that had "purity" as its motto. It was this era that yielded the successes of the 1950s and brought about a new technology of "semiconductor electronics". Experiments with pure crystals provided a powerful stimulus to the develop ment of semiconductor theory. New methods and theories were developed and tested: the effective-mass method for complex bands, the theory of impurity states, and the theory of kinetic phenomena. These developments constitute what is now known as semiconductor phys ics. In the last fifteen years, however, there has been a noticeable shift towards impure semiconductors - a shift which came about because it is precisely the impurities that are essential to a number of major semiconductor devices. Technology needs impure semiconductors, which unlike the first-generation items, are termed "doped" rather than "impure" to indicate that the impurity levels can now be controlled to a certain extent.
The hopping process, which differs substantially from conventional transport processes in crystals, is the central process in the transport phenomena discussed in this book. Throughout the book the term ``hopping'' is defined as the inelastic tunneling transfer of an electron between two localized electronic states centered at different locations. Such processes do not occur in conventional electronic transport in solids, since localized states are not compatible with the translational symmetry of crystals.The rapid growth of interest in hopping transport has followed in the footsteps of the development of physics of disordered systems during the last three decades. The intense interest in disordered solids can be attributed to the technological potential of the new noncrystalline materials, as well as to new fundamental problems discovered in solid state physics when a crystal is no longer translationally symmetric.In the last decade hopping systems such as organic polymers, biological materials, many oxide glasses, mesoscopic systems, and the new high-temperature superconducting materials in their normal state have attracted much interest. New phenomena investigated recently include interference and coherent scattering in variable range hopping conduction, mesoscopic effects, relaxation processes and thermo-electric power, and thermal conductivity caused by hopping transport. This volume presents the reader with a thorough overview of these recent developments, written by leading experts in the various fields.
Disordered materials offer new and unexpected insights into the structure of solids and the ways charge carriers move and interact with their environment. The first part of this review volume presents new results and ideas in the subject dealing with the local bonding structure in amorphous and vitreous semiconductors. These include the local bonding structure in chalcogenide glasses containing metal atoms, the interaction of local vibrational modes with their local bonding environment, and new models for the H-bonding configurations.The second part is devoted to questions of low temperature hopping transport and recombination of photocarriers in disordered semiconductors as a function of frequency and at high electric fields. The reviews by leading experts offer different insights and attempt to address problems from the various angles.
Advances in nanoscale science show that the properties of many materials are dominated by internal structures. In molecular cases, such as window glass and proteins, these internal structures obviously have a network character. However, in many partly disordered electronic materials, almost all attempts at understanding are based on traditional continuum models. This workshop focuses first on the phase diagrams and phase transitions of materials known to be composed of molecular networks. These phase properties characteristically contain remarkable features, such as intermediate phases that lead to reversibility windows in glass transitions as functions of composition. These features arise as a result of self-organization of the internal structures of the intermediate phases. In the protein case, this self-organization is the basis for protein folding. The second focus is on partly disordered electronic materials whose phase properties exhibit the same remarkable features. In fact, the phenomenon of High Temperature Superconductivity, discovered by Bednorz and Mueller in 1986, and now the subject of 75,000 research papers, also arises from such an intermediate phase. More recently discovered electronic phenomena, such as giant magnetoresistance, also are made possible only by the existence of such special phases. This book gives an overview of the methods and results obtained so far by studying the characteristics and properties of nanoscale self-organized networks. It demonstrates the universality of the network approach over a range of disciplines, from protein folding to the newest electronic materials.
Miller and Abrahams' random impedance network is generalized to include non-steady state behavior. The generalized network has the property that for dc it is equivalent to the MA network, and for high frequencies it corresponds to the theory of Pollak and Geballe. In addition to Miller and Abrahams' resistances Zij between states i and j the generalized network includes capacitances Ci connected between the i terminal of Zij and one terminal of a generator Vi. The other terminal of Vi is connected to a 'ground' common to all the generators. The capacitances are related to the equilibrium occupation probability of site i, and the generators are related in a simple way to the imposed field. The network can also be extended to include electronic correlation effects by the inclusion of feedback elements.
This review volume contains articles on the recent developments, new ideas, as well as controversial issues dealing with the general phenomena of hopping transport in disordered systems. Examples of hopping systems of current interest are polymers and biological materials, mesoscopic systems, two- and one-dimensional systems such as MOSFETs, semiconductors near the metal-nonmetal transition, and the new high temperature superconducting materials (in their normal state). The fundamental problems addressed include effects of static and dynamic interactions with phonons, Coulomb interaction, new magnetic effects due to coherent scattering, effects of high electric fields, and relaxation phenomena.