Electronic Properties of Doped Semiconductors

B. I. Shklovskii, A. L. Efros, "Electronic Properties of Doped Semiconductors"
Springer | 1984 | ISBN: 0387129952 | 388 pages | PDF | 10,1 MB

The aim of this book is to present in logical fashion the theory of electronic
states and conduction in doped semiconductors at low temperatures, that is,
in the region where the properties of the electronic states differ most from
those of Bloch waves.
Depending on the doping, the electronic states of a semiconductor at zero
temperature may be localized or delocalized. An important advance in the
theory of disordered systems was the so-called Anderson theorem, which
posits the existence of strictly localized states under certain conditions.
A discussion of this question (Chap. 2) begins the exposition of the theory
of electronic states, which differs from that for ideal crystals in that it must
account for electron-electron interaction even at the lowest electron
concentrations.
To this end, a nonlinear screening theory was developed, based on the
selfconsistent field method (Sect. 3.4). This method does not, however, work in
the vicinity of the Fermi level, where the density of states has interesting and
peculiar features (Chap. 10).
If the Fermi level is in the localized-state region, then conduction is due to
electron hopping and is exponentially dependent on temperature and the impurity
concentration. The hopping conduction phenomenon was identified
long ago, but several major advances have taken place in the last decade. A
theory was developed which describes the temperature, concentration and
magnetic field dependences quantitatively. This theory is based on a new
mathematical discipline known as "percolation theory".
Chapter 5 details the main tenets of percolation theory, replete with bibliography
on the topic.
Although the book is devoted to crystallic semiconductors, many of the
ideas and methods also apply to amorphous semiconductors, so much so that
"amorphous digressions" are an integral part of the text. Occasionally (see
Chap. 9) experimental data on amorphous semiconductors are used to support
certain concepts.
The book is not intended solely as a specialists' monograph, but also as an
extension of an ordinary course in semiconductor theory that touches on a
new range of problems. Chapter 1 and Sects. 4.1 and 11.1 serve to connect this
book with standard courses in the theory of "pure" semiconductors. The
book is aimed at a wide readership: theoretical and experimental physicists,
graduate students, and engineers acquainted with the basics of solid-state
physics.
It is useful to keep in mind that as a rule all questions are discussed twice,
first qualitatively and then quantitatively. For the reader not interested in
mathematical detail the qualitative explanation should suffice.
The authors substantially updated the book for the English edition, adding new results
in percolation theory and hopping conduction. During the five years
since the Russian edition, several significant developments had occurred
in the physics of disordered systems. One of these was the creation in 1979 of
the scaling theory of localization by Anderson with coworkers and Thouless.
This has been incorporated into Chapter 2 of the present edition.
New ideas have also emerged in the understanding of electron-electron interaction
in disordered systems. In 1975 the authors proposed the idea that a Coulomb
gap may form in the vicinity of the Fermi level, which if correct would make it
necessary to revise Mott's law for variable-range hopping conduction. In the
Russian edition, only one section was devoted to this question, but since then,
a number of authors have made both theoretical and experimental contributions
to this subject. In the present edition, a whole new chapter is devoted to this
question (Chapter 14). It describes computer modelling of the Coulomb gap,
the impurity-band structure, and hopping conduction.

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