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1

Markowich, Peter A., Christian A. Ringhofer, and Christian Schmeiser. Semiconductor Equations. Vienna: Springer Vienna, 1990. http://dx.doi.org/10.1007/978-3-7091-6961-2.

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2

1957-, Ringhofer C. A., and Schmeiser C. 1958-, eds. Semiconductor equations. Wien: Springer-Verlag, 1990.

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3

Jüngel, Ansgar. Quasi-hydrodynamic Semiconductor Equations. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8334-4.

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4

Rate equations in semiconductor electronics. Cambridge [Cambridgeshire]: Cambridge University Press, 1985.

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5

Markowich, Peter A. The Stationary Semiconductor Device Equations. Vienna: Springer Vienna, 1986.

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6

Markowich, Peter A. The stationary semiconductor device equations. Wien: Springer-Verlag, 1986.

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7

The stationary semiconductor device equations. Wien: Springer-Verlag, 1986.

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8

Markowich, Peter A. The Stationary Semiconductor Device Equations. Vienna: Springer Vienna, 1986. http://dx.doi.org/10.1007/978-3-7091-3678-2.

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9

Hagley, William Andre. Self-consistent solution of Schrödinger's and Poisson's equations for arbitrary semiconductor heterostructures. Ottawa: National Library of Canada, 1993.

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10

Transport equations for semiconductors. Berlin: Springer, 2009.

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11

Jüngel, Ansgar. Transport Equations for Semiconductors. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89526-8.

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12

Balance equation approach to electron transport In semiconductors. Hackensack, NJ: World Scientific, 2008.

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13

Multigroup equations for the description of the particle transport in semiconductors. New Jersey: World Scientific, 2005.

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14

Galler, Martin. Multigroup equations for the description of the particle transport in semiconductors. Singapore: World Scientific, 2005.

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15

Hänsch, W. The drift diffusion equation and its applications in MOSFET modeling. Wien: Springer-Verlag, 1991.

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16

Hänsch, W. The drift diffusion equation and its applications in MOSFET modeling. Wien: Springer-Verlag, 1991.

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17

Shen, Shun-Qing. Topological Insulators: Dirac Equation in Condensed Matters. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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18

Computation of semiconductor properties using moments of the Inverse Scattering Operator of the Boltzmann Equation. Konstanz: Hartung-Gorre, 2006.

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19

Markowich, Peter A., Christian A. Ringhofer, and Christian Schmeiser. Semiconductor Equations. Springer, 2002.

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20

Carroll, J. E. Rate Equations in Semiconductor Electronics. Cambridge University Press, 1990.

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21

Jüngel, Ansgar. Quasi-hydrodynamic Semiconductor Equations. Springer, 2012.

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22

Markowich, P. A. The Stationary Semiconductor Device Equations (Computational Microelectronics). Springer, 2004.

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23

Quasi-hydrodynamic Semiconductor Equations (Progress in Nonlinear Differential Equations and Their Applications). Birkhäuser Basel, 2001.

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24

Quasi-Hydrodynamic Semiconductor Equations (Progress in Nonlinear Differential Equations and Their Applications, V. 41). Birkhauser, 2000.

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25

Hierarchy Of Semiconductor Equations Relaxation Limits With Initial Layers For Large Innitial Data. Mathematical Society of Japan, 2012.

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26

Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data. Tokyo, Japan: The Mathematical Society of Japan, 2011. http://dx.doi.org/10.2969/msjmemoirs/026010000.

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27

Wolf, E. L. Atoms, Molecules, Crystals and Semiconductor Devices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198769804.003.0005.

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Properties of matter and of electronic devices are described, starting with Bohr’s model of the hydrogen atom. Motion of electrons in a periodic potential is shown to allow energy ranges with free motion separated by energy ranges where no propagating states are possible. Metals and semiconductors are described via Schrodinger’s equation in terms of their structure and their electrical properties. Energy gaps and effective masses are described. The semiconductor pn junction is described as a circuit element and as a photovoltaic device. We now extend Schrodinger’s method to more familiar matter, in the form of atoms, molecules and semiconductors. The solar cell, that produces electrical energy from Sunlight, in fact requires a sophisticated understanding of the semiconductor PN junction.
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28

United States. National Aeronautics and Space Administration., ed. A theoretical stody of photovoltaic converters: Progress report for the period May 16, 1986 to January 1, 1987. Norfolk, Va: Dept. of Mathematical Sciences, College of Sciences, Old Dominion University, 1987.

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29

Kavokin, Alexey V., Jeremy J. Baumberg, Guillaume Malpuech, and Fabrice P. Laussy. Semiclassical description of light–matter coupling. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198782995.003.0004.

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In this chapter we consider light coupling to elementary semiconductor crystal excitations—excitons—and discuss the optical properties of mixed light–matter quasiparticles named exciton-polaritons, which play a decisive role in optical spectra of microcavities. Our considerations are based on the classical Maxwell equations coupled to the material relation accounting for the quantum properties of excitons.
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30

Jüngel, Ansgar. Transport Equations for Semiconductors. Springer, 2010.

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31

Cantor, Brian. The Equations of Materials. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851875.001.0001.

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This book describes some of the important equations of materials and the scientists who derived them. It is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. It is meant to be readable and enjoyable, a primer rather than a textbook, covering only a limited number of topics and not trying to be comprehensive. It is pitched at the level of a final year school student or a first year undergraduate who has been studying the physical sciences and is thinking of specialising into materials science and/or materials engineering, but it should also appeal to many other scientists at other stages of their career. It requires a working knowledge of school maths, mainly algebra and simple calculus, but nothing more complex. It is dedicated to a number of propositions, as follows: 1. The most important equations are often simple and easily explained; 2. The most important equations are often experimental, confirmed time and again; 3. The most important equations have been derived by remarkable scientists who lived interesting lives. Each chapter covers a single equation and materials subject. Each chapter is structured in three sections: first, a description of the equation itself; second, a short biography of the scientist after whom it is named; and third, a discussion of some of the ramifications and applications of the equation. The biographical sections intertwine the personal and professional life of the scientist with contemporary political and scientific developments. The topics included are: Bravais lattices and crystals; Bragg’s law and diffraction; the Gibbs phase rule and phases; Boltzmann’s equation and thermodynamics; the Arrhenius equation and reactions; the Gibbs-Thomson equation and surfaces; Fick’s laws and diffusion; the Scheil equation and solidification; the Avrami equation and phase transformations; Hooke’s law and elasticity; the Burgers vector and plasticity; Griffith’s equation and fracture; and the Fermi level and electrical properties.
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32

Morawetz, Klaus. Deep Impurities with Collision Delay. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0017.

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The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.
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33

Solymar, L., D. Walsh, and R. R. A. Syms. The band theory of solids. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0007.

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The solution of Schrodinger’s equation is discussed for a model in which atoms are represented by potential wells, from which the band structure follows. Three further models are discussed, the Ziman model (which is based on the effect of Bragg reflection upon the wave functions), and the Feynman model (based on coupled equations), and the tight binding model (based on a more realistic solution of the Schrödinger equation). The concept of effective mass is introduced, followed by the effective number of electrons. The difference between metals and insulators based on their band structure is discussed. The concept of holes is introduced. The band structure of divalent metals is explained. For finite temperatures the Fermi–Dirac function is combined with band theory whence the distinction between insulators and semiconductors is derived.
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34

Ando, K., and E. Saitoh. Incoherent spin current. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0002.

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This chapter introduces the concept of incoherent spin current. A diffusive spin current can be driven by spatial inhomogeneous spin density. Such spin flow is formulated using the spin diffusion equation with spin-dependent electrochemical potential. The chapter also proposes a solution to the problem known as the conductivity mismatch problem of spin injection into a semiconductor. A way to overcome the problem is by using a ferromagnetic semiconductor as a spin source; another is to insert a spin-dependent interface resistance at a metal–semiconductor interface.
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35

Solymar, L., D. Walsh, and R. R. A. Syms. Principles of semiconductor devices. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0009.

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p–n junctions are examined initially and the potential distribution in the junction region is derived based on Poisson’s equation. Next the operation of the transistor is discussed, both in terms of the physics and of equivalent circuits. Potential distributions in metal–semiconductor junctions are derived and the concept of surface states is introduced. The physics of tunnel junctions is discussed in terms of their band structure. The properties of varactor diodes are described and the possibility of parametric amplification is touched upon. Further devices discussed are field effect transistors, charge-coupled devices, controlled rectifiers, and the Gunn effect. The fabrication of microelectronic circuits is discussed, followed by the more recent but related field of micro-electro-mechanical systems. The discipline of nanoelectronics is introduced including the role of carbon nanotubes. Finally, the effect of the development of semiconductor technology upon society is discussed.
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36

Succi, Sauro. Boltzmann’s Kinetic Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0002.

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Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.
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37

Guangjun, Mao, ed. Relativistic microscopic quantum transport equation. Hauppauge, N.Y: Nova Science Publishers, 2005.

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38

Shen, Shun-Qing. Topological Insulators: Dirac Equation in Condensed Matters. Springer, 2015.

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39

Shen, Shun-Qing. Topological Insulators: Dirac Equation in Condensed Matter. Springer, 2017.

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40

Shen, Shun-Qing. Topological Insulators: Dirac Equation in Condensed Matter. Springer, 2018.

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41

(Editor), Naoufel Ben Abdallah, Anton Arnold (Editor), Pierre Degond (Editor), Irene M. Gamba (Editor), Robert T. Glassey (Editor), C. David Levermore (Editor), and Christian Ringhofer (Editor), eds. Dispersive Transport Equations and Multiscale Models (The IMA Volumes in Mathematics and its Applications). Springer, 2003.

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42

A, Goldman J., Brennan K. F, and United States. National Aeronautics and Space Administration., eds. Theoretical and material studies of thin-film electroluminescent devices: Sixth six-monthly report for the period 1 November 1987 - 30 April 1988. Atlanta, GA: Georgia Institute of Technology ; [Washington, DC, 1988.

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43

Theoretical and material studies of thin-film electroluminescent devices: Final report. [Washington, DC: National Aeronautics and Space Administration, 1990.

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44

F, Brennan K., and United States. National Aeronautics and Space Administration., eds. Theoretical and material studies of thin-film electroluminescent devices: Second six monthly report for the period 1 October 1985 - 31 March 1986. [Washington, DC: National Aeronautics and Space Administration, 1986.

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