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1999 | Buch

Physical Models of Semiconductor Quantum Devices

verfasst von: Ying Fu, Magnus Willander

Verlag: Springer US

Buchreihe : Electronic Materials Series

insite
SUCHEN

Über dieses Buch

Solid state electronics is undergoing rapid changes driven by heteroepitaxy, lithography, and new device concepts. While ten years ago Si was the material of choice in solid state electronics, now GaAs, InGaAs ,AlAs,InP, Ge,etc. have all become quite important. The advent of semiconductor lasers and integrated optoelectronic circuits has led to a flurry of activities in compound semiconductors. Additionally, the remarkable advances in the thin film epitaxy have allowed active semiconductor devices with sub-three-dimensional properties and built-in controlled biaxial strain due to lattice mismatch. This book addresses three main areas of interest: i) electronic and optical properties oflow­ dimensional semiconductor materials; ii) principal physics of quantum electronic devices, iii) principal physics of quantum optical devices. These areas will provide readers with an intimate knowledge of the new material properties on which novel solid state electronic devices such as quantum diode, and small size transistor, high electron mobility transistor are based, leading to the very front of the development of material and device research. The link between basic physics on which the real devices are based and the output from the real devices is closely observed in the book. Chapter 1 Elemental and compound semicond uctors 1. 1 Crystalline nat ure of solids The intrinsic property of a crystal is that the environment around a given atom or group of atoms is exactly the same as the environment around another atom or similar group of atoms.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Elemental and compound semiconductors
Abstract
The intrinsic property of a crystal is that the environment around a given atom or group of atoms is exactly the same as the environment around another atom or similar group of atoms. To understand and to define the crystal structure, two important concepts are introduced, i.e., the lattice and the basis.
Ying Fu, Magnus Willander
Chapter 2. Electronic processes in semiconductors
Abstract
Density of states is the number of available electronic states per unit volume per unit energy around an energy E. It is observed quantum mechanically that each electronic state can be occupied by two electrons (spin up and down). Here we exclude the magnetic field. In a three-dimensional bulk material, the electronic state is represented by its wave vector k (Bloch theorem). Because of the lattice periodicity,
$$\psi (x,y,z) = \psi (x + {L_x},y,z)$$
we have the following expression for the wave vector k i
$${k_i} = \frac{{2{n_i}\pi }}{{{L_i}}},i = x,y,x$$
(2.1)
where n i is an integer. When L i is large, the spacing between the allowed k values is very small so that we are able to discuss the volume in the k-space that each electronic state occupies
$$\frac{{{{(2\pi )}^3}}}{{{L_x}{L_y}{L_z}}} = \frac{{{{(2\pi )}^3}}}{V}$$
(2.2)
where V=L x L y L z is the volume of the crystal. The total number of electronic states in the k-space is
$$\frac{{2Vdk}}{{{{(2\pi )}^3}}}$$
(2.3)
and the density of states per unit volume is given by
$$N(E)dE = \int_E^{E + dE} {\frac{{2dk}}{{{{(2\pi )}^3}}}} $$
(2.4)
for a three-dimensional system.
Ying Fu, Magnus Willander
Chapter 3. Optical properties of semiconductors
Abstract
In general, the Maxwell equations in differential form
$$\nabla \times H = J + \frac{{\partial D}}{{\partial t}}$$
,
$$\nabla \times E = - \frac{{\partial B}}{{\partial t}}$$
,
$$\nabla \cdot D = \rho $$
,
$$\nabla \cdot B = 0$$
(3.1)
where H is the magnetic field intensity, J the current density, D the electric flux density, E the electric field intensity, B the magnetic field intensity, ρ is the volume charge density.
Ying Fu, Magnus Willander
Chapter 4. Electronic quantum devices
Abstract
To accurately analyze a semiconductor structure which is intended as a self-contained device under various operating conditions, a mathematical model has to be given. The equations which form this mathematical model are commonly called the basic semiconductor equations.
Ying Fu, Magnus Willander
Chapter 5. Quantum optoelectronics
Abstract
A large amount of both theoretical and experimental works has been published concerning the resonant tunneling structure (RTD) leading to a broad range of electrical [1, 2] as well as optical [3, 4] applications. Photoluminescence (PL) characterization of the resonant-tunneling light-emitting diode (RTLED) consists of mainly the recombination of electrons and holes that each tunnel from the opposite contact layers into the central RTD active layer. If the two contact layers are both n +-type, the electrons are majority carriers and holes are photocreated minority carriers (if the contacts are p +-type, the roles of electrons and holes are exchanged) [5]; if one contact is n +-type and the other p +-type, both electrons and holes are majority carriers [6].
Ying Fu, Magnus Willander
Chapter 6. Numerical recipes
Abstract
The concentration of free carriers in the conduction band can be calculated by
$$\begin{gathered} n = 4\pi {\left( {\frac{{2{m^*}{k_B}T}}{{{h^2}}}} \right)^{3/2}}\int_0^\infty {\frac{{{x^{1/2}}dx}}{{\exp (x - \eta ) + 1}}} \hfill \\ = \frac{{2{N_c}}}{{\sqrt \pi }}{F_{1/2}}(\eta ) \hfill \\ \end{gathered} $$
(6.1)
where N c is the effective density of states in the conduction band, m* is the density-of-state effective mass, x = E/k B T is the carrier energy in unit of k B T, η =E f /k B T is the Fermi level in unit of k B T F 1/2 (η) is the Fermi-Dirac integral of order of 1/2.
Ying Fu, Magnus Willander
Backmatter
Metadaten
Titel
Physical Models of Semiconductor Quantum Devices
verfasst von
Ying Fu
Magnus Willander
Copyright-Jahr
1999
Verlag
Springer US
Electronic ISBN
978-1-4615-5141-6
Print ISBN
978-0-7923-8457-1
DOI
https://doi.org/10.1007/978-1-4615-5141-6