Band Theory
Band theory is a concept in solid-state physics that explains the behavior of electrons in a crystalline solid. It describes the energy levels of electrons within a solid, forming bands of allowed energy levels. These bands are separated by energy gaps, and the behavior of electrons within these bands determines the electrical and thermal properties of the material.
6 Key excerpts on "Band Theory"
eBook - ePubGateway to Condensed Matter Physics and Molecular Biophysics
Concepts and Theoretical Perspectives
- Ranjan Chaudhury(Author)
- 2021(Publication Date)
- Apple Academic Press(Publisher)
...In the first chapter, a general introduction to electronic Band Theory is presented. Moreover, various experimental techniques and phenomena associated with the studies of energy bands are also briefly dealt with. In the second chapter, we cover various aspects of magnetism in solids, and we include both microscopic theories as well as the experimental techniques along with some of the effects observed. Applications to some new techniques and devices are also discussed. The third chapter is devoted to lattice dynamics and the origin of phonons. It also contains some manifestations of various types of phonons to different kinds of phenomena and effects. The fourth chapter contains a detailed analysis of the electrons in real solids. It introduces various many-body techniques and effective theories, which are semi-phenomenological in nature. Besides, a bit of surface physics is also included. Here again, some connections to exotic phenomena and new devices are brought out. The fifth chapter deals exclusively with superconductivity. It carries out a fairly detailed analysis of the microscopic and phenomenological theories of superconductivity, for both conventional materials as well as the exotic materials. Moreover, it covers special topics such as magnetic superconductors and high-temperature superconductivity. It also includes various forms of experimental techniques and their applications. The very last chapter deals with the theoretical attempts from a viewpoint of a quantum condensed matter physicist to understand certain important biophysical properties of DNA, a very crucial ingredient of all living systems. Almost all the physical properties of solids can be linked to the following three types of very fundamental and important characteristics: (a) electrical transport, (b) magnetic, and (c) electrical polarization...
eBook - ePubPrinciples of Solar Cells, LEDs and Diodes
The role of the PN junction
- Adrian Kitai(Author)
- 2011(Publication Date)
- Wiley(Publisher)
...on the electron and hole concentrations and mobilities. 7. Introduce the concepts of doped semiconductors and the resulting electrical characteristics. 8. Understand the concept of excess, non-equilibrium carriers generated by either illumination or by current flow due to an external power supply. 9. Introduce the physics of traps and carrier recombination and generation. 10. Introduce alloy semiconductors and the distinction between direct gap and indirect gap semiconductors. 1.1 Introduction A fundamental understanding of electron behaviour in crystalline solids is available using the Band Theory of solids. This theory explains a number of fundamental attributes of electrons in solids including: i. concentrations of charge carriers in semiconductors; ii. electrical conductivity in metals and semiconductors; iii. optical properties such as absorption and photoluminescence; iv. properties associated with junctions and surfaces of semiconductors and metals. The aim of this chapter is to present the theory of the band model, and then to exploit it to describe the important electronic properties of semiconductors. This is essential for a proper understanding of p-n junction devices, which constitute both the photovoltaic (PV) solar cell and the light-emitting diode (LED). 1.2 The Band Theory of Solids There are several ways of explaining the existence of energy bands in crystalline solids. The simplest picture is to consider a single atom with its set of discrete energy levels for its electrons. The electrons occupy quantum states with quantum numbers n, l, m and s denoting the energy level, orbital and spin state of the electrons. Now if a number N of identical atoms are brought together in very close proximity as in a crystal, there is some degree of spatial overlap of the outer electron orbitals. This means that there is a chance that any pair of these outer electrons from adjacent atoms could trade places...
eBook - ePubRadiation Detection
Concepts, Methods, and Devices
- Douglas McGregor, J. Kenneth Shultis(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
...The periodic arrangement of atoms causes the appearance of periodic potentials. This potential periodicity causes bands of allowed states to form, producing quasi-continua of energy states in these bands. The density of allowed energy states in these bands is defined by the density of states function. Gaps between these bands are referred to as energy gaps. The energy band that plays the part of atomic bonding is the valence band, and the energy band that plays the part in electron conduction is the conduction band. The energy gap between the valence band and the conduction band is referred to as the band gap. Energy bands have maxima and minima when defined by energy and crystal momentum in what are known E - k diagrams. Empty states in the valence band are treated as positive particles called “holes”. Because electrons need only lose energy to recombine with a hole in direct band gap semiconductors, the charge carriers have high recombination probabilities, thereby causing short charge carrier lifetimes. Electrons must change both momentum and energy to recombine with holes for semiconductors with indirect band gaps; hence, the charge carrier lifetimes are generally longer than observed for direct band-gap materials. Bands with sharp curvature d 2 E / dk 2 cause the charge carrier effective mass for electrons or holes to decrease. Small effective mass increases the charge carrier mobility. The electrical behavior of semiconductors can be controlled by introducing dopant impurities. Deep dopants can be added into material to increase resistivity and reduce leakage currents in such a way that the material performs in a similar fashion as intrinsic material. The introduction of excess impurities or defect centers causes a reduction in charge carrier lifetime. PROBLEMS 1. For the structure shown in Fig...
eBook - ePub- Wai Kai Chen(Author)
- 2004(Publication Date)
- Academic Press(Publisher)
...These bands are separated by forbidden energy gaps as shown in Figure 6.1. The position and extent of allowed and forbidden energy gaps determine the properties of solids. FIGURE 6.1 Band structures of a Dielectric, a Semiconductor, and a Metal. The shaded regions represent energy levels filled with electrons (two per state to satisfy the Pauli exclusion principle). The important property of electrons is determined by the rule that is called the Pauli exclusion principle. According to this principle, not more than two electrons with different spins can occupy each energy state. Electrons occupy the lowest energy levels first. In semiconductors and dielectrics, almost all the states in the lowest energy bands are filled by electrons, whereas the energy states in the higher energy bands are, by and large, empty. The lower energy bands with mostly filled energy states are called the valence bands. The higher energy bands with mostly empty energy states are called conduction bands. The difference between the highest valence band and the lowest conduction band is called the energy band gap or the energy gap. An electron in a valence band needs the energy equal to or higher than the energy gap to experience a transition from the valence to the conduction band. In a dielectric, the energy gap, E g, is large so that the valence bands are completely filled and conduction bands are totally devoid of electrons. Typically for a dielectric, E g is larger then 5 to 6 eV. For semiconductors, energy band gaps vary between 0.1 eV and 3.5 eV. The energy gap of silicon (Si), which is the most important semiconductor material, is approximately 1.12 eV at room temperature. The energy gap of silicon dioxide—the most widely used dielectric material in microelectronics—is 9 eV...
eBook - ePubNanotechnology
Synthesis to Applications
- Sunipa Roy, Chandan Kumar Ghosh, Chandan Kumar Sarkar(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
...The lattice point is an imaginary, mathematical concept. A group of atoms or molecules known as basis arrange themselves in a unique manner around the lattice points. A unit cell is the smallest volume of a crystal structure having the same symmetry as the whole crystal. The unit cell when repeated along all directions forms the crystal. A unit cell is known as primitive when it has only one lattice point and is known as nonprimitive when it has more than one lattice point (Figure 3.1). FIGURE 3.1 Crystal. The widely used extrinsic semiconductors in the electronic industry are formed by doping of crystal structures. We create free holes (in case of p type) and free electrons (in case of n type) by means of doping such that they can help in conduction. Silicon, germanium, and gallium are widely used in semiconductors. Thus, the crystal structure plays an important role in the creation of semiconductors, which are the basic building blocks of diodes and transistors. 3.3 Energy Bands We know that the energy of the bound electron in an atom is quantized. It occupies atomic orbitals of discrete energy levels. As the atoms combine to form molecules, the atomic orbitals overlap. According to Pauli’s exclusion principle, no two electrons can have the same quantum number in a molecule. In the case of crystal lattices, a large number of identical atoms combine to form a molecule. Here the atomic orbitals split into different energy levels. A large number of closely spaced energy levels are formed. These closely spaced energy levels are known as energy bands. The finite energy gap between two energy bands is known as band gap (Figure 3.2). FIGURE 3.2 Splitting of energy bands. Band structure can be found by solving Schrödinger’s equation, which gives Bloch waves as the solution, of the form (3.1) (3.1) ψ x = u x e i k x where k is the wave vector or constant of motion. The energy E has discontinuities with forbidden gaps for the particles...
eBook - ePubSemiconductor Basics
A Qualitative, Non-mathematical Explanation of How Semiconductors Work and How They are Used
- George Domingo(Author)
- 2020(Publication Date)
- Wiley(Publisher)
...I illustrate this in Figure 2.5. Imagine that the valence band is a parking lot full of cars (electrons), and above it is the conduction band, equivalent to an empty freeway. The cars in the parking lot cannot move because there is no space for them to go to. No cars are on the freeway, so there is no movement up there, either. If I apply a voltage to this material (right, in Figure 2.5), nothing moves. The gap between the parking lot and the freeway is too large for cars to jump, and thus no matter what voltage I apply, the electrons cannot move; there is no current flowing in this material at all. This is the case for insulators. No electrons can move under an applied voltage. Figure 2.5 In an insulator, the valence band is full of electrons, the conduction band is empty, and the separation between the two bands is very large. At this point, I would like to clarify the concept of bands, which can sometimes be confusing. The bands are not a physical location where electrons reside, just as earth's orbit is not a railroad track or a circular road on top of which the earth travels. A cannonball follows a parabolic path even though there is no “path,” pipe, road, or track that the ball rolls over. The concept of energy bands is similar. The electrons are anywhere in the material, but they have energies with values restricted to certain allowed ranges – energy ranges that we call bands. The electrons are not allowed, under any circumstances, to have energy between the highest energy of the valence band and the lowest energy of the conduction band. 2.3 The Conductor Now consider the situation where the valence band is not full of electrons (case 2), as I show in Figure 2.6, or where the bands expand so much that the conduction band encroaches into the valence band (case 5), as I show in Figure 2.7. These two cases are very similar. Even at absolute zero (as I show on the left), there is lots of space for the electrons to move...
