Chap-12 - Chapter 12 Electrical Properties Charge carriers...

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Unformatted text preview: Chapter 12: Electrical Properties Charge carriers and conduction: Charge carriers include all species capable of transporting electrical charge, including electrons, ions, and electron holes. The latter are particularly important for describing the electrical behavior of semiconductors. Direct measurement of the ability of a material to conduct charge is provided by its resistance (R), which is described through Ohm’s law: IR V = Obviously, I and V are the current and voltage, respectively. You all probably understand intuitively that if the length of a wire is doubled, then its resistance is also doubled. Similarly, if the diameter of a wire is reduced while the length is held constant, the resistance will increase. In other words, the resistance is an extrinsic property of the materials, meaning that its value depends on the amount of material present. We would like to understand electrical conduction through intrinsic properties, which depend only on the nature of the material, not the amount of that material. We can define the resistivity ( ρ ) according to: l RA = ρ where A is the cross-sectional area perpendicular to current flow and l is the length. The resistivity is an intrinsic material property, and some typical values are given in table 12.1. Sometimes it is more convenient to use the conductivity ( σ ), another intrinsic material property defined as: ρ σ 1 = The conductivity is the product of several factors, the density of charge carriers (n), the amount of charge (e) each carrier possesses, and the inherent mobility ( μ ) of each carrier, assumed for now to be electrons. Thus the conductivity for most materials is: e e n μ σ | | = The carrier (electron) mobility ( μ e ) quantifies the rapidity of motion of charge carriers in a potential gradient, in analogy to the diffusivity (D), which measures the rapidity of motion of chemical species in a concentration gradient. The mathematics of transport that describes the motion of charge carriers is similar to that which describes the motion of chemical species. Energy levels and energy bands: Electron orbitals in individual atoms are associated with discrete energy levels. When atoms combine to form molecules, these electron orbitals can interact and form new “molecular” orbitals, which have different energies than the original atomic orbitals. This occurs due to the wavelike nature of electrons, which must obey the principles of quantum mechanics. Show figures 12.2 through 12.4. Now imagine extending this principle to a Na solid containing a very large number of Na atoms. In this case, the valence electron orbitals now overlap to form a very large number of closely spaced “band” electron orbitals. Since each of the 3s orbitals in individual Na atoms is only half-filled, the final 3s energy band is also only half-filled. Each of these electron orbitals is delocalized throughout the Na solid, being shared among all of the Na atoms. At low (room) temperature, electrons can easily be...
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Chap-12 - Chapter 12 Electrical Properties Charge carriers...

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