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HR41 - Chapter 41 Conduction of Electricity in Solids In...

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1 Chapter 41 In this chapter we focus on a goal of physics that has become enormously important in the last half century. That goal is to answer the question: What are the mechanisms by which a material conducts, or does not conduct electricity? The answers are complex since they involve applying quantum mechanics not just to individual particles and atoms, but to a tremendous number of particles and atoms grouped together and interacting. Scientists and engineers have made great strides in the quantum physics of materials science, which is why we have computers, calculators, cell phones, and many other types of solid-state devices. We begin by characterizing solids that conduct electricity and those that do not. Conduction of Electricity in Solids 41-
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2 Crystalline solid: solid whose atoms are arranged in a repetitive three-dimensional structure (lattice). Basic unit (unit cell) is repeated throughout the solid. Basic Electrical Properties Electrical Properties of Solids 41- Fig. 41-1 copper silicon or carbon Face-centered cubic Diamond lattice 1. Resisivity ρ : relates how much current an applied electric field produces in the solid (see Section 26-4). Units ohm meter ( m). 1. Temperature coefficient of resistivity α : defined as α =(1/ ρ )( d ρ / dT ). Characterizes how resistivity changes with temperature. Units inverse Kelvin ( K -1 ). 1. Number density of charge carriers n : the number of charge carriers per unit volume. Can be determined from Hall measurements (Section 28-4). Units inverse cubic meter (m -3 )
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3 Electrical Properties of Solids, cont’d 41- Some Electrical Properties of Two Materials Material Properties Unit Copper Silicon Type of conductor Metal Semiconductor Resistivity, ρ m 2x10 -8 3x10 3 Temperature Coeff. of resistivity, α K -1 +4x10 -3 -70x10 -3 Number density of charge carriers, n m -3 9x10 28 1x10 16 Table 41-1
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4 Electronic configuration of copper atom: Energy Levels in a Crystalline Solid 41- Fig. 41-2 1 s 2 2 s 2 2p 6 3 s 2 3 p 6 3 d 10 4 s 1 Fig. 41-3 x N Pauli exclusion→ localized energy states split to accommodate all electrons, e.g., not allowed to have 4 electrons in 1 s state. New states are extended throughout material.
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5 To create a current that moves charge in a given direction, one must be able to excite electrons to higher energy states. If there are no unoccupied higher energy states close to the topmost electrons, no current can flow. In metals, electrons in the highest occupied band can readily jump to higher unoccupied levels. These conduction electrons can move freely throughout the sample, like molecules of gas in a closed container (see free electron model-Section 26-6).
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