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phonons. This name came about because phonons in certain fundamental quantum theory properties bear some resemblance to photons. Each phonon is a delocalized vibrational wave that spans the entire crystal lattice. The lattice waves can form more or less localized wave packets through the superposition of a range of wavelengths of lattice waves. The more or less localized phonon wave packet is completely analogous to the photon and electron wave packets mentioned just above and discussed in Chapter 6. The phonons are moving wave packets of mechanical thermal energy. The phonon wave packet can be thought of as a moving region of relatively localized jiggling of the atoms.

Electron Wave Packets and Phonon Wave Packets Scatter

An electron wave packet that is being accelerated toward the positive direction can interact with a phonon. The phonon causes the positively charged atomic nuclei to move. The negatively charged electron is influenced by the moving positive charges. The interaction of the electron and phonon is called a scattering event and is shown schematically in Figure 19.7. The electron and phonon wave packets are propagating in certain directions. The electron is being accelerated by the electric field when it “collides” with a phonon. Following the scattering event, in general, both wave packets will move in new directions. The electron will again be accelerated by the electric field toward positive. After some time, it will again encounter a phonon, and scatter. Each time the electron scatters, it gives up some of its kinetic energy to a phonon that it got from being accelerated by the electric field (voltage source).

FIGURE 19.7. Cartoon of an electron-phonon scattering event. The interaction of the electron and phonon causes the directions of the wave packet motions to change.

The scattering events do two things. First, they prevent the electrons from moving directly to the positive battery connection. Second, the scattering events add kinetic energy to the phonons. The electron loses energy, and the phonon gains it. The electron-phonon scattering reduces the electrical conductivity of metals because the electrons keep getting bumped, which causes them to move in different directions as they are trying to move to the electrically positive end of the wire. This is called electrical resistance. At very low temperature, there are few phonons, so the electrons can move a long way between scattering events. This makes it easier for the electrons to reach the positive connection. As the temperature is increased, there are more and more phonons because phonons are heat. As the temperature goes up, the electrons propagate less distance before their direction is changed, reducing their ability to reach the positive electrode. The result is that electrical conductivity decreases (the resistance increases) as the temperature increases.

Electron-Phonon Scattering Heats the Metal

Because the scattering events add kinetic energy to the phonons, they raise the metal’s temperature. Temperature is a measure of the heat content of a piece of material. Heat is the kinetic energy of the atomic motions. If there are a lot of electrons moving through the metal undergoing scattering events, then a lot of heat is added to the wire, and the temperature goes up. However, when the temperature goes up, there are even more phonons, more scattering events, and so the temperature goes up more.

This process is what you see when you turn an electric stove to high, and it takes some time for the heating element to glow red. When you first turn on the stove, the heating wire is at room temperature. Current (electrons) is flowing and electron-phonon scattering is occurring, causing the temperature to go up. The increased temperature means there are more phonons and more scattering events, and even more heat is added to the wire. The temperature goes up even more. However, as the temperature goes up, the current goes down because the additional scattering slows the progress of the electrons through the wire. The wire will