In this chapter, we examine applications of quantum mechanics to more complex systems, such as molecules, metals, semiconductors, and superconductors. We review and develop concepts of the previous chapters, including wave functions, orbitals, and quantum states. We also introduce many new concepts, including covalent bonding, rotational energy levels, Fermi energy, energy bands, doping, and Cooper pairs.
- 9.1: Prelude to Condensed Matter Physics
- For centuries, crystalline solids have been prized for their beauty, including gems like diamonds and emeralds, as well as geological crystals of quartz and metallic ores. But the crystalline structures of semiconductors such as silicon have also made possible the electronics industry of today. In this chapter, we study how the structures of solids give them properties from strength and transparency to electrical conductivity.
- 9.2: Types of Molecular Bonds
- Molecules form by two main types of bonds: the ionic bond and the covalent bond. An ionic bond transfers an electron from one atom to another, and a covalent bond shares the electrons. The energy change associated with ionic bonding depends on three main processes: the ionization of an electron from one atom, the acceptance of the electron by the second atom, and the Coulomb attraction of the resulting ions. Covalent bonds involve space-symmetric wave functions.
- 9.3: Molecular Spectra
- Molecules possess vibrational and rotational energy. Energy differences between adjacent vibrational energy levels are larger than those between rotational energy levels. Separation between peaks in an absorption spectrum is inversely related to the moment of inertia. Transitions between vibrational and rotational energy levels follow selection rules.
- 9.4: Bonding in Crystalline Solids
- Packing structures of common ionic salts include FCC and BCC. The density of a crystal is inversely related to the equilibrium constant. The dissociation energy of a salt is large when the equilibrium separation distance is small. The densities and equilibrium radii for common salts (FCC) are nearly the same.
- 9.5: Free Electron Model of Metals
- Metals conduct electricity, and electricity is composed of large numbers of randomly colliding and approximately free electrons. The allowed energy states of an electron are quantized. This quantization appears in the form of very large electron energies, even at \(T = 0 \space K\). The allowed energies of free electrons in a metal depend on electron mass and on the electron number density of the metal.
- 9.6: Band Theory of Solids
- The energy levels of an electron in a crystal can be determined by solving Schrödinger’s equation for a periodic potential and by studying changes to the electron energy structure as atoms are pushed together from a distance. The energy structure of a crystal is characterized by continuous energy bands and energy gaps. The ability of a solid to conduct electricity relies on the energy structure of the solid
- 9.7: Semiconductors and Doping
- The energy structure of a semiconductor can be altered by substituting one type of atom with another (doping). Semiconductor n-type doping creates and fills new energy levels just below the conduction band. Semiconductor p-type doping creates new energy levels just above the valence band. The Hall effect can be used to determine charge, drift velocity, and charge carrier number density of a semiconductor.
- 9.8: Semiconductor Devices
- A diode is produced by an n-p junction. A diode allows current to move in just one direction. In forward biased configuration of a diode, the current increases exponentially with the voltage. A transistor is produced by an n-p-n junction. A transistor is an electric valve that controls the current in a circuit. A transistor is a critical component in audio amplifiers, computers, and many other devices.
- 9.9: Superconductivity
- A superconductor is characterized by two features: the conduction of electrons with zero electrical resistance and the repelling of magnetic field lines. A minimum temperature is required for superconductivity to occur. A strong magnetic field destroys superconductivity. Superconductivity can be explain in terms of Cooper pairs.
Thumbnail: Structure of the diamond crystal. The single carbon atom represented by the dark blue sphere is covalently bonded to the four carbon atoms represented by the light blue spheres.