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9.S: Condensed Matter Physics (Summary)

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    10322
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    Key Terms

    acceptor impurity atom substituted for another in a semiconductor that results in a free electron
    amplifier electrical device that amplifies an electric signal
    base current current drawn from the base n-type material in a transistor
    BCS theory theory of superconductivity based on electron-lattice-electron interactions
    body-centered cubic (BCC) crystal structure in which an ion is surrounded by eight nearest neighbors located at the corners of a unit cell
    breakdown voltage in a diode, the reverse bias voltage needed to cause an avalanche of current
    collector current current drawn from the collector p-type material
    conduction band above the valence band, the next available band in the energy structure of a crystal
    Cooper pair coupled electron pair in a superconductor
    covalent bond bond formed by the sharing of one or more electrons between atoms
    critical magnetic field maximum field required to produce superconductivity
    critical temperature maximum temperature to produce superconductivity
    density of states number of allowed quantum states per unit energy
    depletion layer region near the p-n junction that produces an electric field
    dissociation energy amount of energy needed to break apart a molecule into atoms; also, total energy per ion pair to separate the crystal into isolated ions
    donor impurity atom substituted for another in a semiconductor that results in a free electron hole
    doping alteration of a semiconductor by the substitution of one type of atom with another
    drift velocity average velocity of a randomly moving particle
    electric dipole transition transition between energy levels brought by the absorption or emission of radiation
    electron affinity energy associated with an accepted (bound) electron
    electron number density number of electrons per unit volume
    energy band nearly continuous band of electronic energy levels in a solid
    energy gap gap between energy bands in a solid
    equilibrium separation distance distance between atoms in a molecule
    exchange symmetry how a total wave function changes under the exchange of two electrons
    face-centered cubic (FCC) crystal structure in which an ion is surrounded by six nearest neighbors located at the faces at the faces of a unit cell
    Fermi energy largest energy filled by electrons in a metal at \(\displaystyle T=0K\)
    Fermi factor number that expresses the probability that a state of given energy will be filled
    Fermi temperature effective temperature of electrons with energies equal to the Fermi energy
    forward bias configuration diode configuration that results in high current
    free electron model model of a metal that views electrons as a gas
    hole unoccupied states in an energy band
    hybridization change in the energy structure of an atom in which energetically favorable mixed states participate in bonding
    impurity atom acceptor or donor impurity atom
    impurity band new energy band create by semiconductor doping
    ionic bond bond formed by the Coulomb attraction of a positive and negative ions
    junction transistor electrical valve based on a p-n-p junction
    lattice regular array or arrangement of atoms into a crystal structure
    Madelung constant constant that depends on the geometry of a crystal used to determine the total potential energy of an ion in a crystal
    majority carrier free electrons (or holes) contributed by impurity atoms
    minority carrier free electrons (or holes) produced by thermal excitations across the energy gap
    n-type semiconductor doped semiconductor that conducts electrons
    p-n junction junction formed by joining p- and n-type semiconductors
    p-type semiconductor doped semiconductor that conducts holes
    polyatomic molecule molecule formed of more than one atom
    repulsion constant experimental parameter associated with a repulsive force between ions brought so close together that the exclusion principle is important
    reverse bias configuration diode configuration that results in low current
    rotational energy level energy level associated with the rotational energy of a molecule
    selection rule rule that limits the possible transitions from one quantum state to another
    semiconductor solid with a relatively small energy gap between the lowest completely filled band and the next available unfilled band
    simple cubic basic crystal structure in which each ion is located at the nodes of a three-dimensional grid
    type I superconductor superconducting element, such as aluminum or mercury
    type II superconductor superconducting compound or alloy, such as a transition metal or an actinide series element
    valence band highest energy band that is filled in the energy structure of a crystal
    van der Waals bond bond formed by the attraction of two electrically polarized molecules
    vibrational energy level energy level associated with the vibrational energy of a molecule

    Key Equations

    Electrostatic energy for equilibrium separation distance between atoms \(\displaystyle U_{coul}=−\frac{ke^2}{r_0}\)
    Energy change associated with ionic bonding \(\displaystyle U_{form}=E_{transfer}+U_{coul}+U_{ex}\)
    Critical magnetic field of a superconductor \(\displaystyle B_c(T)=B_c(0)[1−(\frac{T}{T_c})^2]\)
    Rotational energy of a diatomic molecule \(\displaystyle E_r=l(l+1)\frac{ℏ^2}{2I}\)
    Characteristic rotational energy of a molecule \(\displaystyle E_{0r}=\frac{ℏ^2}{2I}\)
    Potential energy associated with the exclusion principle \(\displaystyle U_{ex}=\frac{A}{r^n}\)
    Dissociation energy of a solid \(\displaystyle U_{diss}=α\frac{ke^2}{r_0}(1−\frac{1}{n})\)\(
    oment of inertia of a diatomic molecule with reduced mass \(μ\) \(\displaystyle I=μr^2_0\)
    Electron energy in a metal \(\displaystyle E=\frac{π^2ℏ^2}{2mL^2}(n^2_1+n^2_2+n^2_3)\)
    Electron density of states of a metal \(\displaystyle g(E)=\frac{πV}{2}(\frac{8m_e}{h^2})^{3/2}E^{1/2}\)
    Fermi energy \(\displaystyle E_F=\frac{h^2}{8m_e}(\frac{3N}{πV})^{2/3}\)
    Fermi temperature \(\displaystyle T_F=\frac{E_F}{k_B}\)
    Hall effect \(\displaystyle V_H=uBw\)
    Current versus bias voltage across p-n junction \(\displaystyle I_{net}=I_0(e^{eV_b/k_BT}−1)\)
    Current gain \(\displaystyle I_c=βI_B\)
    Selection rule for rotational energy transitions \(\displaystyle Δl=±1\)
    Selection rule for vibrational energy transitions \(\displaystyle Δn=±1\)

    Summary

    9.1 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.

    • Atoms use a linear combination of wave functions in bonding with other molecules (hybridization).

    9.2 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.

    9.3 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.

    9.4 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 \(\displaystyle T=0K\).

    • The allowed energies of free electrons in a metal depend on electron mass and on the electron number density of the metal.

    • The density of states of an electron in a metal increases with energy, because there are more ways for an electron to fill a high-energy state than a low-energy state.

    • Pauli’s exclusion principle states that only two electrons (spin up and spin down) can occupy the same energy level. Therefore, in filling these energy levels (lowest to highest at \(\displaystyle T=0K\)), the last and largest energy level to be occupied is called the Fermi energy.

    9.5 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.

    9.6 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.

    9.7 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.

    9.8 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.

    Contributors

    Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).