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Engineering LibreTexts

Electronic Properties

  • Page ID
    307
  • Electronic band structure (or simply band structure) of a solid describes those ranges of energy that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.

    • Brillouin Zones
      A Brillouin zone is defined as a Wigner-Seitz primitive cell in the reciprocal lattice. The first Brillouin zone is the smallest volume entirely enclosed by planes that are the perpendicular bisectors of the reciprocal lattice vectors drawn from the origin. The concept of Brillouin zone is particularly important in the consideration of the electronic structure of solids.
    • Compton Effect
      The Compton effect (also called Compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule. The scattered radiation experiences a wavelength shift that cannot be explained in terms of classical wave theory, thus lending support to Einstein's photon theory. The effect was first demonstrated in 1923 by Arthur Holly Compton (for which he received a 1927 Nobel Prize).
    • Debye Model For Specific Heat
      The Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid. This model correctly explains the low temperature dependence of the heat capacity, which is proportional to T³ and also recovers the Dulong-Petit law at high temperatures. However, due to simplifying assumptions, its accuracy suffers at intermediate temperatures.
    • Density of States
      The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy. Bulk properties such as specific heat, paramagnetic susceptibility, and other transport phenomena of conductive solids depend on this function.
    • Electron-Hole Recombination
      Recombination is the mechanism that is utilized by extrinsic semiconductors to equilibrate excess charge carriers through the bringing together and annihilation of oppositely charged carriers. Specifically the annihilation of positively charged holes and negatively charged impurity or free electrons. Recombination results in the release of energy, this energy stems from the act of electrons jumping down from the conduction band in order to recombine with holes generated in the valence band.
    • Energy bands in solids and their calculations
      When a large number of atoms are brought together to form a solid, the number of orbitals becomes exceedingly large, and the difference in energy between them becomes very small, so the levels may be considered to form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. Within an energy band, energy levels are so numerous as to be a near continuum. However, some intervals of energy contain no orbitals, i.e., the forbidden energy levels.
    • Fermi Energy and Fermi Surface
      The Fermi energy is described as the highest energy that the electrons assumes at a temperature of 0 K.
    • Ferroelectricity
      Ferroelectricity is a property observed in certain materials characterized by the presence of a spontaneous electric polarization without the presence of an electric field, much like how ferromagnetism is characterized by a spontaneous, permanent magnetic field. A subclass of piezoelectric and pyroelectric materials, ferroelectric materials are noncentrosymmetric crystals.
    • Hall Effect
      Hall Effect, deflection of conduction carriers by an external magnetic field, was discovered in 1879 by Edwin Hall.
    • Ladder Operators
      Mathematically, a ladder operator is defined as an operator which, when applied to a state, creates a new state with a raised or lowered eigenvalue. Their utility in quantum mechanics follows from their ability to describe the energy spectrum and associated wavefunctions in a more manageable way, without solving differential equations. We will discuss the most prominent example of the use of these operators; the quantum harmonic oscillator.
    • Lattice Vibrations
      Almost all solids with the exception of amorphous solids and glasses have periodic arrays of atoms which form a crystal lattice. The existence of the periodic crystal lattice in solid materials provides a medium for characteristic vibrations. Between the lattice spacing, there are quantized vibrational modes called a phonon. The study of phonon is an important part of solid state physics.
    • Piezoelectricity
      Piezoelectricity is the effect of mechanical strain and electric fields on a material; mechanical strain on piezoelectric materials will produce a polarity in the material, and applying an electric field to a piezoelectric material will create strain within the material. When pressure is applied to a piezoelectric material, a dipole and net polarization are produced in the direction of the applied stress. Piezoelectricity has many application.
    • Real and Reciprocal Crystal Lattices
      Crystal is a three dimensional periodic array of atoms. Crystal lattice is the geometrical pattern of the crystal, where all the atom sites are represented by the geometrical points. There are two classes of crystal lattices. When all of the lattice points are equivalent, it is called Bravais lattice. Otherwise, it is called non-Bravais lattice. The non-Bravais lattice may be regarded as a combination of two or more interpenetrating Bravais lattices with fixed orientations relative to each other
    • Resistivity
      Resistivity is the material property that pertains to how difficult it is for electrical current to flow through said material. Materials with high resistivity are known as insulators while materials with low resistivity are known as conductors. Spanning from 10-8 Ωm to 1020 Ωm, resistivity possess the largest range of values for any physical property. Resistivity is essential in many material applications including resistors, dielectrics, resistive heating, and superconducting.
    • Solving the Ultraviolet Catastrophe
      This is a very interesting story which first time lead people to believe that energies (associated with waves) are quantized rather than continuous. It all started with Black Body radiation when scientist attempted to explain the curve of frequency (or wavelength) vs intensity. Max Planck was first to explain the behavior in 1900, but no one accepted it; as there is no explanation for assuming energy corresponding to particular wavelength quantized rather than continuous.
    • Thermocouples
      This page provides a fundamental discussion of what a thermocouple is and how it works. A thermocouple is a temperature measuring device that can operate in a wide range of temperature. It is created by joining two dissimilar metal and/or semiconductor wires together. Thermocouples are inexpensive to make. However, they have limited accuracy.
    • Thermoelectrics
      Thermoelectrics (TEs) are materials that convert heat to electricity via the Seebeck effect. This unique ability of TEs is dependent upon electronic and thermal properties. The dimensionless figure of merit (zT) is used to quantify TE performance, and is related to the conversion efficiency (η). TEs optimizing energy conversion are currently used in radioisotope thermoelectric generators (RTGs) to generate electricity for spacecraft and other inaccessible power systems.
    • X-ray diffraction, Bragg's law and Laue equation