ELECTRICAL CONDUCTION

• Ohm's Law


  Relates the current (or time rate of charge passage) to the applied voltage
• Electrical resistivity


  Dependence on resistance, specimen cross-sectional area, and distance between measuring points
• Electrical conductivity


  • Used to specify the electrical character of a material
  • The reciprocal of the resistivity
  • Magnitude dependent on the number of electrons available (not all electrons will accelerate in the presence of an electric field)
  • Direct function of the numbers of free electrons and holes

  
• Classification of solids according to conduction of electric current

  • Conductors (metals with conductivities on the order of 10^7 (ohm-m)^-1)
  • Semiconductors (generally from 10^-6 to 10^4 (ohm-m)^-1)
  • Insulators (materials with very low conductivities, ranging between 10^-10 and 10^-20 (ohm-m)^-1)
• Electric current


  • Results from the motion of electrically charged particles in response to forces that act on them from an externally applied electric field
  • Positive charged particles accelerated in the field direction
  • Negatively charged particles accelerated in the opposite direction
• Electric conduction


  Current arises from the flow of electrons in most solids
• Ionic conduction


  For ionic materials a net motion of charged ions is possible that produces a current
• The number of electrons available for electrical conduction is related to the arrangement of electron states or levels with respect to energy, and then the manner in which these states are occupied by electrons

  
• The electrons in most atoms fill only the states having the lowest energies
• Solids are comprised of atoms initially separated but brought together and bonded to form crystalline structures
• At large separation distances, atoms behave independently with their own energy levels and electron configurations
• Close proximity causes electron perturbation by adjacent atoms' electrons and nuclei, leading to the formation of electron energy bands

  
• At the equilibrium spacing, band formation may not occur for the electron subshells nearest the nucleus

  
• The number of states within each band will equal the total of all states contributed by the N atoms
• With regard to occupancy, each energy state may accommodate two electrons, which must have oppositely directed spins
• Furthermore, bands will contain the electrons that resided in the corresponding levels of the isolated atoms

  
• Fermi energy (Ef)


  Energy corresponding to the highest filled state at 0 K
• Types of band structures

  • Partially filled outermost band (typical of some metals like Cu), with the Fermi energy marking the highest filled state
  • Overlapping filled and empty bands (found in metals like magnesium), with the Fermi energy set where N states are filled, accommodating two electrons per state
  • Valence band - One band that is completely filled with electrons
  • Conduction band - Similar to three but empty. Energy band gap lies between the valence and conduction bands.

  
• Fermi energy for insulators and semiconductors lies within the band gap—near its center

  
• In very pure metals, electrons have no energies within the gap
• Insulators have a wide band gap, semiconductors have a narrow band gap
• Free electrons


  Electrons that participate in the conduction process
• Hole


  A charged electronic entity found in semiconductors and insulators, with energy less than the Fermi energy, that participates in electric conduction

  
• In metals, for an electron to be free, it must be excited/promoted into one of the empty and available energy states above the Fermi energy

  
• Very little energy is required to promote electrons into the low-lying empty states above the Fermi energy in metals (the energy of the electric field is enough to excite them)

  
• For insulators and semiconductors, empty states adjacent to the top of the filled valence band are not available. To become free, electrons must be promoted across the energy band gap and into empty states at the bottom of the conduction band

  
• The larger the band gap, the lower is the electrical conductivity at a given temperature
• Increased temperature


  Increased thermal energy (for electron excitement) = more electrons excited
• For electrically insulating materials, electrons are tightly bound to or shared with the individual atoms, and are highly localized and not free to wander throughout the crystal
• For semiconductors, valence electrons are not as strongly bound to the atoms and are more easily removed by thermal excitation than they are for insulators

  
• According to quantum mechanics, there is no interaction between an accelerating electron and atoms in a perfect crystal lattice

  
• Frictional forces


  • Result from the scattering of electrons by imperfections in the crystal lattice, including impurity atoms, vacancies, interstitial atoms, dislocations, and even the thermal vibrations of the atoms themselves
  • Scattering event = lose kinetic energy/change direction of motion
  • Scattering event = resistance to the passage of an electric current (or raises resistivity)

  
• Scattering centers (in metals)

  • Crystalline defects
• Scattering mechanisms

  • Thermal vibrations
  • Impurities
  • Plastic deformation
• Matthiessen's rule


  A mathematical formula that sums the three scattering mechanisms to give the total resistivity
• Drift velocity


  The average electron velocity in the direction of the force imposed by the applied field, which is directly proportional to the electric field
• Electron mobility


  A constant of proportionality that is an indication of the frequency of scattering events

  
• Energy levels


  Quantized energy values of an atom
• Energy bands


  Energy levels that exist at the molecular level
• Energy levels exist at the atomic level