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 Fermienergy
Very little energy is required to promote electrons into the low-lying empty states above the Fermi energy in metals (the energy of the electricfield is enough to excite them)
For insulators and semiconductors, emptystates 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 conductionband
The larger the band gap, the lower is the electricalconductivity at a given temperature
Increased temperature
Increased thermal energy (for electron excitement) = more electrons excited
For electrically insulating materials, electrons are tightlybound to or shared with the individual atoms, and are highly localized and not free to wander throughout the crystal
For semiconductors, valenceelectrons are not as strongly bound to the atoms and are more easily removed by thermalexcitation 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)
Crystallinedefects
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 appliedfield, which is directly proportional to the electric field
Electron mobility
A constant of proportionality that is an indication of the frequency of scattering events