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Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Free carrier concentration is the concentration of free carriers in a doped semiconductor. It is similar to the carrier concentration in a metal and for the purposes of calculating currents or drift velocities can be used in the same way. Free carriers are electrons that have been introduced into the conduction band (valence band) by doping ...
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
The optical Hall effect is an emerging technique for measuring the free charge carrier density, effective mass and mobility parameters in semiconductors. The optical Hall effect measures the analogue of the quasi-static electric-field-induced electrical Hall effect at optical frequencies in conductive and complex layered materials.
N dop is the net density of dopants (either donors or acceptors). When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants. Instead, a measure of the profile of the doping gradients provides an "effective" profile that better matches the profile of the majority carrier density.
The average free time of flight of a carrier and therefore the relaxation time is inversely proportional to the scattering probability. [15] [16] [18] For example, lattice scattering alters the average electron velocity (in the electric-field direction), which in turn alters the tendency to scatter off impurities. There are more complicated ...
where D is the diffusion coefficient for the electron in the considered medium, n is the number of electrons per unit volume (i.e. number density), q is the magnitude of charge of an electron, μ is electron mobility in the medium, and E = −dΦ/dx (Φ potential difference) is the electric field as the potential gradient of the electric potential.
Using the carrier concentration equations given above, the mass action law can be stated as = =, where E g is the band gap energy given by E g = E c − E v. The above equation holds true even for lightly doped extrinsic semiconductors as the product n p {\displaystyle np} is independent of doping concentration.