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The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] =, where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
At low fields, the drift velocity v d is proportional to the electric field E, so mobility μ is constant. This value of μ is called the low-field mobility. As the electric field is increased, however, the carrier velocity increases sublinearly and asymptotically towards a maximum possible value, called the saturation velocity v sat.
Typical values of saturation velocity may vary greatly for different materials, for example for Si it is in the order of 1×10 7 cm/s, for GaAs 1.2×10 7 cm/s, while for 6H-SiC, it is near 2×10 7 cm/s. Typical electric field strengths at which carrier velocity saturates is usually on the order of 10-100 kV/cm.
The drift velocity deals with the average velocity of a particle, such as an electron, due to an electric field. In general, an electron will propagate randomly in a conductor at the Fermi velocity. [5] Free electrons in a conductor follow a random path. Without the presence of an electric field, the electrons have no net velocity.
is the mobility (m 2 /(V·s)). In other words, the electrical mobility of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field: =. For example, the mobility of the sodium ion (Na +) in water at 25 °C is 5.19 × 10 −8 m 2 /(V·s). [1]
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The physical quantity ion mobility K is defined as the proportionality factor between an ion's drift velocity v d in a gas and an electric field of strength E. = After making the necessary adjustments to account for the n0 standard gas density, ion mobilities are often expressed as reduced mobilities.