Electronic Devices and Circuits Engineering Sciences 154

In 1900 Paul Drude (1863-1906) formulated a very powerful model electrical conductivity which we will review here.

References:

Introductory slide presentation on Drude model (source)
Drude model - Solid State Physics lectures from Carleton College -- see in particular:
            Electric conduction in metallic conductors (local copy)

Consider the follow model of a single representative charge carrier moving through a medium with "scattering centers:"

Schematic View of Charge Carrier Motion

More Accurate Representation of Charge Carrier Motion

A statistical equation for describing the "mean drift velocity" in the direction of the field may be written:

where t is the "mean free time" or "relaxation time" (the "mean free path" l is given by t times the "mean thermal velocity", v_therm.   When the field is zero, this equation, obviously, describes the decay of any gross charge carrier motion in any particular direction.  This equation has the simple solution:

where  is the mobility.  Finally, if we have ncharge carriers per unit volume, the net flux of charge carriers per unit time is given by  and the current density by

where   is the electrical conductivity (r is the electrical resistivity).  If we have both negative and positive charge carriers then
 

For metals the number carriers is fixed and the essentially linear temperature dependence of metallic conductivity is attributed to the temperature dependence of the mobility.

Electrical conductivity
of sodium metal