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Mobility

Our basic ideas of charge transport in solids date back to a model proposed by Drude in the late 1890s. It assumes that atoms in metals (the only conductors known at that time) form a crystal lattice and contribute their valence electrons to a gas of free electrons which floats between the ions. In an external electric field E the electrons are accelerated for a certain time before they bounce into an ion and lose their kinetic energy in the collision.

For an estimation of the mean electron velocity v the time derivative in the equation of motion was approximated by the relaxation time τ:

The current density j is easily expressed in terms of the carrier velocity v, their density n and their charge e:

Earlier we defined the specific conductivity σ as product of carrier density, carrier charge, and mobility.

σ = n e μ

Thus, we are able to relate the carrier mobility μ and the relaxation time τ:

In the next paragraphs we will look closer at the different types of collisions, or scattering events, and try to relate them to the relaxation time τ:

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