Carrier - diffusion mobility

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

A. Miller, Transient Grating Studies of Carrier Diffusion and Mobility in Semiconductors... 

The space charge region is denoted by length w, while Lp is the hole (minority carrier) diffusion length. Zp is the minority carrier (hole) lifetime, jp the (minority carrier) hole mobility, and Dp the minority carrier diffusion coefficient. 

Other indirect methods for measuring lifetimes often involve device structures such as p-n junctions. The electron-beam-induced current (EBIC) technique, for example, measures the increase injunction current as an impinging electron beam moves close to the junction, i.e., within a few minority-carrier diffusion lengths. If a diffusion constant can be estimated, say by knowledge of the minority-carrier mobility, then the minority-carrier lifetime can be calculated. However, SI GaAs does not form good junctions, so such methods are really not applicable. 

After this time, the carrier crosses the mobility edge and is trapped in localized states, so that further movement is much slower, although the distance between the sites is larger. During thermalization in extended states the carriers diffuse apart a distance. 

The carrier diffusion coefficient, D, for electrons and Dp for holes, is another important parameter associated with mobility. It is given by... 

In recent years, more complex types of transport processes have been investigated and, from the point of view of solid state science, considerable interest is attached to the study of transport in disordered materials. In glasses, for example, a distribution of jump distances and activation energies are expected for ionic transport. In crystalline materials, the best ionic conductors are those that exhibit considerable disorder of the mobile ion sublattice. At interfaces, minority carrier diffusion and discharge (for example electrons and holes) will take place in a random environment of mobile ions. In polycrystalline materials the lattice structure and transport processes are expected to be strongly perturbed near a grain boundary. 

---