In this chapter we will examine how the various scattering processes discussed in the last two chapters influence transport properties of electrons and holes. In steady state the response of the free carriers to an external electric field is represented by the velocity versus electric field relationship. This relationship is vital to the understanding of electronic devices. There are three regions of the electric field which are important in charge transport:

1. The low electric field region where the velocity-field relation is linear and is defined by the mobility ? through the relation

   v = ? F

   It is usually possible to develop analytic formalisms for this region based on the Boltzmann transport equation.

2. A higher electric field (usually F ? 1 kV/cm), where the v- F relation is no longer linear. To understand the transport in this region one usually requires numerical methods including those based on computer simulations.

3. Finally, at extremely high electric fields ( F ? 10 ⁵ V/cm), the semiconductor "breaks down" either due to impact ionization or due to electrons tunneling from the valence band to the conduction band.

The steady state v- F relationships require an electron to undergo several (usually at least several tens) collisions before reaching steady state. Most collision times are of the order of a picosecond, and since electron velocities are of the order of 10 ⁷ cm/s, it takes an electron several hundred Angstroms of travel before scattering occurs. Transport in...