where is the electrical conductivity. It is in general a tensor but can be assumed as a scalar in most semiconductors

From the microscopic point of view the current density is made up by the moving carriers

where is the elementary charge, and are the electron and hole concentrations, respectively, and and are the mean velocities of electrons and holes, respectively. The electric field accelerates the carriers, but due to various scattering mechanisms the velocity of the carriers is limited:

(2.22) | ||||

(2.23) |

where and are the mobility of electrons and holes, respectively. By inserting these two equations into eqn. (2.21)

and comparing eqn. (2.24) with eqn. (2.20) and eqn. (2.19) the following relations are obtained:

(2.25) | ||

(2.26) |

and for the conductivities:

(2.27) | ||

(2.28) |