We have seen in Section 4.5 that charge is a conserved quantity, i.e. it fulfils the continuity
equation (Eq. (4.34)). Now we will formulate the continuity equation in terms of the
electron and hole concentrations. Therefore we have to take drift, diffusion, and
recombination as well as generation processes into account; the latter are discussed in
Chapter 7.
For electrons, the rate at which the concentration changes is given by
where R and G denote recombination and generation, respectively. For holes, we obtain
In these equations ∂n/∂t (∂p/∂t) is the time rate change in the electron (hole) concentration.
Without any generation or recombination, the number of electrons and holes is
conserved, i.e. Eq. 4.34 can be applied. We thus obtain
where J n (J p ) is the electron (hole) current density.
The equations can be written in a more compact form when introducing substitutions,
R n (R p ) denotes the net thermal recombination-generation rate of electrons (holes), G n (G p )
is the generation rate of electrons (holes) due to other processes, such as photogeneration.
We will discuss these processes in detail in Chapter 7. Substituting Eqs. (6.31), (6.32) and
(6.33) into Eq. (6.30) finally leads to