The processes of excess electron and hole generation and recombination are explored, with definitions of the generation and recombination rates.
$$ G = R \newline R = \frac{n p - n_i^2}{\tau_p (n + n_i) + \tau_n (p + n_i)} $$
Excess electrons and holes move together in what is known as ambipolar transport, instead of moving independently.
$$ D_a = \frac{n D_n + p D_p}{n + p} \mu_a = \frac{n \mu_n + p \mu_p}{n + p} $$
The ambipolar transport equation was derived, focusing on conditions of low injection and extrinsic doping. Under these conditions, both excess electrons and holes diffuse and drift together, aligning with the behavior of minority carriers.
$$ \frac{\partial^2 p}{\partial x^2} - \frac{p - p_0}{L_a^2} = 0 $$
The excess carrier lifetime concept was introduced, helping to describe the lifespan of these carriers.
$$ \tau = \frac{1}{R} $$
Excess carrier behavior was examined over time, space, and both together.
$$ \frac{\partial n}{\partial t} = D_n \frac{\partial^2 n}{\partial x^2} - \frac{n}{\tau_n} $$
The quasi-Fermi levels for both electrons and holes were defined, with the degree of Fermi level splitting used to measure deviations from thermal equilibrium.
$$ n = n_i e^{\frac{F_n - E_i}{k T}} \newline p = n_i e^{\frac{E_i - F_p}{k T}} $$
The Shockley-Read-Hall theory of recombination was discussed, including expressions for minority carrier lifetime and how traps in semiconductors affect the generation and recombination of excess carriers.
$$ R_{SRH} = \frac{n p - n_i^2}{\tau_p (n + n_i) + \tau_n (p + n_i)} $$
Finally, the influence of the semiconductor surface on the behavior of excess carriers was noted, along with the definition of surface recombination velocity.
$$ S = \frac{J_{recomb}}{n} $$