Are the electron and hole densities always equal in an intrinsic semiconductor? In my laser physics book (Laser physics by Hooker and Webb) it is stated that the density of electrons injected into the intrinsic active region of a diode laser is equal to the density of holes. I am not convinced because the electrons do not come from the valence band but rather from a neighbouring n-type layer, and similarly holes come from a p-type layer on the other side. These two processes seem quite independent so why should the electron and hole densities match, particularly when the system is not symmetric between the p-type and n-type layers?
 A: In general, the densities of electrons and holes in the depletion region of a pn junction are not equal, but governed by relation
$$pn=p_B n_B e^{-\varphi_B/V_{th}},$$
where $n_B, p_B$ are bulk carrier densities, $\varphi_B$ is the barrier height and $V_{th}=kB T/q$ (see here). This relation is further modified when the diode is biased. This means that the junction is charged (positively or negatively), even though the whole circuit remains neutral.
However, this is not the carrier density that enters the laser rate equations. Rather, the carrier density entering the semiconductor laser rate equations is the density of the carriers carrying current and recombining in the active region. If the numbers of the electrons and the holes entering this region were different, there would be constant accumulation of charge, i.e., the charge in the region would continuously grow and create potential, reducing the excess carriers current and increasing the current of the carriers that are lacking. No doubt this is what is happening when the laser is turned on. However, in a steady state regime such charge accumulation should have already stopped (otherwise, we are not in a steady state).
Furthermore, it is assumed that these processes are much faster than the emission of photons, and need not be accounted for to describe the lasing dynamics.
