  From the microscopic quantum Langevin equations (QLEs) we derive the
effective semiconductor QLEs and the associated noise correlations which are
valid at a low-injection level and in real devices. Applying the semiconductor
QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula
for the Fano factor of photons which gives the photon-number statistics as a
function of the pump statistics and several parameters of LEDs. Key ingredients
are non-radiative processes, carrier-number dependence of the radiative and
non-radiative lifetimes, and multimodeness of LEDs. The formula is applicable
to the actual cases where the quantum efficiency $\eta$ differs from the
differential quantum efficiency $\eta_{d}$, whereas previous theories
implicitly assumed $\eta = \eta_{d}$. It is also applicable to the cases when
photons in each mode of the cavity are emitted and/or detected inhomogeneously.
When $\eta_{d} < \eta$ at a running point, in particular, our formula predicts
that even a Poissonian pump can produce sub-Poissonian light. This mechanism
for generation of sub-Poissonian light is completely different from those of
previous theories, which assumed sub-Poissonian statistics for the current
injected into the active layers of LEDs. Our results agree with recent
experiments. We also discuss frequency dependence of the photon statistics.
