Recently, interest in optical refrigeration of semiconductors, which is based on photo-luminescence up-conversion,
has drawn extensive attention both theoretically and experimentally. Theoretical descriptions often treat spatially
homogeneous semiconductors, because of their conceptual simplicity. In typical experiments, however,
semiconductors are usually heterostructures designed to reduce non-radiative recombination at the sample's surface.
In particular, GaAs/GaInP structures have been used in experiments. In these structures, the GaAs layers
are usually unintentionally p-doped, while the surface layers of GaInP are n-doped. Recent measurements of the
non-radiative recombiation lifetime yielded values in the desirable inverse microsecond regime, and it is believed
that the non-radiative recombination processes occur mainly at the heterostructure interfaces and its surfaces.
For this reason, it is important to know the spatial density distribution of the excited carriers. Furthermore,
photo-luminescence and carrier lifetime measurements are not spatially resolved, and therefore it is desirable to
have a theory that can simulate lifetime measurements using the spatially varying density profile as an input.
We have developed such a theory, using the simplifying assumption of quasi-thermal equilibrium (at each time
during the photo-luminescence decay process). Using this theory, we are able to relate measurable (i.e. spatially
averaged) lifetime measurements to the underlying non-radiative decay processes that, in our simulations,
occur predominantly at the GaAs/GaInP interface. From this, we find that spatial inhomogeneities in the carrier
density, which are most pronounced at low optical excitation powers, can have appreciable effects on the
interpretation of the lifetime measurements.