  A theoretical model using electron-phonon scattering rate equations is
developed for assessing carrier thermalization under steady-state conditions in
two-dimensional systems. The model is applied to investigate the hot carrier
effect in III-V hot-carrier solar cells with a quantum well absorber. The
question underlying the proposed investigation is: what is the power required
to maintain two populations of electron and hole carriers in a
quasi-equilibrium state at fixed temperatures and quasi-Fermi level splitting?
The obtained answer is that the thermalization power density is reduced in
two-dimensional systems compared to their bulk counterpart, which demonstrates
a confinement-induced enhancement of the hot carrier effect in quantum wells.
This power overall increases with the well thickness, and it is moreover shown
that the intra-subband contribution dominates at small thicknesses while the
inter-subband contribution increases with thickness and dominates in the bulk
limit. Finally, the effects of the thermodynamic state of phonons and screening
are clarified. In particular, the two-dimensional thermalization power density
exhibits a non-monotonic dependence on the thickness of the quantum well layer,
when both out-of-equilibrium longitudinal optical phonons and screening effects
are taken into account. Our theoretical and numerical results provide tracks to
interpret intriguing experimental observations in quantum well physics. They
will also offer guidelines to increase the yield of photovoltaic effect based
on the hot carrier effect using quantum well heterostructures, a result
critical to the research toward high-efficiency solar cell devices.
