  In this paper, we present analytical results for the so-called forward
lateral photovoltage scanning (LPS) problem. The (inverse) LPS model predicts
doping variations in crystal by measuring the current leaving the crystal
generated by a laser at various positions. The forward model consists of a set
of nonlinear elliptic equations coupled with a measuring device modeled by a
resistance. Standard methods to ensure the existence and uniqueness of the
forward model cannot be used in a straightforward manner due to the presence of
an additional generation term modeling the effect of the laser on the crystal.
Hence, we scale the original forward LPS problem and employ a perturbation
approach to derive the leading order system and the correction up to the second
order in an appropriate small parameter. While these simplifications pose no
issues from a physical standpoint, they enable us to demonstrate the analytic
existence and uniqueness of solutions for the simplified system using standard
arguments from elliptic theory adapted to the coupling with the measuring
device.
