We study excited-state phenomena in a variety of semiconductor systems, with
use of the variational and diffusion quantum Monte Carlo (QMC) methods.
Firstly, we consider the formation of charge-carrier complexes in the
Mott-Wannier model, for systems of restricted geometrical freedom (the coupled
quantum well bilayer, and the quantum ring). We find in such systems that
geometrical constraints lead to the characteristic formation of certain
charge-carrier complexes, and highlight how such effects are of relevance to
the interpretation of recent experiments.

Secondly, we illuminate a key difference between two-dimensional systems formed
from geometrical restriction, and those which are truly two-dimensional in
extent, by introduction of the Keldysh interaction. We then study
the formation of charge-carrier complexes in two-dimensional semiconductors and
their heterostructures in the so-called Mott-Wannier-Keldysh model, deriving
appropriate extensions of the Keldysh interaction as necessary.

Thirdly, we undertake a comprehensive survey of the use of continuum QMC
methods to evaluate excited-state properties in a truly ab initio
fashion, establishing best-practices, and presenting energy gap calculations
for several real materials. This includes the first published QMC calculation
of the electronic energy gaps of a two-dimensional semiconductor, phosphorene.

Finally, we propose an extension of the Keldysh interaction which permits the
study of continuum phases, the so-called ``periodic Keldysh interaction'', and
use it to probe the possible Wigner crystallisation of electrons in a
weakly-doped two-dimensional semiconductor.