The inclusion of rare earth arsenide nanoparticles in III-V semiconductor films is an ongoing area of interest for thermoelectric and terahertz sensor research. These films, typically grown by molecular beam epitaxy, have been observed to exhibit strain behavior which is not accurately predicted by simple linear averaging based on alloy composition i.e. Vegard's Law. Although this non-Vegard-like behavior is by no means novel in itself, the cause of the behavior in the specific case of rare earth nanoparticles in III-Vs has not been studied extensively. Researchers have recently begun investigating films co-doped with multiple species of rare earth nanoparticle in order to achieve lattice matching to a particular substrate or to improve thermoelectric properties. The strain behavior of these co-doped films is similarly lacking in study.

In order to rectify this lack of understanding, a systematic study of erbium arsenide and scandium arsenide particles in gallium arsenide is conducted. Films of nanoparticle-doped GaAs are grown by molecular beam epitaxy and are characterized in situ by reflected high-energy electron diffraction and ex situ by high-resolution x-ray diffraction. It is reaffirmed that ErAs produces a superdilation of the GaAs lattice constant and it is newly observed that ScAs produces a supercontraction. The combination of these lattice distortions is roughly linear and is used to correctly predict the relative concentrations required for a lattice-matched co-doped film. GaAs exhibits an asymmetric strain response to rare earth arsenides with positive and negative lattice mismatches, undergoing greater dilation than contraction for nanoparticles of equal mismatch magnitude.

Several mechanisms known to produce superdilation or supercontraction in other doped semiconductor systems are examined and compared with the properties of the ErAs+ScAs:GaAs system to try and explain these behaviors. A new lattice misfit model is proposed which explains the lattice distortions primarily in terms of heavily distorted bond lengths at the interfaces between particles and the surrounding matrix. This model agrees well with measurements of ErAs:GaAs films and is used to predict an interfacial bond length for ScAs:GaAs which can be checked in a future study.