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Self-assembled InAs quantum dots (QDs), which have long hole-spin coherencetimes and are amenable to optical control schemes, have long been explored asbuilding blocks for qubit architectures. One such design consists of verticallystacking two QDs to create a quantum dot molecule (QDM) and using thespin-mixing properties of "molecule-like" coupled hole states for all-opticalqubit manipulation. In this article, the first of two papers, we introduce theincorporation of dilute GaBiAs alloys in the barrier region between the twodots. GaBiAs is expected to increase the spin-mixing of the molecular statesneeded for qubit operations by raising the barrier valence band edge andspin-orbit splitting. Using an atomistic tight-binding model, we compute theproperties of GaBiAs and the modification of hole states that arise when thealloy is used in the barrier of an InAs QDM. An atomistic treatment isnecessary to correctly capture non-traditional alloy effects such as theband-anticrossing valence band. It also allows for the study of configurationalvariances and clustering effects of the alloy. We find that in InAs QDMs with aGaBiAs interdot barrier, electron states are not strongly affected by theinclusion of Bi. However, hole states are much more sensitive to the presenceand configuration of Bi in the barriers. By independently studying thealloy-induced strain and electronic scattering off Bi and As orbitals, weconclude that an initial increase in QDM hole state energy at low Biconcentration is caused by the alloy-induced strain. We further find that thedecrease in QDM hole energy at higher Bi concentrations can only be explainedwhen both alloy strain and orbital effects are considered. In our secondarticle, we use the understanding developed here to discuss how the alloyedbarriers contribute to enhancement in hole spin-mixing and the implications forQDM qubit architectures.

Incorporation of random alloy GaBi$_x$As$_{1-x}$ barriers in InAs quantum dot molecules (I): energy levels and confined hole states