In this paper we present a formalism for the calculation of electron transport through three-terminal junction devices, which have received attention due to their recently demonstrated non-linear electrical properties. The formalism, which is based on the scattering-matrix method, takes quantum interference effects fully into account. Furthermore, the formalism provides numerical stability in the calculations as well as large flexibility in the modelling of arbitrary potential profiles due to the common basis approach used in the formulation. The method is used to calculate the transport properties for Y-shaped three-terminal ballistic junction (TBJ) structures with configurations typical of recently performed experiments. Quantum interference effects are shown to strongly influence the transport characteristics of TBJ structures due to complex scattering of the electrons in the cavity-like coupling window between the three arms of the device. The theoretical approach presented in this paper provides a flexible tool for the study of such quantum interference effects, which may play an important role in the design and functionality of future nanoscale devices based on three-terminal junctions.
