Boundary conditions (BCs) to the Poisson and transport equations for stationary transport processes of non-equilibrium carriers in semiconductor structures are formulated. The applicability of the resulting BCs for several materials (metals, bipolar semiconductors, including ones in the quasineutrality approach, QNA) and their structures are analyzed for both closed and open circuits. As a first step. general BCs for different types of contacts between two materials and between a solid and the vacuum under thermodynamic equilibrium conditions are thoroughly discussed. Later on. BCs are presented for the general case of a contact between a solid (this contact is considered as a "free-surface" in a broad sense) and the vacuum under non-equilibrium conditions. The concept of "free-surface", and its BCs, can be extended and applied to other interfaces such as semiconductor-insulator that is relevant in semiconductor devices. Finally, the case of a hetero-contact between two conducting media under a current flow is addressed. BCs for closed-circuit conditions are presented and it is shown that BCs for open-circuit can be obtained as a limit of the proposed ones when the electric current tends to zero. In all the considered cases the changes operated in the BCs if the QNA is invoked are carefully studied. (C) 2008 Elsevier Ltd. All rights reserved.