A coupling model between a classical Monte Carlo simulator and a Liouville equation solver has been proposed with application to the simulation of vertical transport quantum devices in which extensive regions of the simulation domain behave classically. These devices can be partitioned in regions in which either a classical (Monte Carlo) or a quantum (Wigner formalism) treatment of carrier transport is required making a coupling scheme between adjacent regions necessary. According to this aim, the boundary conditions inferred from the Monte Carlo solver for the integration of the Liouville equation in the quantum regions, as well as the injecting scheme to the Monte Carlo regions provided by the Wigner distribution function at the boundaries have been earlier established. The results of this work, using a resonant tunneling diode as a reference device, show that the proposed technique is promising for the simulation of electron transport in quantum devices. © 1998 Elsevier Science Ltd. All rights reserved.