  The design of electrically driven quantum dot devices for quantum optical
applications asks for modeling approaches combining classical device physics
with quantum mechanics. We connect the well-established fields of
semi-classical semiconductor transport theory and the theory of open quantum
systems to meet this requirement. By coupling the van Roosbroeck system with a
quantum master equation in Lindblad form, we introduce a new hybrid
quantum-classical modeling approach, which provides a comprehensive description
of quantum dot devices on multiple scales: It enables the calculation of
quantum optical figures of merit and the spatially resolved simulation of the
current flow in realistic semiconductor device geometries in a unified way. We
construct the interface between both theories in such a way, that the resulting
hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics.
We show that our approach guarantees the conservation of charge, consistency
with the thermodynamic equilibrium and the second law of thermodynamics. The
feasibility of the approach is demonstrated by numerical simulations of an
electrically driven single-photon source based on a single quantum dot in the
stationary and transient operation regime.
