  State-of-the-art industrial semiconductor device modeling is based on highly
efficient Drift-Diffusion (DD) models that include some quantum corrections for
nanodevices. In contrast, latest academic quantum transport models are based on
the non-equilibrium Green's function (NEGF) method that cover all coherent and
incoherent quantum effects consistently. Carrier recombination and generation
in optoelectronic nanodevices represent an immense numerical challenge when
solved within NEGF. In this work, the numerically efficient B\"uttiker-probe
model is expanded to include electron-hole recombination and generation in the
NEGF framework. Benchmarks of the new multiple-particle B\"{u}ttiker probe
method against state-of-the-art quantum-corrected DD models show quantitative
agreements except in cases of pronounced tunneling and interference effects.
