In organic heterojunction solar cells, the generation of free charge carriers takes place in a multistep process which involves charge transfer (CT) states, that is, bound electron-hole pairs at the interface between donor and acceptor molecules. Past efforts to model the CT-state dissociation during solar cell operation were not able to consistently reproduce the experimentally observed field and temperature dependence. This discrepancy between model and experiment was partly due to the field-dependent free charge carrier collection process, which plays an important role in the widely used bulk heterojunction cell configuration and superimposes a possible field-dependent charge carrier generation process. In order to distinguish between generation and collection of free charge carriers, we propose the planar heterojunction cell configuration as a model system to study the field-dependent charge carrier generation process in organic heterojunction solar cells. We apply this model system to check current CT-state dissociation models against experimental data. Although the models can quantitatively account for the photocurrent's dependence on the applied voltage and the device thickness, they fail to account for the virtually negligible temperature dependence of the field-dependent charge-generation process. This discrepancy is traced back to a common feature of the models: an Arrhenius-like temperature dependence, distinctive of all processes involving a thermally activated jump over an energy barrier. As a solution to the problem, we introduce an exciton dissociation model based on a field-dependent tunnel process and demonstrate its consistency with the experimental observations. Our results indicate that the current microscopic picture of the charge-generation process in organic heterojunction solar cells being limited by the CT-state dissociation process needs to be reconsidered.