Organic semiconductors, which serve as the active component in devices, such as solar cells, light-emitting diodes and field-effect transistors(1), often exhibit highly unipolar charge transport, meaning that they predominantly conduct either electrons or holes. Here, we identify an energy window inside which organic semiconductors do not experience charge trapping for device-relevant thicknesses in the range of 100 to 300 nm, leading to trap-free charge transport of both carriers. When the ionization energy of a material surpasses 6eV, hole trapping will limit the hole transport, whereas an electron affinity lower than 3.6 eV will give rise to trap-limited electron transport. When both energy levels are within this window, trap-free bipolar charge transport occurs. Based on simulations, water clusters are proposed to be the source of hole trapping. Organic semiconductors with energy levels situated within this energy window may lead to optoelectronic devices with enhanced performance. However, for blue-emitting light-emitting diodes, which require an energy gap of 3 eV, removing or disabling charge traps will remain a challenge.