We investigate Si/0.85Ge0.15 fully depleted-SOI tunnel FET (TFET) devices operated in the electron-hole bilayer (EHB) mode. The application of negative bias on front gate and positive bias on back gate results in confined hole and electron layers that are expected to enable vertical band-to-band tunneling (BTBT). The idea of the EHB-TFET device is to enhance the tunneling current by expanding the BTBT generation area from the narrow lateral source/channel junction to the entire channel region. Our systematic measurements on a variety of TFETs with variable geometry and channel materials do not offer support to this attractive concept. Self-consistent simulations confirm that the vertical BTBT transitions do not produce an appreciable current in our devices, due to size-and bias-induced quantization, effective mass anisotropy, and incomplete formation of the bilayer. We examine the conditions for efficient vertical BTBT to occur and show that they cannot be met simultaneously, at least in Si or Si/SiGe devices.