In tunnel field-effect transistors (tFETs), the preferred mechanism for switching occurs by alignment (on) or misalignment (off) of two energy levels or band edges. Unfortunately, energy levels are never perfectly sharp. When a quantum dot interacts with a wire, its energy is broadened. Its actual spectral shape controls the current/voltage response of such transistor switches, from on (aligned) to off (misaligned). The most common model of spectral line shape is the Lorentzian, which falls off as reciprocal energy offset squared. Unfortunately, this is too slow a turnoff, algebraically, to be useful as a transistor switch. Electronic switches generally demand an on/off ratio of at least a million. Steep exponentially falling spectral tails would be needed for rapid off-state switching. This requires a new electronic feature, not previously recognized: narrowband, heavy-effective mass, quantum wire electrical contacts, to the tunneling quantum states. These are a necessity for spectrally sharp switching.