Fundamental Conductance ÷ Voltage Limit in Low Voltage Tunnel Switches

There is a fundamental conductance ÷ voltage limit in low voltage (<4kT/q) tunnel switching devices that obtain a sharp turn off by relying upon the band edges to abruptly cut off the available density of states. The Fermi occupation probabilities are thermally broadened by 4kbT. However, current is only allowed to flow in a narrow energy range limited by the applied voltage, V. This means that if we apply a voltage less than 4kbT/q, the conductance will be reduced by at least qV/4kbT. Even with a perfect tunneling probability of 1 in a perfect quantum channel, the conductance quantum would be diminished by qV/4kT. Attempts at lowering the operating voltage below <4kT/q must come at the expense of smaller conductance.