Fundamental Conductance Voltage Limit in Low Voltage Tunnel Switches

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