Fundamental Conductance <inline-formula> <tex-math notation="TeX">\(\div \) </tex-math></inline-formula> Voltage Limit in Low Voltage Tunnel Switches

There is a fundamental conductance ÷ voltage limit in low voltage (<;4k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T/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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T. 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T/q is applied, the conductance will be reduced by at least qV/4k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T. Even with a perfect tunneling probability of 1 in a perfect quantum channel, the conductance quantum would be diminished by qV/4k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T. Attempts at lowering the operating voltage below <;4k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> T/q must come at the expense of smaller conductance.