Beating Boltzmann’s tyranny: Surpassing lower limit on computing energy consumption

The collaboration of researchers from three FLEET nodes showed that transistors based on topological insulators rather than conventional semiconductors could reduce the gate voltage by half, and the energy used by each transistor by a factor of four.

This overcomes the famous Boltzmann’s tyranny, which puts a lower limit on transistor switching energy.

The research discovered something surprising: a gate voltage applied to a topological insulator could create a barrier to electron flow that is larger than the voltage itself times the electron charge, a result previously thought impossible.

Transistors switch on and off based on application of a gate voltage, with the energy used to charge up the gate electrode lost each time each transistor switches. With literally billions of transistors turning on and off billions of times each second, this adds up to a lot of energy.

In conventional semiconductor transistors, a gate voltage shifts the semiconductor’s ‘bandgap’ (or the range of energies within which electrons are forbidden) to allow (the ‘on’ state) or block (the ‘off’ state) incoming electrons.

In an ideal transistor, 1 volt applied to the gate would move up the range of energies blocked by 1 electron-volt. But leakage ‘tyranny’ puts a lower limit on that switching energy.

With electrons' energies inherently ‘smeared out’, there are always a few electrons with sufficiently-high energy to make it over the barrier. This ‘leakage’ current represents wasted energy.

To avoid wasted leakage current requires a minimum gate voltage that puts a lower limit on switching energy.

Named ‘Boltzmann’s tyranny’, after the scientist who first described the ‘smearing’ of the energies of particles by temperature, this limits how small the operating gate voltage can be for a transistor, no matter what material it is made of.

However, FLEET researchers wondered whether Boltzmann’s tyranny could be overcome in a new type of transistor using topological insulators, switched via an electric field rather than gate voltage.

Two-dimensional topological insulators can function as the ‘on’ state of a new type of transistor, with current carried by the conducting edges.

The conducting state of a such a material can be changed by an electric field, switching the material from dissipationless conduction (a topological insulator with a negative bandgap) to non-conduction (effectively, functioning as a regular semiconductor, with a positive bandgap blocking electron flow).

Crucially, the team found that, unlike a regular semiconductor, the increase in the bandgap in the topological insulator could be larger than the voltage applied to the gate, beating Boltzmann’s tyranny.

The next steps will be to confirm these findings in the laboratory, using candidate materials such as bismuthene, with FLEET working to synthesise these new materials, characterise them, and incorporate them into electronic devices.

Back to Research theme 1: Topological materials