Motivation. My postdoctoral work focused on ratchets – far-from-equilibrium devices that transport particles using local asymmetries, rather than overall biases. Ratchets are rectifiers – they extract directional motion from non-directed sources of energy, like chemical energy and Brownian motion. Biological motors in the body use ratchet mechanisms, and produce motion very efficiently, even in the highly-damped biological conditions, where the thermal noise is actually orders of magnitude stronger than the chemical energy available. We want to understand how the ratcheting applies to electrons, especially under highly-damped conditions, like in low-mobility organic semiconductors. Very little experimental work has been done on electron ratchets, and so we mainly seek to improve our understanding of the mechanism, with an eye toward possible future applications in solar cells or other electronic devices.

This work was part of an Energy Frontiers Research Center (EFRC) of the Department of Energy, called the Center for Bio-inspired Energy Science.

Ratchet principles. Three conditions are needed to achieve transport: (i) breaking the spatial inversion symmetry, for instance by applying an electric field with periodic asymmetric repeat units (e.g., a sawtooth potential); (ii) breaking temporal symmetry, typically assured by energy dissipation; and (iii) energy input to keep the system away from equilibrium (otherwise rectification would be prohibited by the 2^nd law of thermodynamics). In a flashing ratchet, we combine conditions i and iii by oscillating (flashing) a periodic sawtooth-shaped potential, so that both spatial asymmetry and energy are applied together. All of our work is in damped systems, so condition ii is satisfied by the dissipative energy loss. As an aside, some researchers have constructed non-dissipative ratchets (sometimes called Hamiltonian ratchets) using optical traps and cold atom clusters, so they must use asymmetric temporal drives to achieve transport. We have recently published an introduction to ratchets, accessible to a wide scientific audience, and I highly recommend perusing that work for a detailed explanation of ratcheting, and some thoughts my colleagues and I have on the field (Lau, Kedem et al., Mater. Horiz. 2017).

A new design. My main work was designing, fabricating and characterizing an experimental flashing electron ratchet. The device is similar to field effect transistors, in a co-planar, bottom-gate geometry. An array of “finger electrodes” (FEs) with an asymmetric thickness profile applied an electric field to an organic semiconductor transport layer above, inducing a current between source and drain electrodes made of the same metal. As a ratchet, the device produces a short-circuit current – current flows between the source and drain electrodes with no applied source-drain bias, or work-function difference between them. The current is produced due to the local asymmetries in the applied field, but without an overall asymmetry (bias). The current is very sensitive to the oscillation frequency, as ratcheting is a dynamic steady-state.

We have previously found in a theoretical study that the shape of the potential critically impacts the direction and magnitude of the ratchet current (see “Potential shape” below), and so developed an experimental design that enables the application of a wide range of potential shapes, and allows us to examine general behaviors. The photoactive transport layer (P3HT:PCBM) enables the modulation of charge carrier density using light, and revealed that sometimes, increasing the carrier density can actually reduce the ratchet current, matching previous theoretical predictions. For the first time in a flashing ratchet device, the ratchet is powered by an unbiased temporal drive, a sine wave, rather than an on/off or sin^2 drive. This will enable the future use of energy sources such as electromagnetic radiation to power a ratchet. We explore the symmetry-breaking mechanism responsible in other studies (see “Temporal drive” and “Ratcheting beyond 1D” below). We detail the design, fabrication, and characterization of the new ratchet device in a 2017 PNAS paper (Kedem et al., PNAS 2017).

Temporal drive. We initially drove our ratchet using a simple sine wave; work in the literature used basic on/off drives. But, surely the temporal drive can be optimized? There has been very little work in the literature, so we set out to explore the topic. We replaced the sine wave with a square wave, and modified the duty ratio (the fraction of time spent in the positive state). We find a rather complicated relationship, but the behavior can be approximated very well with a previously published analytical model. With it, we explain the symmetry-breaking mechanism that enables the use of unbiased drives (sine, 0.5 duty ratio square), and explain how to optimize the current (Kedem et al., Nano Lett. 2017).

Ratcheting beyond 1D. Almost all ratchet theory papers use 1D models. However, experimental ratchets typically have a 3D transport layer, which, due to symmetry, can be treated as 2D. Usually the electric field is applied by electrodes under the transport layer, meaning the field is asymmetric in the z-direction (thickness) – it is a 2D potential, rather than 1D. In this work we classically simulated charged nanoparticles in water, transported by time-oscillating ratchet potentials. We found that the non-uniformity in the z-direction means the thickness of the transport layer is extremely important for effective transport. In agreement with the experimental studies on electron ratchets, we found that the decay in the z-direction allows us to use sine wave temporal drive, something which is not possible in 1D models (Kedem et al., ACS Nano 2017). In this new symmetry-breaking mechanism in ratchets, spatial asymmetry is used in place of temporal asymmetry.

Interparticle interaction. When ratcheting multiple particles, those particles can interact with one another, for example by Coulombic repulsion for charged particles of the same-sign charge. As the concentration of particles grows, so does the impact of interparticle interactions on the properties of the transport process. In this classical simulation study we set out to explore how repulsive interparticle interactions modify the observed transport, both the overall performance, and the microscopic details of the process. We found that with increasing particle concentration, higher driving frequencies can be used, which produce faster transport. At low driving frequencies, high particle densities enable a new transport mode, resulting from the weak trapping of particles in wells (Kedem and Weiss, J. Phys. Chem. C 2019).

Potential shape. Typically, both theory and experiments in the ratchet field use a simple sawtooth shape, either a piecewise linear (sharp sawtooth), or a biharmonic (sum of two sine waves) with a specific set of pre-factors. But how sensitive is the performance to the shape itself? What if instead of one asymmetric shape, we choose another, slightly different one? My colleague, Bryan Lau, led a study to answer this question, using quantum-mechanical simulations of an electron ratchet. We varied the shape of the potential, as well as the damping strength in the system. We identified two different ratcheting mechanisms, at low and high damping regimes, and found that the ratchet current is extremely sensitive to the shape of the potential – a small change of the shape can result in a nullification or even a reversal of the current. Current reversals are the most puzzling property of ratchet, and in this work we provided an intuitive explanation for one class of reversals (Lau et al., Phys. Rev. E 2016).

A below-bandgap photovoltaic. Regular solar-cells rely on exciting electrons across a bandgap. Any energy beyond the band-gap is lost, and photons with energy below the bandgap cannot be used. My colleague, Bryan Lau, led a study exploring a new type of photovoltaic device, which can use below-bandgap photons (far-IR, THz range) to produce a current. The work used semi-classical simulations of a slab of Si with an asymmetric strain gradient. The strain splits and shifts conduction band energy levels, and a periodic asymmetric strain gradient will result in a like potential. The simulated device can harness below-bandgap, unpolarized, incoherent light to produce a current. Though the calculated efficiency was low, this proof-of-principle is very promising, and future simulation and experimental work will improve the performance (Lau et al., Adv. Energy Mater. 2017).