Single-molecule transistors: logical successors to silicon?
The first transistor, made more than 60 years ago at Bell Labs, was a couple of inches across. Today, a typical laptop computer uses a processor chip that contains well over a billion transistors, each one with electrodes separated by less than 50 nm of silicon. This continual drive for miniaturization, with the density of transistors doubling roughly every two years, was first noted by Intel co-founder Gordon Moore in 1965, and has been such a mainstay of electronics development that it is now enshrined as “Moore’s law”. These billions of transistors are made by “top down” methods that involve depositing thin layers of materials, patterning nanoscale stencils and effectively carving away the unwanted bits. The end result is billions of individual components on a single chip.
Miniaturization cannot go on forever. We are beginning to run into the problem that the silicon, copper wiring and oxide insulating layers in these devices are all made out of atoms, each about 0.3 nm across. Moreover, when we try to think about how electrons act in small numbers of atoms, we know that we have to worry about orbitals and chemical bonds – quantum mechanics rules at these scales.
In 1974 Ari Aviram and Mark Ratner from the IBM Thomas J Watson Research Center in New York saw the writing on the wall. Rather than giving up on electronics at the molecular scale, they suggested turning lemons into lemonade: using molecules themselves as electronic components. In particular, they suggested making a simple electronic device, a rectifier, by designing a molecule with one end that likes to give up an electron and another end that likes to accept an electron. If individual molecules were able to replace bulk electrical components, then manufacturing and miniaturization might continue all the way down to the atomic scale. After all, chemists can produce enormous numbers (1023) of exactly identical nanometer-scale molecules at a time in a beaker. If each one could take the place of a transistor, that would be enough components for 50 trillion processors.
However, early optimism about single-molecule devices as replacements for semiconductor nanoelectronics has been tempered by an appreciation of the enormous challenges that need to be overcome. For example, having 1023 components is not useful if they all have to be positioned with atomic precision to work correctly. We also need to have a good understanding of how such devices would behave. Remember, the enormous success of silicon electronics has been built on decades of physics, chemistry, materials science and electrical-engineering knowledge. Finally, because individual molecules are so small, it can be incredibly challenging to “see” what is going on in single-molecule devices.
Recent experimental successes, however, have led to a growing appreciation that single-molecule electronic devices can teach us an enormous amount about the physics and physical chemistry that will be relevant in electronics on the single-nanometer scale. As the portfolio of experimental techniques grows beyond simple DC electronic measurements of current as a function of voltage, we are getting a much better sense of the physics relevant at these tiny scales, such as the microscopic origins of dissipation and the importance of electron–electron interactions at the nanoscale.
Moving charge through a molecule
Before we try to do anything too exotic, it is important to understand the basic physics of electronic conduction through molecules. The vast majority of single-molecule electronic measurements so far have focused on precisely this – making sure that we can make single-molecule devices and understanding how electrons move through them. Measuring simple electronic conduction is relatively straightforward: apply a voltage across some device of interest and measure the flow of current at some temperature. The form of the current as a function of these two parameters (temperature and voltage) can reveal much about the physics at work.
The tricky bit is that small molecules exist on the single-nanometer scale, and electron motion at these distances is very different to that in macroscopic wires. The quantum nature of the electrons needs to be taken into account. Think about an electron approaching a barrier. Classically, an electron with too little energy to overcome the barrier would be reflected 100% of the time. Quantum mechanically, however, the electron can “tunnel” through the barrier with a probability that depends exponentially on the barrier height and geometry. A related way to think about this is that quantum-mechanical uncertainty allows “virtual” states that violate classical energy conservation as long as the violation is sufficiently brief. Tunnelling and virtual states are part and parcel of charge motion on the molecular scale.
To understand the electronic states involved in conduction, consider two metal electrodes separated by an individual molecule. In isolation, the molecule has a discrete spectrum of states called molecular orbitals. Because the electrons on the molecule are jammed into such a small region, confinement and the electron–electron repulsion cause these states to differ in energy by quite a bit. For example, the differences in the molecular energy levels in dye molecules correspond to the energy of photons of visible light.
On the other hand, in the metal electrodes, we can usually think of the electrons as wavelike, and because the electrodes are comparatively big, there are many wavelike states, with very minor energy differences between them, so their states look continuous. The Pauli principle means that we can think of each state as only holding two electrons, each with opposite spin. The energy of the highest occupied state is called the chemical potential. As the temperature is increased, electrons can be kicked into higher energy states by thermal fluctuations.
Attaching the molecule to one or both of the metal electrodes changes the situation. Just as atomic orbitals can be coupled to form molecular orbitals, the molecular states couple to the wavelike states in the metal, thus smearing out the molecular energy electrons will rearrange themselves to occupy the lowest available states of the whole system, even if that means transferring charge between the molecule and the metal. Alignment between molecular and metal levels, which critically affects tunnelling and therefore conduction, turns out to depend in detail on the metals, the molecule and the precise molecule–metal binding.
Now consider applying a voltage between the source and drain electrodes. What happens? The system is driven out of equilibrium, with the source and drain having different chemical potentials, and electrons can start flowing across the device. How they do this depends on where the molecular levels sit.
If the voltage aligns a molecular level with the chemical potential of one electrode and there are empty states available on the other side, electrons can move from source to drain by resonant tunnelling. Under the best of circumstances, this conduction process via a single resonant state results in a conductance of 2e2/h, where e is the charge on the electron and h is Planck’s constant. Known as the quantum of conductance, it is about 13 kΩ when translated into a resistance. Such perfect transmission is commonly observed when electrodes are connected by a chain of metal atoms. Molecular conductances are typically orders of magnitude lower, although recent observations by Jan van Ruitenbeek and co-workers at Leiden University in the Netherlands show that high conductances are possible with certain simple molecules such as H2.
Even without a molecular level available for the direct flow of electrons, some current can still flow, thanks to quantum tunnelling through virtual states. From the point of view of an electron at the highest occupied state in one of the electrodes, the situation looks like tunnelling through an effective barrier that is set by the energies of the molecular orbitals. Finally, the spin of the electron also has profound effects on electrical conduction. Suppose that there is an unpaired electron localized on the molecule. An electron of opposite spin could pair up with the localized electron, but electron–electron repulsion forbids this classically. Still, such a paired state can be a virtual state in a higher-order magnetic dance that flips the localized spin and transfers an electron across the device. This is called the Kondo effect and it can lead to the perfect transmission of electrons in devices even without level alignment.
All sorts of subtleties crop up once the system is driven out of equilibrium. The electrons that do make it through the device are “hot” – out of thermal equilibrium with the electrodes. Such electrons can also dump energy into other degrees of freedom, like molecular vibrations or molecular bonds. These inelastic processes have been of huge interest to physicists in recent years. Identifying particular molecular vibrations through their effect on the conductance can confirm that current really is flowing through the molecule of interest. Furthermore, how energy flows through the electrons and vibrational modes is related both to fundamental questions of irreversibility and to practical concerns about power dissipation in nanodevices.
Measuring single-molecule electrical properties requires getting a single molecule between two electrodes. This can be a real challenge because everything tends to move on the atomic scale (particularly near room temperature), including the molecules and the atomic surfaces of the electrodes. One common approach is the mechanical breakjunction technique. Two pieces of metal (either a metal tip and a flat surface, or two ends of a broken metal wire) are brought in and out of contact, with molecules (on the surfaces or in surrounding solution) occasionally getting between the electrodes.
By measuring the conductance throughout the breaking process, histograms of conductance can be compiled. If certain junction configurations are favored by chemistry and atomic bonding, and therefore show up often in the experiment, there will be peaks in the histograms at particular values of conductance. Break junctions were originally developed by van Ruitenbeek and collaborators in the early 1990s to examine atomic-scale metal junctions, and were first applied to study molecules by Mark Reed of Yale University and collaborators in 1997. Recent work, particularly that of N J Tao’s group at Arizona State University, Latha Venkataraman’s group at Columbia University and Christian Schönenberger’s group at Basel University, has shown that peaks at low conductances can be identified with off-resonant conduction through individual molecules. Another form of measurement comes from building the single-molecule analogy to transistors. A gate electrode is employed to shift the molecular levels relative to the source and drain. This is difficult in break junctions, but it is possible if a molecular junction can be made flat on a chip.
The most common method of doing this, which was originally developed by Hongkun Park and Paul McEuen in the late 1990s at the University of California, Berkeley (UCB), starts with a pre-formed metal strip and uses a high-density current to push metal atoms around until the strip breaks into electrodes separated by a nanoscale gap. This is called electromigration and it can be used to make source and drain electrodes that are separated at the single-nanometer scale. As the probability of an electron tunnelling across the gap depends so strongly on distance, the conductance of such a junction is dominated by a volume comparable to that of a single molecule, centered on the point where the electrodes are closest. If the metal is initially coated in a layer of molecules of interest, a molecule may end up within this critical volume after electromigration. Empirically, this seems to work about 10–30% of the time, depending on the details of the process and the molecules.
A gate electrode lying under the junction has some coupling to the tunnelling region, and under ideal circumstances can shift the molecular levels enough to allow changes in the molecular charge state (oxidation and reduction, in the chemist’s lingo). Huge challenges in these experiments include the lack of direct microscopy to confirm the presence of a particular molecule in the junction, and the microscopic variation in configuration from device to device. Great care and many control experiments are needed to draw useful conclusions from such singlemolecule transistors (SMTs). Recently Dan Ralph’s group at Cornell University has been able to create a gated mechanical break junction, combining the electronic tunability of an SMT with the geometric engineering possible in mechanical junctions. The main advantages of SMTs are their geometric stability, allowing temperature- and magnetic- field dependent measurements with comparative ease, and the ability to change molecular charge states.
SMT transport experiments have demonstrated vibrational effects, and have been used extensively to examine Kondo physics in a variety of molecules with both normal and ferromagnetic electrodes. Beyond current and voltage Current as a function of voltage can only tell us so much about what is taking place in a single-molecule junction. Recently there has been a great deal of interest in moving beyond “simple” conductance, to tease more information from these nanoscale systems. For example, rather than just measuring the current, you can measure noise – the fluctuations in the current. Noise in equilibrium is determined by the thermal fluctuations of the electrons and provides a means of assessing temperature. When charge is pushed through the molecule, additional “shot noise” results from the fact that charge is not continuous but comes in “lumps” of individual electrons. The noise can reveal if interactions lead to the electrons moving in a correlated way. Such measurements have been reported by van Ruitenbeek’s group in individual D2 molecules using a break junction, and predictions exist for pronounced noise signatures of electron– vibrational coupling in molecular junctions.
Similarly, instead of applying a voltage across a molecule, the UCB groups led by Rachel Segalman and Arunava Majumdar have forced the two electrodes to have differing temperatures and monitored the voltage that appears across the molecule. These are pioneering measurements of thermopower, which can provide information about the alignment of the molecule and electrode energy levels. There is great interest in understanding dissipation and heating in single-molecule junctions, and some way of determining the effective local temperature of the molecule would be a good start.
One approach taken by Tao’s group is to look at either the mechanical force required to break a single- molecule junction or the distance such a junction may be stretched, as a function of voltage (and therefore current). While the interpretation can be subtle, comparisons between data at various voltages and data at different equilibrium temperatures allow you to infer an effective junction temperature. Finally, optical measurements of single-molecule junctions may provide another route to similar information. We recently demonstrated that the electrodes in electromigrated junctions are extremely effective optical antennas. The electrodes capture incident light and effectively focus it down to the molecular junction, and similarly allow the molecule to radiate efficiently. This is perfect for doing Raman spectroscopy on individual molecules.
The ultimate limit
Despite some birth pangs, the field of single-molecule electronic devices is alive and well. New efforts are being made to incorporate electronic correlations, spin effects and excited states into theoretical treatments. At the same time, combining conduction with other, complementary, techniques is giving us more tools to examine these tiny structures. Single-molecule electronic devices are unlikely to replace semiconductor technologies soon. However, single-molecule devices are outstanding tools for examining basic physics issues relevant to any sufficiently nanosized electronic device. It is critical that we develop an understanding of the flow of energy, the mechanisms of dissipation and the engineering of surfaces at the molecular scale. Single-molecule devices are a fascinating laboratory system with which to explore these issues. While silicon is likely to continue dominating nanoelectronics technologies for a long time, these molecular experiments are shedding light on the limits of electronic devices.
