SPM break junction is probably the most widely used method for studying electron transport in single-molecule junctions. It usually utilizes scanning tunneling microscope or atomic force microscope facilities (Figure 2(a)). In the experiments, a macroscopic hydrogen-flame-annealed metal tip is indented into a metal-coated substrate electrode onto which a self-assembled monolayer is prepared and subsequently withdrawn (Figure 2(b)) [14,21]. The tip motion is often feedback controlled via voltage applied to the piezo-actuator for better reproducibility of the data [22]. The junction stretching speed during conductance trace measurements is defined by the sweep rate of the piezo-voltage, and is typically several tens of nanometer per second. The conductance trace measurements in most of the SPM break junction experiments were implemented in a liquid environment by placing the tip and the substrate in a Teflon cell filled with solvent.

The SPM approach has contributed considerably to advancing our understanding of electron transport in single molecules. Measurements on alkanedithiols have revealed an exponential decrease in the single-molecule conductance with the number of methylenes in the backbone that manifested tunneling electron transport through the saturated molecules [14,23–27]. Exponential decay of the conductance with the molecular length has also been reported for various π-conjugated molecules, e.g., oligophenylenes [28], oligopeptides [29], caltenoid polyenes [30], oligothiophenes [31], and oligo(phenylene ethinylene) [32], and these molecules showed smaller tunneling decay constant owing to the role of delocalized HOMO and LUMO. A tunneling to hopping transition of charge conduction through a molecular wire was also confirmed by extending the measurements to long length molecules [32–34]. While these results reported smaller conductance for longer molecules, peculiar length dependence has been observed for short oligothiophenes, where terthiophenes exhibited lower single-molecule conductance than tetrathiophenes [35]. This was attributed to a smaller charge injection barrier for tetrathiophenes having HOMO levels closer to the Au electrode Fermi level. The role of molecular orbital levels on single-molecule tunneling conductance has been demonstrated by beautiful experiments by Venkataraman et al. [36]. They used many types of substituent molecules that donate or withdraw electrons to raise (lower) or lower (raise) the HOMO (LUMO) of benzenediamines, and find that the single molecule conductance increases with donor-like substituents, thereby suggested dominant role of HOMO on the conductance [36].

Besides the Fermi alignment issue, a suitable anchoring group for developing highly conductive and stable molecular junctions has been pursued, which is important from viewpoint of electronics device applications. Thiol (SH) has been the most frequently employed anchor group because one can exploit the strong Au-S bonds to form a stable metal-molecule-metal structure when using Au electrodes. However, the wide variation in the Au-S contact motif, whether it binds to top, bridge, or hollow sites of Au surface, gives rise to a broad distribution of the single-molecule conductance not suitable for device applications [37–39]. Furthermore, thiol was theoretically predicted to not be an optimal choice from the viewpoint of contact transparency [37], which was later corroborated by a photoelectron spectroscopy study on a monolayer [40–42]. Thus, to find metal-molecule links with superior stability and electronic coupling than Au-S linkages, many kinds of anchoring groups have been tested including pyridine [14]], amine [26,43,44], carboxylic acid [23], isocyanide [45,46], phosphine [24], selenol [47,48], and even C₆₀ [49] using archetypical molecule wires such as alkanes and phenylenes. Amine (NH₂) is found to provide more well-defined metal-molecule contact geometries because it can only be bonded to atop sites via its lone pair [26,43,44]. This idea was also applied to thiols; the single-molecule conductance distribution became narrowed by replacing thiols with methyl thiols [24], which was ascribed to the selective metal-molecule contact configurations for bonding between the sulfur lone pair of methyl thiols and the undercoordinated atop Au atoms on the electrode surface. Although incorporation of methyls to saturate the anchor units is proven to be effective approach for restricting the contact configuration variations, it also resulted in weaker metal-molecule bonds, which should be avoided for the sake of building robust single-molecule devices [50–52]. Recently, amazing results were reported by Cheng et al. [53]. They used Au break junctions and measured single-molecule conductance of alkanes with both ends terminated with trimethyl tin groups. It was found that the trimethyltin units tend to dissociate on the Au surface and at the same time the alkane chain creates covalent Au-C sigma bonds at both the ends. This new type of metal-molecule bonding design offered single alkanes with 100 times higher conductance compared to the other conventional anchors together with a narrow conductance distribution and excellent bond strength of 3.0 eV [53].

The careful and systematic SPM break junction experiments have led to the advance in understanding and control of electron transport in single molecules and provided a useful guideline for constructing robust and highly conductive molecular junctions. Beyond this, there is growing interest in using SPM to construct and realize single-molecule device concepts such as single molecule diodes and transistors. However, thermal drift poses a critical difficulty in holding molecular bridges for more than 10 s at room temperatures, and such research is often possible only under cryogenic vacuum conditions. In this sense, EBJ and MCBJ techniques have advantages in that they possess superior mechanical stability as described below.

MCBJ consists of a free-standing metal wire fixed on a flexible beam (Figure 3) [11]. Usually, phosphor bronze plate coated with thick polyimide layer is used for the substrate. As the name implies, the principle of MCBJ is essentially the same as that of SPM break junction approach; mechanical manipulation of distance between the two facing electrodes to form a metal/molecule/metal system. The difference lies in the way we move the electrodes; whereas SPM directly moves the tip with piezo-actuator displacements, MCBJ makes use of substrate deflection caused by piezo-driven pushing rod motion to indirectly displace the positions of two free-standing electrodes on the substrate (Figure 3) [11]. The ingenious structure of MCBJ enables fine tuning of the inter-electrode distance. The pushing rod displacement is translated into the electrode displacement with the attenuation factor r [11,54]. Micro-fabricating the metal nanobridge, r can be made smaller than 10⁻⁴, which allows control of the electrode displacement at sub-picometer resolution by nanometer-level manipulation of the pushing rod displacements with a piezo-element [11,55,56]. At the same time, mechanical loop of micro-fabricated MCBJs, defined by the length of the nanobridge, is reduced to several micrometers. This amazingly short mechanical loop gives outstanding mechanical stability necessary for forming and holding single-molecule junctions for prolong time at room temperatures [11].

In addition to their applications for studying single-molecule electron transport, the unique capability of micro-fabricated MCBJs of adjusting the electrode gap distance at sub-picometer precision has been utilized for studying the stability and current carrying capacity of individual organic molecular wire at room temperatures [57,58]. In these works, single-molecule junctions were repeatedly formed and broken by the break junction method with a slow junction elongation speed down to 0.6 pm/s.

Special care was taken to avoid possible effects of Au nanocontact thinning processes on the molecular junction stability and meanwhile to optimize the production efficiency [59,60]. For this purpose, the Au junction stretching speed was multistep feedback controlled in the pre-breakdown stage [59,60]. This automated metal/molecule/metal structure fabrication method was recently exploited in an interesting break junction experiments using a STM system customarily designed to suppress mechanical drift [61]. Because the molecular junction breakdown is a thermally activated stochastic event, the holding duration, or the lifetime, of single-molecule bridges is described in Arrhenius form as: (1) τ = ( 1 / f ) exp [ ( E B − α F − β V b ) / k B T eff ]where f, E_B, αF, βV_b, k_B, and T_effare the attempt frequency, the barrier energy for junction breakdown, the mechanical tensile forces [62,63], the current-induced forces [64–66], Boltzmann factor, and the contact temperature including the local electrical heating effects [67–70]. In the experiments, τ could be deduced from the duration of sustaining the single-molecule conductance state during junction breaking [57]. The breakdown mechanism was found to be classified into three different regimes with respect to the displacement speed [59]. At high strain rates, the tensile force exerted on both sides of the contact during elastic deformation dominates, and it tends to dissociate under a certain amount of force, as has also been observed in SPM break junction measurements [68,71]. When the elongation speed is lowered, effects of thermal fluctuations become non-negligible, and the force necessary to break the junction decreases logarithmically to zero with decreasing stretching rates [59]. The natural lifetime can be assessed either indirectly by extrapolating the stretching rate dependence of the junction lifetime to zero breakdown force or directly under a slow-enough elongation rates whereas contribution of thermal fluctuations becomes predominant and junction breaks spontaneously [58]. For Au single-atom contacts, the breakdown force approaches zero at the stretching rate below 6 pm/s. The room temperature average contact lifetime at this low strain rate regime took a constant value of about 10 s, suggesting self-breaking of a Au-Au link with a bonding energy of 0.8 eV under negligible influence of the mechanical forces [59]. Benzenedithiol single-molecule junctions were found to be much more stable, as expected from the strong Au-S binding energy of 1.6 eV, with the natural lifetime of 50,000 s [58]. However, this junction lifetime was also too short for Au-S bonds to dissociate thermally at room temperatures, suggesting contact breakdown at the Au-Au bonds in the bank. In contrast, benzenediamines can be hold for 0.2 s on average, shorter lived than Au single atom contacts [51]. This clearly indicates that the diamine molecules rupture at the NH₂-Au links with bond energy of 0.7 eV. These findings not only shed light on the formation and breakdown mechanisms of molecular junctions, but also prove the potential of micro-fabricated MCBJs for quantitatively evaluating the single-molecule device stability [51].

The self-breaking method to rupture molecular bridges without external mechanical forces also offers a platform useful for studying heat dissipation [67–69,72]. Under the high-field, electron-phonon interactions induce considerable local heating in molecular conductors [68,69,72]. Understanding and controlling the electrical heating mechanism is an important issue as it strictly limits the current carrying capacity of single-molecule devices. The rise in the effective temperature T_eff of single-molecule junctions can be estimated by examining the lifetime decay with the applied voltage using Equation (1). In SPM break junctions, substantial influence of external forces on the junction lifetime is inevitable as thermal drift becomes problematic under slow stretching rate conditions [73]. This complicates the T_eff deduction from the analyses of the junction holding time. In contrast, the zero-force conditions attained in the self-breaking approach simplifies the description of the molecular bridge lifetime as τ = (1/f)exp[E_B/k_BT_eff]. The voltage dependence of T_eff deduced in this way for Au/single-benzenedithiol/Au junctions [58] revealed effective temperature increases of up to 170 K from the ambient temperature at V_b = 1 V with T_eff ∼ (V_b)^1/2 as derived theoretically [68]. On the other hand, the local temperature of Au single atom contacts measured under the same conditions showed a negligible increase in T_eff demonstrating marginal influence of local heating, which was attributed to the effective lattice cooling by heat conduction to the bulk [66,74]. This manifested a large thermal resistance at the Au-benzenedithiol contacts due to the phonon mismatch between the high energy optical vibration modes of benzenedithiols and the low energy acoustic phonons of the Au electrodes that impedes heat dissipation from the junction to the electrodes [68]. As it is difficult to dissipate the local heat generated in the junctions vertically through the substrate, which is the strategy applicable for graphene [75] and carbon nanotube devices [76], development of phonon-transparent electrode-molecule contacts is perhaps essential for achieving high current carrying capacity of single-molecule bridges.

Pioneering studies on three-terminal single-molecule devices utilized electromigration to form two electrodes separated by a nanometer gap for constructing molecular bridges [3–5,77]. This fascinating idea can be imagined as an electrical version of a mechanical break junction approach replacing the mechanical forces with electron wind forces (Figure 4). When a voltage ramp is applied to a lithographically defined metal nanowire, it ruptures at the nano-constriction under the huge current density that induces Joule-heat-activated electromigration of the contact atoms [78,79]. Usually, a self-assembled monolayer is prepared on the metal wire. The molecules are thermally diffused on the surface during the electrical breaking and a few of them become trapped in the electrode gap by chance, whereby a metal/molecule/metal structure is formed. There are several technical advantages in the electromigration break junction approach. Most importantly, the planar device architecture is compatible with silicon technology and amenable for integrating additional functionality such as electronic gating using a three-terminal device configuration. The electrode gap defined by the solid-state nanoelectrodes on the substrate is also highly mechanically stable. On the contrary, the gap distance is not controllable in the post-breaking stage unlike the case for mechanical break junctions that allow adjustment of the electrode positions to form a gap of arbitrary size. Therefore, the fabrication yield of molecular junctions is often very low. Moreover, metal nano-clusters are nucleated during electromigration processes, which are then trapped in the electrode gap and behave like molecules by creating parasitic electron conduction pathways and showing Coulomb blockade and Kondo effects that mimic electrical characteristics of single-molecule junctions [80–82].

Recently, improvements have been introduced to the original electromigrated gap formation method for achieving better reproducibility and yield [83–85]. Instead of using a single ramp to rapture a metal nano-junction, the bias voltage is feedback controlled by decrease in the conductance associated with the electromigration thinning (Figure 4(a,b)) [83]. This enables regulation of the self-accelerating nature of the electromigration failure processes and prevents the junction from undergoing overcurrent breakdown leading to considerably large electrode gaps. The active electrical breaking proceeds until the nano-constriction evolves into atomic size wire, after then the junction is left to break spontaneously by thermal fluctuations under a low voltage (Figure 4(c)). Electrode gaps fabricated in this way can be made as small as 1 to 2 nm (Figure 4(d)). Perhaps, the most important benefit of employing this self-breaking technique is the fact that the somewhat gentle way of contact breaking does not involve formation of metal nanoparticles [84,85].

It is important to understand the underlying physics of the electromigration junction breakdown. Electrical breaking of metallic nanocontacts occurs via the current-induced forces and the local heating. Which factor becomes critical depends on material. It is predicted theoretically that contact tends to break by local heating when the heat cannot be removedefficiently from the contact to the bulk leads by thermal conduction [86]. On the other hand, when the lattice cooling is effective, the contact breaks under high current density by the current-induced forces [58,74,86]. Systematic studies should be carried out to shed light on this intriguing subject. Although the electromigration-induced wire breaking approach lacks the controllability of the electrode gap distance, the planar solid-state electrode architecture is more attractive than the mechanical break junction methods from view point of large-scale integration of arrays of single-molecule devices, and may find future applications not only in molecular electronics but also as a biosensing platform in the emerging field of nanopore sequencing [87,88].

In fact, three-terminal single-molecule device concepts have long been explored using the electromigration break junction method. In these experiments, identification of the molecule species in the electrode gap is crucial for dealing with the nanoparticle nucleation issue. In this context, increasing effort has been devoted to incorporate spectroscopic techniques such as Raman spectroscopy and inelastic electron tunneling spectroscopy (IETS) in break junction experiments, which serve to ensure the presence of target molecules between the electrodes thereby improving the measurement data reliability as summarized below.

Mechanical break junction methods have proven to be a useful tool for determining the electrical conductance of molecular tunneling bridges at the single-molecule level by the fact that theoretical calculations of the electron transport in molecular junctions in the elastic tunneling regime can now quantitatively explain the break junction measurements [17]. Beyond the fundamental studies on single-molecule electron transport, active control of the electronic properties is pursued for molecular electronics devices [16,19]. Owing to the various techniques developed for fabricating metal/molecule/metal systems (e.g., mechanical and electromigration break junctions, cross-bar junctions, and nanopore junctions) experimentalists are now able to form stable molecular bridges and explore the functionalities by examining the dynamic response of the electrical characteristics to the external fields.

An essential ingredient for conducting reliable single-molecule device characteristics has been a technique that can identify molecular signatures of the molecule in the junction. In the early discussions of quantized conductance of metal quantum point contacts, high resolution transmission electron microscopy (TEM) has played an important role by elucidating the evolution of metallic single-atom chains by in situ observations of thermally-driven shrinkage of a nano-junction; and meanwhile simultaneous measurements of the conductance traces provided solid evidence of conductance quantization in the Au single-atom contacts [12,13]. Applications of the TEM approach to single-molecule junction characterizations will no doubt revolutionize the field of single-molecule electronics by providing valuable information in situ concerning molecular conformations and metal-molecule contact configurations at the atomic level. Unfortunately, however, organic molecules can be easily burned out by heat generated upon irradiating high-energy electron beam. Therefore, TEM observations of molecular junctions have not been realized (except for fullerenes possessing high temperature stability [89–91]).

A conductor capable of changing its impedance between two distinct levels controllably and repeatedly can be used as a switching device for storing information as we do so with flash memories. The nanometer size of single-molecule switches promises applications for memory devices by realizing unprecedented integration densities. For this, it is important to demonstrate high speed conductance switching with a long retention period and good endurance by single-molecule junctions under ambient conditions.

Binary switching of single-molecule conductance was first inferred in scanning tunneling microscopy studies of individual molecules adsorbed on a surface [126,127]. Isolated alkanedithiol molecules embedded in alkanethiol self-assembled monolayer on a Au (111) surface were imaged as bright spots. The single-molecule images revealed blinking of the bright dots in the consecutive images of the same area. This phenomenon was attributed to on-off of the conductance states of the alkanedithiols associated with breaking and formation of the Au-S links. The blinking frequency was found to increase at high temperatures, suggesting thermally activated bond breaking processes at the metal-molecule contacts [127]. In break junction experiments, the two-level stochastic switching has also been observed in various metal/molecule/metal junctions, which were attributed to thermal fluctuations of the electrode-molecule bonding sites and concomitant change in the electrode-molecule coupling strength [128–130]. These findings indicate that binary switches can be made by exploiting the geometrical dependence of the single-molecule conductance through developing a way to control the molecular conformations and metal-molecule contact configurations [131].

A diode is a two-terminal electronic component that facilitates current flow in one (forward) bias direction and suppresses under the opposite (reverse) direction. Molecular design for diodes is essentially similar to the p-n junction configuration and consists of donor and acceptor molecules connected via σbond (Figure 9(a)) [1]. For the donor (D) and the acceptor (A), electron donating and withdrawing substituents are often used to chemically engineer the frontier molecular orbital levels of π-conjugated units, while the σ link serves as an insulating barrier for electrically separating the two segments. Original device concept exploits the energetically facile acceptor-to-donor electron transfer in D-σ-A systems for current rectifications [1]. Nevertheless, asymmetric I-V characteristics can arise from many factors. In the early experiments on Langmuir-Blodgett films of C₆H₁₃Q-3CNQ, both positive and negative rectifications were observed [152–155]. The variation was explained by the electrostatic shifts of the molecular orbital levels that could cause rectification characteristics opposite to the Aviram-Ratner mechanism depending on the conditions for resonance between the electrode Fermi level and HOMO or LUMO [156,157]. Using mechanical break junction techniques, it was also found that difference in the electrode-molecule coupling at the both sides can give asymmetric I-V behavior even for essentially symmetric molecules [158,159]. These issues complicate the interpretation of the experimentally observed rectification characteristics of molecular junctions.

The first single-molecule diodes have been fabricated using a lithographically defined MCBJ [160]. The molecules had a donor-acceptor structure with one of the phenyl group being functionalized with four fluorine atoms. The electronic states of the two functional units were localized by reducing the overlap of their π-orbitals using the large torsion by steric hindrance of methylenes at the D-A link. Molecular junctions were formed using dithiol anchoring groups with Au MCBJ electrodes. Rectification behavior was observed with the current ratio of up to 10. The I-V asymmetry was due to the different heights of the conductance steps at the positive and negative biases that originated from crossing of the occupied and the unoccupied molecular orbital levels by virtue of their electrostatic shifts under the applied bias. Contributions of metal-molecule contacts were also found to be negligible by measuring D-D and A-A molecules as controls that gave symmetric IVs. Although density functional theory calculations nicely explained the electron transport characteristics, the random nature of the molecular orientations in the MCBJ approach led to junction-to-junction variation in the I-V curves and posed a difficulty to clarify the actual bias direction along the D-A molecule [160]. Recent SPM break junction experiments by Díez-Pérez et al. [161] incorporated two different protection groups to control the orientations of diode molecules. They formed a self-assembled monolayer of dipyrimidinyl-diphenyl molecules on a Au (111) substrate by deprotecting the thiol at the diphenyl sides. Removing the protecting group at the dipyrimidinyl side allowed formation of molecular junctions by approaching a Au tip to the substrate via S-Au bonds. This excellent procedure regulated the orientation of molecules to align vertically with the dipyrimidinyl unit heading upward, whereby enabling unambiguous definition of the bias direction. The single-molecule conductance was determined using the repeated break junction method, which was then used as a reference for fabricating single-molecule junctions, ahereas symmetric IVs were acquired for tetraphenyl molecules, the dipyrimidinyl-diphenyl molecules clearly demonstrated rectification characteristics with the average current ratio of 5.

The fact that the current was suppressed in the negative bias regime suggested an important role of asymmetric electrode-molecule coupling that yields lower threshold voltage in the positive bias regime for attaining resonance between the anode and the molecular HOMO (Figure 9(b)) [162]. It has now become technically available to form single-molecule diodes with well-defined molecular orientations. The low rectification ratio is the remaining issue, which requires improved design of D-σ-A architecture. One way may be to pursue the molecular level structure with small energy gap between the donor HOMO and the acceptor LUMO so as to utilize the delocalized resonance states under electrostatic crossing of these two levels.

Most of today's integrated circuit chips are based on metal-oxide-semiconductor field effect transistors (MOSFETs). As the gate length is already far below 100 nm and continues to become smaller, the solid-state silicon devices are starting to face fundamental physical limits, e.g., dopant fluctuations, short channel effects, and oxide-gate tunneling. Whether single-molecule junctions can find applications as FETs is of practical interest for further downscaling of transistors to sub-10 nm scale.

Theoretical verifications of back-gated single-molecule transistors have predicted that the conductance can be modulated by the gate-field induced electrostatic shifts of the molecular energy levels with respect to the electrode Fermi level [163,164]. However, screening by the charge rearrangements in the electrode is suggested to weaken the gate effect considerably for the nanometer scale gate length of molecular junctions [165]. A challenge to form single-molecule FETs has thus been to put a gate electrode at the vicinity of the molecule.

Development of single-molecule FETs has been vigorously explored in the past decades. Three-terminal molecular junctions were fabricated often by utilizing electromigration break junction method to form source and drain metallic electrodes with nanometer separation on a bottom gate electrode using a silicon micro-fabrication technology [3,77]. To minimize the gate-to-molecule distance and thereby overcoming the screening effects, Al was frequently employed for the gate electrode material wherein ultra-thin Al₂O₃ natural oxide layer served as the gate dielectric. Gate modulation of single-molecule conductance has been demonstrated for various types of π-conjugated molecules [3–5,166–169]. These experiments observed staircase-like structures in the I-V curves. The differential conductance plotted against the source-drain and gate voltage revealed diamond shaped profiles that manifests Coulomb blockade in a weakly coupled molecule to the leads. Although interesting phenomena such as single electron tunneling and Kondo effects have been found in this weak coupling regime, demonstration of the original concept of single-molecule FETs, i.e., continuous modulation of the single molecule conductance by electrostatic modification of the energy gap between the frontier levels and the electrode Fermi level, required fabrication of molecular junctions with stronger electrode-molecule coupling.

The role of electrode-molecule coupling strength on the gate modulation of single-molecule electron transport has been investigated by Danilov et al. [170]. In this ingenious work, electrode-molecule coupling was tailored by incorporating CH₂ units at both sides of the oligophenylene-vinylene that served as tunneling barrier for localizing the electronic states on the molecule and weaken the electronic coupling to Au leads. By forming three-terminal single-molecule junctions using the mask-defined nanogap device with an Al₂O₃/Al bottom-gate configuration, they found non-linear I-V curves with no conductance gap at low voltages for oligophenylene-vinylene molecules anchored directly to the Au electrodes via S-Au bonds, suggesting coherent tunneling of electrons through the molecule. For these molecules, the differential conductance changed little with the gate voltage. The absence of Coulomb blockade signatures indicated strong coupling at the electrode-molecule contacts that smeared out the single electron charging effects. On the other hand, the junction conductance decreased by orders of magnitude for the same molecules with CH₂ barriers inserted. Current flowing through the molecules could be modified appreciably by the gate voltage and revealed Coulomb diamond in the differential conductance diagram. These results directly showed the critical role of electrode-molecule coupling on the electron transport characteristics [168]. Unfortunately, however, large gate modulation of the conductance was not achieved, presumably because of the weak gate coupling by screening of the electrostatic field due to the proximity of the electrodes.

Recently, the first proof-of-principle demonstration of single-molecule FETs has been reported by Song et al. [171]. In this excellent experiment, benzenedithiol molecules were bridged between electrode nanogap formed using the electromigration break junction method, and a back gate device configuration with conventional Al₂O₃/Al electrode was used to investigate the electrostatic modulation of current flowing through the molecule (Figure 10(a)). Au/single-benezenedithiol/Au structure is one of the most widely studied π-conjugated molecules with electronic states delocalized over the entire junction [22,117]. The electron transport is coherent tunneling as suggested by the gap-less non-linear I-V characteristics with the G_SMC spanning vastly from 0.1 G₀ to 0.0001 G₀ depending on the molecular conformations and the metal-molecule motifs [117]. Although the yield was not so high, less than 10%, the devices with low-bias conductance of 0.01 G₀ that corresponds to typical single-molecule conductance of Au-benzenedithiol-Au junction [22] exhibited a large modulation of the I-V curves with the gate voltage. Transition voltage spectroscopy was performed to investigate the gate modulation of the energy gap between the electrode Fermi energy and the nearest molecular level [166–168]. In this method, voltage where a minimum in (lnI/V²) versus 1/V plots occurs is deduced. This transition voltage can be utilized as a qualitative measure of the charge injection barrier height that corresponds to the energy level whereat the broadened resonance level contributes to the conductance at a certain extent [172–175] (it should also be noted however that care is needed when assessing molecular orbital levels from the transition voltage unless the electrostatic potential profile along the current-carrying molecular junction is uncertain, as is the case in most of the experiments [174,176,177].).

The positive linear scaling of the transition voltage with the gate voltage was an indication of electron transport through the HOMO level [171]. The gate coupling strength, which was about 0.2 eV/V, could also be estimated from the slope. In addition to this, IETS analyses were applied to the molecular junctions. The vibrational spectra showed pronounced peaks at well-defined voltages corresponding to the IETS-active vibration modes of Au/benzenedithiol/Au systems. Furthermore, it was found that the peak height became significantly enhanced with increasing the gate voltage. These findings not only served to validate the presence of current-carrying benzenedithiol in the electrode gap but also inferred strong coupling between the HOMO and the molecular vibrational modes at near resonance [171,178]. Overall results supported gate modulation of the single-molecule conductance via the electrostatic tuning of the molecular orbital levels (Figure 10(b)). Although single-molecule FETs have proven to work as predicted theoretically, the low device yield is a critical issue. Technical barriers to be overcome include formation of well-defined metal-molecule contacts with strong coupling, controls of gate-to-molecule distance, and mitigating the electrode screening. Perhaps, these challenges can be overcome in part by exploiting graphene as source and drain electrodes [88,179]: the atomic-sheet geometry provides sub-nanometer gaps between the molecular bridges to the bottom gate and also reduces the screening effects.

Thermoelectric energy conversion efficiency is represented by the material's dimensionless figure of merit ZT = σS²T/κ, where σ is the electrical conductivity, S = −ΔV/ΔT is the thermopower (or Seebeck coefficient), and κ is the thermal conductivity. It has long been pursued to develop thermoelectric materials with ZT > 3. However, achieving enhancement of σ and decrease in κ at the same time is intrinsically difficult in bulk compounds because heat is carried not only by photons but also by charge carriers so that a rise in the electrical conductivity is counteracted by the concomitant increase in the electronic contribution of thermal conductivity as stated in the Wiedemann Franz law. This has been a critical barrier for attaining ZT > 1 despite the fact that (Bi,Sb)Te alloys were found to possessZT ∼ 1 already in 1950s [180].

Recently, an increasing amount of research is focusing on utilizing low-dimensional nanostructures for improving ZT of bulk materials [181,182]. Quantum well superlattices have proven to be a promising system that allows independent control of the thermal conductivity through the increased phonon scattering rates at the interfaces [181,183]. By this effect, unprecedented ZT > 2 has been reported for Be₂Te₃/Sb₂Te₃ [184]. Another potential strategy is to exploit charge confinements in a quantum dot, which makes use of a delta-function distribution of the density of states at the discrete energy levels to obtain high thermopower [185,186]. As single-molecule junctions share essentially the same feature, Lorentzian distribution of density of states at HOMO and LUMO levels defined by the molecule-electrode coupling strength, they may also be potentially important thermoelectric materials [187,188].

Advances in theoretical modeling of the conductance and the thermopower of a single-molecule junction offer a physical picture for how to improve the power factor σS² [72,189–192]. As thermoelectric generator operates under zero bias voltage, G in the expression of ZT corresponds to the electron transmission of a single-molecule junction at the Fermi level E_F, which can be described as: (2) G = ( 2 e 2 / h ) T ( E ) | E F

The transmission function is determined by the frontier molecular orbital levels (E_HOMO and E_LUMO) and the metal-molecule coupling at the left (Γ_left) and right side (Γ_right) of the junction that broadens the HOMO and LUMO energies. Analytical expression of T(E) is derived as: (3) T ( E ) = ∑ ( Γ left Γ right ) / [ ( E − E i ) + ( Γ left + Γ right ) 2 / 4 ]from single-particle scattering theory, where summation is over E_i = E_HOMO and E_LUMO [189]. This predicts that G takes a maximum at the resonance when the nearest molecular orbital level aligns with the electrode Fermi level that makes T(E) ∼ 1 for a symmetric junction with Γ_left ∼ Γ_right. Similar to the conductance, thermopower is determined by the line shape of the transmission curve at the Fermi level E_F. The simplified Landauer expression within a single-particle picture of Seebeck coefficient of single-molecule junctions under assumptions of low temperatures and a far-from-resonance condition is written as: (4) S = − ( π 2 k B 2 T 0 / 3 e T ( E ) ) ( ∂ T ( E ) / ∂ E ) | E Fwhere k_B and T₀ are the Boltzmann constant and the temperature of the junction, respectively [189]. It is anticipated from the Lorentzian-shaped transmission curves peaked at the HOMO and LUMO energy levels that ∂T(E)/∂E attains a maximum and changes its sign at near the resonance states. These theoretical aspects predict qualitatively that both G and S can be optimized by bringing the HOMO (Figure 11(b)) or the LUMO level (Figure 11(c)) close to the chemical potential [187].

Recent experiments have demonstrated that indeed thermopower of off-resonance single-molecule tunneling junctions behaves as expected from the theories [72]. The thermoelectric transport through a junction can be measured in a relatively simple way [193]. The method is based on the SPM break junction technique. Molecular bridges were formed by approaching a metal tip to a conductive substrate coated with a self-assembled monolayer of target molecules until the tip-substrate conductance reached a set value. To induce measurable thermoelectric voltage, a temperature gradient ΔT was applied by heating the substrate while keeping the tip at the ambient temperature. Subsequently, analogous to the single-molecule conductance measurements that monitor temporal change of the current flowing through the molecules under a constant bias voltage during junction stretching [14], thermopower was measured by recording the voltage ΔV required to cancel the thermal current between the tip and the substrate under the constant temperature gradient ΔT [193]. The thermoelectric voltage stayed at a constant voltage with relatively large fluctuations for a certain period and gradually decreased to zero as the electrodes were pulled apart, which manifested that ΔV is insensitive to the number of molecules bridging the electrodes. This is in sharp contrast to the electrical conductance of molecular junctions that increases with the number of current-carrying molecules. The thermopower could be deduced by exploring the linear dependence of ΔV on ΔT. Since the measured voltage includes thermoelectric power of Au electrodes, the junction thermopower was estimated through S = S_Au − ΔV/ΔT, where S_Au ∼ 1.94 μV/K is the Seebeck coefficient of bulk Au at 300 K [193].

One of the remarkable outcomes of the thermopower measurements is that whether a single-molecule junction is n type or p type can be judged from the sign of the thermoelectric voltage, as is usually done for bulk materials [189]. The theoretical expression of S indicates its dependence on the transmission curve line shape ∂T(E)/∂E. From this, vanishingly small thermopower is expected when E_F aligns at the center of the HOMO-LUMO gap. On the other hand, when E_F is shifted closer to the HOMO (LUMO) level, ∂T(E)/∂E takes a negative (positive) value and S is positive (negative); or conversely, positive S signifies that E_F is closer to HOMO, and vice versa [189]. Reddy et al. have found positive S for 1,4-benzenedithiols bridged between the Au electrodes, suggesting HOMO contributions to the electrical conductance [193]. This was in accordance with the results obtained by the gate modulation of molecular orbital levels. Furthermore, Widawsky et al. [194] positive and negative S for molecular junctions with Au-NH₂ and Au-pyridine contacts, respectively. They could simultaneously measure the single-molecule conductance of these molecules, and quantitatively explained the results by the density functional theory calculations [194].

Molecular length dependence of the thermopower has also been explored for better understanding of thermoelectric transport in single-molecule junctions [195]. It has been well-established that an increase in the molecule length L leads to an exponential decay of the tunneling conductance as G = G_Cexp(−β_GL), where G_C is the contact resistance and β_Gis the decay constant [14,23–27]. In contrast, the Seebeck coefficient of oligophenylenedithiols increased linearly with the number of phenyl rings [193,195]. Furthermore, oligophenylenediamines also showed similar S − L dependence but the intercept at L = 0 was low. From this observation, the length-dependent thermopower of the aromatic molecular junctions was described as S = S_C + β_SL, where S_C denotes the contact thermopower that can be optimized by the choice of anchoring group and β_S is a coefficient. The linear increase in S was explained by the shrinking of the HOMO-LUMO gap with increasing the length of the molecule that reduces energy gap between the Fermi level and the frontier molecular orbital levels [195]. This clearly shows that the thermopower of single-molecule junctions is insensitive to the contact coupling, as predicted by Paulsson and Datta [189].

Interestingly, the junction-to-junction variations of the thermoelectric voltage were found to become more expansive with increasing L [196]. Moreover, the distribution of S was unaffected by adding a steric hindrance to reduce twisting angle between the phenyl rings of the oligophenylenedithiols. As S is less affected by Γ in the far from resonance regime, the distributions of the measured thermoelectric voltage can be attributed to a variation in the HOMO-Fermi level alignment presumably stemming from the difference in the contact motifs, the molecular orientations with respect to Au electrodes, and the interactions with nearby molecules [196]. The variation in the thermovoltage cannot be explained by the simplified model of Equation (4) [72], and continues to be an important issue to be resolved in future studies.

Although the thermopower is enhanced by increasing the molecular length [193,195], it also leads to exponential decrease of the conductance [196]. As such, the overall effect cannot improve the power factor. Therefore, along with the increased fluctuations of G and S, using a long molecular wire may not be a good choice for developing high-ZT single-molecule devices.

Perhaps adjusting the Fermi level alignment in situ by gate modulation of the molecular orbital levels may be a suitable way to optimize the power factor. This approach has already demonstrated to be useful for improving the thermoelectric properties of Si nanowires [197]. An alternative strategy was also suggested by Baheti et al. [198]. They chemically tuned the HOMO level by dressing a molecule with donor or acceptor substituents. It was found that the Seebeck coefficient of p-type 1,4-benzenedithiols can be increased by adding electron donating methyl units, or decreased by decollating with electron withdrawing atoms such as F and Cl. These results can be interpreted by a shift of the HOMO level close to (away from) the Fermi level with the donor (accepter) groups. Though not yet verified, this method can in principle raise both G and S simultaneously as the conductance also increases with decreasing the HOMO-Fermi level energy gap for p-type molecules [198].

Much has been learned about thermoelectric transport in single-molecule junctions through the excellent experimental and theoretical studies. Recently, high thermopower has been reported for n-type single-fullerene molecules, and further improvements in the power factor can be expected with the chemical doping strategy [199]. For the prospect of high-ZT single-molecule thermoelectric devices, however, it is indispensable to evaluate and control the heat transport through single-molecule junctions and attain low κ [189]. Several studies have reported indirect estimations of the single-molecule thermal conductance [200,201]. Wang et al. [200] investigated the cross-plane thermal conductance of a self-assembled monolayer of alkanethiols by measuring the time required for a laser pulse heat to transfer through the molecules. The single-molecule thermal conductance of 50 pW/K was deduced from the obtained monolayer thermal conductance and the area density of the alkanethiols [200]. Another experiment examined heat dissipation in current-carrying benzenedithiol single-molecule junctions [201]. From the dissipated power and the estimated junction effective temperature, single-molecule junction thermal conductance was assessed to be 40 pW/K [201]. Although these experiments suggest that molecular junctions possess relatively low κ, heat transport in single-molecule bridges is largely unknown. Particularly, from a practical viewpoint, heat leakage by radiation and convection may become crucial issues considering the small size and the low thermal conductivity of single-molecule junctions. Future efforts should aim at direct measurements of thermal conductivity at the single-molecule level. This may be accomplished by developing nanostructures consisting of a heat source and a temperature sensor. One such system has already been fabricated for evaluating Joule heating in atomic-sized contacts [202].