Introduction

A temperature gradient in a material induces diffusion of majority charge carriers from the hot to the cold region and builds electric voltage there. This thermoelectric effect enables direct conversion of thermal energy into electricity or vice versa without need of mechanical components; an ideal route for power generation being a silent and greenhouse gas emission-free technology. A fundamental issue in thermoelectric generators has been the low efficiency of the constituent materials, which are required to possess conflicting properties of low thermal conductivity and electrical resistivity in addition to high thermopower1,2. This so-called phonon-glass electron-crystal concept has led to significant improvements of the thermoelectric figure of merit in bulk materials though yet to reach an acceptable level for the practical applications1,2,3,4.

An emerging approach for high-performance thermoelectric materials is to exploit quantum effects in low-dimensional nanostructures that provides high electronic density of states for enhanced Seebeck coefficients5,6. Thermoelectric transport in atomic and molecular junctions, confined systems with discrete states, has recently been studied intensively in this respect7,8,9,10,11,12,13. Significant enhancement of thermopower was reported in Bi quantum point contacts attaining several mV/K10. Positive and negative thermovoltage was also found in metal-molecule-metal bridges in where current was carried through the highest occupied and lowest unoccupied molecular orbitals, respectively; a key finding in constructing thermoelectric devices with molecular junctions11. Despite the progress, however, little experimental efforts have been devoted to elucidate the high sensitivity of thermoelectric power on the atomic junction configurations; an essential feature that needs to be understood and controlled for tailoring the unique properties in such quantum systems12,13,14.

Here we describe a method for evaluating the geometrical dependence of thermopower in nanoscale conductors. We developed a microheater-embedded mechanically-controllable break junction (MCBJ). It combines the ability to control the local temperature at the microfabricated electrical resistance Pt heater15 with the MCBJ technique for repeatedly forming stable atomic and molecular junctions of varying configurations16 (Fig. 1a–b; fabrication procedures are available in Methods section and Supplementary Information Fig. S1). We imposed a temperature gradient by applying a dc voltage Vh to the Pt heater and performed simultaneous measurements of the electrical conductance G and the thermoelectric voltage ΔV of Au atom-sized constrictions repeatedly at room temperatures in a vacuum (Fig. 1a–b; see also Fig. S1).

Figure 1
figure 1

Simultaneous measurements of single-atom conductance and thermoelectric voltage.

(a–b), Scanning electron micrographs of a heater-embedded mechanically-controllable break junction. It consists of a Au nanobridge and a Pt microheater fabricated on thin Al2O3 layers patterned on a polyimide-coated phosphor-bronze substrate. A temperature gradient was created at the junction by electrically heating the Pt heater through applying a dc voltage Vh. (c), Au single-atom contacts were formed by exerting tensile forces on the junctions through controlling a deflection of the substrate via a piezo-control. Concurrent recording of the junction conductance G and the thermoelectric voltage ΔV were conducted under constant Vh. The voltage source was switched off upon measuring ΔV. (d), Time traces of G and ΔV during stretching of a Au nanocontact at room temperatures in a vacuum under Vh = 0.5 V and 2.0 V. Conductance decreased in a stepwise fashion and exhibited a plateau at one unit of conductance quantum signifying formation of Au single-atom chains. Meanwhile, ΔV showed large fluctuations ascribed to a change in the electronic structure.

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Results

Slowly stretching a Au nanocontact, G measured at the applied voltage Vb = 0.1 V decreased to zero in a stepwise manner reflecting atom rearrangements during elastic/plastic deformations that cause discontinuous changes in the cross-sectional area at a nanoconstriction (Fig. 1d)17. When a contact is narrowed and becomes comparable to the Fermi wavelength λF, which is about 0.5 nm, we enter into a full quantum limit wherein G complies with Landauer formula (i = 1, 2, 3 ··· n)18. Here, Ti is the transmission coefficient in the ith channel and G0 = 2e2/h is the conductance quantum. Plateaus appeared at near 1 G0 signify formation of Au single-atom chains with a fully-open channel for charge transmission17,19. The staircase-like structure was observed in all the G − t traces acquired in a range of Vh from 0 to 3 V. In contrast, the thermoelectric voltage simultaneously recorded with G responded sharply to the Vh conditions: ΔV is several μV at Vh = 0.5 V but increases by an order of magnitude at Vh = 2.0 V (Fig. 1d; background voltage has been subtracted using the data obtained at Vh = 0 V as explained in Supplementary Information Figs. S2 and S3). Furthermore, ΔV fluctuated substantially upon mechanical elongation in the course of tensile loading manifesting geometry-sensitive thermoelectricity in atom-sized junctions (Figs. S4 and S5).

Statistical distributions of G and ΔV were explored to investigate thermoelectric transport in ballistic Au nanocontacts. Conductance histograms constructed with 50 G-t curves exhibit peaks at integer multiples of 2e2/h with slight deviations attributable to the virtual series resistance Rs of 800 Ω associated with defect scattering in the electron reservoirs (Fig. 2a)17,20. The low-conductance feature in the histogram below 1 G0 suggests adsorption of gas molecules on the junction surface that affects the conductance of Au single-atom contacts21,22. On the other hand, ΔV exhibits single-peak distributions (Fig. 2b inset). Here, the center of the peak, ΔVp, represents the thermoelectric voltage generated at relatively large junctions having G of 5 to 8 G0. The plots reveal monotonic increase of ΔVp with Vh2 (blue line in Fig. 2b), which manifests that one side of the Au nanocontact has been heated to an elevated temperature via the Joule heat dissipated at the current-carrying Pt coil (Supplementary Information Fig. S6).

Figure 2
figure 2

Quantized thermoelectric voltage in ballistic Au atom-sized contacts.

(a), Conductance histogram showing peaks at multiple integer of 2e2/h. Dotted lines mark the expected quantized conductance states with a virtual serial resistance Rs of 800 Ω. (b), Plots of the thermoelectric voltage of Au nanocontacts ΔVp extracted by Gaussian fitting to the ΔV distributions (inset) as a function of the voltage applied to the Pt microheater Vh. Dotted line is a quadratic fit to the plots. Monotonic increase in ΔVp with Vh2 suggests heating of the contact via the Joule heat occurring at the biased Pt coil. (c), Average ΔV, ΔVave, plotted against the corrected junction conductance Gc = 1/(1/G − Rs) with the serial resistance Rs = 800 Ω. Solid lines are Gaussian fits to the distribution with dotted lines indicating their center positions, Gm,i (i = 1, 2, 3). The oscillation of ΔVave at above 1 G0 is in close agreement with the quantized thermoelectric power expected in a ballistic one dimensional system. Color coding denotes peaks positioned at Gm,i: black = Gm,1, blue = Gm,2 and green = Gm,3. (d), Gm,i obtained in a range of Vh from 2.0 V to 3.0 V. Dotted lines show the average values. (e), Standard deviation Q of ΔV plotted against Gc. Dotted lines denote the conductance GSD,i whereat Q shows local maxima. Blue line is the theoretical Q derived from the coherent backscattering model. (f), Plots of the peak positions GSD,i extracted from (e). Dotted lines are at the average conductance.

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To reveal any quantum confinement effects in thermoelectricity in Au nanocontacts at a single-atom level, we deduced the average together with the standard deviations and plotted with respect to the junction conductance (Figs. 2c–f), where N is the number of thermoelectric voltage data ΔVi within a conductance window of 0.02 G0. Interestingly, whereas ΔVave is almost constant in a high conductance regime, several peaks are detected at Gm,i below 3 G0 (note that the influence of the series resistance Rs = 800 Ω is subtracted from G as Gc = 1/(1/G − Rs) in Fig. 2c). We find that these characteristic peaks emerge at a well-defined conductance of Gm,1 = 0.70 G0, Gm,2 = 1.54 G0 and Gm,3 = 2.30 G0 irrespective of Vh (Fig. 2d; see also Figs. S7 and S8). This fairly agrees with thermopower oscillations expected to take place in the quantum regime of a ballistic conductor that anticipates ΔV maxima at (n + 0.5 G0) [n = 1, 2, 3, ···]23,24.

The quantum nature of electron transport in atomic junctions is also identified in the thermo-voltage fluctuations. Q − G plots at Vh = 2.0 V reveal strong suppression of the thermoelectric voltage fluctuations at nG0 (Fig. 2e; G is corrected by Rs = 800 Ω similar to the case in Fig. 2c). This characteristic property is reproduced in the Vh range measured (Fig. 2f). Theoretically, fluctuations of thermopower stemming from coherent electron backscattering in vicinity of the contact scales with , which in fact predicts Q minima when Ti of all the contributing channels is either 0 or 114,25 and therefore agrees with the transmission-dependent suppression of noise in the thermoelectric voltage observed here. More quantitatively, we extracted up to two peak positions in the Q − G plots, GSD,i (i = 1, 2) and plotted against Vh (Fig. 2e). The average values are GSD,1 = 1.59 ± 0.18 G0 and GSD,2 = 2.41 ± 0.30 G0. Meanwhile, the backscattering model4 yields local Q maxima at 1.56 G0 and 2.61 G0, which are in accordance with the experimental GSD,i within 2% and 8% error for GSD,1 and GSD,2, respectively.

The above results indicate predominant roles of quantum confinement effects on the thermoelectric transport in ballistic atom-sized contacts. We demonstrate herein that the conductance-dependent thermoelectric power also provides insight into the geometry-sensitive electronic structures of Au single-atom chains. As depicted in Fig. 2c, ΔV tends to show a deep minimum at one unit of the conductance quantum and attains a positive maximum at around 0.6 G0. This can be interpreted qualitatively as arising from weakening of contact-lead coupling in single-atom chains under elongation26,27. In an unstrained fully transparent single-atom contact, s-electrons are delocalized along the chains and the peak of a broad transmission curve is located at the Fermi level EF (Fig. 3b)26. Under this condition, the thermoelectric power is very small (Regime I)9,13. In contrast, the coupling is weakened as Au-Au bonds are stretched that contributes to shift and narrow the transmission curve26. In a weak coupling case, Sc is defined as Sc = 28, which increases rapidly as moving slightly away from the resonance condition (Regime II). On the other hand, further straining leads to concomitant decrease in G and Sc (Regime III)26,28.

Figure 3
figure 3

Geometry-sensitive thermoelectric voltage of single-atom contacts.

(a), G and ΔV traces at Vh = 2.0 V and (b), the corresponding transmission curves deduced for different stages of contact stretching. The transmission peak is at around the electrode Fermi level EF when G is close to 1 G0. At this point, ΔV is very small (Region I). Pulling the junction, a single-atom chain is elongated that weakens contact-lead coupling and shifts the narrowed transmission curve. Whereas the single-atom conductance tends to be zero in a stepwise manner, this first gives rise to a rapid increase (Region II) followed by monotonic decrease in ΔV (Region III). (c–d), Sign inversion of thermoelectric voltage in single-atom contacts. Negative ΔV was found occasionally at below 1 G0. A transition occurs at Gt. (e), The positive-to-negative transition of the thermoelectric voltage is ascribable to the existence of a local minimum in the transmission curve near EF.

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Interestingly, the thermoelectric power of single-atom contacts in many cases changed from positive to negative (Fig. 3c–d). Depending on the contact mechanics, in conjunction with a possible influence of gas molecule adsorptions29, a single-atom contact evolves into various motif with different transmission lineshapes26,30. Sign inversion can take place when a transmission valley crosses over the Fermi level (Fig. 3e), where at the same time thermoelectric voltage would become much sensitive to a change in the electronic structure giving rise to large fluctuations in ΔV (Fig. 2e). The negative ΔVave thus indicates formations of atomic chains with a local minimum of transmission at near the Fermi level (Fig. 3e)26.

Particular interest lies in estimating thermopower of single-atom contacts from the ΔV measurements; a prerequisite for evaluation of the thermoelectric performance. It requires analyses of the actual temperature gradient ΔTc at the junction. For this, we utilized the lifetime τ of single-atom contacts as atomic thermometer described as τ = f0−1exp(−EB/kBTc)31,32. Here, f0 = 3 × 1012 Hz, EB, kB and Tc denote the attempt frequency, the critical bond strength in the contact, Boltzmann factor and the effective temperature at a breakpoint in the atomic wires. The average lifetime τave acquired from 1 G0 plateau lengths (Fig. 4a, inset; see also Fig. S9) decayed exponentially with Vh (Fig. 4a) suggesting steady increase in Tc with Vh33. Extrapolation of the log(τave) − Vh dependence to Vh = 0 V gives EB = 0.82 eV, typical for Au single-atom contacts. We back-calculated Tc from τave using the energy barrier height (Fig. 4b). As it is clear from Figs. 2b and S6 that the contact heats up with Vh2, due to the fact that the Joule heat at the heater carrying current I increases with the power IVh = Vh2/R, where R is the resistance of the Pt coil, we fit the Tc - Vh plots as a function of Vh2 to deduce the local temperature gradient formed at the Au single-atom wire ΔTc (the cold side is assumed to be remained at the ambient temperature7). The relatively low Tc compared to the local temperature at the microheater under elevated Vh (Fig. S6) is ascribed to heat leakage through the Au lead and Al2O3 layer. The thermopower of the Au single-atom chain Sc is deduced from ΔVc, which is the maximal positive ΔV at G < 1 G0. Noticeably, we find that ΔVc rises linearly with ΔTc at low ΔTc and tends to increase faster at ΔTc > 15 K (Fig. 4c). Accordingly, the acquired Sc obtained through Sc = SAu − ΔVc/ΔTc (Fig. S10) is around −4 μV/K at low ΔTc whereas it decreases to −6 to −8 μV/K under larger ΔTc.

Figure 4
figure 4

Thermopower of Au single-atom contacts.

(a), The average holding time τ of single-atom contacts (inset) that demonstrates exponential decay with Vh. (b), The effective temperature Tc at the hot side of single-atom chains obtained from (a). Broken line is a quadratic fit to the plot. (c), Thermovoltage of single-atom contacts ΔVc obtained from the peak at Gm,1 (red), Gm,2 (green) and Gm,3 (blue) plotted against the local temperature gradient ΔTc. Dotted line is a linear fit at ΔTc < 15 K. (d), Thermopower Sc of single-atom contacts.

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Discussion

The present results indicate that what largely determines the thermopower of Au atom-sized contacts is the geometry at their bank region that gives rise to both positive and negative ΔV irrespective of the conductance (Fig. S5). This geometrical dependence, which is characterized as a random noise due to the stochastic nature of the mechanical deformation processes during contact elongation, can be smoothed by data averaging, by which the intrinsic quantum properties of atom-sized junctions, such as the conductance-dependent thermopower oscillation, becomes observable. Here, it is noticeable that the experiment performed by Ludoph and van Ruitenbeek14 in a cryogenic vacuum failed to detect the oscillation behavior in Au nanocontacts ascribed to the considerable fluctuation in the thermopower data14. The discrepancy stems presumably from the fact that we finely controlled the contact mechanics via a feedback mechanism to hinder fusing of the contact during the formation processes (the junction conductance was below 15 G0 throughout the experiments), which enabled to make the structure of the electrodes in the bank relatively intact leading to diminished thermopower fluctuations derived from the electron backscattering. On the other hand, such procedure was not incorporated in the previous work14 implying a large structural variation in the bulk electrodes involved in the break-junction measurement. This manifests the importance of having special care to preserve the geometry of bulk regions in order to evaluate the quantum effects on the thermoelectric properties of nanocontacts.

The negative sign of the Seebeck coefficient of Au nanocontacts found here is in agreement with theory that predicts thermopower quantization at Sc = kBln2/e(n + 1/2) ~ −60/(n + 1/2) μV/K for the nth sub-band in a ballistic one-dimensional system23,34, where kB and e are the Boltzmann constant and the electron charge, respectively. Moreover, as shown in Fig. 4c, Sc obtained at Gm,2 is larger than that at Gm,3. This can also be explained by the theoretical model that anticipates smaller thermoelectric power at higher sub-band states. Quantitatively, however, the theoretical thermopower for n = 1 should be a factor of 1.7 higher than that at n = 2, whereas the ratio of the experimental Sc at Gm,2 and Gm,3, which should correspond to the first and the second sub-band states, is approximately 1.4. In addition, the measured Seebeck coefficients are an order of magnitude smaller than the theoretical value. These discrepancies presumably stem from the assumption that the local temperature at one side of the contact remains at the ambient even under high Vh conditions that may not be applicable for Au atom-sized contacts considering the high thermal conductivity of gold: unlike molecular junctions13, thermal transport through the heat-conductive metallic nanocontact would make the actual temperature gradient smaller than ΔTc, which leads to underestimation of Sc.

Methods

Fabrication of heater-embedded MCBJs

Heater-embedded MCBJs are fabricated as follows. We first formed a 4 μm-thick polyimide layer on a mirror-polished surface of a 0.5 mm-thick phosphor bronze substrate by spin-coating and baking on a hot plate. We then rendered a microelectrode pattern by a photolithography method using a photoresist AZ-5206E. Subsequently, a Au/Cr multilayer of thickness 25 nm/5 nm was deposited by a radio-frequency magnetron sputtering. The substrate was then immersed in N, N-dimethylformamide (DMF) for more than 8 hours and ultrasonicated for lift off. After that, we delineated an Al2O3 thin film pattern by an electron-beam lithography method using a resist ZEP-520A-7. Al2O3 of 25 nm thickness was then deposited using the sputtering method followed by a lift-off in DMF. On the Al2O3, a heater pattern is drawn by the EB lithography. By depositing 40 nm thick Pt by the sputtering and removing the resist in DMF, we obtained Pt nanowire of 350 nm width. Following this, we further fabricated a 100 nm thick Au nanowire with a narrow constriction of 100 nm width at the middle using the same lithography and sputtering processes. The sample was then exposed to isotropic reactive ion etching (50 W, O2) to remove the polyimide underneath the Au nanowire. As a result, we obtained a Au nanobridge of length about 2 μm. This geometry provides the attenuation factor r of 3 × 10−4 17, which enables fine-control of the tensile displacements on the junction at sub-picometer level.

Formation of gold single-atom contacts

We formed Au single-atom contacts using a self-breaking technique. Specifically, we mounted a heater-integrated MCBJ on a stage in a three-point bending configuration and evacuated the sample chamber to below 10−5 Torr. The MCBJ substrate was then bended mechanically from the back using a piezo-driven pushing rod at room temperatures. Meanwhile, the electrical conductance G of the junction was monitored at a bias voltage Vb of 0.1 V. Here, the conductance was used as a reference to control the stretching speed vd of the junction: vd was kept at 6 nm/s at G > 10 G0 until G decreases to 10 G0 where the stretching rate is lowered to 0.6 nm/s and finally to vd = 0.0006 nm/s when it fell below 5 G0. After breakdown, we moved the piezo-element in the opposite direction and formed a contact. During the formation process, a special care was taken to make conductance not to exceed 15 G0 so as to prevent fusing of the contact. This conductance feedback control of contact mechanics allowed forming and holding single-atom contacts for prolonged time necessary for conducting the thermoelectric voltage measurements33.

Thermoelectric voltage and electrical conductance measurements

Simultaneous measurements of the thermoelectric voltage and the electrical conductance were performed when G decreases below 8 G0 during the feedback controlled stretching of Au nanocontacts. For this, a dc voltage Vh was applied to the Pt microheater by a picoammeter-source unit (Keithley model 6487) to impose a temperature gradient on the junction via heat conduction through the Al2O3 layer. The picoammeter was also exploited for calibration of the Pt microheater (Fig. S6). Note that the polyimide layer is used not only for electrical insulation but also as a thermal insulator for impeding heat leakage through the substrate. In the break junction measurements, G was measured under a voltage of Vb = 0.1 V using another ammeter (Keithley model 6487). A protection resistance of 10 kΩ was connected to prevent from overcurrent breakdown of fused junctions. After each conductance measurement, voltage across the junction was recorded using a nanovoltmeter (Keithley model 2182) with voltage source being switched off. The sampling rate of the simultaneous recording was approximately 3 Hz.

Pt microheater calibration

In prior to the break junction experiments, we carried out a calibration of the Pt heater (Fig. S6). We controlled the temperature of the sample stage T0 using a resistive heater and a thermometer attached to it using a temperature controller (Scientific Instruments model 9700). The resistance of the microheater RPt was then recorded using a picoammeter-source (Keithley model 6487) at various T0 above room temperatures. After that, RPt – Vh characteristics were measured by the same ammeter. The thus quantitated RPt – T0 relationship was used as a calibration curve to deduce the local temperature at the microheater under elevated Vh conditions during the thermoelectric voltage measurements.

Data analysis

Background in the thermoelectric voltage measurements was calibrated by measuring the Vm – G dependence with no heat added and subtracting it from the data at Vh > 0 V. After that, the thermoelectric voltage ΔV was deduced as ΔV = Vm(1 + 12900/G/Rp), where G and Rp are the junction conductance in G0 unit and the resistance of the 10 kΩ protective resistor. ΔVave and Q were calculated from ΔV data binned at 0.01 G0, which were obtained in the consecutive 50 junction opening/closing processes. ΔVc were extracted by Gaussian fitting to the ΔVave in the positive regime within a conductance window of 0 to 1 G0.