Supporting Information: Engineering the thermopower of C 60 molecular junctions

Transcription

1 Supporting Information: Engineering the thermopower of C 60 molecular junctions Charalambos Evangeli, Katalin Gillemot, Edmund Leary, M. Teresa González, Gabino Rubio-Bollinger, Colin J. Lambert, NicolásAgraït 1. Substrate preparation and experimental setup The C 60 molecules are deposited using the drop casting technique from a very dilute ( M) 1,2,4-trichlorobenzene solution. Specifically, a drop of the solution is left on an annealed gold surface for about 3 minutes, and then is blown off with dry nitrogen and allowed to dry for a couple of hours. Once the sample is dry we mount it on a homebuilt STM and let it stabilize for about one hour in order to minimize the thermal drift. Using this procedure we are able to deposit isolated molecules both on terraces and step edges as shown in Figure 1e. The molecules at steps are generally more stable under scanning. For larger concentrations the formation of C 60 islands become favored. In order to measure the thermopower of the molecular junction, we have modified our STM setup by adding a surface mount 1kOhm resistor which acts as a heater to the tip holder while the substrate was maintained at room temperature. A thermocouple connected to the tip and sample holders was used to monitor the resulting temperature difference, which was set to 12 K, and 25 K in the herein reported experiments, the sample is maintained at approximately at 25 ºC. We found that the temperature stabilized in about 15 minutes, and the thermal drift increased making necessary to use fast imaging to locate the isolated molecules. 2. Building the experimental conductance histograms The conductance histograms in Fig.1g of the main text represent the conductance values when contact is established between a single C 60 and the Au-tip (blue curve in Fig.1g) and a single C 60 and a C 60 -tip (black curve in Fig.1g). In the first case we select points spanning 0.1 nm after the abrupt jump or marked change of slope in the conductance during approach as illustrated for several approach curves in Fig. S1a. In the second case, contact between the two C 60 s is marked by a more gradual change in slope that 1

2 develops in a shoulder. We select the data points spanning this shoulder up to the point where the conductance starts increasing again as illustrated in Fig. S2a. Comparison of these contact conductance histograms with the standard conductance histograms, which take into account the whole conductance traces, shows that for the single C 60 junctions (Fig.S1b), they differ strongly, since none of the peaks in the whole conductance histogram (blue curve in Fig.S1b) corresponds to the Au-C 60 -Au contact formation. In contrast for the C 60 dimer both peaks coincide. Figure S1 a, Approach curves for a bare gold tip on four different isolated C 60 molecules (blue). Contact points are plotted in red. b, Conductance histogram for the whole conductance traces (blue) and for the contact points (red). c, 2d histogram of 77 approach curves on isolated C 60 molecules. 2

3 Figure S2 a, Approach curves for a C 60 -tip on four different isolated C 60 molecules (blue). Contact points are plotted in red. b, Conductance histogram for the whole conductance traces (blue) and for the contact points (red). c, 2d histogram of 38 approach curves on isolated C 60 molecules. 3. Thermal circuit By heating the tip we not only establish a temperature difference between the tip and the substrate of the STM but also a temperature gradient across the copper wire connecting the tip to the current circuit, that gives rise to an additional thermoelectric voltage. We use the value for the thermopower of Cu from reference 4 of the main text, 1.85 µv/k, which is much smaller than the thermopower of the C 60 molecular junctions. Considering the equivalent circuit in Fig. S3, we can write and consequently the voltage offset is given by 3

4 Figure S3 Equivalent thermal circuit of the setup for the calculation of the thermopower. The substrate and body of the STM are at ambient temperature T c while tip is heated to a temperature of T h = T c + ΔT above ambient temperature. S is the thermopower of the molecular junction and S Cu is the thermopower of the copper wire use for connecting the tip. V bias is the bias voltage imposed by the control electronics of the STM. 4. Simultaneous measurement of thermopower and conductance during approach and retraction For the sake of clarity, in Fig.3 we only presented the thermopower and conductance acquired as the tip approaches the sample, however in our experiments we always acquire these two magnitudes both for approach and retraction, which provides us with valuable insight on the effect of contact formation on the molecule. After contacting a single C 60 molecule with an Au-tip, the similarity of approach and retraction curves shows that the molecule remains quite unaltered, although sometimes it is transferred to the tip (see Fig. S4a-b and c-d). In contrast, after contacting a C 60 molecule with a C 60 - tip, one of the two C 60 molecules is expelled from the junction and the retraction curves are similar to those obtained for a single C 60 junction (see Fig. S4e-f and g-h). 4

5 Figure S4 Approach and retraction traces of simultaneous conductance thermopower measurements. a, Conductance (blue) and thermopower (green) acquired during approach of a gold tip on an individual C 60 molecule. b, Conductance (red) and thermopower (magenta) acquired during the retraction following the approach shown in a. The temperature difference was ΔT = 25 K. c and d, Another example of approach and retraction curves of a gold tip on an individual C 60 molecule. In this case ΔT = 12 K. The thermopower points corresponding to the Au-C 60 -Au contact have been highlighted in yellow. e, Conductance (blue) and thermopower (green) acquired during approach of a C 60 -tip on an individual C 60 molecule. f, Conductance (red) and thermopower (magenta) acquired during the retraction following the approach shown in e. The temperature difference was ΔT = 25 K. g and h, Another example of approach and retraction curves of a C 60 -tip on an individual C 60 molecule. In this case ΔT = 12 K. The thermopower points corresponding to Au-C 60 -C 60 -Au contact have been highlighted in yellow. 5

6 5. Computational methods Electronic and transport calculations of the C 60 junctions are carried out using the abinitio code SMEAGOL 5, which uses the Hamiltonian provided by DFT code SIESTA. SIESTA 1 employs norm-conserving pseudo-potentials to account for the core electrons, and a linear combination of pseudo-atomic orbitals. SMEAGOL divides the entire nanoscale junction into three parts; the left and the right bulk electrodes with <111> surface orientations and the extended molecule that consists of the C 60 (s) and the topmost gold layers modelling the tip of the electrode. SMEAGOL uses the Hamiltonian derived from SIESTA to calculate self-consistently the density matrix, the transmission coefficients τ(e) of the electrons from one electrode into the other. The DFT calculations were performed with a double zeta polarized basis set, an energy cutoff of 200 Ry to define the real space grid, the Local Density Approximation (LDA) with Caperley-Alder parametrization 2 and Troullier-Martins type non-relativistic, normconserving pseudopotentials 3. We varied the mesh and the vacuum size to check that results were independent of the chosen values. In all calculations the molecules between the electrodes were fully relaxed. The electrodes were assigned flat gold <111> surfaces to realistically model the large surface areas of STM tips and the substrates. The equilibrium distance between an electrode and a C 60 was obtained by computing the total energy versus distance and choosing the distance corresponding to the energy minimum. Our results of 0.22 nm are in good agreement with the previously reported numerical distances 4. The analysed systems are depicted on Figure S5. In all cases, the orientation of the C 60 s towards the Au was chosen such that a C-C bond between a hexagon and a pentagon was closest to the Au surface. As a test we also examined the single C 60 case with four other orientations (namely a hexagon facing the Au surface, a pentagon facing the Au surface, a bond between two hexagons facing the Au surface, and a single atom facing the Au surface). We have found that the results for S and ZT were rather insensitive this orientation. Nevertheless, for completeness, in all the theoretical histograms for the single C 60 case, all of the above orientations are included. The calculations ran over a wide range of electrode separations, the exact distance ranges can be found in Table 1. For the dimer, at a C 60 -C 60 separation of 0.34 nm, (the usual carbon-carbon interlayer distance) the top C 60 moves sideways and slides across the lower C 60, while lowering the top electrode. This leads to a plateau in the conductance trace (see blue curve Figure 3e, main text), similar to that in the blue experimental curve for the dimer in Figs. 3d and 1f in main text. In the case of the C 60 trimers we only allowed vertical movement by systematically running the calculations over a range of different distances d 1 and d 2 between the C 60 pairs. 6

7 We focused on the zero bias limit and then computed the conductance, the thermopower and the figure of merit at the temperature of T = 300 K. To calculate these quantites 6,7 it is useful to introduce the non-normalised probability distribution P(E) defined by, where τ(ε) is the transmission coefficient for electrons of energy E passing from one electrode to the other, f(e) the Fermi-Dirac function, whose moments are denoted, where E F is the Fermi energy. The conductance, G is 2, where e is the electronic charge, h is the Planck constant, and T is the temperature. The thermopower S is the thermal conductance κ is and the figure of merit ZT is 1, 2 1, 1. 1 All our results were obtained using the above formulae. As an aside, for E close to E F, if τ(e) varies only slowly with E on the scale of k B T then these expressions take the well known forms: 2,,, 7

8 where /3 is is the Lorentz number. Figure S5 Geometrical setups for the theoretical calculations. a, Monomers. b, dimmers. c, trimers. Red arrows indicate moving variables, while black arrows indicate fixed distances. z is the electrode separation, c = 0.22 nm and is fixed, d, d 1 and d 2 are varied. a, In the single C 60 case, the distance between the substrate and the C 60 was kept fixed while the top electrode was moved over a wide range of distances in the vertical direction. b, For the C 60 dimer, both buckyballs were fixed to the electrodes. The top complex was first lowered onto the bottom one until a given separation between the two C 60 -s was reached. Then we modelled a rolling/squeezing sequence by lowering it further while allowing a sideways movement, until the top C 60 was next to the buckyball lying on the substrate. The path of the top complex is noted by the blue arrow. c, For the C 60 trimer, the distance between the electrodes and the closest C 60 -s were fixed, while the distances d 1 and d 2 between the middle buckyball and the others were changed systematically. References: 8

9 1. Soler, J., Artacho, E., Gale, J., Garcia, A., Junquera, J., Ordejon, P. & Sanchez- Portal, D., The SIESTA method for ab initio order-n materials simulation. J. Phys.: Condens. Matter 14, (2002). 2. Perdew, J. P. & Zunger, A., Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, (1981). 3. Troullier, N. & Martins, J. L., Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 43, (1991). 4. Wang L. & Cheng H., Density functional study of the adsorption of a C 60 monolayer on Ag(111) and Au(111) surfaces. Phy.Rev. B 69, (2004). 5. Rocha, A., Garcia-Suarez, V., Bailey, S., Lambert, C. J., Ferrer, J. & Sanvito, S., Spin and Molecular Electronics in Atomically Generated Orbital Landscapes. Phys. Rev. B 73, (2006). 6. Sivan, U. & Imry, Y., Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge. Phys. Rev. B. 33, 551 (1986). 7. Butcher, P.N., Thermal and electrical transport formalism for electronic microstructures with many terminals. J. Phys.: Condens. Matt.2, 4869 (1990). 6. Building histograms from the theoretical calculations Since (-df(e)/de) is peaked at the Fermi energy E F, whereas τ(e) possesses peaks in the vicinity of the HOMO and LUMO levels of the C 60 s, the moments L i, defined above are sensitive to the positions of the HOMO and LUMO levels relative to E F. Variations in the orientations of the C 60 (s) towards the Au surface and to each other and changes in the electrode separation cause the HOMO and LUMO peaks to be shifted relative to the E F. Furthermore, image charges due to screening by the electrodes change the positions of the HOMO and LUMO levels relative to E F, during approach and retraction, by amounts which depend on the detailed atomic arrangement of the electrodes. For example, Malen et al. 1,2 report that during thermopower measurements on thiol bound molecules they observed a rather large shift of the HOMO level relative to the Fermi energy. They also found that this in part is caused by the change of the contact geometry, the orbital hybridization and intermolecular interactions. In view of these unknown fluctuations in E F we computed curves of τ(e) for a range of electrode separations and evaluated the moments L i for each electrode separation and for a range of values of E F relative to the bare DFT value E F =0 obtained from SIESTA. These results were then used to build histograms of thermoelectric coefficients. Fig. S6 shows an example of transmission curves for a monomer, dimer 9

10 and trimer. Transport through a single C 60 is LUMO dominated 3,4,5, leading to negative values for S, in agreement with our experiments. For each electrode separation, we used ca. 30 shifts in E F with a ev step size, yielding a series of E F s in the gap, with a maximum shift of -0.5 ev. As an example of the results of this procedure, Figure S7. shows theoretical approaching curves of S versus separation z, for the single C 60 case at different values of E F. Figure S6 Example transmission curves for single C 60 (blue dots), C 60 dimer (black dash) and C 60 trimer (green line). The thick vertical red line indicates the position of the bare Fermi energy obtained by DFT, while the black dashed vertical lines give examples of nearby E F s at which positions the thermal coefficients were recalculated. Figure S7 Theoretical approaching curves of the thermopower for a single C 60 obtained by recalculating S at a number of different E F s, shifted by amounts shown in the legend relative to the bare DFT value. The numbers in the legend show the shift in ev. The C 60 was oriented with a C-C bond between a hexagon and a pentagon facing the substrate. 10

11 In Table 1, all the resulting histograms are plotted without any sorting of the data. These results for S and ZT are also shown in Fig. 4b,c,e,f,g,h of the main text, and to aid comparison with results for the conductance, the results for S and ZT are reproduced here. Table 1 Theoretical histograms without sorting the data., and ZT av refer to average, δ to standard deviation. ΔE F gives the range of Fermi energy shifts from the bare DFT Fermi energy. Δd, Δd 1 and Δd 2 are the ranges of the distances d, d 1 and d 2 in Figure S1. Note that as a comparison Tables 1, 2 and 3 have the same scales and bin sizes. Since the range of fluctuations in E F in the experiments is not known precisely, and since our experimental histograms only use measurements obtained after making contact with the tip, we attempted to compare our theoretical data to the experiments by using only a smaller range of electrode separations and Fermi energy shifts then before, when creating the histograms (see Table 2.). By only using the values in a range of 0.3 nm for the electrode separations and simultaneously using only the values 11

12 corresponding to ev shifts to the Fermi energy for the monomer, and ev for the dimer, we were able to get a good fit to the experimental histograms for both G and S at the same time. Table 2 Theoretical results after sorting the data to best match the experiments., and ZT av refer to average, δ to standard deviation. ΔE F gives the range of Fermi energy shifts from the bare DFT Fermi energy. Δd is the range of the distance d in Figure S5. Note that as a comparison Tables 1, 2 and 3 have the same scales and bin sizes. To understand the origin of the large values observed for ZT, we have also sorted our data to yield higher average ZT values then the ones without any kind of sorting. From the data for the single C 60 case in Table 3. we can see that such high figures of merit values result from the energy points in the steep parts of the transmission curves near the original DFT Fermi energy, where both G and S take up large values. We have found the same for the dimers and trimers as well. 12

13 Table 3 Theoretical results after sorting the data to yield high average ZT for the single C 60 case., and ZT av refer to average, δ to standard deviation. ΔE F gives the range of Fermi energy shifts from the bare DFT Fermi energy. Δd is the range of the distance d in Figure S5. Note that as a comparison Tables 1, 2 and 3 have the same scales and bin sizes. References: 1. Malen, J. A., Doak, P., Baheti, K., Tilley, T. D., Majumdar, A. & Segalman, R. A., The Nature of Transport Variations in Molecular Heterojunction Electronics. Nano Lett. 9, 10, (2009). 2. Malen, J. A., Yee, S. K., Majumdar, A. & Segalman, R. A., Fundamentals of energy transport, energy conversion, and thermal properties in organic-inorganic heterojunctions. Chem. Phys. Lett. 491, (2010). 3. Palacios, J. J., Pérez-Jiménez, A. J., Louis, E. & Vergés, J. A., Electronic transport through C 60 molecules. Nanothechnology 12, (2000). 4. Zheng, X., Dai, Z. & Zheng, Z. The size effects of electrodes in molecular devices: an ab initio study on the transport properties of C 60. J. Phys.: Condens. Matter 21, (2009). 5. Yee, S. K., Malen, J. A., Majumdar, A. & Segalman, R., Thermoelectricity in Fullerene Metal Heterojunctions. Nano Lett. 11, 4089 (2011). 13