Mohammed
Noori‡
ab,
Hatef
Sadeghi‡
*a,
Qusiy
Al-Galiby‡
ac,
Steven W. D.
Bailey
a and
Colin J.
Lambert‡
*a
aQuantum Technology Centre, Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK. E-mail: h.sadeghi@lancaster.ac.uk; c.lambert@lancaster.ac.uk
bDepartment of Physics, Collage of Science, Thi-Qar University, Thi-Qar, Iraq
cDepartment of Physics, Collage of Education, Al Qadisiyah University, Iraq
First published on 19th June 2017
We investigated the thermoelectric properties of flat-stacked 5,15-diphenylporphyrins containing divalent metal ions Ni, Co, Cu or Zn, which are strongly coordinated with the nitrogens of pyridyl coated gold electrodes. Changing metal atom has little effect on the thermal conductance due to the phonons. The room-temperature Seebeck coefficients of these junctions are rather high, ranging from 90 μV K−1 for Cu, Ni and Zn-porphyrins to −16 μV K−1 for Co-porphyrin. These values could be further increased by lowering molecular energy levels relative to the DFT-predicted Fermi energy. In contrast, the phonon contribution to the thermal conductance of these junctions is rather insensitive to the choice of metal atom. The thermopower, thermal conductance and electrical conductance combined to yield the room-temperature values for the thermoelectric figure of merit ZT ranging from 1.6 for Cu porphyrin to ∼0.02 for Ni-porphyrin.
Here, in an effort to further enhance the thermoelectric performance of single-molecule junctions by controlling phonon transport while maintaining good electrical contact, we examine the effect of coating the electrodes with functional units, which form coordination bonds with the molecule of interest. As an example, we examine junctions formed from 5,15-diphenylporphyrins containing divalent metal ions Ni, Co, Cu or Zn, which are strongly coordinated with the nitrogens of pyridyl coated gold electrodes. Porphyrins are attractive as building blocks for molecular-scale devices, because they are conjugated, rigid, chemically stable molecules and their properties could be modified by coordinating a variety of metallic ions (metallo-porphyrins).25–33 In what follows our aim is to explore the potential of the metallo-porphyrin-based molecular junctions shown in Fig. 1a for high-efficiency thermoelectricity. Since the in-plane electrical conductance of porphyrins is rather low, we consider “cross-plane” junctions in which the current flows perpendicular to the porphyrin plane.34 A shown in Fig. 1b, a porphyrin plane is contacted to gold electrodes via pyridyl groups attached to the gold by thiol anchors, with the plane of the porphyrin stacked perpendicular to the direction of charge transport.
From the point of view of optimising thermoelectric properties, junctions formed from these molecules are of interest, because by varying the metal atom (denoted χ in Fig. 1) residing in the core of the organic porphyrin framework, the molecular energy levels can be tuned relative to the Fermi energy EF of the electrodes and if energy levels are close enough to EF, then this should lead to transport resonances, which enhance the thermopower.35 In what follows, we shall demonstrate that this is indeed the case and that large positive and negative thermopowers are achievable. Moreover, our calculations show that although the thermal conductance due to the phonons dominates the total thermal conductance, high values of ZT are obtained.
Recent experiments and theory show that the conductances G of the metallo-porphyrins are enhanced when they are sandwiched between two gold electrodes with pyridine-4-yl-methanethiol anchors (Fig. 1b).34,36 Since large G is desirable, the 5,15-diphenylporphyrins (χ-DPP) studied in this paper contains metal atoms χ = Co, Cu, Ni or Zn, which are strongly coordinated with the nitrogens of pyridyl coated gold electrodes (Fig. 1a). Our aim in this paper is to investigate the thermoelectric properties of these metallo-porphyrins devices when the metal atom is varied.
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Fig. 2 (a–d) show the electronic transmission coefficients T(E) = T↑el(E) + T↓el(E) as a function of energy E for χ-DPP with χ = Co, Cu, Zn and Ni. |
Due to the presence of thiol anchors, the DFT-predicted Fermi energy is close to the HOMO transmission resonances of each χ-DPP and the slope of Tσel(EF) is negative. Hence from eqn (S5) of the ESI,† one expects the Seebeck coefficient S to be positive. Using the Landauer formula (see ESI†), the electrical conductance was calculated from the transmission coefficient shown in Fig. 2.
The electrical conductances (Fig. S2 of the ESI†) follow the trend GZn > GCu > GCo > GNi in agreement with the experimental values of Zn-DPP 8.2 × 10−2, Cu-DPP 4.4 × 10−2, Co-DPP 2.2 × 10−2 and Ni-DPP 1.8 × 10−2.33
To calculate the vibrational modes of each structure, we use the harmonic approximation to construct the dynamical matrix D and a Green's function approach to calculate the phononic transmission coefficient Tph(ω) for phonons with energy ℏω passing through the device as explained in ref. 35. Fig. 3 shows the phonon transmission coefficients for each χ-DPP.
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Fig. 3 (a–d) Phonon transmission coefficient as a function of ℏω for χ-DPP with χ = Co, Cu, Zn and Ni. |
The thermal conductance of the junction (κ = κph + κel) is obtained by summing the contributions from both electrons (κel) and phonons (κph). The electronic (phononic) thermal conductances are calculated from the electronic (phononic) transmission coefficients (as described in ref. 35).
Comparison between Fig. 4a and b shows that in the vicinity of DFT Fermi energy, the main source of the thermal conductance in these junctions is due to phonons, whose room-temperature contribution is relatively insensitive to the choice of metal atom, varying between 6 and 10 pW K−1 depending on the choice. The inset of Fig. 4b shows the cumulative distribution of eigenvalues (integrated density of states) of each molecule and reveals that the lower frequency modes of the Co porphyrin in the region 0 to 1.5 meV are pushed to higher frequencies, leading to a low-frequency transmission gap below 3 meV. This reflects the higher binding energy of a single pyridyl group to the Co metal atom compared with the other. (These follow the trend Co = −1.2 eV, Zn = −1.2 eV, Cu = −0.4 eV and Ni = −0.17 eV.) (These follow the trend Co = −1.2 eV, Zn = −1.2 eV, Cu = −0.4 eV and Ni = −0.17 eV.)
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Fig. 4 (a) Show electronic contribution of the thermal conductance κel and (b) show phononic contribution of the thermal conductance κph for DPP with Co, Cu, Zn and Ni. |
Consequently the low-frequency cumulative distribution of Co and the low-temperature thermal conductance initially lies below that of the others and then rises with a steeper slope. Fig. 3c shows that Zn also has a low-frequency transmission gap below 1 meV, which suppresses the low-temperature phonon thermal conductance.
Fig. 5 shows the Seebeck coefficient S and total figure of merit ZT over a range of Fermi energies at room temperature for each metallo-porphyrin. Fig. 5a demonstrates that both the magnitude and sign of S are sensitive to the metal atom at the centre of the DPP, which determine the location of transport resonances relative to the Fermi energy. Since the Fermi energy from DFT is not necessarily reliable, we have presented results for a range of Fermi energies (Fig. 5a).
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Fig. 5 Show (a) Seebeck coefficient S (thermopower) and (b) total figure of merit ZT over a range of Fermi energies at room temperature for each metallo-porphyrin. |
For the junctions discussed in this paper, the conductances have been measured experimentally36 so we have estimated the Fermi energy by comparing these measurements with our calculated conductances. This yields a value of EF = −0.03 eV, compared with the DFT-predicted Fermi energy. Table 1 shows the Seebeck coefficients of porphyrins in the presence of Cu, and then Co, Zn and Ni at EF = −0.03 eV. The predicted trend is SCu > SNi > SZn > SCo and when combined with the higher Cu CPP the yield room-temperature values of ZT range from 1.66 for Cu porphyrin to 0.07 for Zn porphyrin, as shown in Fig. 5b.
Metallic | S (μV K−1) | ZT | ||
---|---|---|---|---|
E F = −0.03 eV | E F = 0.0 eV | E F = −0.03 eV | E F = 0.0 eV | |
Cu | +90 | +182 | 1.66 | 3.22 |
Co | −16 | +77 | 0.05 | 0.92 |
Zn | −23 | +72 | 0.07 | 0.56 |
Ni | −32 | +66 | 0.018 | 0.05 |
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp02229h |
‡ These author contributed equally to this work. |
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