Resonant heating and substrate-mediated cooling of a single C60 molecule in a tunnel junction

We study the influence of different metallic substrates on the electron induced heating and heat dissipation of single C60 molecules in the junction of a low temperature scanning tunneling microscope. The electron current passing through the molecule produces a large amount of heat due to electron-phonon coupling, eventually leading to thermal decomposition of the fullerene cage. The power for decomposition varies with electron energy and reflects the resonance structure participating in the transport. The average value for thermal decomposition of C60 on Cu(110) amounts to 21 $\mu$W, while it is much lower on Pb(111) (2.9 $\mu$W) and on Au(111) (1.0 $\mu$W). We ascribe this difference to the amount of charge transfer into C60 upon adsorption on the different surfaces, which facilitates molecular vibron quenching by electron-hole pair creation.


INTRODUCTION
A single molecule junction that is exposed to the flow of an electron current will experience an increase of temperature due to the heat generated by conduction electrons. Recent theoretical studies predicted that Joule heating in molecular junctions can be large enough to affect the reliability of molecular devices [1]. The temperature of a molecular junction is difficult to estimate. Recent experimental approaches have found agreement in that a single molecule device can easily reach several hundreds of degrees under normal operation (flow of microwatts when powered with 1 Volt) [2,3,4,5]. For most molecules, such temperature reaches the limit of thermal degradation. Therefore, a deeper knowledge of the microscopic mechanisms of heat generation and dissipation on the nanoscale is required in order to improve the performance of a molecular device.
The temperature at the junction is a consequence of an equilibrium between heating and dissipation of heat away from the molecule. Heat generation is essentially caused by scattering of electrons with molecular vibrations. Heat dissipation is expected to follow several mechanisms involved in the coupling of the hot molecule with the substrate acting as an external cold bath. According to this, the temperature reached by a single molecule during electron transport should depend on the lead's material. Furthermore, one would expect that both the phonon bandwidth and the electronic density of states around the Fermi energy should govern a priori the mechanisms of heat dissipation (cooling) and, hence, the molecular temperature.
In this paper we analyze the effect of the lead's material on the heat dissipated during electron transport through a single molecule. We use a low temperature scanning tunneling microscope (STM) to inject an electron current through a single fullerene adsorbed onto clean metal surfaces of different nature. Rather than measuring the temperature reached by the single molecule, we follow the approach described in our previous work [5]. We look for certain current and sample bias (V s ) values at which the molecule under the STM tip undergoes an irreversible thermal degradation. The applied power required to reach the decomposition limit (P dec ) varies slightly with the electron energy (eV s ) in a sequence that resembles the energy alignment of the fullerene resonances for every metal substrate, confirming a resonant mechanism of electron heating [6]. However, we also find that the mean values of P dec (P dec ) depend more strongly on the substrate onto which the fullerenes are adsorbed. The way that P dec scales for different metals cannot be explained in terms of intrinsic properties of each material. Instead, the observed trend seems to be a result of the mechanism of interaction between metal and molecule. In particular, we find a correlation between the behavior P dec and the amount of charge transfer into molecular unoccupied states, as resolved using local spectroscopy measurements of C 60 molecules on the different substrates. Hence, our results suggest that charge transfer processes at the metal-molecule contact provide an effective pathway to dissipate heat from a hot molecule through the creation of e-h pairs. The experiments were performed in a custom-made ultra-high vacuum STM, which is operated at a temperature of 5 K. We chose Cu(110), Pb(111) and Au(111) single crystals as substrates because of their different properties regarding chemical reactivity, as well as phonon band widths and densities of states at the Fermi energy (E F ). Cleaning of the metal substrates was performed by standard sputtering-annealing cycles under ultra-high vacuum, ensuring an atomically clean and flat metal surface. Indentations of the STM tip into the substrate while applying a tip-sample bias were used to clean the tips in regular intervals. The tips are therefore believed to be composed of the same material as the substrate. A arXiv:0803.2222v1 [cond-mat.mtrl-sci] 14 Mar 2008 sub-monolayer coverage of C 60 molecules was deposited from a Knudsen cell on the metal surfaces at room temperature. On Cu(110) the system was further annealed to 470 K to ensure that the molecules self-assemble in ordered domains and populate a thermally stable adsorption state. The structure and electronic configuration of the molecular layers were characterized using STM and scanning tunneling spectroscopy (STS) measurements (Fig. 1  On Cu(110), C 60 forms ordered islands with a pseudohexagonal structure ( Fig. 1 (a)), in which the fullerenes adopt a well-defined adsorption configuration with a pentagon-hexagon C-C bond pointing upwards [5,7]. An STS spectrum on these molecules ( Fig. 1 (d)) resolves a clear spectroscopic fingerprint characterized by a sharp resonance at ∼1.5 eV above the Fermi level and associated to the alignment of the LUMO+1 resonance (LUMO: lowest unoccupied molecular orbital).
The LUMO resonance appears as a broader peak centered at ∼0.2 eV and is partially occupied.
Fullerene adsorption on Pb(111) at room temperature results in highly ordered hexagonal islands ( Fig. 1 (b)). Here, scanning tunneling spectroscopy reveals the LUMO and LUMO+1 derived resonances as in Cu(110) but more pronounced and with a characteristic split structure due to the breaking of degeneracy upon adsorption [8] (Fig. 1 (e)). The energetic alignment of the LUMO close to E F , with a small tail crossing it, indicates a small amount of charge transfer into C 60 .
C 60 islands on Au(111) evidence a similar hexagonal lattice as on Pb(111) (Fig. 1 (c)), but with large variety regarding molecular orientations [9], as one can determine from intramolecular structure resembling the lobed shape of the LUMO resonance [10]. Both LUMO and LUMO+1 resonances are resolved in STS spectra as pronounced peaks, independently of the molecular orientation [11]. The LUMO peak appears located far from E F , at ∼ 0.8 eV, thus indicating that charge transfer from the substrate is very small [12].

C60 DECOMPOSITION ON METAL SURFACES
In our experiment, we approach the STM tip a distance Z towards a single C 60 molecule while holding the sample bias V s constant. During approach we record the current flowing through the molecular junction (I(Z)). The tunnel regime is revealed by an exponential increase of I(Z) with diminishing gap distance. At a certain approach distance the I(Z) curves deviate smoothly from the exponential dependence, indicating the onset of a tip-molecule contact [3]. The conductivity at this point is a small fraction of G 0 (G 0 = 77.5 µS). For small positive sample bias the molecule remains intact upon contact formation and even further indentations of severalÅngstroms, leading to a stable junction with the molecule contacted by the STM tip on the one side, and the metal surface, on the other [3,5]. In this case, the integrity of the indented molecule after tip contact can be verified by its appearance in the STM images and, especially, by its electronic fingerprint in dI/dV s spectra. Fig. 3 shows, for the case of Pb(111), the effect of approaching a molecule at bias voltages above a threshold value of V s = 1.0 V . A sharp drop appears in the I(Z) curves before reaching the contact regime [13], denoting the occurrence of an irreversible change in the junction (Fig. 3 (c)). Similar results can also be found on Cu(110) and on Au(111) V s > 1.5 V . After this current drop STM images reveal that the molecule is transformed into a lower feature (Fig. 3 (d)) and the characteristic resonances of the fullerene icosahedral cavity are absent from its corresponding STS spectrum (Fig.  3 (e)). Hence, the discontinuous current drop is a fingerprint of degradation of the fullerene cage. The precise way in which the C 60 decomposes can not be determined in detail in our measurements. The effect is observed solely on the molecule selected for the tip approach and shows a high reproducibility, as depicted in Fig. 3  on Cu(110) [14]. A mechanical breaking of the fullerene cage can be excluded since the process takes places before a tip-molecule contact is formed (i.e. in the tunneling regime). We can then conclude that the decomposition is a current induced thermal process. The current I dec at which the C 60 decomposition occurs can be taken from the I(Z) approach curves. I dec turns out to show very reproducible values distinctive for every metal substrate and a clear dependence on the bias voltage used during the tip approach. Fig. 4 shows the statistical average of I dec plotted vs. V s for all three surfaces. Adsorbed on Cu(110), C 60 molecules can withstand currents of several tens of microamperes, typically one order of magnitude larger than for C 60 on Pb(111) or Au(111). In general, I dec decreases monotonously as the applied bias is increased. Additionally, some faint steps can be inferred. This substructure becomes more evident when we plot instead the applied power necessary to decompose the molecule, P dec = V s × I dec (Fig. 4  (b-d)).
The monotonous decrease of I dec transforms in a fairly flat behaviour of P dec with the applied bias. Fig. 4 (b-d) shows that the average power applied for degradation depends strongly on the substrate used: P dec ∼ 21 µW for Cu(110), P dec ∼ 2.9 µW for Pb(111), and P dec ∼ 1 µW for Au(111). Superimposed to these values, the stepped substructure appears now more pronounced. The structure is correlated with the alignment of the unoccupied states of the C 60 molecule, also shown in Fig. 4 (b-d).
In general we find that P dec decreases whenever a new resonance (here the LUMO+1 and LUMO+2) enters the conduction energy window. Hence, the molecular resonance structure is reflected in the power needed to decompose a molecule. Next, we interprete the origin of this resonant substructure (section 4) and of the strong substrate dependence of the applied power for degradation P dec (section 5).

MOLECULAR HEATING AND COOLING MECHANISMS
The origin of the sub-structure in the P dec vs. V s plots can be understood from current theoretical models describing the electron-induced heating of single molecules during electron transport [15,16]. Heat inside the molecule is generated by inelastic scattering of tunneling electrons with molecular vibrations (Fig. 5 (a)). For the large tunneling rates used in our experiment electron scattering leads to a non-equilibrium distribution of excited modes, whose internal energy can be associated with a molecular temperature T m . For a certain set of current and bias values, T m depends on the balance between the heat generated by the inelastic scattering of electrons with molecular modes, and heat dissipated into the "cold" electrode, in our experiment at 5 K [6,15,17]. Recent calculations [6] have shown that when a new resonance level E r enters into the transport energy window (hence, when eV s > E r ) a steep temperature increase takes place in the molecule as a consequence of more vibronic levels being accessible (Fig. 5 (a)). Hence, the increase in temperature upon crossing a resonance level manifests itself as a step-like decrease of the corresponding decomposition current I dec and power P dec , as shown in the plots of Fig. 4.
In contrast to this, tunnel electrons can also absorb vibrons of a hot molecule (Fig. 5 (b)), leading to a reduced heat generation. When the sample bias lies right below a resonance level eV s ≤ E r ) this cooling mechanism can be very effective and, eventually, causes a lower rise of molecular temperature with V s [5]. This behavior translates into plateaus in I dec and increase in P dec at bias values below the corresponding resonance energy. Qualitatively, the combination of both heating and cooling processes accounts well for the correspondence between the stepped (oscillating) behavior of the I dec (P dec ) plots and the resonant structure of the molecule in Fig. 4 [18]. However, it cannot explain the striking differences of P dec found for the different substrates. Since the mechanisms of heating/cooling by tunneling electrons depend on the coupling between tunnel electrons and molecular vibrons they are not expected to vary much on the different substrates. Hence, the large differences in P dec must be related to substrate mediated mechanisms of cooling the molecule.

SUBSTRATE DEPENDENCE OF DECOMPOSITION POWER
Further mechanisms of molecular cooling are those in which molecular hot modes decay by creating quasiparticle excitations in the substrate (either e-h pairs or phonons). In agreement with our findings, these excitations do not depend on the sample bias but may vary depending on the substrate's electronic and phononic properties. Decay of molecular vibrons into substrate phonons plays a minor role in cooling the molecule, since this mechanism is limited by the phonon band width of the substrates (Fig. 6 (a)). The Cu(110) phonon band is approximately 42 meV wide and therefore larger than in Pb(111) (14 meV [19]) and in Au(111)(16 meV [20]). However, the 174 internal modes of C 60 have energies between 33 meV and 200 meV. Hence, substrate phonons are expected to be primarily coupled to external molecular vibrations of the C 60 molecule with respect to the surface, which do not contribute to the thermal decomposition of the fullerene cage.
The most important contribution to the observed substrate dependence of P dec is the varying efficiencies of molecular cooling through electron-hole pair creation ( Fig. 6 (b)) [21]. Since the final states lie at excitation energies in the order of the vibrational band width of the molecule, the decay rate scales with the density of states around E F . On Cu(110) and Au(111), surface states provide most of the available states in this energy region, according to available data of DOS at E F [22]. It can therefore be expected, that e-h pair creation is favoured on Cu(110) with respect to the gold surface, in agreement with our observations. However, this mechanism fails to explain the intermediate P dec value found for degradation of C 60 on Pb(111), since this metal surface has no surface state, and whose density of bulk states at E F is also the lowest of all three metals [22].
To solve this puzzle we note that the absorption of molecular vibrons through excitation of electron-hole pairs rather depends on the density of states around E F in the C 60 molecule coming from the surface [5,23]. Therefore, this dissipation channel should not be viewed as an intrinsic property of the substrate material, but as a consequence of the molecule-surface interaction. In our case, we could experimentally determine that the LUMO derived resonances of C 60 on different metals exhibit a different degree of weight at the Fermi energy, associated to different amounts of charge transfer from the surface. In fact, the degree of charge transfer (increasing from Au(111) over Pb(111) to Cu(110), as shown in Fig. 7 (a-c)), follows the trend found for P dec in Fig. 4. This allows us to depict a qualitative picture, in which charge transfer from the metal causes an increase of the density of molecular states around E F . This favours the generation of e-h pairs at the molecule, which are then reflected back into the metal where they recombine. The rate of heat dissipation thus increases with the charge transfer, causing that a larger power is required to thermally degrade the single molecule. Ignoring additional mechanisms and effects like hybridization of metal and molecule states, which probably could also play an important role here, our results hint that charging a single molecule in contact with a metal electrode can help to sustain larger current densities crossing through a single molecule.

SUMMARY
Our experiments reveal that electronic currents in the range of 0.1-20 µA and powers in the order of 1-30 µW are sufficient to generate heat in single C 60 molecules leading to thermal decomposition on metal surfaces. The decomposition power results from the balance of molecular heating and cooling. While the former is substrate independent, the latter varies on the different substrates as a function of charge transfer into the molecule. Charge transfer assures an effective quenching of molecular vibrons into electron-hole pairs. In order to increase the current density a molecular junction can sustain, it is desirable to choose a substrate where molecular adsorption leads to a partial filling of molecular states by substrate electrons.
We thank Alessio Gagliardi and Alessandro Pecchia for helpful discussions. This research was supported by the Deutsche Forschungsgemeinschaft, through the collaborative projects SPP 1243 and SFB 658.