Thermal origin of light emission in non-resonant and resonant tunnel junctions

Electron tunneling is associated with light emission. In order to elucidate its generating mechanism, we provide a novel experimental ansatz that employs fixed-distance epitaxial graphene as metallic electrodes. In contrast to previous experiments, this permits an unobscured light spread from the tunnel junction, enabling both a reliable calibration of the visible to infrared emission spectrum and a detailed analysis of the dependence of the parameters involved. In an open, non-resonant geometry, the emitted light is perfectly characterized by a Planck spectrum. In an electromagnetically resonant environment, resonant radiation is added to the thermal spectrum, both being strictly proportional in intensity. In full agreement with a simple heat conduction model, we provide evidence that in both cases the light emission stems from a hot electronic subsystem in interaction with its linear electromagnetic environment. These very clear results should resolve any ambiguity about the mechanism of light emission in nano contacts.

When electrons tunnel from a metal to a metal driven by a voltage V , they enter the opposite electrode as hot injected electrons. Their energy/heat is then redistributed within the electronic system via electron-electron scattering. In graphene, this electronic thermalization appears within 20 fs to 30 fs, similar timescales are observed in common metals. 17 On much longer timescales, in the picosecond range, electron phonon cooling sets in, which is transferring the heat out of the electronic system. 18,19 Hence, within picoseconds the Joule heat is conserved in the electronic system and spreads outwards obeying the heat diffusion equation. In the stationary state, this means that at the injection spot the electron system is overheated in a two-fold sense: (i) there is a spatial decay of effective temperature T el,hot (r) towards equilibrium in the electronic system and (ii) this temperature detaches thermally from the underlying vibrational system.
The simplest description of the stationary case can be made by consulting the phenomenological Wiedemann-Franz-law. 20 We assume that there is a hot spot with radius r 1 at the junction where the heat is injected into the electronic system. Further there is electronic cooling towards a thermally equilibrated bath with temperature T B at a larger radius r 2 , where the heat is transferred to the lattice. Because in this inner region, the transport is purely electronic, the thermal conductivity λ = LσT (The Lorenz number L equals π 2 k 2 B /(3e 2 ) in a Drude description) determines the thermal gradient, σ is the electrical conductivity. As a result, at the tunnel junction, the electronic temperature is determined by for two dimensional heat spread. Note that in the high temperature limit T el,hot ∝ √ P el .
When we insert realistic numbers for a graphene tunnel junction, temperatures of a few thousand Kelvin can be reached. Such a hot electron system, however, emits light with a thermal spectrum. While we do not expect quantitative predictive power from this model, we will see that despite its simplicity (as compared to the models used in Refs. 7,8,15 ) this model gives a convincing description of nearly all phenomena.
The graphene nanojunctions are fabricated in a stepwise process. Starting with a lithographically defined graphene constriction, a controlled electroburning protocol 21 is performed, which leads via a graphene point contact (GPC) regime close to quantum conductance in which presumably a single carbon bond forms the junction, to finally a graphene tunnel contact (GTC).
First, we discuss the tunnel regime (GTC, Fig. 1a), in which the tunnel resistance is at least 100 kΩ. The IV characteristics display nonlinearities, from which we infer that the graphene lattice is interrupted. The tunnel pathway and the termination of the graphene sheet at the narrowest point is unknown. We focus on the observation that light is emitted from a narrow spot of approximately one micrometer size, i. e. at or below the optical resolution limit, when the voltage exceeds ≈1.5 V. We performed a spectral analysis of the emitted light in the visible and near-infrared regime with two different detectors. A careful spectral calibration was performed by replacing the sample holder by a macroscopic heated cavity with controlled temperature. Its blackbody radiation served as standard to calibrate the full optical pathway and the detectors. Reliable results were obtained above 550 nm, at lower wavelengths the calibration provides inaccuracies and is not further considered. We performed a Planck fit to the infrared part of the data (1000 nm to 1600 nm), for which the temperature T Planck and a proportionality constant are the only free parameters. 22 It matches well and results in temperatures well beyond 2000 K, see Fig. 1c. We assign this broad signal to thermal radiation, which will become much more evident when going one step back in our fabrication scheme.
Before the electroburning process reaches the tunnel regime an important threshold in conductance is the GPC regime in which the junction conductance is close to quantum con-ductance. In the description of charge transport through nanojunctions, it plays a particular role because here the transmission, the shot noise amplitude and the light emission should be strongly dependent on details. 11, 23,24 In graphene, the contact is then presumably formed by a single or few C-C bonds, 25,26 c. f. Fig. 1b. This regime is particularly stable: when applying a voltage to the GPC, under ambient conditions its light emission can be seen with the bare eye up to a bias voltage of approximately 3 V, beyond which the device fails. For a sample mounted in cryogenic vacuum, the voltage range can be significantly extended up to 8 V, sometimes even 10 V. The data have strong similarity to the GTC case, in particular the curves increase monotonously with bias. Here however, for any voltage, we find excellent match of the full emission spectra to Planck's formula (see Fig. 1d), reaching 2300 K at 8 V. Notably, despite both graphene and SiC are extremely robust materials, at these temperatures SiC would thermally decompose. 27,28 Even in the presence of air, T Planck as high as 1600 K was observed, a temperature at which the graphene electrodes would simply burn away. We conclude from these purely experimental findings that in GPCs there are subsystems at different temperatures. As dissipation starts with an electronic process which is subsequently cooled by electron-phonon relaxation processes, 19,29 we can assign the light emission with its T Planck to the electronic system, whereas in particular the carbon lattice must be significantly colder, below the degradation threshold. Given the similarity and the continuous evolution of the spectra it can be concluded that also in the GTC regime similar physics rule, i. e. a hot electron subsystem determines the light emission.
Within the picture of an overheated electron temperature at the junction, the differences between GTC and GPC can readily be understood: In the GTC case, a large fraction of the applied voltage drops along the tunnel distance, i. e. within roughly 1 nm. The result is a hot electron subsystem, the diameter of which can be estimated to be less than the electron-phonon scattering length scale, in accordance with the resolution limited spot.
When, however, the junction is in the GPC case, the point contact resistance, the spreading resistance and the electric leads are all in the 10 kΩ range, hence, the sharp voltage drop at the nanojunction is strongly diminished. This goes along with a reduced electronic temperature. Another qualitative confirmation can be achieved by changing the material (quasifreestanding bilayer graphene on SiC is used, see S.I. section 6) such that the electron-phonon scattering rate is lowered. There, much higher electronic temperatures can be achieved with the same applied bias, extending light emission into the so called overbias regime, 4 a category that turns out to be irrelevant. Because in the GPC case the spectral information is particularly clear and the stability is outstanding, it is well suited to study the underlying mechanisms in detail.
First, the concept of the overheated electronic subsystem is investigated. According to Eq. (1), T el,hot (P el ) is essentially linear above a certain threshold. The large spectral range gives immediate access to the Planck temperature. Indeed, the data follow a linear relation, however with a kink that presumably indicates that an additional cooling mechanism comes into play, see Fig. 2a. We suspect that a fraction of the injected electrons above the work function of graphene leave the material and thus reduce P el . In a next step, we investigate the power dependence of the emitted light. Because the junction distance is fixed and the material system SiC/graphene withstands very high electric fields, we have access to an unusually broad range. Fig. 2b presents the intensity measured via avalanche photo detectors, i. e. counting photons up to approximately 900 nm. In this representation, the intensity appears as a straight line over six orders of magnitude in intensity, which emphasizes that only one, clearly defined mechanism rules over the entire range. This behavior can readily be understood: when inserting Eq. (1) into Planck's law, such a behavior follows immediately (see S.I. section 4). Hence, these high-quality spectra and voltage dependencies prove that the origin of light emission is thermal and the simple heating model is presumably the simplest valid description.
We now readdress the tunnel regime (GTC). As we can determine the Planck temperature from the infrared part of the spectrum, we subtract the Planck part from the experimental data and obtain a resonance-like contribution, centered around 720 nm, see Fig. 2c, which appeared as shoulder-like anomaly in Fig. 1c. Its intensity increases with increasing voltage without a spectral shift. Even the peak shape is maintained but slightly differs from sample to sample like a fingerprint. This feature, being absent in GPCs, is sensitive to atomistic details of the tunnel junction and offers opportunities: we understand it as a local resonant electromagnetic environment of the tunnel process. To conclude, we measured voltage dependent spectra of light emission when electrons tunnel from graphene to graphene. The extensive data show unambiguously that the light source is essentially a hot electronic subsystem, far above the lattice temperature, in agreement with a simple heat-spread model. Sharp tunnel gaps provide further an electromagnetic resonance, which reveals that the thermal light can be spectrally shaped: hot electrons, thermal radiation and resonant excitation are rigidly connected phenomena. According to our experiments, in tunnel junctions with point-like injection, the luminescence is driven by Joule heating of the electronic system.
• This work was supported by the Deutsche Forschungsgemeinschaft (DFG), Project No.
• The authors declare that they have no competing financial interests.
•  P l a n c k i n t e n s i t y [ a . u . ] d Figure 2: (a) Planck temperature as derived from the Planck spectra as a function of √ P el of a GPC sample. Two strictly linear regions can be identified in full accordance to Eq. 1, the kink may indicate a crossover in cooling mechanisms. (b) Intensity dependencies on P −1/2 el (GPC and GTC samples), which on the logarithmic scale appears as a straight line over six orders of magnitude (the constant dark count rate has been subtracted). (c) Analysis of the shoulder-like feature in Fig. 1c, which appears as a self-similar resonance. (d) The amplitude of the latter scales strictly linear with the amplitude of the underlying blackbody radiation. The simplicity of all parameter dependencies (dashed straight lines are guides to the eye) is remarkable and underscores the validity of the model.