Main

Immediately after photoexcitation of an optoelectronic device, energetic electrons scatter with other high-energy and ambient charge carriers to form a thermalized hot electron gas, which further cools by dissipating excess energy to the lattice. Owing to the short distance travelled by charge carriers between electron–electron scattering events in solids18, equilibration among the electrons occurs on timescales from tens of femtoseconds to picoseconds19,20. In graphene, a low-dimensional material with much enhanced Coulomb interaction21, electron thermalization is known to occur on extremely fast timescales (<30 fs; refs 22,23,24,25), reflecting the extremely short transit length between scattering events. Most analyses of graphene have, therefore, treated its electrons as being instantaneously thermalized26,27,28,29, and slightly non-thermal electronic behaviour has thus far only been reported in pump-probe experiments with ultrashort (∼10 fs) laser pulses and low excitation density8,9. Owing to such short time (femtosecond) and length (nanometre) scales, it is challenging to detect and control the thermalization process in graphene or, more generally, in any solid-state systems.

In this letter, we report an approach to probe and manipulate the electron thermalization in graphene by introducing a new energy transport channel that competes with the thermalization process. Such an additional dynamical pathway is realized in a vdW heterostructure30 that consists of a G–BN–G stack (Fig. 1a–c). In this layered structure, the photoexcited electrons in one graphene layer can travel vertically to the other graphene layer through the very thin middle BN layer (blue dashed arrow in Fig. 1b). Given the close proximity of these layers, interlayer charge transport can occur on extremely fast timescales31, and thus compete directly with the intralayer thermalization process (red arrows in Fig. 1b). In our experiment, we have observed such competing processes by measuring the interlayer photocurrent under different bias and excitation conditions. Remarkably, by adjusting the interlayer bias voltage or varying the excitation photon energy, we can control the interlayer charge transport to occur slower or faster than the intralayer thermalization, thus tuning the thermalization process. Our experiments not only provide valuable insight into the electron dynamics of graphene, but also demonstrate a means to manipulate electron thermalization in low-dimensional materials.

Figure 1: Interlayer photocurrent of a G–BN–G device.
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a, Schematic of a G–BN–G device under optical excitation. b, Schematic of intralayer thermalization and interlayer transport of the optically excited carriers. c, Band alignment between graphene and BN. BN has a band gap of ∼5.9 eV, and the Dirac point of graphene is located ∼1.3 eV (Δ) above the edge of the BN valence band33. d, Optical image of a G–BN–G device, which consists of a top exfoliated graphene layer (white line), a 14-nm-thick BN flake, and a bottom graphene layer grown by chemical vapour deposition (dashed red line). e,f, Scanning images of interlayer photocurrent at interlayer bias Vb = −0.5 and 0.5 V, respectively. g, Interlayer photocurrent as a function of Vb with and without light illumination. All measurements were carried out with 600-nm optical excitation from a supercontinuum laser at T = 100 K. The incident laser power is 500 μW for e,f and 100 μW for g.

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We fabricated the G–BN–G heterostructure devices on Si/SiO2 substrates by mechanically co-laminating graphene sheets and hexagonal boron nitride (BN) flakes32 with 5–30 nm thickness (Fig. 1a, d; see Methods). In our experiment, we applied a bias voltage Vb between the top and bottom graphene and measured the corresponding interlayer current I under optical excitation. The main light source is a broadband supercontinuum laser that provides bright semi-continuous radiation from wavelength λ = 450 to 2,000 nm (see Methods). To probe the interlayer current in the time domain, we also used femtosecond laser pulses from an 80 MHz Ti:sapphire oscillator. We have measured four G–BN–G devices with monolayer graphene and two devices with few-layer (≤four layers) graphene, and found similar results. The device characteristics are therefore insensitive to a slight change of graphene layer thickness.

Figure 1d–f shows the optical image of a G–BN–G device and the corresponding device characterization using scanning photocurrent microscopy. Photocurrent images at interlayer bias voltages Vb = −0.5 and 0.5 V under laser excitation at a wavelength of 600 nm show that the photocurrent I appears only in the area where the two graphene layers overlap with each other. The photocurrent magnitude increases significantly with Vb, and its direction flips with the sign of bias voltage (Fig. 1g). We do not observe any current in the absence of illumination, indicating that optical excitation is necessary to generate a measurable interlayer current in our G–BN–G devices. On the basis of recent first-principles calculations33, the graphene Dirac point is located at Δ ∼ 1.3 eV above the BN valence band edge, and ∼4.5 eV below the conduction band edge (shown schematically in Fig. 1c), in agreement with dark tunnelling measurements15,16. This suggests that, because the potential energy barrier Δ is much smaller for positive charge carriers (holes) than for electrons, the interlayer current is mediated predominantly by holes.

The photocurrent in our G–BN–G devices exhibits a complex dependence on excitation laser power P, interlayer bias Vb, and excitation photon energy ℏω (Fig. 2). Although the photocurrent generally increases with laser power, it exhibits both linear and superlinear power dependences, depending sensitively on bias voltage and photon energy. If we keep a constant bias Vb = 5 V, I increases superlinearly with P at ℏω = 1.75 eV (red dots in the left panel of Fig. 2a), yet gradually becomes linear as the photon energy increases to ℏω = 2.43 eV (purple squares). If we instead keep a constant photon energy ℏω = 2.10 eV, the photocurrent increases superlinearly with P at Vb = 1.5 V (red dots in the right panel of Fig. 2a), then gradually becomes linear as the bias increases to Vb = 10 V (purple squares).

Figure 2: Two different regimes of interlayer photocurrent in a G–BN–G device.
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a, Photocurrent I as a function of excitation laser power P, at constant interlayer bias Vb = 5 V but increasing photon energies ℏω = 1.75, 2.10, 2.25 and 2.43 eV (left panel), and at constant photon energy ℏω = 2.10 eV but increasing bias Vb = 1.5, 3.75, 5 and 10 V (right panel). For better comparison, the current and laser power are normalized, and the data are fitted with a power law I ∼ Pγ. The raw data are shown in the Supplementary Information. b, Colour map of γ as a function of Vb and ℏω. The colour scale is customized to make the area with γ > 1 (Region A) and γ = 1 ± 0.02 (Region B) appear red–yellow and blue, respectively. The black dashed lines are contours corresponding to tunnelling times of 2, 7, 100 and 1,000 fs, predicted by our model described in the text. c, Schematics depicting the thermionic emission and the direct carrier tunnelling as the dominant photocurrent mechanism, respectively, for Region A and B in b. All measurements were carried out with a supercontinuum laser at T = 100 K.

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Remarkably, the complexity of the photocurrent variations can be efficiently captured by a single fitting parameter γ, which we obtained by fitting all photocurrent versus power data with a simple power law I ∼ Pγ. Figure 2b, our main result, shows γ over a wide range of bias voltage and photon energy. The data is separated into several distinct regions, labelled A and B, highlighting the superlinear (γ > 1, red–yellow colour) and linear (γ = 1 ± 0.02, blue) power dependence of the photocurrent, respectively. The value of γ demonstrates a clear and gradual transition from γ ∼ 3 at low bias and photon energy (regime A) to γ ∼ 1 at high bias voltage and photon energy (regime B; see Supplementary Information).

We attribute the complex photocurrent behaviour to the transition between two distinct processes, thermionic emission and direct carrier tunnelling, both of which mediate charge carrier transit through the G–BN–G heterostructure (Fig. 2c). In thermionic emission, the photoexcited carriers remain in the graphene, scatter with one another, and quickly reach thermal equilibrium among themselves. High-energy carriers in the hot tail of the resultant thermal distribution have sufficient energy to overcome the potential energy barrier Δ, and will travel to the other graphene layer34,35,36. Whereas previous studies29,37 have shown that the temperature of hot carriers in graphene scales with laser power approximately as T ∼ P1/3, the population of thermionically emitted carriers increases exponentially with the temperature for the high BN barrier. We therefore expect an overall superlinear dependence of the photocurrent on the laser power34 (see Supplementary Information). This behaviour matches well with our observation at low Vb/ℏω (Regime A in Fig. 2b, c).

In contrast, at high Vb/ℏω, the effective BN barrier is reduced, allowing the excited carriers to tunnel from one graphene layer to the other before they scatter with other carriers. Given the energy height and thickness of the BN potential energy barrier, optical excitation is necessary to assist the tunnelling process15,16. The photon-assisted tunnelling current then scales with the number of initial photoexcited carriers and, therefore, increases linearly with laser power. This behaviour matches well with the observed linear power dependence of photocurrent at high Vb/ℏω (Regime B in Fig. 2b, c).

To confirm that electron thermalization dominates the photocurrent response in the thermionic regime, we performed photocurrent measurements using a Ti:sapphire femtosecond laser at low Vb/ℏω. At a photon energy of 1.55 eV, photoexcitation with short pulses (90-fs duration) produces a photocurrent that is orders of magnitude higher than that with a supercontinuum laser (pulse duration ∼90 ps) at the same fluence, indicating that shorter pulses produce a higher transient electronic temperature. In addition, we measured the photocurrent under photoexcitation by two identical laser pulses with orthogonal polarization (Methods) and varying temporal separation29,37. We observed strong positive two-pulse correlation in the photocurrent signal, which exhibits a short component (< 100 fs) and a long component (∼1 ps; Fig. 3 and Methods). These results, consistent with thermionic emission, are similar to the previously reported two-pulse correlation of hot photoluminescence3, a phenomenon that arises from hot carriers at the high-energy tail of the thermal distribution in graphene. Moreover, positive correlation in the two-pulse photocurrent measurement immediately excludes direct carrier tunnelling with a linear P-dependence as the main photocurrent mechanism at low Vb. We thus conclude that the observed photocurrent at low Vb/ℏω arises from high-energy thermalized carriers in graphene.

Figure 3: Two-pulse correlation of interlayer photocurrent in a G–BN–G device.
figure 3

a, Photocurrent at Vb = 0.1 V, as a function of temporal separation between two identical but cross-polarized excitation pulses. The incident fluences of each beam are 0.74, 1.95 and 3.54 J cm−2. The pulse duration is 90 fs and the photon energy is 1.55 eV. b,c, The time constants of the fast and slow components, respectively, at different incident fluences. They are extracted by fitting the correlation data with a symmetric biexponential function convolved with a Gaussian function of width 130 fs. All measurements were carried out with a Ti:sapphire laser at T = 300 K.

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In the photon-assisted tunnelling regime (high bias voltage and photon energy), electron tunnelling is described by the Fowler–Nordheim (FN) formalism. For electrons tunnelling through a triangular barrier in the presence of a high electric field, the current–voltage characteristics take the form38:

Here m is the carrier effective mass in the barrier region, and the width d is determined by the BN thickness (see Supplementary Information).

The FN model exhibits several features that serve as fingerprints of a non-thermal carrier tunnelling process, and can be compared directly with experiment. Equation (1) suggests a linear relationship between ln(I/Vb2) and 1/Vb, with a bias-independent slope −β. To examine the regime over which this behaviour holds, we analysed the I–Vb data taken under supercontinuum laser excitation. Figure 4a shows ln(I/Vb2) versus 1/Vb at positive bias over a range of photon energies. At high bias or photon energy (Region B in Fig. 2c), we observed a linear relationship that breaks down at low Vb/ℏω, where thermionic emission dominates (Region A). We extracted the slope (−β) from the linear fits, and found that β2/3 scales linearly with the excitation photon energy ℏω, consistent with equation (2) (red dots in Fig. 4b). From fitting the data and comparing to equation (2), we estimate the barrier height from the x-axis intercept to be Δ = 1.25 eV. Similar results were obtained at negative bias (see Supplementary Information), with a slightly higher estimated barrier height Δ = 1.31 eV (blue dots in Fig. 4b). These values agree well with the predicted potential barrier (∼1.3 eV) between graphene and BN by first-principles calculations33, and confirm that the photocurrent is dominated by direct carrier tunnelling at high Vb/ℏω.

Figure 4: Experimental signatures of direct Fowler–Nordheim carrier tunnelling.
figure 4

a, ln(I/Vb2) as a function of 1/Vb at different excitation photon energies in the range ℏω = 2–2.48 eV. The blue lines highlight the linear behaviour at high bias, with a slope of −β. b, β2/3 as a function of ℏω at positive bias (red dots) and negative bias (blue dots). The lines are linear fits with x-intercepts at 2Δ, where Δ = 1.25 and 1.31 eV correspond to the barrier height in the Fowler–Nordheim formula (equation (2) in the text). c, d2I/dVb2 map as a function of Vb and ℏω. The black lines highlight two oscillation features with a separation of 200 meV. All measurements were carried out with a supercontinuum laser at T = 100 K.

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By adjusting the interlayer bias voltage and excitation photon energy, we can tune the interlayer transport process, thus allowing us to pinpoint the regime in which both processes occur on similar timescales. For direct carrier tunnelling, the average lifetime of photoexcited carriers τtun can be estimated as τtun = τ/T(E) ∼ h/ΔET(E), where τ ∼ h/ΔE is approximated from the uncertainty principle (see Supplementary Information), h is Planck’s constant, ΔE is the energy difference between initial and final states, and T(E) is the Wentzel–Kramers–Brillouin (WKB) transmission probability38,39. Both T(E) and τ depend on the excitation energy and bias voltage, whereas T(E) also contains information about the barrier height and effective mass in BN (see Supplementary Information). As a function of bias voltage and photon energy, this model predicts that the average lifetime remains constant over a series of lines in ℏω versus Vb space. Figure 2b shows several of these lines (black dashed lines) and the corresponding times (τtun = 2, 7, 100 and 1,000 fs). Carrier tunnelling occurs faster at high Vb/ℏω than at low Vb/ℏω, with τtun ranging from 1 fs to almost infinity (near zero bias voltage). Our estimate of τtun exhibits remarkable agreement with experiment. In particular, the contour at τtun = 7 fs effectively captures the main transition (blue to red) between features in our photocurrent image. Furthermore, the fit implies a carrier thermalization time of the order of 10 fs in graphene, which indeed matches excellently the results from other ultrafast experiments23.

In the regime for which the thermalization time matches the carrier lifetime of tunnelling (white–red areas in Fig. 2b), we also observed peculiar behaviours in the I–Vb characteristics, indicating a strong transition between direct tunnelling and thermionic emission. Particularly, we observed an abrupt change of linearity between ln(I/Vb2) and 1/Vb (Fig. 4a), which signifies the breakdown of the FN approximation as Vb/ℏω decreases, and hence a diminishing contribution from non-thermal carrier tunnelling. Intriguingly, at the onset of FN tunnelling, weak oscillations in the ln(I/Vb2) versus 1/Vb plot can be seen. These can be more easily observed by plotting d2I/dVb2, which changes between negative and positive values as Vb/ℏω increases (blue and red stripes in Fig. 4c). We also observe an additional replica oscillation feature that appears parallel to, yet ∼200 meV above, the major oscillation feature in the d2I/dVb2 map. These subtle features may indicate resonance effects in the FN tunnelling regime, whose origin could be related to field emission resonances40 due to spatial confinement or resonant phonon emission38,41,42. More work, beyond the scope of this manuscript, will be needed to investigate in depth the origin of these resonances.

Methods

Device fabrication.

We fabricated G–BN–G heterostructure devices on Si/SiO2 substrates. The graphene layers were prepared either by mechanical exfoliation of graphite or by chemical vapour deposition (CVD) on a copper surface. In the heterostructure, the bottom layer was either exfoliated graphene, or transferred CVD graphene that was patterned into strips by e-beam lithography and O2 plasma etching. The middle BN flake was exfoliated from high-quality bulk crystals onto methyl methacrylate (MMA) polymer and transferred onto the bottom graphene. The top graphene layer was similarly exfoliated onto MMA polymer and transferred onto the BN. Finally, we deposited 0.8/80-nm Cr/Au electrodes with e-beam lithography and thermal evaporation.

Photocurrent measurements.

We carried out the photocurrent experiment in a confocal microscope. The devices are mounted in an optical cryostat cooled by liquid helium, with controllable temperature in the range of 4–300 K. The excitation beam comes from a broadband supercontinuum fibre laser (Fianium and SuperK). The beam, with wavelength tunable by means of a monochromator, is focused onto the samples with a spot diameter of ∼1 μm. By using a piezoelectrically controlled mirror, we can scan the beam across the whole device area to obtain photocurrent images. The current is measured by using a lock-in preamplifier at an optical chopper frequency of 77 or 740 Hz.

Two-pulse correlation measurements.

We have carried out time-domain photocurrent measurements with an 80-MHz Ti:sapphire oscillator (Tsunami) that generates femtosecond laser pulses with central wavelength 800 nm. The laser is separated into two equally intense beams with controllable path-length difference, and focused onto the devices with a spot diameter of ∼2 μm. Photocurrent was measured as a function of temporal separation between the two pulses. To suppress the interference at zero time delay, the polarizations of the two beams were set to be orthogonal to each other by a half-wave plate. A set of neutral density filters was used to adjust the pump fluence. We have characterized the pulse duration with second harmonic autocorrelation. From the autocorrelation width (∼130 fs), we determined a pulse duration of ∼90 fs at our sample position. The response time of the devices is extracted by fitting the photocurrent correlation data with a symmetric biexponential function convolved with a Gaussian function of width ∼130 fs.