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Supplementary Information for Tuning ultrafast electron thermalization pathways in a van der Waals heterostructure

Qiong Ma1†, Trond I. Andersen1†, Nityan L. Nair1†, Nathaniel M. Gabor1*, Mathieu Massicotte2, Chun Hung Lui1, Andrea F. Young1, Wenjing Fang3, Kenji Watanabe4, Takashi Taniguchi4, Jing Kong3, Nuh Gedik1, Frank H. L. Koppens2, Pablo Jarillo-Herrero1*

†These authors contributed equally to this work.

*Correspondence to: [email protected]; [email protected]

1 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 2 ICFO, Mediterranean Technology Park, Castelldefels (Barcelona) 08860, Spain 3 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 4 National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

Contents:S1. Details of devicesS2. Modeling of the interlayer current after thermalization of photo-excited carriers S3. Relative contributions between lower-energy tunneling and higher-energy thermionic emission after thermalizationS4. Estimation of the average lifetime of photocarriers in the direct tunneling regime S5. Fowler-Nordheim tunneling with extraction of barrier heightS6. Discussions about the contribution from BN defects S7. Additional data and figures

In this supplementary material, S1 describes the details of the devices from which data in the main text was gathered. In Section S2-S4, we provide a theoretical model that was used to fully simulate our system and strongly supports our claims in the main text. S2 and S3 focus on the regime where the photo-excited carriers fully thermalize before crossing the BN barrier, which leads to well-defined electronic temperatures in the graphene layers, from which we can calculate the interlayer current contributions from carriers of different energies. The calculation shows that in the regime of our interest, lower-energy tunneling current contributes little compared with the higher-energy thermionic emission due to the strongly suppressed transmission probability for low-energy carriers, which leads to a highly super-linear power dependence. As discussed in the main text, the electron thermalization is turned off at high bias voltage and photon energy, since direct vertical extraction into BN then supersedes thermalization. Thus, in Section S4, we focus on estimating the direct extraction time from uncertainty principle and tunneling probability, which is then used to estimate a bound on the thermalization time. In all the simulations, the top and bottom layers are both monolayer

Tuning ultrafast electron thermalization pathways in a van der Waals heterostructure

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graphene and are charge neutral at zero bias. In reality, the devices are asymmetric, as manifested in the experimental data. Section S5 describes in detail the Fowler-Nordheim model we used in the main text to support the non-thermal carrier tunneling and extract the barrier height. Section S6 includes some additional data and figures. Considering the large number of symbols employed in this SI, we use Vbias instead of Vb throughout this text. S1. Details of devices in the main text

The data shown in the main text come from two similar devices, which behave very similarly in all the measurements presented in the main text. Table S1 summarizes the structures of the devices and the assembly methods, as well as which figure comes from which device. The exfoliated MLG on BN has very little extrinsic doping, while the few-layer graphene and CVD MLG are heavily doped and shows very weak modulation with gating.

Device number Top layer Bottom layer

BN thickness

(nm) Assembly method

Main Figure

1 Exfoliated monolayer graphene

CVD monolayer graphene 14 dry-transfer1,2 1 and 3

2 Exfoliated bilayer graphene

Exfoliated four-layer graphene 20 dry-transfer 2 and 4

Table S1| Device details used in the main text. S2. Modeling of the interlayer current after thermalization of photo-excited carriers

As shown in Figure S1a, we model the heterostructure as multiple parallel plate capacitors, containing four plates separated by dielectrics. The two middle plates correspond to the top and bottom graphene layers, while the outermost plates account for gating effects. We define the electrochemical, electrostatic and chemical potentials of the electrons in plate i as eVi, Ui and μi, respectively (i = 1, 2, 3, 4), where eVi = Ui + μi. The dielectric constant and thickness between consecutive plates i and i+1 are �� and di,i+1, respectively, allowing us to find the electrostatic potential difference from Gauss’ law:

�� − �� = ∑ ��

�� = − ∑ ��

�� (S1)

where �� is the charge density of plate j (electron density is positive and hole density is negative). The sums ∑ �� and ∑ ��

�� here represent the total charge densities below and above capacitor i, respectively. These are opposite, since the field outside the capacitor is zero, giving:

�� = 0 (S2)

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Writing the electrochemical potential differences as the sum of the chemical and electrostatic potential differences, we then find:

�(�� − ��) = �� − �� − ��

�� = �� − �� − ��

� (S3)

�(�� − ��) = �� − �� − ��

�� = �� − �� − ��

� (S4)

�(�� − ��) = �� − �� + ��

�� = �� − �� + ��

� (S5)

where �� = ��

= �� is the capacitance per area and elementary charge. We can reduce

equations (S2-5) to: −�� = ��(�� − ��) − (�� − ��)� + ��(�� − ��) − (�� − ��)� (S6) �� = ��(�� − ��) − (�� − ��)� − ��(�� − ��) − (�� − ��)� (S7)

which obey the mirror symmetry between the two layers of graphene. In reality, we do not have a top gate, so we set �� = 0. Furthermore, the back gate dielectric SiO2 is much thicker (~ 300 nm) than the interlayer BN dielectric (~ 10 nm), and the dielectric constants of BN and SiO2 are similar, so we approximate �� = 0 in equation (S7) as well. It can be seen from fig. S1 that V3 − V2 = Vbias as well as V4 − V3 = VBG, and by changing the subscripts i = 2, 3 to t (top) and b (bottom), we get the simple form:

�� = −�� = � �� − (��)� � (S8)

with C = �/(de) (� and d are the dielectric constant and thickness of BN, respectively). We note that the above derivation is based on the assumption that there is no residual doping, meaning that the top and bottom graphene are chemically undoped, i.e., nb = nt = 0 and μb = μt = 0 at zero bias voltage. In order to incorporate residual doping, we can rewrite (S8) as

�� = −�� = � �� − (��)� � (S9)

where �� = �� − ��, �� = �� − ��, �� = �� − �� and �� = �� − �� (subscript 0 refers to quantities measured at Vbias = 0).

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SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3620


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graphene and are charge neutral at zero bias. In reality, the devices are asymmetric, as manifested in the experimental data. Section S5 describes in detail the Fowler-Nordheim model we used in the main text to support the non-thermal carrier tunneling and extract the barrier height. Section S6 includes some additional data and figures. Considering the large number of symbols employed in this SI, we use Vbias instead of Vb throughout this text. S1. Details of devices in the main text

The data shown in the main text come from two similar devices, which behave very similarly in all the measurements presented in the main text. Table S1 summarizes the structures of the devices and the assembly methods, as well as which figure comes from which device. The exfoliated MLG on BN has very little extrinsic doping, while the few-layer graphene and CVD MLG are heavily doped and shows very weak modulation with gating.

Device number Top layer Bottom layer

BN thickness

(nm) Assembly method

Main Figure

1 Exfoliated monolayer graphene

CVD monolayer graphene 14 dry-transfer1,2 1 and 3

2 Exfoliated bilayer graphene

Exfoliated four-layer graphene 20 dry-transfer 2 and 4

Table S1| Device details used in the main text. S2. Modeling of the interlayer current after thermalization of photo-excited carriers

As shown in Figure S1a, we model the heterostructure as multiple parallel plate capacitors, containing four plates separated by dielectrics. The two middle plates correspond to the top and bottom graphene layers, while the outermost plates account for gating effects. We define the electrochemical, electrostatic and chemical potentials of the electrons in plate i as eVi, Ui and μi, respectively (i = 1, 2, 3, 4), where eVi = Ui + μi. The dielectric constant and thickness between consecutive plates i and i+1 are �� and di,i+1, respectively, allowing us to find the electrostatic potential difference from Gauss’ law:

�� − �� = ∑ ��

�� = − ∑ ��

�� (S1)

where �� is the charge density of plate j (electron density is positive and hole density is negative). The sums ∑ �� and ∑ ��

�� here represent the total charge densities below and above capacitor i, respectively. These are opposite, since the field outside the capacitor is zero, giving:

�� = 0 (S2)

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Writing the electrochemical potential differences as the sum of the chemical and electrostatic potential differences, we then find:

�(�� − ��) = �� − �� − ��

�� = �� − �� − ��

� (S3)

�(�� − ��) = �� − �� − ��

�� = �� − �� − ��

� (S4)

�(�� − ��) = �� − �� + ��

�� = �� − �� + ��

� (S5)

where �� = ��

= �� is the capacitance per area and elementary charge. We can reduce

equations (S2-5) to: −�� = ��(�� − ��) − (�� − ��)� + ��(�� − ��) − (�� − ��)� (S6) �� = ��(�� − ��) − (�� − ��)� − ��(�� − ��) − (�� − ��)� (S7)

which obey the mirror symmetry between the two layers of graphene. In reality, we do not have a top gate, so we set �� = 0. Furthermore, the back gate dielectric SiO2 is much thicker (~ 300 nm) than the interlayer BN dielectric (~ 10 nm), and the dielectric constants of BN and SiO2 are similar, so we approximate �� = 0 in equation (S7) as well. It can be seen from fig. S1 that V3 − V2 = Vbias as well as V4 − V3 = VBG, and by changing the subscripts i = 2, 3 to t (top) and b (bottom), we get the simple form:

�� = −�� = � �� − (��)� � (S8)

with C = �/(de) (� and d are the dielectric constant and thickness of BN, respectively). We note that the above derivation is based on the assumption that there is no residual doping, meaning that the top and bottom graphene are chemically undoped, i.e., nb = nt = 0 and μb = μt = 0 at zero bias voltage. In order to incorporate residual doping, we can rewrite (S8) as

�� = −�� = � �� − (��)� � (S9)

where �� = �� − ��, �� = �� − ��, �� = �� − �� and �� = �� − �� (subscript 0 refers to quantities measured at Vbias = 0).




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figure S1| Schematic of the heterostructure and its band alignment. a, We model the stack as a series of capacitors. Plate 1 and 4 are top and back gates, respectively. Plate 2 and 3 are the top and bottom graphene layers. Blue layers are dielectrics. b, Band alignment between the two graphene layers and relevant symbols used in the text. Integrating over carrier energies in each flake gives another two expressions relating �� and ��: �� = � ��(�∞

� ) � ��(�� )�� − � ��(��∞

) � �1 − ��(�� )�� (S10)

�� = � (� + ��) � ��(�∞

� ) � ��(�� )�� − � (� + ��) � ��(��∞

) � �1 − ��(�� )�� (S11) where � = �� . Here, ��(�) and ��(�� ) = (�(��)�� + 1)�� are the density of states and Fermi-Dirac distribution of layer i, respectively. The need for equation (S11) comes from the fact that the system can reach very high electronic temperatures (~103 K) after optical pumping and we are interested in features that appear close to the charge neutrality points of the graphene layers. We can thus not assume that �� , so the Sommerfeld expansion is invalid, preventing us from simply using a heat capacity linear in temperature to convert changes in total energy to electronic temperature. Equations (S9-11) relate the carrier density n, electronic temperature T, chemical potential � and total energy E of the two flakes implicitly at any given point in time, providing a good framework for modeling the system temporally throughout the course of a laser pulse. At each time step, we first let the energy evolve with time and then use equations (S9-11) to update the remaining variables as well. The time evolution of energy is formulated by considering the emission of both optical (OP)3,4 and acoustic (AC) phonons, the latter of which includes both supercollision5,6 (SC) and normal collision (NC) cooling mechanisms7:

�� = �� (�) − 9.62 �� (��)��

ℏ�� (�� − ��)��

��

− �� (��)ℏ��(�� − ��)��

− ��

ℏ � ��(�� )��(�)(1 −∞

�∞

��(� − �� ))��(�−��)��

� � = �� (S12)

�� = ��2��

�� = 2ℏ��

where �� (�) is the absorbed laser intensity at time t, ��(��) is the electron-acoustic (optical) phonon coupling constant, T0 is the lattice temperature, �� is the Fermi wave number, s is the sound speed in graphene, �� is the Boltzmann constant, N is the number of spin/valley flavors, l is the mean free path, D is the deformation potential, a is the bond length in graphene, �� is the mass density, and �� = 197 meV is the optical phonon energy. Together, equations (S9-12) allow for describing the time evolution of the system completely, given the bias voltage and laser power. In S3, we show how the interlayer current can be evaluated at each time step from � and T of both layers.

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The above analysis is based on the assumption that photo-excited carriers thermalize and form a hot Fermi-Dirac distribution with an effective temperature T before generating vertical electric current, which is not always the case (see S4). Moreover, equation (S12) does not include the complete set of cooling channels. Lateral diffusion of hot carriers away from the excitation spot is expected to act as an additional cooling pathway on a time scale of ~ 1 ps (beam spot size (~ 1 μm) divided by the Fermi velocity of electron). In addition, the interlayer current itself cools the system by vertical hot carrier extraction, which could dominate over conventional electron-lattice cooling and lateral diffusion. S3. Relative contributions from under-barrier tunneling and above-barrier thermionic emission after thermalization

We will first consider the simple case of no residual doping in either graphene layers, and focus on the situation where carriers thermalize before crossing the barrier. For a certain Fermi-Dirac distribution at temperature T, there will be carriers (in this case holes) with energies both below and above the barrier. While the former have to rely on quantum tunneling to cross the BN, the latter can be classically emitted over the barrier (thermionic emission). In both cases, the number of holes with energy E moving from the bottom (top) to the top (bottom) layer is proportional to the hole occupancy in the bottom (top) layer ��(� − ��(�))(� − ��(� − ��(�), ��(�), ��(�))) and the electron occupancy/hole vacancy in the top (bottom) layer ��(� − ��(�))��(� −��(�), ��(�), ��(�)), since the Pauli exclusion principle entails that carriers can only move into available states. The interlayer current also scales with the transmission probability ��(�, ��, ��), which is found using the WKB method:

Tr(�) =

�� √��∗

��(��) �(Δ� � �� − �)�� − (�� − �)�

�� Δ� � �� (��, ��)�� √��∗

��(��) (Δ� � �� (��, ��) − �)�� Δ� � �� (��, ��) � � � Δ� � �� (��, ��)

� � � Δ� � �� (��, ��) (S13)

Here Δ� is the barrier height in an ungated, zero-biased system, and ��(�) is the electrostatic potential of the top (bottom) flake, which equals its Dirac point energy (Figure S1b). Since the BN barrier is pinned to the Dirac cones, its slanted part goes from Δ� � �� at the top graphene side to Δ� � �� at the bottom. Here, quantum tunneling occurs in the two first energy intervals, the latter of which represents the slanted region of the BN barrier, and the third interval corresponds to thermionic emission. Subtracting the current in the two opposite directions and integrating over all energies then gives:

�� ∝ � ��(�, ��, ��)��(� − ��)��(� − ��)(��(� − ��, ��, ��) − ��(� − ��, ��, ��))��

(S14) We note that the competition between the exponentially decaying ��(� − ��)��(� −




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��)�� )) (Figure S2a red) and the exponentially increasing transmission probability �� ) (Figure S2a blue) governs the balance between thermionic emission and quantum tunneling. Thus, at high electronic temperatures, the Fermi-Dirac tail is long, so there are many carriers with sufficient energy to move over the BN barrier and thermionic emission thus dominates. At lower temperatures, on the other hand, the Fermi-Dirac distribution decays so quickly that tunneling low-energy electrons contribute the most to the interlayer current.

figure S2| Competition between tunneling and thermionic emission after thermalization. a, Hole occupancy-related term (red) and transmission probability (blue) for holes with different energies at effective temperature Tt = Tb = 4000 K and Vbias = 4V. The BN thickness is 30 nm. Note that we use the hole energy, which is opposite of the electron energy, and E=0 is at the Fermi level of the grounded electrode. The striped area represents the classically forbidden region (tunneling). b, The contribution to interlayer current (product of the two terms in (a)) as a function of hole energy at different effective temperatures. The hole energy that contributes the most to the current clearly increases with temperature, leading to a transition from tunneling to thermionic emission. The product of the two terms (the integrand in equation (S14)) gives the current contribution at each hole energy, which is shown in Figure S2b at different electronic temperatures. We see here that the hole energy that contributes the most to interlayer current increases with electronic temperature, causing a transition from tunneling (current in shaded area) to thermionic emission (above shaded area). Note that we here refer to a transition between processes that occur after thermalization and not a change in whether thermalization occurs or not. This is therefore not the same as the transition in power dependence that is focused on in the main text. More importantly, the area under the curve, which equals the total interlayer current, clearly increases highly superlinearly with temperature. This is further investigated in Figure S3a, showing the total interlayer current (the integral in equation (S14)) as a function of the electronic temperature. In order to understand how this relates to the power dependence, however, we need to further consider how the electronic temperature varies with laser power. In order to get a semi-quantitative sense of the power dependence, we simply use equation (S12) for now, without considering cooling due to vertical convection and lateral diffusion. The peak electronic temperature is shown in Figure S3b over the course of a pulse, plotted against the laser power.

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Evidently, the electronic temperature is in fact weakly sublinear in power, which is why intralayer current shows a sublinear power dependence6,8. In the case of interlayer current, however, this is overruled by the highly superlinear dependence of current on temperature, leaving current superlinear in power (Figure S3c). Further investigating the transition between under-barrier tunneling dominated current and over-barrier thermionic emission, we define a transition temperature T* at which the two contributions are equal. Thus, the thermionic current dominates when T > T*, while tunneling contributes the most when T < T*. As shown in Figure S5, the transition temperature can be tuned down by reducing the bias voltage or increasing the barrier thickness, since both disfavor tunneling. This is supported by the recent observation of a clear transition between the two mechanisms as temperature increases in a G-WS2-G sandwiched device9 . Since the barrier height of WS2 for graphene is considerably lower than that of BN, this device type allows for observing the transition at very low electronic temperatures without the use of laser excitation. Moreover, the isotherms are linear, suggesting that the transition temperature is tightly connected with the electric field across the BN.

figure S3| Superlinearity of the interlayer current generated after thermalization. Vbias = 4 V and the BN thickness is 20 nm. a, Highly superlinear dependence of Iinter on electronic temperature, assuming the top and bottom are at the same temperature. b, Maximum electronic temperature through the course of a laser pulse, simulated for the 90 femtosecond ultrafast laser (upper panel) and for the 90 picosecond super-continuum laser (lower panel) vs. incident laser power. c, Normalized Iinter vs. laser power (blue curve). The superlinearity in (a) overrules the sublinearity in (b), causing Iinter to depend highly superlinearly on laser power. Red curve is the power law fitting and the extracted exponent of the power law is ~ 3.4.




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figure S4| Simulated I-V curve in the thermionic regime based on equations S9-14, which shows good agreement with the experimental data at photon energy ~ 1.8 eV. The asymmetry between positive and negative bias is originating from different absorption and different residual doping levels of the top and bottom graphene layers.

figure S5| The transition temperature T＊ plotted against BN thickness d and bias voltage Vbias. Decreasing d and increasing |Vbias| favors tunneling, and thus increases the transition temperature. The linear isotherms suggest that T＊depends strongly on the electric field across the BN.

S4. Estimation of the average lifetime of photocarriers in the direct tunneling regime

In this work, we heuristically estimate τtun of photoexcited carriers through the uncertainty principle and tunneling probabilities. We assume that τ is the carrier lifetime for being staying in

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one graphene layer with transmission probability one. Since BN serves as a barrier in between, the real lifetime will be increased due to suppressed transmission probability. For instance, if the transmission probability is 0.1, only one out of ten holes can successfully cross the barrier. This effectively increases the lifetime to 10 τ. Therefore, we can calculate the carrier lifetime as τtun = τ/Tr(E), where Tr(E) is the transmission probability as calculated in the above, affected by the excitation energy ��, the interlayer bias voltage Vbias and the barrier height Δ. Note that in the main text, we used T(E). Here Tr(E) is to differentiate from temperature T used extensively in the above. The only question that remains is how to estimate the time τ. Intuitively, τ will be strongly dependent on Vbias that accelerates the hole movement, and also the excitation energy �� since it influences the initial kinetic energy. Accurate calculation of the time is complicated, requiring knowledge about the time and position dependent wave function evolving in an electric field. Thus we take an alternate approach by using the uncertainty principle ��ℎ��, where h is the Planck constant and �� is the energy difference between the excited state of a hole in one graphene layer to the Fermi level of the other graphene layer, which is roughly ~ ��

� � �|��| (figure S6). Therefore,

�� ∼ ℎ��2 � �|��|

1��(�) (S15)

In figure S7, we plot τtun as a function of �� and Vbias within the same parameter range as in the experiment. In this range, the lifetime estimated from the above approach ranges from 1 fs to almost infinity. Since the estimation of �� is very rough, we check how the coefficients of �� and Vbias will influence the number and the shape. We can see from figure S7 that both the time scale and the iso-time contour shape are not very sensitive to the coefficients of �� and Vbias. Especially the contour shape is mostly decided by the transmission probability. The calculation is done by using BN thickness ~ 20 nm (measured thickness of that particular device in the power dependent measurement) and barrier height ~ 1.3 eV.




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figure S6| In our model, the initial state is the excited state of a hole in one graphene layer (ℏ�

� below the Dirac point) and the final state is the Fermi level of the other graphene layer. Therefore, the energy difference is �� ℏ�

� � �|��| � �. We notice that in the direct-tunneling regime, ℏ�� and |��| are

generally much higher than the possibly achieved chemical potential � (< 300 meV) of graphene, and we thus further simplify it to �� ℏ�

� � �|��|.

figure S7| Iso-τtun contours in the parameter space of ℏω and Vbias. Here we investigated different coefficients of ℏω and Vbias, from which we see that the shape of the iso-time contours depends mostly on the transmission coefficients, rather than the relative ratio between ℏω and Vbias in the energy difference

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��. S5. Fowler-Nordheim tunneling model with extraction of barrier height and effective mass

Fowler-Nordheim tunneling describes electron tunneling in a high electric field that tilts the barrier. This is suitable for the direct tunneling case in our experiment, which occurs at eVb much greater than barrier height Δ . The tunneling current generated from the Fowler-Nordheim formula takes the form of

�(��) = ��

1��∗�� − 4�√2�∗��

�� (S1�)

Here e is the electron charge, m0 is the rest mass of a free electron, m* is the hole effective mass in BN, A is the effective tunneling area, V is the bias voltage, d is the thickness of the barrier and � = � − ��

� is the barrier height for photo excited carriers. Note that the formula is originally acquired for absolute zero temperature T = 0, where only carriers near the Fermi level have enough probability and population to tunnel. And this is consistent with our case where all photocarriers are at a single energy level. The above equation (16) can be rewritten in a different form that makes it easier to fit with experimental quantities:

ln �(��)��

� = ln ��1��∗�� − 4�√2�∗��

� ��

1��

(S17)

In this form, it is clear that at a certain photon energy ��, ln �(��)�� is simply linear in �

��.

Thus in the direct tunneling regime, we should observe linearity if we plot ln �(��)�� against �

��,

which is well exhibited in Figure 4a and figure S6. Moreover, if we investigate further the linear

coefficient (the slope), which we define as � = ��√��∗�� , a simple transformation gives that

�� = �4√2 ��

��

(�∗)�� − ��

2 � (S18) Therefore, there is another linear relation between �� and �� as exhibited in the main Figure 4b. We can extract the barrier height from the intersection with β = 0, which equals to 2Δ.




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figure S8| Fowler-Nordheim description of I-V for both positive and negative bias voltages in a larger range for the same device as shown in Figure 4a.

figure S9| Wavelength dependence in the thermionic emission regime. In the thermionic emission regime, photo excited carriers will first thermalize and from a Fermi-Dirac distribution with enhanced temperature. And the subsequent process will only depend on the hot distribution. Therefore, the generated current will be mostly decided by the absorbed power instead of photon energy. The red dots are photocurrent at Vbias = 0.1 V as a function of wavelength (photon energy) for a constant incident laser power. The variation can be accounted for by the substrate-induced interference that modulates the local

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field. Blue line is the cubic of calculated actual absorbed power by graphene. The photocurrent matches with the cubic of absorbed power because the power dependence roughly follows the cubic power law. S6. Discussions about the contribution from BN defects

The photo-induced doping effect, where the doping level of graphene is modified by light

excitation, was observed in G-BN devices on SiO2 substrate in Ju et. al.10. The explanation given

in Ref [10] is that the light actives BN defects (dopants) and excites free electrons into the

conduction band, where they can move to the graphene. We have considered whether the BN

defect can play any roles in our observations. As shown in figure S10, if there are dopant states

(primarily defect type, according to Ref [10]) that can be photo-excited, the absorbed photons

excite electrons from the defect states into the conduction band, from which they flow into the

anode electrode (left cone in figure S10). However, there is still a very high barrier (~ 2 eV for

the highest photon energy used in our measurements) for the electrons to travel from the cathode

electrode to the defect level in BN in order to close the current loop. This process cannot

compete with the hole tunneling process due to excitation of graphene, for which the barrier

height is only ~ 1.3 eV, even in the absence of photo-excitation.

In fact, we did not observe any photodoping effect in our study, meaning the Dirac point of

graphene is always at the same gate voltage throughout all the measurements. Moreover, we

found that the photodoping phenomenon only appears when boron nitride is sitting on the SiO2

substrate. If we eliminate the BN-SiO2 interface, such as in a top gated graphene device with BN

as the gate dielectric11,12 or inserting a piece of metal underneath BN as a local bottom gate13,

this additional doping effect will be completely gone. We are now making efforts to understand

the various observations.




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figure S10| Band alignment of a G-BN-G device and an (unsupported) current generating mechanism based on defect states. Electrons are excited from defect states into the BN conduction band and move to the anode (left) electrode. Since the barrier height is ~ 4.5 eV for electrons, and the defect state is maximally 2.5 eV (highest �� in our measurements) below the conduction band, electrons in the cathode electrode face a ~ 2 eV barrier to close the current loop by recombining the defect sites. S7. Additional data and figures

figure S11| Raw data of the power dependence in a log-log scale for Vbias = 10 V (a) and Vbias = 5 V (b). As distinguished by different colors, photon energies �� = 2.48, 2.25, 2.03, 1.94, 1.85, 1.70, respectively.

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As shown in the log scale, the current has a large overlapping range. Therefore, The distinct power dependence is trustable.

figure S12| Photocurrent as a function of photon energy at bias V = 10 V, 8 V, 6 V and 4 V at a very low incident laser power P = 0.14 μW at �� = 2.48 eV. We have taken into account the local field effect to make sure the actually absorbed power is the same for different photon energies. We chose the very low laser power to suppress the contribution of thermionic emission at low photon energies in order to observe a clear onset of the photocurrent due to direct tunneling. And indeed, it matches with the onset of direct tunneling (linear regime) in the power dependence plot (Figure 2b).

figure S13| a, Highly superlinear power dependence with femtosecond laser at a very low bias Vbias = 0.1 V. b, Same as the main figure Figure 3a. Inset: each curve is normalized to its respective lowest value. The dispersion of the three curves indicates slightly different superlinearity at different delay times (different effective laser intensities).




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References: 1 Dean, C. et al. Boron nitride substrates for high-quality graphene electronics. Nat

Nanotechnol 5, 722-726 (2010). 2 Hunt, B. et al. Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals

Heterostructure. Science 340, 1427-1430 (2013). 3 Song, J. C., Tielrooij, K. J., Koppens, F. H. & Levitov, L. S. Photoexcited carrier

dynamics and impact-excitation cascade in graphene. Phys Rev B 87, 155429 (2013). 4 Tielrooij, K. et al. Photoexcitation cascade and multiple hot-carrier generation in

graphene. Nat Phys 9, 248-252 (2013). 5 Song, J. C., Reizer, M. Y. & Levitov, L. S. Disorder-assisted electron-phonon scattering

and cooling pathways in graphene. Phys Rev Lett 109, 106602 (2012). 6 Graham, M. W., Shi, S.-F., Ralph, D. C., Park, J. & McEuen, P. L. Photocurrent

measurements of supercollision cooling in graphene. Nat Phys 9, 103-108 (2013). 7 Bistritzer, R. & MacDonald, A. Electronic cooling in graphene. Phys Rev Lett 102,

206410 (2009). 8 Sun, D. et al. Ultrafast hot-carrier-dominated photocurrent in graphene. Nat

Nanotechnol 7, 114-118 (2012). 9 Georgiou, T. et al. Vertical field-effect transistor based on graphene-WS2

heterostructures for flexible and transparent electronics. Nat Nanotechnol 8, 100-103 (2013).

10 Ju, L. et al. Photoinduced doping in heterostructures of graphene and boron nitride. Nat Nanotechnol 9, 348–352 (2014).

11 Gabor, N. M. et al. Hot carrier–assisted intrinsic photoresponse in graphene. Science 334, 648-652 (2011).

12 Ma, Q. et al. Competing Channels for Hot-Electron Cooling in Graphene. Phys Rev Lett 112, 247401 (2014).

13 Woessner, A. et al. Near-field photocurrent nanoscopy on bare and encapsulated graphene. arXiv preprint arXiv:1508.07864 (2015).




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