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Hot-Carrier Cooling in High-Quality Graphene Is Intrinsically Limited by Optical Phonons
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  • Eva A. A. Pogna
    Eva A. A. Pogna
    NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127 Pisa, Italy
    Department of Physics, Politecnico di Milano, 20133 Milan, Italy
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    Orcidhttps://orcid.org/0000-0003-4779-3549
  • Xiaoyu Jia
    Xiaoyu Jia
    Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany
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  • Alessandro Principi
    Alessandro Principi
    School of Physics and Astronomy, University of Manchester, M13 9PL Manchester, U.K.
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  • Alexander Block
    Alexander Block
    Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST & CSIC, Campus UAB, Bellaterra, Barcelona 08193, Spain
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  • Luca Banszerus
    Luca Banszerus
    JARA-FIT and second Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU
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    Orcidhttps://orcid.org/0000-0002-1855-1287
  • Jincan Zhang
    Jincan Zhang
    Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
    Beijing Graphene Institute, Beijing 100095, P. R. China
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  • Xiaoting Liu
    Xiaoting Liu
    Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
    Beijing Graphene Institute, Beijing 100095, P. R. China
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  • Thibault Sohier
    Thibault Sohier
    NanoMat/Q-Mat/CESAM, Université de Liège (B5), B-4000 Liège, Belgium
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  • Stiven Forti
    Stiven Forti
    Center for Nanotechnology Innovation IIT@NEST, Piazza San Silvestro 12, 56127 Pisa, Italy
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  • Karuppasamy Soundarapandian
    Karuppasamy Soundarapandian
    ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
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  • Bernat Terrés
    Bernat Terrés
    ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
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  • Jake D. Mehew
    Jake D. Mehew
    Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST & CSIC, Campus UAB, Bellaterra, Barcelona 08193, Spain
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  • Chiara Trovatello
    Chiara Trovatello
    Department of Physics, Politecnico di Milano, 20133 Milan, Italy
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    Orcidhttps://orcid.org/0000-0002-8150-9743
  • Camilla Coletti
    Camilla Coletti
    Center for Nanotechnology Innovation IIT@NEST, Piazza San Silvestro 12, 56127 Pisa, Italy
    Graphene Laboratories, Via Morego 30, 16163 Genova, Italy
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    Orcidhttps://orcid.org/0000-0002-8134-7633
  • Frank H. L. Koppens
    Frank H. L. Koppens
    ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
    ICREA - Institució Catalana de Reçerca i Estudis Avancats, 08010 Barcelona, Spain
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    Orcidhttps://orcid.org/0000-0001-9764-6120
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    Mischa Bonn
    Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany
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  • Hai I. Wang
    Hai I. Wang
    Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany
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    Orcidhttps://orcid.org/0000-0003-0940-3984
  • Niek van Hulst
    Niek van Hulst
    ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
    ICREA - Institució Catalana de Reçerca i Estudis Avancats, 08010 Barcelona, Spain
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    Orcidhttps://orcid.org/0000-0003-4630-1776
  • Matthieu J. Verstraete
    Matthieu J. Verstraete
    NanoMat/Q-Mat/CESAM, Université de Liège (B5), B-4000 Liège, Belgium
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  • Hailin Peng
    Hailin Peng
    Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
    Beijing Graphene Institute, Beijing 100095, P. R. China
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    Orcidhttps://orcid.org/0000-0003-1569-0238
  • Zhongfan Liu
    Zhongfan Liu
    Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
    Beijing Graphene Institute, Beijing 100095, P. R. China
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    Orcidhttps://orcid.org/0000-0003-0065-7988
  • Christoph Stampfer
    Christoph Stampfer
    JARA-FIT and second Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU
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  • Giulio Cerullo
    Giulio Cerullo
    Department of Physics, Politecnico di Milano, 20133 Milan, Italy
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  • Klaas-Jan Tielrooij*
    Klaas-Jan Tielrooij
    Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST & CSIC, Campus UAB, Bellaterra, Barcelona 08193, Spain
    *E-mail: [email protected]
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    Orcidhttps://orcid.org/0000-0002-0055-6231
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ACS Nano

Cite this: ACS Nano 2021, 15, 7, 11285–11295
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https://doi.org/10.1021/acsnano.0c10864
Published June 17, 2021

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Abstract

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Many promising optoelectronic devices, such as broadband photodetectors, nonlinear frequency converters, and building blocks for data communication systems, exploit photoexcited charge carriers in graphene. For these systems, it is essential to understand the relaxation dynamics after photoexcitation. These dynamics contain a sub-100 fs thermalization phase, which occurs through carrier–carrier scattering and leads to a carrier distribution with an elevated temperature. This is followed by a picosecond cooling phase, where different phonon systems play a role: graphene acoustic and optical phonons, and substrate phonons. Here, we address the cooling pathway of two technologically relevant systems, both consisting of high-quality graphene with a mobility >10 000 cm2 V–1 s–1 and environments that do not efficiently take up electronic heat from graphene: WSe2-encapsulated graphene and suspended graphene. We study the cooling dynamics using ultrafast pump–probe spectroscopy at room temperature. Cooling via disorder-assisted acoustic phonon scattering and out-of-plane heat transfer to substrate phonons is relatively inefficient in these systems, suggesting a cooling time of tens of picoseconds. However, we observe much faster cooling, on a time scale of a few picoseconds. We attribute this to an intrinsic cooling mechanism, where carriers in the high-energy tail of the hot-carrier distribution emit optical phonons. This creates a permanent heat sink, as carriers efficiently rethermalize. We develop a macroscopic model that explains the observed dynamics, where cooling is eventually limited by optical-to-acoustic phonon coupling. These fundamental insights will guide the development of graphene-based optoelectronic devices.

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Introduction

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The ultrafast dynamics of photoexcited charge carriers in graphene have received ample attention, initially driven by fundamental scientific interest in the intriguing electron–electron and electron–phonon interactions; cf. refs (1−5). More recently, interest has multiplied as a result of the emergence of highly promising technological applications that exploit these ultrafast dynamics. One example is ultrafast photodetection of visible (VIS) and infrared light, (6,7) and even terahertz (THz) radiation. (8−10) The ultrafast electronic response of graphene to incoming light has also led to the development of several concepts with relevance for data communication technologies, including modulators and receivers, (11−13) and is demonstrated to be crucial for tailoring nonlinear photonics applications. (14−17) Part of the aforementioned applications, for instance photodetectors and receivers, exploit the ultrafast photothermoelectric effect in graphene, (18,19) where a longer hot-carrier cooling time leads to an increased photoresponse. Other applications, such as modulators, could instead benefit from a short cooling time, as this can lead to a higher modulation speed, i.e., to a broader bandwidth. Generally, these applications require high-quality graphene with a high electrical mobility. Clearly, it is crucial to properly understand the cooling dynamics of hot carriers in graphene, and in particular to identify the intrinsic mechanism that ultimately determines the cooling process in high-quality systems.
The decay of photoexcited charges in graphene occurs through a variety of dynamical processes that are the result of the specific properties of Dirac electrons and graphene phonons. Photoexcited charge carriers in graphene first undergo thermalization on a <100 fs time scale, which occurs through carrier–carrier scattering and leads to a state with an elevated carrier temperature, i.e., a broadened Fermi–Dirac distribution. (2−4,20) This photoinduced heating process is very efficient (5,21) and, due to the small electronic heat capacity of graphene, (22) the electron temperature Te can be increased significantly (Te ≫ 500 K). The hot-carrier state then relaxes back to the ground state with the electronic system at ambient temperature. This cooling process occurs through the interaction between charge carriers and graphene optical phonons, graphene acoustic phonons, and substrate phonons in nearby materials. These phonon-induced relaxation mechanisms have intricate dependencies on intrinsic (sample-dependent) parameters (such as disorder density and intrinsic doping), as well as extrinsic experimental parameters (such as photon energy, incident fluence, and ambient temperature). Thus, determining the dominant cooling channel(s) for excited graphene charge carriers has been challenging.
It is generally believed that charge carriers with enough kinetic energy can relax on an ultrafast time scale of a few hundred femtoseconds by interacting with strongly coupled optical phonons. (2,23,24) These are the optical phonons at the Γ and K points with an energy of 0.2 and 0.16 eV, respectively. (25) Thus, charge carriers with an excess energy >0.16 eV above the chemical potential can efficiently cool by optical phonon emission. (26) Carriers with an excess energy <0.16 eV can only couple to acoustic phonons, generally resulting in very inefficient cooling with decay times up to the nanosecond range. (27) In the case of graphene with significant disorder, however, coupling to acoustic phonons becomes much more efficient through disorder-assisted scattering. By scattering with defects, the large momentum mismatch between electrons and acoustic phonons is overcome. (28) This disorder-assisted “supercollision” cooling process leads to typical cooling times of a few picoseconds at room temperature, as measured by electrical, (29) optical, (30,31) and optoelectronic (32) techniques. Since disorder also limits the electrical mobility, this disorder-assisted cooling mechanism tends to play an increasingly important role for graphene with lower electrical mobility. Currently, there are contrasting views in the literature regarding the role of different cooling mechanisms. In particular, some studies, such as ref (26), question the role of supercollision cooling.
In the case of graphene with a mobility above 10 000 cm2 V–1 s–1, which we here refer to as “high-quality graphene”, the disorder density is low enough that disorder-assisted cooling will not play an important role. Recent experiments on high-quality hBN-encapsulated graphene with a mobility above 30 000 cm2 V–1 s–1, however, did not show a strong increase in cooling time. (33) This is because a parallel relaxation mechanism emerges in these heterostructures: hot carriers in graphene can decay through near-field interaction with hyperbolic phonon polaritons of the hBN. (33−35) Hyperbolic phonon polaritons occur in spectral regions, where the in- and out-of-plane permittivities (ϵ∥ and ϵ⊥, respectively) have opposite signs, i.e., the permittivity product ϵ∥·ϵ⊥ is negative. (36) These hyperbolic spectral regions contain a high density of optical modes, which are accessible via near-field interaction with a large range of momentum vectors. As a result, out-of-plane super-Planckian cooling for hBN-encapsulated graphene occurs with a decay time of a few picoseconds at room temperature. (33−35)
Here, we aim to unveil the intrinsic physical mechanism that ultimately limits the cooling of hot carriers in high-quality graphene. We address this question using time-resolved optical measurements of the cooling dynamics in two specifically chosen material systems: WSe2-encapsulated graphene and suspended graphene. Both systems contain “high-quality” graphene, according to our definition of having a mobility >10 000 cm2 V–1 s–1, which is high enough to make “supercollision” cooling inefficient. Furthermore, they have basically nonhyperbolic environments, such that out-of-plane cooling to hyperbolic phonons does not play any role. We show that, despite eliminating these two relaxation channels, cooling still happens on a time scale of a few picoseconds. We attribute this to the high-energy tail of the hot-carrier distribution, where electrons with an energy >0.16 eV above the chemical potential reside. These electrons lose energy by coupling to optical phonons, which in turn couple to graphene acoustic phonons, while the electronic system continuously rethermalizes. Probing the transient optical properties of graphene in the VIS, near-infrared (NIR), and THz ranges, we will show that this cooling mechanism is consistent with the experimentally obtained cooling dynamics.

Results and Discussion

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Cooling Dynamics in High-Quality WSe2-Encapsulated Graphene

The first material system we study is WSe2-encapsulated graphene (see Figure 1a). Encapsulation with materials offering atomically planar surfaces via van der Waals stacking, is a successful route for obtaining high-quality graphene, suppressing rippling, preserving high carrier mobility (37) and partially screening long-distance Coulomb scattering with substrate charges. (38) Besides hBN, WSe2 is arguably one of the most promising encapsulation materials for various technological applications of graphene. (39) One of the main reasons is that it leads to a very high room-temperature mobility, which in a recent study reached up to 350 000 cm2 V–1 s–1 for hBN/graphene/WSe2. (40) Our sample of WSe2-encapsulated monolayer graphene was prepared using exfoliation and dry transfer. The WSe2 flakes were obtained by adhesive tape exfoliation of WSe2 crystals in the trigonal prismatic phase synthesized by chemical vapor transport, as detailed in the Methods. Bottom and top WSe2 flakes are 63 and 61 nm thick, respectively, as measured by atomic force microscopy (see Figure 1b and the Supporting Information). The WSe2/graphene/WSe2 heterostructure was transferred onto a 280 μm thick CaF2 substrate that is transparent for VIS and NIR light and allows for pump–probe measurements in transmission geometry.

Figure 1

Figure 1. Characterization of the WSe2-encapsulated graphene sample. (a) Sketch of the encapsulated graphene prepared by exfoliation and dry transfer of two flakes of WSe2 and monolayer graphene. (41) (b) Atomic force microscopy image of the sample, used to determine the thicknesses of the WSe2 flakes. (c) Raman spectra of fully encapsulated graphene (blue line) and of semiencapsulated graphene (black line) obtained with 532 nm laser source. Encapsulation gives rise to a background, reduced graphene Raman signatures’ (G and 2D peaks) intensity, and a clear blue shift of the 2D peak. (d, e) Maps of the 2D peak frequency ω2D (d) and width Γ2D (e) extracted from Raman spectra at different positions on the sample fitted with a Voigt function centered in ω2D. (f, g) Statistical distribution of ω2D (f) and Γ2D (g) in the encapsulated graphene obtained from the maps in panels d and e. The narrow width suggests a high electrical mobility.

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We first characterize the WSe2-encapsulated graphene using Raman spectroscopy with a 532 nm laser source (see Methods for details), in order to assess the quality of graphene and extract an estimation of its Fermi energy and charge mobility. In the regions where graphene is semiencapsulated, the Raman fingerprints of graphene, the G-peak and 2D-peak, are clearly visible (see Figure 1c). In the fully encapsulated region, the spectrum is dominated by a large background. Nevertheless, by extending the exposure time, we can identify the G-peak with center frequency of ωG ∼ 1584 cm–1 and width of ΓG ∼ 20 cm–1 (spectra in the Supporting Information). From the G-peak position and width we estimate that |EF| ≤ 0.1 eV, in agreement with a previous observation for graphene supported by single-layer WSe2. (40) Examining the 2D-peak at many positions in the encapsulated portion of graphene, we find that it is blue-shifted from ∼2689 to ∼2710 cm–1 after encapsulation; see Figure 1d. The distribution of the 2D-peak widths Γ2D in Figure 1 is centered at 18 cm–1, indicating that WSe2-encapsulated graphene has a rather homogeneous strain distribution, with little intravalley scattering and high mobility. (42) On the basis of the empirical correlation of ref (43), the measured Γ2D corresponds to a mobility of ∼80 000 cm2 V–1 s–1. In order to verify this estimate, we measured the transport properties at room temperature of a similar WSe2-encapsulated graphene heterostructure with two metal contacts and a backgate. We obtained an electron (hole) mobility of ∼39 000 cm2 V–1 s–1 (∼36 000 cm2 V–1 s–1, see Supporting Information). With such high mobility values, disorder-assisted “supercollision” cooling predicts a characteristic cooling time scale of >10 ps (see Supporting Information).
Having established the high quality of our WSe2-encapsulated graphene sample, we now study its hot-carrier cooling dynamics. We perform time-resolved transient absorption (TA) measurements in the NIR range using a high-sensitivity microscope (see Methods for details on the experimental setup), which effectively serves as an ultrafast electronic thermometer. All experiments are performed under ambient conditions and at room temperature, monitoring the time-dependent differential transmission ΔT/T(t). We use pump pulses at 1550 nm (0.8 eV) with a 40 MHz repetition rate and probe pulses at 1700 nm (0.729 eV). These photon energies are chosen well below the band gap of WSe2 (∼1.35 eV for multilayer WSe2), to avoid photoexcitation of charges in the encapsulant (see reflectance measurements in the Supporting Information). Thus, the role of the WSe2 is solely that of a dielectric environment. The pump pulses are absorbed in graphene, where they induce carrier heating, i.e., a broadening of the Fermi–Dirac distribution of the electronic system. The probe pulses are sensitive to this because the broadening leads to Pauli blocking of the interband transitions at the probe photon energy. Therefore, the pump-induced increase in probe transmission is a measure of the electronic temperature. Accordingly, the ΔT/T signal in Figure 2a is positive, indicating pump-induced transmission increase, i.e., absorption bleaching. We can distinguish between fully encapsulated and semiencapsulated graphene regions in Figure 2a, as the former gives rise to a lower transient signal (at a time delay of ∼100 fs), which is likely the result of strong Fresnel reflections at the air–WSe2 and WSe2–graphene interfaces.

Figure 2

Figure 2. Hot-carrier cooling dynamics of WSe2-encapsulated graphene. (a) Transient transmission ΔT/T maps at a fixed time delay t = 100 fs between pump and probe pulses acquired with pump at 0.8 eV (1550 nm) and probe at 0.729 eV (1700 nm). White lines indicate the edges of WSe2 flakes extracted from an optical image. The panel on the right shows a zoom of the left panel, and the black cross indicates the location in the fully encapsulated region, where the ΔT/T dynamics are measured. (b) Comparison of normalized ΔT/T relaxation dynamics of graphene encapsulated by WSe2 (blue dots) and hBN (black dots), using a pump fluence of ∼1 μJ/cm2 in both cases. Encapsulation with hBN gives rise to faster dynamics, which we attribute to out-of-plane cooling to hyperbolic phonons of hBN. (33−35) This cooling mechanism is much less efficient for WSe2 encapsulation. (c) ΔT/T dynamics (dots) for WSe2-encapsulated graphene at five different pump fluences from 0.2 to 2 μJ/cm2. The positive ΔT/T is due to pump-induced heating, leading to Pauli blocking of probe interband transitions. The solid lines are the calculated ΔT/T dynamics, based on the intrinsic hot-electron cooling mechanism via the combination of optical-phonon emission, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (d) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel c. Here, fast decay due to the electron-optical-phonon coupling is followed by slower decay via optical-to-acoustic phonon coupling. The former component shows up very strongly in the TA signal as a consequence of the strongly superlinear relation between the TA signal ΔT/T and the change in carrier temperature ΔTe.

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Figure 2b shows the relaxation dynamics of the ΔT/T signal of WSe2-encapsulated graphene and compares it to the dynamics for hBN-encapsulated graphene. The decay in WSe2-encapsulated graphene is significantly slower: the signal decays to 10% of the initial value (at time zero) after a time delay of ∼5.5 ps for WSe2-encapsulated graphene, instead of a delay of ∼2 ps for the hBN-encapsulated graphene. As shown recently, in high-quality, hBN-encapsulated graphene, hot-carrier cooling is dominated by out-of-plane coupling to hyperbolic phonons in hBN. (33−35) Since the hyperbolic nature of hBN is crucial for making this cooling channel efficient, (34) we study the hyperbolicity of WSe2 using ab initio density functional theory calculations. The comparison of in-plane and out-of-plane permittivities of WSe2 and hBN, reported in the Supporting Information, shows that WSe2 is much less hyperbolic than hBN. Therefore, out-of-plane cooling to the phonons in the encapsulant will be relatively inefficient in WSe2-encapsulated graphene, in qualitative agreement with the slower cooling that we observe. Quantitatively, however, both disorder-assisted “supercollision” cooling and out-of-plane cooling to the encapsulant would predict longer cooling times (see Supporting Information), well above 10 ps for the WSe2-encapsulated graphene sample, which is not what we observe.
In order to explain the relatively fast cooling dynamics observed in the WSe2-encapsulated graphene, we therefore consider an intrinsic cooling mechanism, based on the coupling of electrons with energy >0.16 eV above the chemical potential to optical phonons. The optical phonons, at the Γ and K points, in turn, are anharmonically coupled to acoustic phonons. An important ingredient for this cooling channel is the continuous rethermalization of the electronic system. Microscopically, this means that once the electrons with high enough energy (more than 0.16 eV above the chemical potential) have relaxed by coupling to optical phonons, the remaining electrons will rethermalize through carrier–carrier scattering. This means that some electrons will end up with an energy that is high enough to emit optical phonons. Even at an electron temperature of 300 K, there is a significant fraction of electrons that can emit optical phonons. As a result, this is a rather efficient cooling channel for graphene at room temperature. We will describe the analytical model of this cooling mechanism in more detail in the following discussion and in the Supporting Information.
We calculate the cooling dynamics and compare the results to the experimental data. In the calculation, we also take into account the superlinear relation connecting the ΔT/T signal to the change in carrier temperature. As shown in Figure 2c, the experimental data and calculated signal are in good agreement when we use an optical-to-acoustic phonon decay time of 2 ps and a Fermi energy of 0.1 eV. This optical phonon lifetime lies within the range 1.2–2.55 ps, previously reported (44−48) for graphene. Figure 2d shows the temperature dynamics corresponding to the calculated transient signals in Figure 2c, which are clearly nonexponential. The fast initial decay corresponds to efficient coupling to optical phonons, whereas the slower subsequent decay is the result of the hot-phonon bottleneck, where optical phonons are cooling to acoustic phonons.

Cooling Dynamics in High-Quality Suspended Graphene

In order to determine if this cooling mechanism is intrinsic to graphene, we study a second technologically relevant material system in which any thermal exchange with the environment is inherently excluded: high-quality suspended graphene. This sample contains large-area graphene grown by chemical vapor deposition (CVD), which was then transferred onto a transmission electron microscopy (TEM) grid; see Figure 3a. This was achieved through a polymer-free approach, using the method described in ref (49). As a TEM grid we used holey carbon, which is convenient as it has locations with relatively large holes with a diameter exceeding 10 μm. It has been shown that the graphene in such samples has a mobility well over 10 000 cm2 V–1 s–1. (50) Given the large area and high quality of graphene prepared by this fabrication approach, which is furthermore scalable, this is a highly promising material system for a broad range of electronic and optoelectronic applications.

Figure 3

Figure 3. Characterization of suspended high-quality graphene. (a) Sketch of graphene suspended on a holey carbon film. (b) Scanning electron microscopy images of suspended graphene on holey carbon, showing relatively large hole sizes and high yield. (c) TEM image of the suspended graphene, showing the absence of disorder. (d) Plot of 2D peak frequency ω2D as a function of G peak frequency ωG. Dashed lines represent the expected dependence in the strain-free (red dot-dot-dashed line) and doping-free (blue dot-dashed line) material. (e) Fermi energy EF distribution extracted from vector decomposition of peaks positions in panel d, (51) and centered at |EF| ≈ 0.18 eV. (f) Obtained distribution of 2D-peak widths, indicating a mobility of >17 000 cm2 V–1 s–1, following calculations of ref (43).

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We characterize our suspended graphene sample using various microscopic techniques; see Figure 3. First, we show an image taken using scanning electron microscopy, evidencing excellent graphene coverage of the holes and providing an indication of hole sizes (see Figure 3b). TEM measurements furthermore show an atomically perfect lattice (see Figure 3c). We then perform Raman spectroscopy, in order to estimate the Fermi energy and charge mobility of the suspended graphene. Performing a strain-doping analysis of the G-peak and 2D-peak, obtained from several positions on the sample (see Figure 3d), we obtain a distribution of carrier densities (see Figure 3e), which corresponds to an average Fermi energy of ∼0.18 eV. Using the measured width of the 2D-peaks in Figure 3e and the empirical correlation of ref (43), we extract a mobility of >17 000 cm2 V–1 s–1. This result is in agreement with electrical measurements performed on a sample of suspended graphene, prepared in an identical way; see ref (50). The extracted mobility confirms the high quality of the sample, for which disorder-assisted ”supercollision” cooling predicts a cooling time >10 ps (see Supporting Information).
Having established the high quality of our suspended graphene sample, we now study its hot-carrier cooling dynamics using time-resolved transient absorption microscopy (see Methods for details on the experimental setup). We use a pump tuned at 400 nm (3.1 eV) and a probe at 800 nm (1.55 eV). Similar to the NIR TA measurements, we observe photoinduced bleaching (ΔT/T > 0) of the probe, due to heating-induced Pauli blocking. The ΔT/T map at zero time delay (overlapping pump and probe pulses) in Figure 4a shows that we can resolve the individual holes spatially and that a clearly distinctive transient signal comes from inside—from the suspended graphene. For this experiment we use relatively small spot sizes (see Methods), in order to resolve individual suspended regions.

Figure 4

Figure 4. Hot-carrier cooling dynamics of suspended graphene. (a) Transient transmission ΔT/T map at time zero, showing individual holes where graphene is suspended, acquired with pump tuned at 3.1 eV (400 nm) and probe at 1.55 eV (800 nm). (b) ΔT/T dynamics (colored dots) for suspended graphene at five different pump fluences from 3 to 38 μJ/cm2. The positive ΔT/T results from the pump-induced carrier heating that leads to decreased interband conductivity due to Pauli blocking, and thus decreased absorption of the NIR probe light. The colored lines are the calculated ΔT/T dynamics, based on the intrinsic cooling mechanism where hot electrons cool via the combination of emission of optical phonons, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (c) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel b. Here, a fast decay due to electron-optical-phonon coupling is followed by a slower decay due to optical-to-acoustic phonon coupling.

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The experimental TA dynamics of our high-quality suspended graphene sample are shown in Figure 4b for five different fluences. Similar transient optical responses were observed in suspended graphene prepared by exfoliation, in the VIS (400 nm pump, 800 nm probe), (52) and in the NIR (830 nm pump, 1100–1400 nm probe). (24) We describe the dynamics with the same cooling mechanism as for WSe2-encapsulated graphene, with the same optical-to-acoustic phonon coupling time of 2 ps (details in the Supporting Information). For this sample we use an EF = 0.15 eV, close to the experimentally determined average value. Figure 4c reports the temperature dynamics corresponding to the ΔT/T dynamics in Figure 4b, again showing an initial fast decay due to coupling between electrons and optical phonons, followed by slower decay due to optical phonons coupling to acoustic phonons.
As a final experimental test, we complement our TA measurements on suspended graphene, which probe interband transitions, with optical-pump THz probe (OPTP) measurements, which probe intraband transitions; see Figure S3 of Supporting Information. Despite the different optical transitions that are probed, both techniques essentially function as ultrafast electrical thermometers for graphene. This is because in both cases the probe absorption is affected by pump-induced changes in the carrier temperature. The observed OPTP dynamics, reported in the Supporting Information, can be described with the same model as before, confirming the validity of this intrinsic cooling mechanism.
We now discuss in more detail the cooling mechanism that we have used to describe the experimentally obtained cooling dynamics (schematically shown in Figure 5a). First, we note that in many early time-resolved studies on graphene the dynamics were explained using a qualitatively similar mechanism involving electrons decaying to optical phonons, and a hot-phonon bottleneck; cf. refs (24), (46), (52), and (53). Some of these studies applied a phenomenological two- (or three-) temperature model for electron cooling via optical phonons (and acoustic phonons), which is (implicitly) based on (re)thermalization of the electronic system. Also using electrical transport measurements, signatures of cooling via optical phonons were identified (for bilayer graphene). (54) This cooling mechanism, however, was often thought to only mediate cooling for carriers with high enough energy to couple directly to optical phonons (55) and was typically used for experiments with relatively high fluence and therefore relatively high electron temperatures. For the rest of the carriers in the hot-carrier distribution, and for cooling of systems with relatively low electron temperature, alternative cooling channels were considered. In particular, for cooling below a carrier temperature of ∼1500 K, disorder-assisted “supercollision cooling” to graphene acoustic phonons (28−30,32) and out-of-plane cooling to (hyperbolic) substrate phonons, (33−35) which can both give rise to picosecond cooling at room temperature, were thought to be the dominant mechanisms. In 2016, a microscopic, numerical, simulation of the cooling dynamics of hot carriers in graphene was presented, based on electron-to-optical phonon coupling, and including rethermalization of the carrier system. (26) The calculated cooling times were used to explain qualitative trends in decay times measured by OPTP in samples of multilayer epitaxial graphene on SiC and monolayer graphene grown by CVD. These results motivated us to (re)consider cooling via optical phonons as the intrinsic cooling pathway for high-quality graphene, where disorder-assisted cooling and out-of-plane cooling are inefficient. The cooling mechanism is schematically explained in Figure 5a. We consider two phonon baths, Γ and K phonons, and we capture qualitatively the effect of temperature smearing of the electron Fermi surface in the phonon density of states. The latter is important, because we are dealing with elevated temperatures that lead to a smeared-out Fermi surface.

Figure 5

Figure 5. Hot-carrier cooling dynamics in high-quality graphene. (a) Process of electronic cooling explained through schematics of the carrier density N as a function of carrier energy for three electron temperatures (1200, 800, and 400 K). Cooling occurs through a combination of (i) optical phonon emission by electrons with energy >0.16 eV above the chemical potential (red-shaded area), (ii) rethermalization of the electronic distribution, and (iii) anharmonic coupling of optical phonons to acoustic phonons. (b) Calculated “instantaneous” cooling time for a given initial electron temperature for three different Fermi energies. (c) Calculated cooling time as a function of lattice temperature TL for a very small ΔTe and EF = 0.03 eV. For panels b and c, cooling occurs through optical phonon emission and continuous rethermalization of the electronic system. The hot-phonon bottleneck is not included.

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We developed an analytical model to describe the hot-carrier cooling dynamics in graphene. The details of the derivation are shown in the Supporting Information. Briefly, we solve the following rate equations for the electron temperature Te(t), and phonon temperature Tα(t):
(1)
The left-hand side of the first rate equation contains the electronic heat capacity Ce(Te(t)) and the temporal derivative of the electron temperature. For each electronic temperature, the chemical potential is obtained by imposing that the total carrier density is fixed. The description of electrons in terms of a single temperature and chemical potential implicitly assumes that electron–electron interband scattering processes occur on a much shorter time scale than the electron–phonon dynamics. The dependence of the chemical potential on carrier temperature that we use (see Supporting Information) correspond to those that follow from conservation of total carrier density, where both intraband and interband carrier–carrier scattering are taken into account. The right-hand side of eq 1 describes the emission of optical phonons, where the sum is over the two optical phonon modes (labeled by α), at the Γ and K point, ωα is the frequency of mode α, and is the rate of α-phonon emission. We calculate this rate analytically using a Boltzmann-equation approach, which contains one important input parameter, namely, the electron–phonon coupling strength. For this, we use the value 11.4 eV/Å, obtained by density functional theory calculations, and verified by experiments. (56) The left-hand side of the second rate equation contains , where nα(Tα) is the phonon occupation function. Its right-hand side contains a first term due to the emission of optical phonons by electrons, where the parameter Mα(Te) measures the size of the portion (an annulus) of the phonon Brillouin zone that is heated in the electron-cooling process. This parameter depends, assuming the phonon dispersion to be flat, on the maximum momentum that can be exchanged between electrons and phonons, and thus on the electron temperature Te. The second term describes the decay of optical phonons to acoustic phonons, where Tα(0) is the equilibrium phonon temperature, i.e., the lattice temperature TL. For the optical phonon decay term, we use the parameter γα as a phenomenological damping rate. There are essentially two adjustable parameters in our calculations: the optical phonon lifetime γα–1, and the parameter v that governs the temperature dependence of the phonon number density (see Supporting Information). We note that this thermodynamic model, characterized by a single electronic temperature and chemical potential, is based on underlying microscopic carrier–carrier interactions that lead to carrier (re)thermalization, as well as carrier–phonon and phonon–phonon interactions that lead to carrier cooling.
We have seen that this analytical model is able to accurately describe the experimentally obtained cooling dynamics. The hot-phonon bottleneck, occurring when the density of emitted optical phonons is so high that they cannot completely decay into acoustic phonons and part of their energy is scattered back to the electronic system, becomes more and more important with increasing initial Te, and it leads to an overall slower cooling of the graphene hot carriers. For applications operating with a small heating ΔTe, however, cooling is ultimately determined by electron-optical-phonon cooling. This regime is likely relevant for applications that require low power consumption with low light intensities. Therefore, we analytically study the cooling in the absence of the hot-phonon bottleneck, i.e., when γα → ∞. We calculate that in this case, cooling at room temperature takes between ∼500 fs, for EF = 0.3 eV, and ∼1.4 ps for 0.1 eV. Cooling to optical phonons will quickly become less efficient upon decreasing the lattice temperature TL. Around 200 K, we find a cooling time around 5 ps, whereas this increases to ∼4 ns at 100 K (see Figure 5c). We note that when ΔTe is not small, the effect of increased cooling time with decreased lattice temperature is much weaker. Thus, obtaining a longer intrinsic cooling time requires a reduction of both TL and ΔTe.
As a final discussion, we mention another physical mechanism that can play a significant role in the cooling process of hot carriers in high-mobility graphene (see Supporting Information for details). This mechanism is “diffusive cooling”, where the electron system cools down by in-plane heat diffusion out of the initially heated spot. Until now, this mechanism was mainly considered in the case of micron-sized channels of ultrahigh-quality graphene (≫10 000 cm2/(V s)) and at cryogenic temperatures. (22,57) Cooling via diffusion depends on the electronic heat diffusivity D, which increases with charge mobility and Fermi energy. (58) In the case of pump–probe measurements, the observed evolution of the electron temperature increase due to lateral heat diffusion depends on both pump and probe spot sizes (σpump and σpr, respectively), according to (see Supporting Information):
(2)
Using this equation, we calculate that, for spot sizes below 1 μm, “diffusive cooling” can become the dominant cooling channel in high-mobility graphene samples, even at room temperature. In the measurements we performed on WSe2-encapsulated graphene, “diffusive cooling” does not play a large role, due to the relatively large spot sizes that we used (see Figure S12 of the Supporting Information). However, for the measurements on suspended graphene, with smaller spot sizes, it is very likely that “diffusive cooling” contributes to the probed cooling dynamics, in particular in the tail of the dynamics. It is also conceivable that this leads to an overestimation of the optical phonon decay rate γα. We do note that this “diffusive cooling” is not an intrinsic cooling mechanism, since its contribution becomes negligible for sufficiently large spot sizes.

Conclusion

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Using three different time-resolved measurement techniques (NIR TA, VIS TA, and OPTP) and two different high-quality, technologically relevant, graphene systems (WSe2-encapsulated and suspended CVD graphene), we have shown that hot carriers decay through an intrinsic mechanism involving optical phonon emission and constant rethermalization of the electronic system. Electrons with an energy >0.16 eV above the chemical potential couple to optical phonons, which in turn decay to acoustic phonons while the electronic system continuously rethermalizes. The electron-to-optical-phonon cooling component gives rise to subpicosecond cooling. Due to the hot-phonon bottleneck governed by the anharmonic coupling of optical to acoustic phonons, an approximately biexponential cooling occurs, where the second decay component has a characteristic time scale of a few picoseconds. The overall decay becomes slower for increasing initial electron temperature (higher incident fluence) due to the hot-phonon bottleneck. Whereas previous studies considered a similar mechanism for cooling of high-energy carriers, we here show that this is the intrinsically limiting cooling mechanism for high-mobility graphene, also under relatively low incident fluences and therefore lower electron temperatures. Our analytical model suggests that this mechanism will quickly become less efficient upon decreasing the ambient temperature TL, provided that also the amount of heating is small ΔTe < TL. Thus, operating graphene with low incident fluence and at reduced ambient temperatures is likely a promising approach to optimize optoelectronic applications exploiting hot carriers in graphene.

Methods

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High-Sensitivity Transient Absorption Microscopy

The transient absorption microscope for measurements in the NIR is custom-built starting from a Er-doped fiber laser (Toptica-Femto fiber pro) generating 300 mW, 150 fs pulses centered at 1550 nm with 40 MHz repetition rate. A portion of the output of the laser is used as the pump pulse, and it is modulated with an acousto-optic modulator operating at 1 MHz. The NIR probe pulse is obtained by a supercontinuum (SC) generation focusing part of the laser fundamental in a highly nonlinear fiber. The high-energy component of the SC and the fundamental frequency are filtered out with a long-pass filter cutting at 1600 nm, and the component at 1700 nm is selected with a double-grating monochromator with 5 nm spectral resolution. The pump and the probe are collinearly focused on the sample with an objective (Olympus-LCPLN-IR with magnification 100× and NA = 0.85) over a spot size of 2.8 (3.0) μm for the probe (pump) pulse. The probe transmitted by the sample is collected with an achromatic doublet with a 8 mm focal length and detected by an InGaAs balanced amplified photodiode with 4 MHz bandwidth. The component of the probe at the modulation frequency is measured with a lock-in amplifier (HFLI, Zurich Instruments) using 300 ms effective time constant resulting in a ΔT/T sensitivity below 10–6. Transient transmission dynamics is monitored by changing the pump–probe time delay with an optical delay line, while the pump–probe maps (images) at fixed time-delay are acquired by moving the sample with a motorized three-axis piezo-stack linear stage (Newport NPXYZ100). Image size of 120 × 120 pixels is used in the experiment. The width of the cross-correlation between pump and probe pulses at the sample is ∼210 fs.
The transient absorption measurements in the VIS on suspended graphene are performed using 400 nm pump and 800 nm probe pulses with 150 fs pulses at 76 MHz repetition rate. Both pump and probe pulses are carefully overlapped and focused at the same focal plane with a 40×/0.6 NA objective to focal spot sizes of 1.35 and 0.9 μm, respectively. The pump beam is modulated with an optical chopper at 6.4 kHz. The probe is delayed temporally with a mechanical delay line and detected in transmission on a balanced photodiode via lock-in detection. Further details of the setup are described in ref (59).

Raman Spectroscopy

For Raman characterization, we used an inVia confocal Raman spectrometer from Renishaw plc, equipped with 473 and 532 nm CW laser sources. The laser beam was focused onto the sample through a 100× objective lens, with 0.89 NA. The nominal fwhm of the Gaussian beam at the focus is estimated to be ∼1 μm, and the step size for the maps is set to 4 μm. The laser power hitting the sample in the selected configurations for the measurements were 1.6 mW for the 473 nm laser and 0.7 mW for the 532 nm. With an exposure time per pixel of 60 s, the fluence was 122 and 53 mJ/μm2, respectively. Depending on the measurement, a 1800 lines/mm grating or a denser 2400 lines/mm were used. The spectra are calibrated with respect to the Si peak at 520 cm–1.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.0c10864.

  • Hyperbolic cooling model, cooling dynamics probed with terahertz pulses, topography of encapsulated graphene, electron mobility of WSe2-encapsulated graphene, Raman characterization of WSe2-encapsulated graphene, fully encapsulated vs semiencapsulated graphene, differential reflectance of WSe2-encapsulated graphene, cooling due to lateral heat diffusion, cooling via disorder-assisted acoustic phonon scattering, cooling via optical phonons (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Eva A. A. Pogna - NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, 56127 Pisa, Italy;  Department of Physics, Politecnico di Milano, 20133 Milan, Italy;  Orcidhttps://orcid.org/0000-0003-4779-3549
    • Xiaoyu Jia - Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany
    • Alessandro Principi - School of Physics and Astronomy, University of Manchester, M13 9PL Manchester, U.K.
    • Alexander Block - Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST & CSIC, Campus UAB, Bellaterra, Barcelona 08193, Spain
    • Luca Banszerus - JARA-FIT and second Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU;  Orcidhttps://orcid.org/0000-0002-1855-1287
    • Jincan Zhang - Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China;  Beijing Graphene Institute, Beijing 100095, P. R. China
    • Xiaoting Liu - Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China;  Beijing Graphene Institute, Beijing 100095, P. R. China
    • Thibault Sohier - NanoMat/Q-Mat/CESAM, Université de Liège (B5), B-4000 Liège, Belgium
    • Stiven Forti - Center for Nanotechnology Innovation IIT@NEST, Piazza San Silvestro 12, 56127 Pisa, Italy
    • Karuppasamy Soundarapandian - ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
    • Bernat Terrés - ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain
    • Jake D. Mehew - Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST & CSIC, Campus UAB, Bellaterra, Barcelona 08193, Spain
    • Chiara Trovatello - Department of Physics, Politecnico di Milano, 20133 Milan, Italy;  Orcidhttps://orcid.org/0000-0002-8150-9743
    • Camilla Coletti - Center for Nanotechnology Innovation IIT@NEST, Piazza San Silvestro 12, 56127 Pisa, Italy;  Graphene Laboratories, Via Morego 30, 16163 Genova, Italy;  Orcidhttps://orcid.org/0000-0002-8134-7633
    • Frank H. L. Koppens - ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain;  ICREA - Institució Catalana de Reçerca i Estudis Avancats, 08010 Barcelona, Spain;  Orcidhttps://orcid.org/0000-0001-9764-6120
    • Mischa Bonn - Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany;  Orcidhttps://orcid.org/0000-0001-6851-8453
    • Hai I. Wang - Max-Planck-Institut für Polymerforschung, 55128 Mainz, Germany;  Orcidhttps://orcid.org/0000-0003-0940-3984
    • Niek van Hulst - ICFO - Institut de Ciències Fotòniques, BIST, Castelldefels, Barcelona 08860, Spain;  ICREA - Institució Catalana de Reçerca i Estudis Avancats, 08010 Barcelona, Spain;  Orcidhttps://orcid.org/0000-0003-4630-1776
    • Matthieu J. Verstraete - NanoMat/Q-Mat/CESAM, Université de Liège (B5), B-4000 Liège, Belgium
    • Hailin Peng - Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China;  Beijing Graphene Institute, Beijing 100095, P. R. China;  Orcidhttps://orcid.org/0000-0003-1569-0238
    • Zhongfan Liu - Center for Nanochemistry, College of Chemistry and Molecular Engineering, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China;  Beijing Graphene Institute, Beijing 100095, P. R. China;  Orcidhttps://orcid.org/0000-0003-0065-7988
    • Christoph Stampfer - JARA-FIT and second Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU;  Orcidhttps://orcid.org/0000-0002-4958-7362
    • Giulio Cerullo - Department of Physics, Politecnico di Milano, 20133 Milan, Italy
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We would like to thank Andrea Tomadin for discussions. The authors acknowledge funding from the European Union Horizon 2020 Programme under Grant Agreement No. 881603 Graphene Core 3. ICN2 was supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). A.P. acknowledges support from the European Commission under the EU Horizon 2020 MSCA-RISE-2019 programme (project 873028 HYDROTRONICS) and from the Leverhulme Trust under grant RPG-2019-363. K.J.T. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 804349 (ERC StG CUHL), RyC fellowship No. RYC-2017-22330, and IAE project PID2019-111673GB-I00 and financial support through the MAINZ Visiting Professorship. X.J. acknowledges the support from the Max Planck Graduate Center with the Johannes Gutenberg-Universität Mainz (MPGC). J.Z. acknowledges the support from National Natural Science Foundation of China (No. 52072042). Z.L. acknowledges the support from National Natural Science Foundation of China (No. 51520105003). T.S. acknowledges support from the University of Liege under Special Funds for Research, IPD-STEMA Programme. M.J.V. gratefully acknowledges funding from the Belgian Fonds National de la Recherche Scientifique (FNRS) under PDR grant T.0103.19-ALPS. Computational resources were provided by CECI (FRS-FNRS G.A. 2.5020.11) and the Zenobe Tier-1 supercomputer (Gouvernement Wallon G.A. 1117545) and by a PRACE-3IP DECI grant 2DSpin and Pylight on Beskow (G.A. 653838 of H2020). ICFO was supported by the Severo Ochoa program for Centers of Excellence in R&D (CEX2019-000910-S), Fundació Privada Cellex, Fundació Privada Mir-Puig, and the Generalitat de Catalunya through the CERCA program. N.v.H. acknowledges funding by the European Commission (ERC AdG 670949-LightNet), the Spanish Plan Nacional (PGC2018-096875-BI00), and the Catalan AGAUR (2017SGR1369).

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    Nature Nanotechnology (2009), 4 (12), 839-843CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
    Graphene research so far has focused on electronic rather than photonic applications, in spite of its impressive optical properties. These include its ability to absorb ∼2% of incident light over a broad wavelength range despite being just one atom thick. Here, we demonstrate ultrafast transistor-based photodetectors made from single- and few-layer graphene. The photoresponse does not degrade for optical intensity modulations up to 40 GHz, and further anal. suggests that the intrinsic bandwidth may exceed 500 GHz. The generation and transport of photocarriers in graphene differ fundamentally from those in photodetectors made from conventional semiconductors as a result of the unique photonic and electronic properties of the graphene. This leads to a remarkably high bandwidth, zero source-drain bias and dark current operation, and good internal quantum efficiency.
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  7. 7
    Koppens, F. H. L.; Mueller, T.; Avouris, P.; Ferrari, A. C.; Vitiello, M. S.; Polini, M. Photodetectors Based on Graphene, Other Two-Dimensional Materials and Hybrid Systems. Nat. Nanotechnol. 2014, 9, 780– 793,  DOI: 10.1038/nnano.2014.215
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    7
    Photodetectors based on graphene, other two-dimensional materials and hybrid systems
    Koppens, F. H. L.; Mueller, T.; Avouris, Ph.; Ferrari, A. C.; Vitiello, M. S.; Polini, M.
    Nature Nanotechnology (2014), 9 (10), 780-793CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
    A review. Graphene and other 2-dimensional materials, such as transition metal dichalcogenides, have rapidly established themselves as intriguing building blocks for optoelectronic applications, with a strong focus on various photodetection platforms. The versatility of these material systems enables their application in areas including ultrafast and ultrasensitive detection of light in the UV, visible, IR and terahertz frequency ranges. These detectors can be integrated with other photonic components based on the same material, as well as with silicon photonic and electronic technologies. Here, the authors provide an overview and evaluation of state-of-the-art photodetectors based on graphene, other 2-dimensional materials, and hybrid systems based on the combination of different 2-dimensional crystals or of 2-dimensional crystals and other (nano)materials, such as plasmonic nanoparticles, semiconductors, quantum dots, or their integration with (silicon) waveguides.
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  8. 8
    Bandurin, D. A.; Svintsov, D.; Gayduchenko, I.; Xu, S. G.; Principi, A.; Moskotin, M.; Tretyakov, I.; Yagodkin, D.; Zhukov, S.; Taniguchi, T.; Watanabe, K.; Grigorieva, I. V.; Polini, M.; Goltsman, G. N.; Geim, A. K.; Fedoro, G. Resonant Terahertz Detection Using Graphene Plasmons. Nat. Commun. 2018, 9, 5392,  DOI: 10.1038/s41467-018-07848-w
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    8
    Resonant terahertz detection using graphene plasmons
    Bandurin, Denis A.; Svintsov, Dmitry; Gayduchenko, Igor; Xu, Shuigang G.; Principi, Alessandro; Moskotin, Maxim; Tretyakov, Ivan; Yagodkin, Denis; Zhukov, Sergey; Taniguchi, Takashi; Watanabe, Kenji; Grigorieva, Irina V.; Polini, Marco; Goltsman, Gregory N.; Geim, Andre K.; Fedorov, Georgy
    Nature Communications (2018), 9 (1), 5392CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Plasmons, collective oscillations of electron systems, can efficiently couple light and elec. current, and thus can be used to create sub-wavelength photodetectors, radiation mixers, and on-chip spectrometers. Despite considerable effort, it has proven challenging to implement plasmonic devices operating at terahertz frequencies. The material capable to meet this challenge is graphene as it supports long-lived elec. tunable plasmons. Here we demonstrate plasmon-assisted resonant detection of terahertz radiation by antenna-coupled graphene transistors that act as both plasmonic Fabry-Perot cavities and rectifying elements. By varying the plasmon velocity using gate voltage, we tune our detectors between multiple resonant modes and exploit this functionality to measure plasmon wavelength and lifetime in bilayer graphene as well as to probe collective modes in its moire´ minibands. Our devices offer a convenient tool for further plasmonic research that is often exceedingly difficult under non-ambient conditions (e.g. cryogenic temps.) and promise a viable route for various photonic applications.
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  9. 9
    Castilla, S.; Terrés, B.; Autore, M.; Viti, L.; Li, J.; Nikitin, A. Y.; Vangelidis, I.; Watanabe, K.; Taniguchi, T.; Lidorikis, E.; Vitiello, M. S.; Hillenbrand, R.; Tielrooij, K.-J.; Koppens, F. H. L. Fast and Sensitive Terahertz Detection Using an Antenna-Integrated Graphene pn Junction. Nano Lett. 2019, 19, 2765– 2773,  DOI: 10.1021/acs.nanolett.8b04171
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    9
    Fast and Sensitive Terahertz Detection Using an Antenna-Integrated Graphene pn Junction
    Castilla, Sebastian; Terres, Bernat; Autore, Marta; Viti, Leonardo; Li, Jian; Nikitin, Alexey Y.; Vangelidis, Ioannis; Watanabe, Kenji; Taniguchi, Takashi; Lidorikis, Elefterios; Vitiello, Miriam S.; Hillenbrand, Rainer; Tielrooij, Klaas-Jan; Koppens, Frank H. L.
    Nano Letters (2019), 19 (5), 2765-2773CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Although the detection of light at THz frequencies is important for a large range of applications, current detectors typically have several disadvantages in terms of sensitivity, speed, operating temp., and spectral range. Graphene was used as a photoactive material to overcome all of these limitations in 1 device. A novel detector for far-IR radiation that exploits the photothermoelec. (PTE) effect was introduced, based on a design that employs a dual-gated, dipolar antenna with a gap of ∼100 nm. This narrow-gap antenna simultaneously creates a pn junction in a graphene channel located above the antenna and strongly concs. the incoming radiation at this pn junction, where the photoresponse is created. This novel detector has an excellent sensitivity, with a noise-equiv. power of 80 pW/√(Hz) at room temp., a response time <30 ns (setup-limited), a high dynamic range (linear power dependence over >3 orders of magnitude) and broadband operation (measured range 1.8-4.2 THz, antenna-limited), which fulfills a combination that is currently missing in the state-of-the-art detectors. From the agreement obtained between expt., anal. model, and numerical simulations, a solid understanding of how the PTE effect gives rise to a THz-induced photoresponse, which is very valuable for further detector optimization was reached.
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  10. 10
    Viti, L.; Purdie, D. G.; Lombardo, A.; Ferrari, A. C.; Vitiello, M. S. HBN-Encapsulated, Graphene-Based, Room-Temperature Terahertz Receivers, with High Speed and Low Noise. Nano Lett. 2020, 20, 3169– 3177,  DOI: 10.1021/acs.nanolett.9b05207
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    10
    HBN-Encapsulated, Graphene-based, Room-temperature Terahertz Receivers, with High Speed and Low Noise
    Viti, Leonardo; Purdie, David G.; Lombardo, Antonio; Ferrari, Andrea C.; Vitiello, Miriam S.
    Nano Letters (2020), 20 (5), 3169-3177CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Uncooled terahertz photodetectors (PDs) showing fast (ps) response and high sensitivity (noise equiv. power (NEP) < nW/Hz1/2) over a broad (0.5-10 THz) frequency range are needed for applications in high-resoln. spectroscopy (relative accuracy ~ 10-11), metrol., quantum information, security, imaging, optical communications. However, present terahertz receivers cannot provide the required balance between sensitivity, speed, operation temp., and frequency range. Here, we demonstrate uncooled terahertz PDs combining the low (~ 2000 kB μm-2) electronic sp. heat of high mobility (>50 000 cm2 V-1 s-1) hexagonal boron nitride-encapsulated graphene, with asym. field enhancement produced by a bow-tie antenna, resonating at 3 THz. This produces a strong photo-thermoelec. conversion, which simultaneously leads to a combination of high sensitivity (NEP ≤ 160 pW Hz-1/2), fast response time (≤3.3 ns), and a 4 orders of magnitude dynamic range, making our devices the fastest, broad-band, low-noise, room-temp. terahertz PD, to date.
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  11. 11
    Liu, M.; Yin, X.; Ulin-Avila, E.; Geng, B.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang, X. A Graphene-Based Broadband Optical Modulator. Nature 2011, 474, 64– 67,  DOI: 10.1038/nature10067
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    11
    A graphene-based broadband optical modulator
    Liu, Ming; Yin, Xiaobo; Ulin-Avila, Erick; Geng, Baisong; Zentgraf, Thomas; Ju, Long; Wang, Feng; Zhang, Xiang
    Nature (London, United Kingdom) (2011), 474 (7349), 64-67CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Integrated optical modulators with high modulation speed, small footprint and large optical bandwidth are poised to be the enabling devices for on-chip optical interconnects. Semiconductor modulators have therefore been heavily researched over the past few years. However, the device footprint of Si-based modulators is of the order of millimeters, owing to its weak electrooptical properties. Ge and compd. semiconductors, however, face the major challenge of integration with existing Si electronics and photonics platforms. Integrating Si modulators with high-quality-factor optical resonators increases the modulation strength, but these devices suffer from intrinsic narrow bandwidth and require sophisticated optical design; they also have stringent fabrication requirements and limited temp. tolerances. Finding a complementary metal-oxide-semiconductor (CMOS)-compatible material with adequate modulation speed and strength has therefore become a task of not only scientific interest, but also industrial importance. Here the authors exptl. demonstrate a broadband, high-speed, waveguide-integrated electroabsorption modulator based on monolayer graphene. By elec. tuning the Fermi level of the graphene sheet, the authors demonstrate modulation of the guided light at frequencies over 1 GHz, together with a broad operation spectrum that ranges from 1.35 to 1.6 μm under ambient conditions. The high modulation efficiency of graphene results in an active device area of merely 25 μm2, which is among the smallest to date. This graphene-based optical modulation mechanism, with combined advantages of compact footprint, low operation voltage and ultrafast modulation speed across a broad range of wavelengths, can enable novel architectures for on-chip optical communications.
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  12. 12
    Romagnoli, M.; Sorianello, V.; Midrio, M.; Koppens, F. H. L.; Huyghebaert, C.; Neumaier, D.; Galli, P.; Templ, W.; Ferrari, A. C. Graphene-Based Integrated Photonics for Next-Generation Datacom and Telecom. Nat. Rev. Mater. 2018, 3, 392– 414,  DOI: 10.1038/s41578-018-0040-9
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    12
    Graphene-based integrated photonics for next-generation datacom and telecom
    Romagnoli, Marco; Sorianello, Vito; Midrio, Michele; Koppens, Frank H. L.; Huyghebaert, Cedric; Neumaier, Daniel; Galli, Paola; Templ, Wolfgang; D'Errico, Antonio; Ferrari, Andrea C.
    Nature Reviews Materials (2018), 3 (10), 392-414CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
    A review: Graphene is an ideal material for optoelectronic applications. Its photonic properties give several advantages and complementarities over Si photonics. For example, graphene enables both electro-absorption and electro-refraction modulation with an electro-optical index change exceeding 10-3. It can be used for optical add-drop multiplexing with voltage control, eliminating the current dissipation used for the thermal detuning of microresonators, and for thermoelec.-based ultrafast optical detectors that generate a voltage without transimpedance amplifiers. Here, we present our vision for graphene-based integrated photonics. We review graphene-based transceivers and compare them with existing technologies. Strategies for improving power consumption, manufacturability and wafer-scale integration are addressed. We outline a roadmap of the technol. requirements to meet the demands of the datacom and telecom markets. We show that graphene-based integrated photonics could enable ultrahigh spatial bandwidth d., low power consumption for board connectivity and connectivity between data centers, access networks and metropolitan, core, regional and long-haul optical communications.
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  13. 13
    Muench, J. E.; Ruocco, A.; Giambra, M. A.; Miseikis, V.; Zhang, D.; Wang, J.; Watson, H. F. Y.; Park, G. C.; Akhavan, S.; Sorianello, V.; Midrio, M.; Tomadin, A.; Coletti, C.; Romagnoli, M.; Ferrari, A. C.; Goykhman, I. Waveguide-Integrated, Plasmonic Enhanced Graphene Photodetectors. Nano Lett. 2019, 19, 7632– 7644,  DOI: 10.1021/acs.nanolett.9b02238
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    13
    Waveguide-Integrated, Plasmonic Enhanced Graphene Photodetectors
    Muench, Jakob E.; Ruocco, Alfonso; Giambra, Marco A.; Miseikis, Vaidotas; Zhang, Dengke; Wang, Junjia; Watson, Hannah F. Y.; Park, Gyeong C.; Akhavan, Shahab; Sorianello, Vito; Midrio, Michele; Tomadin, Andrea; Coletti, Camilla; Romagnoli, Marco; Ferrari, Andrea C.; Goykhman, Ilya
    Nano Letters (2019), 19 (11), 7632-7644CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    We present a micrometer scale, on-chip integrated, plasmonic enhanced graphene photodetector (GPD) for telecom wavelengths operating at zero dark current. The GPD is designed to directly generate a photovoltage, is made of chem. vapor deposited single layer graphene, and has an external responsivity of ∼12.2V/W with a 3dB bandwidth of ∼42GHz. We utilize Au split-gates to electrostatically create a p-n-junction and simultaneously guide a surface plasmon polariton gap-mode. This increases light-graphene interaction and optical absorption and results in an increased electronic temp. and steeper temp. gradient across the GPD channel. This paves the way to compact, on-chip integrated, power-efficient graphene based photodetectors for receivers in tele and datacom modules.
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  14. 14
    Hafez, H. A.; Kovalev, S.; Deinert, J. C.; Mics, Z.; Green, B.; Awari, N.; Chen, M.; Germanskiy, S.; Lehnert, U.; Teichert, J.; Wang, Z.; Tielrooij, K. J.; Liu, Z.; Chen, Z.; Narita, A.; Müllen, K.; Bonn, M.; Gensch, M.; Turchinovich, D. Extremely Efficient Terahertz High-Harmonic Generation in Graphene by Hot Dirac Fermions. Nature 2018, 561, 507– 511,  DOI: 10.1038/s41586-018-0508-1
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    14
    Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions
    Hafez, Hassan A.; Kovalev, Sergey; Deinert, Jan-Christoph; Mics, Zoltan; Green, Bertram; Awari, Nilesh; Chen, Min; Germanskiy, Semyon; Lehnert, Ulf; Teichert, Jochen; Wang, Zhe; Tielrooij, Klaas-Jan; Liu, Zhaoyang; Chen, Zongping; Narita, Akimitsu; Muellen, Klaus; Bonn, Mischa; Gensch, Michael; Turchinovich, Dmitry
    Nature (London, United Kingdom) (2018), 561 (7724), 507-511CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
    Multiple optical harmonic generation-the multiplication of photon energy as a result of nonlinear interaction between light and matter-is a key technol. in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency, and the generation of frequency combs. Owing to the unique electronic band structure of graphene, which features massless Dirac fermions1-3, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technol. important terahertz frequencies4-6. However, these predictions have yet to be confirmed exptl. under technol. relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temp. and under ambient conditions, driven by terahertz fields of only tens of kilovolts per cm, and with field conversion efficiencies in excess of 10-3, 10-4 and 10-5 for the third, fifth and seventh terahertz harmonics, resp. These conversion efficiencies are remarkably high, given that the electromagnetic interaction occurs in a single at. layer. The key to such extremely efficient generation of terahertz high harmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were obsd. directly in the time domain as electromagnetic field oscillations at these newly synthesized higher frequencies. The effective nonlinear optical coeffs. of graphene for the third, fifth and seventh harmonics exceed the resp. nonlinear coeffs. of typical solids by 7-18 orders of magnitude7-9. Our results provide a direct pathway to highly efficient terahertz frequency synthesis using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.
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  15. 15
    Soavi, G.; Wang, G.; Rostami, H.; Purdie, D. G.; De Fazio, D.; Ma, T.; Luo, B.; Wang, J.; Ott, A. K.; Yoon, D.; Bourelle, S. A.; Muench, J. E.; Goykhman, I.; Dal Conte, S.; Celebrano, M.; Tomadin, A.; Polini, M.; Cerullo, G.; Ferrari, A. C. Broadband, Electrically Tunable Third-Harmonic Generation in Graphene. Nat. Nanotechnol. 2018, 13, 583– 588,  DOI: 10.1038/s41565-018-0145-8
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    15
    Broadband, electrically tunable third-harmonic generation in graphene
    Soavi, Giancarlo; Wang, Gang; Rostami, Habib; Purdie, David G.; De Fazio, Domenico; Ma, Teng; Luo, Birong; Wang, Junjia; Ott, Anna K.; Yoon, Duhee; Bourelle, Sean A.; Muench, Jakob E.; Goykhman, Ilya; Dal Conte, Stefano; Celebrano, Michele; Tomadin, Andrea; Polini, Marco; Cerullo, Giulio; Ferrari, Andrea C.
    Nature Nanotechnology (2018), 13 (7), 583-588CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
    Optical harmonic generation occurs when high intensity light (>1010 W m-2) interacts with a nonlinear material. Elec. control of the nonlinear optical response enables applications such as gate-tunable switches and frequency converters. Graphene displays exceptionally strong light-matter interaction and elec. and broadband tunable third-order nonlinear susceptibility. Here, we show that the third-harmonic generation efficiency in graphene can be increased by almost two orders of magnitude by controlling the Fermi energy and the incident photon energy. This enhancement is due to logarithmic resonances in the imaginary part of the nonlinear cond. arising from resonant multiphoton transitions. Thanks to the linear dispersion of the massless Dirac fermions, gate controllable third-harmonic enhancement can be achieved over an ultrabroad bandwidth, paving the way for elec. tunable broadband frequency converters for applications in optical communications and signal processing.
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  16. 16
    Soavi, G.; Wang, G.; Rostami, H.; Tomadin, A.; Balci, O.; Paradisanos, I.; Pogna, E. A. A.; Cerullo, G.; Lidorikis, E.; Polini, M.; Ferrari, A. C. Hot Electrons Modulation of Third-Harmonic Generation in Graphene. ACS Photonics 2019, 6, 2841– 2849,  DOI: 10.1021/acsphotonics.9b00928
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    16
    Hot Electrons Modulation of Third-Harmonic Generation in Graphene
    Soavi, Giancarlo; Wang, Gang; Rostami, Habib; Tomadin, Andrea; Balci, Osman; Paradisanos, I.; Pogna, Eva A. A.; Cerullo, Giulio; Lidorikis, Elefterios; Polini, Marco; Ferrari, Andrea C.
    ACS Photonics (2019), 6 (11), 2841-2849CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Hot electrons dominate the ultrafast optical and electronic properties of metals and semiconductors and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power-law expected for a third harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency converters, can be affected by changes in the electronic temp., which might occur due to increase of absorbed optical power or Joule heating.
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  17. 17
    Deinert, J.-C.; Iranzo, D. A.; Perez, R.; Jia, X.; Hafez, H. A.; Ilyakov, I.; Awari, N.; Chen, M.; Bawatna, M.; Ponomaryov, A. N.; Germanskiy, S.; Bonn, M.; Koppens, F. H. L.; Turchinovich, D.; Gensch, M.; Kovalev, S.; Tielrooij, K.-J. Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics. ACS Nano 2021, 15, 1145– 1154,  DOI: 10.1021/acsnano.0c08106
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    17
    Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics
    Deinert, Jan-Christoph; Alcaraz Iranzo, David; Perez, Raul; Jia, Xiaoyu; Hafez, Hassan A.; Ilyakov, Igor; Awari, Nilesh; Chen, Min; Bawatna, Mohammed; Ponomaryov, Alexey N.; Germanskiy, Semyon; Bonn, Mischa; Koppens, Frank H. L.; Turchinovich, Dmitry; Gensch, Michael; Kovalev, Sergey; Tielrooij, Klaas-Jan
    ACS Nano (2021), 15 (1), 1145-1154CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Nonlinear optics is an increasingly important field for scientific and technol. applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and a small material footprint. Ideally, the material system should allow for chip integration and room-temp. operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear optical conversion efficiency. Here, we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3 x 10-8 m2/V2, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to a third-harmonic signal with an intensity that is 3 orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ~ 1% using a moderate field strength of ~ 30 kV/cm. Finally, we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the ninth harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for com. viable, CMOS-compatible, room-temp., chip-integrated, THz nonlinear conversion applications.
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  18. 18
    Gabor, N. M.; Song, J. C.; Ma, Q.; Nair, N. L.; Taychatanapat, T.; Watanabe, K.; Taniguchi, T.; Levitov, L. S.; Jarillo-Herrero, P. Hot Carrier-Assisted Intrinsic Photoresponse in Graphene. Science 2011, 334, 648– 652,  DOI: 10.1126/science.1211384
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    18
    Hot Carrier-Assisted Intrinsic Photoresponse in Graphene
    Gabor, Nathaniel M.; Song, Justin C. W.; Ma, Qiong; Nair, Nityan L.; Taychatanapat, Thiti; Watanabe, Kenji; Taniguchi, Takashi; Levitov, Leonid S.; Jarillo-Herrero, Pablo
    Science (Washington, DC, United States) (2011), 334 (6056), 648-652CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    We report on the intrinsic optoelectronic response of high-quality dual-gated monolayer and bilayer graphene p-n junction devices. Local laser excitation (of wavelength 850 nm) at the p-n interface leads to striking six-fold photovoltage patterns as a function of bottom- and top-gate voltages. These patterns, together with the measured spatial and d. dependence of the photoresponse, provide strong evidence that nonlocal hot carrier transport, rather than the photovoltaic effect, dominates the intrinsic photoresponse in graphene. This regime, which features a long-lived and spatially distributed hot carrier population, may offer a path to hot carrier-assisted thermoelec. technologies for efficient solar energy harvesting.
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  19. 19
    Tielrooij, K.-J.; Piatkowski, L.; Massicotte, M.; Woessner, A.; Ma, Q.; Lee, Y.; Myhro, K. S.; Lau, C. N.; Jarillo-Herrero, P.; van Hulst, N. F.; Koppens, F. H. L. Generation of Photovoltage in Graphene on a Femtosecond Timescale through Efficient Carrier Heating. Nat. Nanotechnol. 2015, 10, 437– 443,  DOI: 10.1038/nnano.2015.54
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    19
    Generation of photovoltage in graphene on a femtosecond timescale through efficient carrier heating
    Tielrooij, K. J.; Piatkowski, L.; Massicotte, M.; Woessner, A.; Ma, Q.; Lee, Y.; Myhro, K. S.; Lau, C. N.; Jarillo-Herrero, P.; van Hulst, N. F.; Koppens, F. H. L.
    Nature Nanotechnology (2015), 10 (5), 437-443CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
    Graphene is a promising material for ultrafast and broadband photodetection. Earlier studies have addressed the general operation of graphene-based photothermoelec. devices and the switching speed, which is limited by the charge carrier cooling time, on the order of picoseconds. However, the generation of the photovoltage could occur at a much faster timescale, as it is assocd. with the carrier heating time. Here, the authors measure the photovoltage generation time and find it to be faster than 50 fs. As a proof-of-principle application of this ultrafast photodetector, the authors use graphene to directly measure, elec., the pulse duration of a sub-50 fs laser pulse. The observation that carrier heating is ultrafast suggests that energy from absorbed photons can be efficiently transferred to carrier heat. To study this, the authors examine the spectral response and find a const. spectral responsivity of between 500 and 1,500 nm. This is consistent with efficient electron heating. These results are promising for ultrafast femtosecond and broadband photodetector applications.
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    Iglesias, J. M.; Pascual, E.; Martín, M. J.; Rengel, R. Relevance of Collinear Processes to the Ultrafast Dynamics of Photoexcited Carriers in Graphene. Phys. E 2020, 123, 114211,  DOI: 10.1016/j.physe.2020.114211
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    20
    Relevance of collinear processes to the ultrafast dynamics of photoexcited carriers in graphene
    Iglesias, Jose Manuel; Pascual, Elena; Martin, Maria J.; Rengel, Raul
    Physica E: Low-Dimensional Systems & Nanostructures (Amsterdam, Netherlands) (2020), 123 (), 114211CODEN: PELNFM; ISSN:1386-9477. (Elsevier B.V.)
    The importance of interband transitions on the ultrafast relaxation process in photoexcited pristine graphene is evaluated by means of an ensemble Monte Carlo simulator. Impact ionization and Auger recombination in the collinear limit are considered, together with phonon-induced generation and recombination and intraband scattering mechanisms. The results show that collinear impact ionization is dominant in the first 100 fs, creating an important excess carrier population that is finally eliminated in the picosecond scale, together with the photoexcited population, by Auger and optical phonon-assisted recombination. The hot phonon effect is also important, stimulating phonon absorption and indirectly reducing the net collinear recombination in the hundreds of femtosecond range. The substrate type is an important factor, appeasing collinear impact ionization via screening and creating addnl. cooling channels that speed up the relaxation process. The results evidence that interband collinear generation processes are crit. to explain the fastest stages of the relaxation process in graphene.
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  21. 21
    Tomadin, A.; Hornett, S. M.; Wang, H. I.; Alexeev, E. M.; Candini, A.; Coletti, C.; Turchinovich, D.; Kläui, M.; Bonn, M.; Koppens, F. H. L.; Hendry, E.; Polini, M.; Tielrooij, K.-J. The Ultrafast Dynamics and Conductivity of Photoexcited Graphene at Different Fermi Energies. Sci. Adv. 2018, 4, eaar5313,  DOI: 10.1126/sciadv.aar5313
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    Fong, K. C.; Wollman, E. E.; Ravi, H.; Chen, W.; Clerk, A. A.; Shaw, M. D.; Leduc, H. G.; Schwab, K. C. Measurement of the Electronic Thermal Conductance Channels and Heat Capacity of Graphene at Low Temperature. Phys. Rev. X 2013, 3, 41008,  DOI: 10.1103/PhysRevX.3.041008
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    Measurement of the electronic thermal conductance channels and heat capacity of graphene at low temperature
    Fong, Kin Chung; Wollman, Emma E.; Ravi, Harish; Chen, Wei; Clerk, Aashish A.; Shaw, M. D.; Leduc, H. G.; Schwab, K. C.
    Physical Review X (2013), 3 (4), 041008CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    The ability to transport energy is a fundamental property of the two-dimensional Dirac fermions in graphene. Electronic thermal transport in this system is relatively unexplored and is expected to show unique fundamental properties and to play an important role in future applications of graphene, including optoelectronics, plasmonics, and ultrasensitive bolometry. Here, we present measurements of bipolar thermal conductances due to electron diffusion and electron-phonon coupling and infer the electronic sp. heat, with a min. value of 10kB (10-22 J/K) per square micron. We test the validity of the Wiedemann-Franz law and find that the Lorenz no. equals 1.32 × (π2/3)(kB/e)2. The electron-phonon thermal conductance has a temp. power law T2 at high doping levels, and the coupling parameter is consistent with recent theory, indicating its enhancement by impurity scattering. We demonstrate control of the thermal conductance by elec. gating and by suppressing the diffusion channel using NbTiN superconducting electrodes, which sets the stage for future graphene-based single-microwave photon detection.
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    Kampfrath, T.; Perfetti, L.; Schapper, F.; Frischkorn, C.; Wolf, M. Strongly Coupled Optical Phonons in the Ultrafast Dynamics of the Electronic Energy and Current Relaxation in Graphite. Phys. Rev. Lett. 2005, 95, 187403,  DOI: 10.1103/PhysRevLett.95.187403
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    23
    Strongly Coupled Optical Phonons in the Ultrafast Dynamics of the Electronic Energy and Current Relaxation in Graphite
    Kampfrath, Tobias; Perfetti, Luca; Schapper, Florian; Frischkorn, Christian; Wolf, Martin
    Physical Review Letters (2005), 95 (18), 187403/1-187403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Ultrafast charge carrier dynamics in graphite has been investigated by time-resolved terahertz spectroscopy. Anal. of the transient dielec. function and model calcns. show that more than 90% of the initially deposited excitation energy is transferred to a few strongly coupled lattice vibrations within 500 fs. These hot optical phonons also substantially contribute to the striking increase of the Drude relaxation rate obsd. during the first picosecond after photoexcitation. The subsequent cooling of the hot phonons yields a lifetime est. of 7 ps for these modes.
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    Hale, P. J.; Hornett, S. M.; Moger, J.; Horsell, D. W.; Hendry, E. Hot Phonon Decay in Supported and Suspended Exfoliated Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 121404,  DOI: 10.1103/PhysRevB.83.121404
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    24
    Hot phonon decay in supported and suspended exfoliated graphene
    Hale, P. J.; Hornett, S. M.; Moger, J.; Horsell, D. W.; Hendry, E.
    Physical Review B: Condensed Matter and Materials Physics (2011), 83 (12), 121404/1-121404/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Near IR pump-probe spectroscopy was used to measure the ultrafast dynamics of photoexcited charge carriers in monolayer and multilayer graphene. The authors observe 2 decay processes occurring on 100-fs and 2-ps time scales. The 1st is attributed to the rapid electron-phonon thermalization in the system. The 2nd time scale is due to the slow decay of hot phonons. Using a simple theor. model the authors calc. the hot phonon decay rate and show that it is significantly faster in monolayer flakes than in multilayer ones. The authors observe this enhanced decay rate in both supported and suspended flakes and thereby demonstrate that it has an intrinsic origin. Possible decay mechanisms, such as flexural phonons, that could cause such an enhancement are discussed.
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    Mounet, N.; Marzari, N. First-Principles Determination of the Structural, Vibrational and Thermodynamic Properties of Diamond, Graphite, and Derivatives. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 205214,  DOI: 10.1103/PhysRevB.71.205214
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    25
    First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives
    Mounet, Nicolas; Marzari, Nicola
    Physical Review B: Condensed Matter and Materials Physics (2005), 71 (20), 205214/1-205214/14CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    The structural, dynamical, and thermodn. properties of diamond, graphite and layered derivs. (graphene, rhombohedral graphite) are computed using a combination of d.-functional theory total-energy calcns. and d.-functional perturbation theory lattice dynamics in the generalized gradient approxn. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the assocd. elastic consts. and phonon dispersions. Both the C33 elastic const. and the Γ to A phonon dispersions are brought to close agreement with available data once the exptl. c/a is chosen for the calcns. The vibrational free energy and the thermal expansion, the temp. dependence of the elastic moduli and the sp. heat are calcd. using the quasiharmonic approxn. Graphite shows a distinctive in-plane neg. thermal-expansion coeff. that reaches its lowest value around room temp., in very good agreement with expts. Thermal contraction in graphene is three times as large; in both cases, bending acoustic modes are responsible for the contraction, in a direct manifestation of the membrane effect predicted by Lifshitz over 50 years ago. Stacking directly affects the bending modes, explaining the large numerical difference between the thermal-contraction coeffs. in graphite and graphene, notwithstanding their common phys. origin.
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    Mihnev, M. T.; Kadi, F.; Divin, C. J.; Winzer, T.; Lee, S.; Liu, C.-h.; Zhong, Z.; Berger, C.; Heer, W. A. D.; Malic, E.; Knorr, A.; Norris, T. B. Microscopic Origins of the Terahertz Carrier Relaxation and Cooling Dynamics in Graphene. Nat. Commun. 2016, 7, 11617,  DOI: 10.1038/ncomms11617
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    26
    Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene
    Mihnev, Momchil T.; Kadi, Faris; Divin, Charles J.; Winzer, Torben; Lee, Seunghyun; Liu, Che-Hung; Zhong, Zhaohui; Berger, Claire; de Heer, Walt A.; Malic, Ermin; Knorr, Andreas; Norris, Theodore B.
    Nature Communications (2016), 7 (), 11617CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier-carrier interactions and carrier-phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent expts. on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of obsd. signals within phenomenol. frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated exptl. and theor. program, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modeling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amts. of disorder and with either high or low doping levels. The theory reproduces the obsd. dynamics quant. without the need to invoke any fitting parameters, phenomenol. models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier-carrier scattering, which maintains a thermalized carrier distribution, and carrier-optical-phonon scattering, which removes energy from the carrier liq.
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    Bistritzer, R.; MacDonald, A. H. Electronic Cooling in Graphene. Phys. Rev. Lett. 2009, 102, 206410,  DOI: 10.1103/PhysRevLett.102.206410
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    Electronic Cooling in Graphene
    Bistritzer, R.; MacDonald, A. H.
    Physical Review Letters (2009), 102 (20), 206410/1-206410/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Energy transfer to acoustic phonons is the dominant low-temp. cooling channel of electrons in a crystal. For cold neutral graphene we find that the weak cooling power of its acoustic modes relative to their heat capacity leads to a power-law decay of the electronic temp. when far from equil. For heavily doped graphene a high electronic temp. is shown to initially decrease linearly with time at a rate proportional to n3/2 with n being the electronic d. The temp. at which cooling via optical phonon emission begins to dominate depends on graphene carrier d.
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    Song, J. C. W.; Reizer, M. Y.; Levitov, L. S. Disorder-Assisted Electron-Phonon Scattering and Cooling Pathways in Graphene. Phys. Rev. Lett. 2012, 109, 106602,  DOI: 10.1103/PhysRevLett.109.106602
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    Disorder-assisted electron-phonon scattering and cooling pathways in graphene
    Song, Justin C. W.; Reizer, Michael Y.; Levitov, Leonid S.
    Physical Review Letters (2012), 109 (10), 106602/1-106602/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We predict that graphene is a unique system where disorder-assisted scattering (supercollisions) dominates electron-lattice cooling over a wide range of temps., up to room temp. This is so because for momentum-conserving electron-phonon scattering the energy transfer per collision is severely constrained due to a small Fermi surface size. The characteristic T3 temp. dependence and power-law cooling dynamics provide clear exptl. signatures of this new cooling mechanism. The cooling rate can be changed by orders of magnitude by varying the amt. of disorder providing means for a variety of new applications that rely on hot-carrier transport.
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    Betz, A. C.; Jhang, S. H.; Pallecchi, E.; Ferreira, R.; Fève, G.; Berroir, J.-M.; Plaçais, B. Supercollision Cooling in Undoped Graphene. Nat. Phys. 2013, 9, 109– 112,  DOI: 10.1038/nphys2494
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    Supercollision cooling in undoped graphene
    Betz, A. C.; Jhang, S. H.; Pallecchi, E.; Ferreira, R.; Feve, G.; Berroir, J.-M.; Placais, B.
    Nature Physics (2013), 9 (2), 109-112CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
    Carrier mobility in solids is generally limited by electron-impurity or electron-phonon scattering, depending on the most frequently occurring event. Three-body collisions between carriers and both phonons and impurities are rare; they are denoted supercollisions. Elusive in electronic transport they should emerge in relaxation processes as they allow for larger energy transfers. This is the case in undoped graphene, where the small Fermi surface drastically restricts the allowed phonon energy in ordinary collisions. Using elec. heating and sensitive noise thermometry we report on supercollision cooling in diffusive monolayer graphene. At low carrier d. and high phonon temp. the Joule power P obeys a PTe3 law as a function of electronic temp. Te. It overrules the linear law expected for ordinary collisions which has recently been obsd. in resistivity measurements. The cubic law is characteristic of supercollisions and departs from the Te4 dependence recently reported for doped graphene below the Bloch-Grueneisen temp. These supercollisions are important for applications of graphene in bolometry and photo-detection.
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    Graham, M. W.; Shi, S.-F.; Wang, Z.; Ralph, D. C.; Park, J.; McEuen, P. L. Transient Absorption and Photocurrent Microscopy Show that Hot Electron Supercollisions Describe the Rate-Limiting Relaxation Step in Graphene. Nano Lett. 2013, 13, 5497– 502,  DOI: 10.1021/nl4030787
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    30
    Transient Absorption and Photocurrent Microscopy Show That Hot Electron Supercollisions Describe the Rate-Limiting Relaxation Step in Graphene
    Graham, Matt W.; Shi, Su-Fei; Wang, Zenghui; Ralph, Daniel C.; Park, Jiwoong; McEuen, Paul L.
    Nano Letters (2013), 13 (11), 5497-5502CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Using transient absorption (TA) microscopy as a hot electron thermometer, disorder-assisted acoustic-phonon supercollisions (SCs) best describe the rate-limiting relaxation step in graphene over a wide range of lattice temps. (Tl = 5-300 K), Fermi energies (EF = ± 0.35 eV), and optical probe energies (∼0.3-1.1 eV). Comparison with simultaneously collected transient photocurrent, an independent hot electron thermometer, confirms that the rate-limiting optical and elec. response in graphene are best described by the SC-heat dissipation rate model, H = A(Te3 - Tl3). The authors' data further show that the electron cooling rate in substrate-supported graphene is twice as fast as in suspended graphene sheets, consistent with SC model prediction for disorder.
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    Alencar, T. V.; Silva, M. G.; Malard, L. M.; de Paula, A. M. Defect-Induced Supercollision Cooling of Photoexcited Carriers in Graphene. Nano Lett. 2014, 14, 5621– 5624,  DOI: 10.1021/nl502163d
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    Defect-Induced Supercollision Cooling of Photoexcited Carriers in Graphene
    Alencar, Thonimar V.; Silva, Mychel G.; Malard, Leandro M.; de Paula, Ana M.
    Nano Letters (2014), 14 (10), 5621-5624CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Defects play a fundamental role in the energy relaxation of hot photoexcited carriers in graphene, thus a complete understanding of these processes are vital for improving the development of graphene devices. Recently, it was theor. predicted and exptl. demonstrated that defect-assisted acoustic phonon supercollision, the collision between a carrier and both an acoustic phonon and a defect, is an important energy relaxation process for carriers with excess energy below the optical phonon emission. Here, the authors studied samples with defects optically generated in a controlled manner to exptl. probe the supercollision model as a function of the defect d. The authors present pump and probe transient absorption measurements showing that the decay time decreases as the d. of defect increases as predicted by the supercollision model.
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    Graham, M. W.; Shi, S. F.; Ralph, D. C.; Park, J.; McEuen, P. L. Photocurrent Measurements of Supercollision Cooling in Graphene. Nat. Phys. 2013, 9, 103– 108,  DOI: 10.1038/nphys2493
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    Photocurrent measurements of supercollision cooling in graphene
    Graham, Matt W.; Shi, Su-Fei; Ralph, Daniel C.; Park, Jiwoong; McEuen, Paul L.
    Nature Physics (2013), 9 (2), 103-108CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
    The cooling of hot electrons in graphene is the crit. process underlying the operation of exciting new graphene-based optoelectronic and plasmonic devices, but the nature of this cooling is controversial. We ext. the hot-electron cooling rate near the Fermi level by using graphene as a novel photothermal thermometer that measures the electron temp. (T(t)) as it cools dynamically. We find the photocurrent generated from graphene p-n junctions is well described by the energy dissipation rate CdT/dt = -A(T3-Tl3), where the heat capacity is C = αT and Tl is the base lattice temp. These results are in disagreement with predictions of electron-phonon emission in a disorder-free graphene system, but in excellent quant. agreement with recent predictions of a disorder-enhanced supercollision cooling mechanism. We find that the supercollision model provides a complete and unified picture of energy loss near the Fermi level over the wide range of electronic (15 to ∼ 3,000 K) and lattice (10-295 K) temps. investigated.
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    Tielrooij, K.-J.; Hesp, N. C. H.; Principi, A.; Lundeberg, M. B.; Pogna, E. A. A.; Banszerus, L.; Mics, Z.; Massicotte, M.; Schmidt, P.; Davydovskaya, D.; Purdie, D. G.; Goykhman, I.; Soavi, G.; Lombardo, A.; Watanabe, K.; Taniguchi, T.; Bonn, M.; Turchinovich, D.; Stampfer, C.; Ferrari, A. C.; Cerullo, G.; Polini, M.; Koppens, F. H. L. Out-of-Plane Heat Transfer in van der Waals Stacks through Electron-Hyperbolic Phonon Coupling. Nat. Nanotechnol. 2018, 13, 41– 46,  DOI: 10.1038/s41565-017-0008-8
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    Out-of-plane heat transfer in van der Waals stacks through electron-hyperbolic phonon coupling
    Tielrooij, Klaas-Jan; Hesp, Niels C. H.; Principi, Alessandro; Lundeberg, Mark B.; Pogna, Eva A. A.; Banszerus, Luca; Mics, Zoltan; Massicotte, Mathieu; Schmidt, Peter; Davydovskaya, Diana; Purdie, David G.; Goykhman, Ilya; Soavi, Giancarlo; Lombardo, Antonio; Watanabe, Kenji; Taniguchi, Takashi; Bonn, Mischa; Turchinovich, Dmitry; Stampfer, Christoph; Ferrari, Andrea C.; Cerullo, Giulio; Polini, Marco; Koppens, Frank H. L.
    Nature Nanotechnology (2018), 13 (1), 41-46CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
    Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior elec. and optoelectronic properties. Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier d. and lattice temp., and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.
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    Principi, A.; Lundeberg, M. B.; Hesp, N. C.; Tielrooij, K. J.; Koppens, F. H.; Polini, M. Super-Planckian Electron Cooling in a van der Waals Stack. Phys. Rev. Lett. 2017, 118, 126804,  DOI: 10.1103/PhysRevLett.118.126804
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    Super-Planckian electron cooling in a van der Waals stack
    Principi, Alessandro; Lundeberg, Mark B.; Hesp, Niels C. H.; Tielrooij, Klaas-Jan
    Physical Review Letters (2017), 118 (12), 126804/1-126804/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Radiative heat transfer (RHT) between macroscopic bodies at sepns. that are much smaller than the thermal wavelength is ruled by evanescent electromagnetic modes and can be orders of magnitude more efficient than its far-field counterpart, which is described by the Stefan-Boltzmann law. In this Letter, we present a microscopic theory of RHT in van derWaals stacks comprising graphene and a natural hyperbolic material, i.e., hexagonal boron nitride (hBN). We demonstrate that RHT between hot carriers in graphene and hyperbolic phonon polaritons in hBN is extremely efficient at room temp., leading to picosecond time scales for the carrier cooling dynamics.
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    Yang, W.; Berthou, S.; Lu, X.; Wilmart, Q.; Denis, A.; Rosticher, M.; Taniguchi, T.; Watanabe, K.; Fève, G.; Berroir, J.-m.; Zhang, G.; Voisin, C.; Baudin, E.; Plaçais, B. A Graphene Zener-Klein Transistor Cooled by a Hyperbolic Substrate. Nat. Nanotechnol. 2018, 13, 47– 52,  DOI: 10.1038/s41565-017-0007-9
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    A graphene Zener-Klein transistor cooled by a hyperbolic substrate
    Yang, Wei; Berthou, Simon; Lu, Xiaobo; Wilmart, Quentin; Denis, Anne; Rosticher, Michael; Taniguchi, Takashi; Watanabe, Kenji; Feve, Gwendal; Berroir, Jean-Marc; Zhang, Guangyu; Voisin, Christophe; Baudin, Emmanuel; Placais, Bernard
    Nature Nanotechnology (2018), 13 (1), 47-52CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
    The engineering of cooling mechanisms is a bottleneck in nanoelectronics. Thermal exchanges in diffusive graphene are mostly driven by defect-assisted acoustic phonon scattering, but the case of high-mobility graphene on hexagonal boron nitride (hBN) is radically different, with a prominent contribution of remote phonons from the substrate. Bilayer graphene on a hBN transistor with a local gate is driven in a regime where almost perfect current satn. is achieved by compensation of the decrease in the carrier d. and Zener-Klein tunnelling (ZKT) at high bias. Using noise thermometry, we show that the ZKT triggers a new cooling pathway due to the emission of hyperbolic phonon polaritons in hBN by out-of-equil. electron-hole pairs beyond the super-Planckian regime. The combination of ZKT transport and hyperbolic phonon polariton cooling renders graphene on BN transistors a valuable nanotechnol. for power devices and RF electronics.
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  36. 36
    Caldwell, J. D.; Kretinin, A. V.; Chen, Y.; Giannini, V.; Fogler, M. M.; Francescato, Y.; Ellis, C. T.; Tischler, J. G.; Woods, C. R.; Giles, A. J.; Hong, M.; Watanabe, K.; Taniguchi, T.; Maier, S. A.; Novoselov, K. S. Sub-Diffractional Volume-Confined Polaritons in the Natural Hyperbolic Material Hexagonal Boron Nitride. Nat. Commun. 2014, 5, 5521,  DOI: 10.1038/ncomms6221
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    Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722– 726,  DOI: 10.1038/nnano.2010.172
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    Boron nitride substrates for high-quality graphene electronics
    Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J.
    Nature Nanotechnology (2010), 5 (10), 722-726CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
    Graphene devices on std. SiO2 substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielecs. that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal BN (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice const. similar to that of graphite, and has large optical phonon modes and a large elec. bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by a mech. transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO2. These devices also show reduced roughness, intrinsic doping and chem. reactivity. The ability to assemble cryst. layered materials in a controlled way permits the fabrication of graphene devices on other promising dielecs. and allows for the realization of more complex graphene heterostructures.
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  38. 38
    Wang, L.; Meric, I.; Huang, P.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 2013, 342, 614– 617,  DOI: 10.1126/science.1244358
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    One-Dimensional Electrical Contact to a Two-Dimensional Material
    Wang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R.
    Science (Washington, DC, United States) (2013), 342 (6158), 614-617CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal B nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality elec. contact. Here, the authors report a contact geometry in which the authors metalize only the 1-dimensional edge of a 2-dimensional graphene layer. In addn. to outperforming conventional surface contacts, the edge-contact geometry allows a complete sepn. of the layer assembly and contact metalization processes. In graphene heterostructures, this enables high electronic performance, including low-temp. ballistic transport over distances longer than 15 μm, and room-temp. mobility comparable to the theor. phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2-dimensional materials.
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  39. 39
    Banszerus, L.; Janssen, H.; Otto, M.; Epping, A.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Neumaier, D.; Stampfer, C. Identifying Suitable Substrates for High-Quality Graphene-Based Heterostructures. 2D Mater. 2017, 4, 025030,  DOI: 10.1088/2053-1583/aa5b0f
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    Identifying suitable substrates for high-quality graphene-based heterostructures
    Banszerus, L.; Janssen, H.; Otto, M.; Epping, A.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Neumaier, D.; Stampfer, C.
    2D Materials (2017), 4 (2), 025030/1-025030/8CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
    We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chem. vapor deposited (CVD) graphene-based heterostuctures on a large no. of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By applying a hBN-assisted, contamination free, dry transfer process for CVD graphene, high-quality heterostructures with low doping densities and low strain variations are assembled. The Raman spectra of these pristine heterostructures are sensitive to substrate-induced doping and strain variations and are thus used to probe the suitability of the substrate material for potential high-quality graphene devices. We find that the flatness of the substrate material is a key figure for gaining, or preserving high-quality graphene.
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  40. 40
    Banszerus, L.; Sohier, T.; Epping, A.; Winkler, F.; Libisch, F.; Haupt, F.; Watanabe, K.; Taniguchi, T.; Müller-Caspary, K.; Marzari, N.; Mauri, F.; Beschoten, B.; Stampfer, C. Extraordinary High Room-Temperature Carrier Mobility in Graphene-WSe2 Heterostructures. arXiv:1909.09523 http://arxiv.org/abs/1909.09523 (accessed December 25, 2020).
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    Backes, C.; Abdelkader, A. M.; Alonso, C.; Andrieux-Ledier, A.; Arenal, R.; Azpeitia, J.; Balakrishnan, N.; Banszerus, L.; Barjon, J.; Bartali, R.; Bellani, S.; Berger, C.; Berger, R.; Ortega, M. M.; Bernard, C.; Beton, P. H.; Beyer, A.; Bianco, A.; Bøggild, P.; Bonaccorso, A. Production and Processing of Graphene and Related Materials. 2D Mater. 2020, 7, 022001,  DOI: 10.1088/2053-1583/ab1e0a
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    Production and processing of graphene and related materials
    Backes, Claudia; Abdelkader, Amr M.; Alonso, Concepcion; Andrieux-Ledier, Amandine; Arenal, Raul; Azpeitia, Jon; Balakrishnan, Nilanthy; Banszerus, Luca; Barjon, Julien; Bartali, Ruben; Bellani, Sebastiano; Berger, Claire; Berger, Reinhard; Ortega, M. M. Bernal; Bernard, Carlo; Beton, Peter H.; Beyer, Andre; Bianco, Alberto; Boeggild, Peter B.; Bonaccorso, Francesco; Barin, Gabriela Borin; Botas, Cristina; Bueno, Rebeca A.; Carriazo, Daniel; Gomez, Andres Castellanos; Christian, Meganne; Ciesielski, Artur; Ciuk, Tymoteusz; Cole, Matthew T.; Coleman, Jonathan; Coletti, Camilla; Crema, Luigi; Cun, Huanyao; Dasler, Daniela; De Fazio, Domenico; Diez, Noel; Drieschner, Simon; Duesberg, Georg S.; Fasel, Roman; Feng, Xinliang; Fina, Alberto; Forti, Stiven; Galiotis, Costas; Garberoglio, Giovanni; Garcia, Jorge M.; Garrido, Jose Antonio; Gibertini, Marco; Goelzhaeuser, Armin; Gomez, Julio; Greber, Thomas; Hauke, Frank; Hemmi, Adrian; Hernandez-Rodriguez, Irene; Hirsch, Andreas; Hodge, Stephen A.; Huttel, Yves; Jepsen, Peter U.; Jimenez, Ignacio; Kaiser, Ute; Kaplas, Tommi; Kim, Hokwon; Kis, Andras; Papagelis, Konstantinos; Kostarelos, Kostas; Krajewska, Aleksandra; Lee, Kangho; Li, Changfeng; Lipsanen, Harri; Liscio, Andrea; Lohe, Martin R.; Loiseau, Annick; Lombardi, Lucia; Lopez, Maria Francisca; Martin, Oliver; Martin, Cristina; Martinez, Lidia; Martin-Gago, Joseangel; Martinez, Jose Ignacio; Marzari, Nicola; Mayoral, Alvaro; Mcmanus, John; Melucci, Manuela; Mendez, Javier; Merino, Cesar; Merino, Pablo; Meyer, Andreas P.; Miniussi, Elisa; Miseikis, Vaidotas; Mishra, Neeraj; Morandi, Vittorio; Munuera, Carmen; Munoz, Roberto; Nolan, Hugo; Ortolani, Luca; Ott, Annak; Palacio, Irene; Palermo, Vincenzo; Parthenios, John; Pasternak, Iwona; Patane, Amalia; Prato, Maurizio; Prevost, Henri; Prudkovskiy, Vladimir; Pugno, Nicola; Rojo, Teofilo; Rossi, Antonio; Ruffieux, Pascal; Samori, Paolo; Schue, Leonard; Setijadi, Eki; Seyller, Thomas; Speranza, Giorgio; Stampfer, Christoph; Stenger, Ingrid; Strupinski, Wlodek; Svirko, Yuri; Taioli, Simone; Bkteo, Kenneth; Testi, Matteo; Tomarchio, Flavia; Tortello, Mauro; Treossi, Emanuele; Turchanin, Andrey; Vazquez, Ester; Villaro, Elvira; Whelan, Patrick R.; Xia, Zhenyuan; Yakimova, Rositza; Yang, Sheng; Yazdi, G. Reza; Yim, Chanyoung; Yoon, Duhee; Zhang, Xianghui; Zhuang, Xiaodong; Colombo, Luigi; Ferrari, Andrea C.; Garcia-Hernandez, Mar
    2D Materials (2020), 7 (2), 022001CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
    We present an overview of the main techniques for prodn. and processing of graphene and related materials (GRMs), as well as the key characterization procedures. We adopt a 'hands-on' approach, providing practical details and procedures as derived from literature as well as from the authors' experience, in order to enable the reader to reproduce the results.
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  42. 42
    Neumann, C.; Banszerus, L.; Schmitz, M.; Reichardt, S.; Sonntag, J.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Stampfer, C. Line Shape of the Raman 2D Peak of Graphene in van der Waals Heterostructures. Phys. Status Solidi B 2016, 253, 2326– 2330,  DOI: 10.1002/pssb.201600283
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    Line shape of the Raman 2D peak of graphene in van der Waals heterostructures
    Neumann, Christoph; Banszerus, Luca; Schmitz, Michael; Reichardt, Sven; Sonntag, Jens; Taniguchi, Takashi; Watanabe, Kenji; Beschoten, Bernd; Stampfer, Christoph
    Physica Status Solidi B: Basic Solid State Physics (2016), 253 (12), 2326-2330CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The Raman 2D line of graphene is widely used for device characterization and during device fabrication as it contains valuable information on, e.g., the direction and magnitude of mech. strain and doping. Here, we present systematic asymmetries in the 2D line shape of exfoliated graphene and graphene grown by chem. vapor deposition. Both graphene crystals are fully encapsulated in van der Waals heterostructures, where hexagonal boron nitride and tungsten diselenide are used as substrate materials. In both material stacks, we find very low doping values and extremely homogeneous strain distributions in the graphene crystal, which is a hall mark of the outstanding electronic quality of these samples. By fitting double Lorentzian functions to the spectra to account for the contributions of inner and outer processes to the 2D peak, we find that the splitting of the sub-peaks, 6.6±0.5cm-1 (hBN-Gr-WSe2) and 8.9±1.0cm-1 (hBN-Gr-hBN), is significantly lower than the values reported in previous studies on suspended graphene.
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    Robinson, J. A.; Wetherington, M.; Tedesco, J. L.; Campbell, P. M.; Weng, X.; Stitt, J.; Fanton, M. A.; Frantz, E.; Snyder, D.; VanMil, B. L.; Jernigan, G. G.; Rachael, L. M. W.; Eddy, C. R.; Gaskill, D. K. Correlating Raman Spectral Signatures with Carrier Mobility in Epitaxial Graphene: A Guide to Achieving High Mobility on the Wafer Scale. Nano Lett. 2009, 9, 2873– 2876,  DOI: 10.1021/nl901073g
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    Correlating Raman Spectral Signatures with Carrier Mobility in Epitaxial Graphene: A Guide to Achieving High Mobility on the Wafer Scale
    Robinson, Joshua A.; Wetherington, Maxwell; Tedesco, Joseph L.; Campbell, Paul M.; Weng, Xiaojun; Stitt, Joseph; Fanton, Mark A.; Frantz, Eric; Snyder, David; Van Mil, Brenda L.; Jernigan, Glenn G.; Myers-Ward, Rachael L.; Eddy, Charles R.; Gaskill, D. Kurt
    Nano Letters (2009), 9 (8), 2873-2876CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    The authors report a direct correlation between carrier mobility and Raman topog. of epitaxial graphene (EG) grown on silicon carbide (SiC). The authors show the Hall mobility of material on SiC(0001) is highly dependent on thickness and monolayer strain uniformity. Addnl., the authors achieve high mobility epitaxial graphene (18100 cm2/(V s) at room temp.) on SiC(0001‾) and show that carrier mobility depends strongly on the graphene layer stacking.
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    Kang, K.; Abdula, D.; Cahill, D. G.; Shim, M. Lifetimes of Optical Phonons in Graphene and Graphite by Time-Resolved Incoherent Anti-Stokes Raman Scattering. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 165405,  DOI: 10.1103/PhysRevB.81.165405
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    Lifetimes of optical phonons in graphene and graphite by time-resolved incoherent anti-Stokes Raman scattering
    Kang, Kwangu; Abdula, Daner; Cahill, David G.; Shim, Moonsub
    Physical Review B: Condensed Matter and Materials Physics (2010), 81 (16), 165405/1-165405/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We report lifetimes of optical phonons (OPs) in graphene and graphite measured by time-resolved anti-Stokes Raman scattering. Lifetimes in graphite and monolayer graphene are 2.4 and 1.2 ps, resp. For graphite and graphene with more than five layers, the lifetimes decrease with increasing temp. as ∼1/T, indicating the dominance of anharmonic processes in the decay of the OP population. The decrease in lifetime with decreasing no. of layers suggests an addnl. decay channel through which excitations in graphene interact directly with lattice vibrations of the a-SiO2 substrate.
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    Lui, C. H.; Mak, K. F.; Shan, J.; Heinz, T. F. Ultrafast Photoluminescence from Graphene. Phys. Rev. Lett. 2010, 105, 127404,  DOI: 10.1103/PhysRevLett.105.127404
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    Ultrafast Photoluminescence from Graphene
    Lui, Chun Hung; Mak, Kin Fai; Shan, Jie; Heinz, Tony F.
    Physical Review Letters (2010), 105 (12), 127404/1-127404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Since graphene has no band gap, photoluminescence is not expected from relaxed charge carriers. The authors have, however, obsd. significant light emission from graphene under excitation by ultrashort (30-fs) laser pulses. Light emission occurs across the visible spectral range (1.7-3.5 eV), with emitted photon energies exceeding that of the excitation laser (1.5 eV). The emission exhibits a nonlinear dependence on the laser fluence. In 2-pulse correlation measurements, a dominant relaxation time of tens of femtoseconds is obsd. A 2-temp. model describing the electrons and their interaction with strongly coupled optical phonons can account for the exptl. observations.
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    Wang, H.; Strait, J. H.; George, P. A.; Shivaraman, S.; Shields, V. B.; Chandrashekhar, M.; Hwang, J.; Rana, F.; Spencer, M. G.; Ruiz-Vargas, C. S.; Park, J. Ultrafast Relaxation Dynamics of Hot Optical Phonons in Graphene. Appl. Phys. Lett. 2010, 96, 081917,  DOI: 10.1063/1.3291615
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    Ultrafast relaxation dynamics of hot optical phonons in graphene
    Wang, Haining; Strait, Jared H.; George, Paul A.; Shivaraman, Shriram; Shields, Virgil B.; Chandrashekhar, M. V. S.; Hwang, Jeonghyun; Rana, Farhan; Spencer, Michael G.; Ruiz-Vargas, Carlos S.; Park, Jiwoong
    Applied Physics Letters (2010), 96 (8), 081917/1-081917/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    Using ultrafast optical pump-probe spectroscopy, the authors study the relaxation dynamics of hot optical phonons in few-layer and multilayer graphene films grown by epitaxy on Si carbide substrates and by CVD on Ni substrates. In the 1st few hundred femtoseconds after photoexcitation, the hot carriers lose most of their energy to the generation of hot optical phonons which then present the main bottleneck to subsequent cooling. Optical phonon cooling on short time scales is independent of the graphene growth technique, the no. of layers, and the type of the substrate. Av. phonon lifetimes in the 2.5-2.55 ps range were found. The authors model the relaxation dynamics of the coupled carrier-phonon system with rate equations and find a good agreement between the exptl. data and the theory. The extd. optical phonon lifetimes agree very well with the theory based on anharmonic phonon interactions. (c) 2010 American Institute of Physics.
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    Wu, S.; Liu, W. T.; Liang, X.; Schuck, P. J.; Wang, F.; Shen, Y. R.; Salmeron, M. Hot Phonon Dynamics in Graphene. Nano Lett. 2012, 12, 5495– 5499,  DOI: 10.1021/nl301997r
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    Hot Phonon Dynamics in Graphene
    Wu, Shiwei; Liu, Wei-Tao; Liang, Xiaogan; Schuck, P. James; Wang, Feng; Shen, Y. Ron; Salmeron, Miquel
    Nano Letters (2012), 12 (11), 5495-5499CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    The dynamics of hot phonons in supported, suspended, and gated monolayer graphene was studied by using time-resolved anti-Stokes Raman spectroscopy. We found that the hot phonon relaxation is dominated by phonon-phonon interaction in graphene, and strongly affected by the interaction between graphene and the substrate. Relaxation via carrier-phonon coupling, known as Landau damping, is ineffective for hot phonons which are in thermal equil. with excited carriers. Our findings provide a basis for better management of energy dissipation in graphene devices.
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    Bonini, N.; Lazzeri, M.; Marzari, N.; Mauri, F. Phonon Anharmonicities in Graphite and Graphene. Phys. Rev. Lett. 2007, 99, 176802,  DOI: 10.1103/PhysRevLett.99.176802
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    Phonon Anharmonicities in Graphite and Graphene
    Bonini, Nicola; Lazzeri, Michele; Marzari, Nicola; Mauri, Francesco
    Physical Review Letters (2007), 99 (17), 176802/1-176802/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The authors det. from 1st principles the finite-temp. properties - linewidths, line shifts, and lifetimes - of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E2g mode decreases with temp.; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate IR-active E1u mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A'1 mode at K dominate over E2g at Γ and couple strongly with acoustic phonons, highlighting how ballistic transport in C-based interconnects requires careful engineering of phonon decays and thermalization.
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    Zhang, J.; Lin, L.; Sun, L.; Huang, Y.; Koh, A. L.; Dang, W.; Yin, J.; Wang, M.; Tan, C.; Li, T.; Tan, Z.; Liu, Z.; Peng, H. Clean Transfer of Large Graphene Single Crystals for High-Intactness Suspended Membranes and Liquid Cells. Adv. Mater. 2017, 29, 1700639,  DOI: 10.1002/adma.201700639
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    Lin, L.; Zhang, J.; Su, H.; Li, J.; Sun, L.; Wang, Z.; Xu, F.; Liu, C.; Lopatin, S.; Zhu, Y.; Jia, K.; Chen, S.; Rui, D.; Sun, J.; Xue, R.; Gao, P.; Kang, N.; Han, Y.; Xu, H. Q.; Cao, Y. Towards Super-Clean Graphene. Nat. Commun. 2019, 10, 1912,  DOI: 10.1038/s41467-019-09565-4
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    Towards super-clean graphene
    Lin Li; Zhang Jincan; Sun Luzhao; Jia Kaicheng; Peng Hailin; Liu Zhongfan; Zhang Jincan; Li Jiayu; Sun Luzhao; Su Haisheng; Cao Yang; Tian Zhongqun; Ren Bin; Li Jiayu; Rui Dingran; Kang Ning; Xu H Q; Li Jiayu; Wang Zihao; Novoselov K S; Xu Fan; Liu Chang; Lopatin Sergei; Zhu Yihan; Han Yu; Chen Shulin; Sun Jingyu; Sun Jingyu; Xue Ruiwen; Gao Peng; Peng Hailin; Liu Zhongfan
    Nature communications (2019), 10 (1), 1912 ISSN:.
    Impurities produced during the synthesis process of a material pose detrimental impacts upon the intrinsic properties and device performances of the as-obtained product. This effect is especially pronounced in graphene, where surface contamination has long been a critical, unresolved issue, given graphene's two-dimensionality. Here we report the origins of surface contamination of graphene, which is primarily rooted in chemical vapour deposition production at elevated temperatures, rather than during transfer and storage. In turn, we demonstrate a design of Cu substrate architecture towards the scalable production of super-clean graphene (>99% clean regions). The readily available, super-clean graphene sheets contribute to an enhancement in the optical transparency and thermal conductivity, an exceptionally lower-level of electrical contact resistance and intrinsically hydrophilic nature. This work not only opens up frontiers for graphene growth but also provides exciting opportunities for the utilization of as-obtained super-clean graphene films for advanced applications.
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    Lee, J. E.; Ahn, G.; Shim, J.; Lee, Y. S.; Ryu, S. Optical Separation of Mechanical Strain from Charge Doping in Graphene. Nat. Commun. 2012, 3, 1024,  DOI: 10.1038/ncomms2022
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    Optical separation of mechanical strain from charge doping in graphene
    Lee Ji Eun; Ahn Gwanghyun; Shim Jihye; Lee Young Sik; Ryu Sunmin
    Nature communications (2012), 3 (), 1024 ISSN:.
    Because of its superior stretchability, graphene exhibits rich structural deformation behaviours and its strain engineering has proven useful in modifying its electronic and magnetic properties. Despite the strain-sensitivity of the Raman G and 2D modes, the optical characterization of the native strain in graphene on silica substrates has been hampered by excess charges interfering with both modes. Here we show that the effects of strain and charges can be optically separated from each other by correlation analysis of the two modes, enabling simple quantification of both. Graphene with in-plane strain randomly occurring between -0.2% and 0.4% undergoes modest compression (-0.3%) and significant hole doping on thermal treatments. This study suggests that substrate-mediated mechanical strain is a ubiquitous phenomenon in two-dimensional materials. The proposed analysis will be of great use in characterizing graphene-based materials and devices.
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    Malard, L. M.; Mak, K. F.; Neto, A. C.; Peres, N.; Heinz, T. F. Observation of Intra-and Inter-Band Transitions in the Transient Optical Response of Graphene. New J. Phys. 2013, 15, 015009,  DOI: 10.1088/1367-2630/15/1/015009
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    Observation of intra- and inter-band transitions in the transient optical response of graphene
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Published June 17, 2021

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  • Abstract

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    Figure 1

    Figure 1. Characterization of the WSe2-encapsulated graphene sample. (a) Sketch of the encapsulated graphene prepared by exfoliation and dry transfer of two flakes of WSe2 and monolayer graphene. (41) (b) Atomic force microscopy image of the sample, used to determine the thicknesses of the WSe2 flakes. (c) Raman spectra of fully encapsulated graphene (blue line) and of semiencapsulated graphene (black line) obtained with 532 nm laser source. Encapsulation gives rise to a background, reduced graphene Raman signatures’ (G and 2D peaks) intensity, and a clear blue shift of the 2D peak. (d, e) Maps of the 2D peak frequency ω2D (d) and width Γ2D (e) extracted from Raman spectra at different positions on the sample fitted with a Voigt function centered in ω2D. (f, g) Statistical distribution of ω2D (f) and Γ2D (g) in the encapsulated graphene obtained from the maps in panels d and e. The narrow width suggests a high electrical mobility.

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    Figure 2

    Figure 2. Hot-carrier cooling dynamics of WSe2-encapsulated graphene. (a) Transient transmission ΔT/T maps at a fixed time delay t = 100 fs between pump and probe pulses acquired with pump at 0.8 eV (1550 nm) and probe at 0.729 eV (1700 nm). White lines indicate the edges of WSe2 flakes extracted from an optical image. The panel on the right shows a zoom of the left panel, and the black cross indicates the location in the fully encapsulated region, where the ΔT/T dynamics are measured. (b) Comparison of normalized ΔT/T relaxation dynamics of graphene encapsulated by WSe2 (blue dots) and hBN (black dots), using a pump fluence of ∼1 μJ/cm2 in both cases. Encapsulation with hBN gives rise to faster dynamics, which we attribute to out-of-plane cooling to hyperbolic phonons of hBN. (33−35) This cooling mechanism is much less efficient for WSe2 encapsulation. (c) ΔT/T dynamics (dots) for WSe2-encapsulated graphene at five different pump fluences from 0.2 to 2 μJ/cm2. The positive ΔT/T is due to pump-induced heating, leading to Pauli blocking of probe interband transitions. The solid lines are the calculated ΔT/T dynamics, based on the intrinsic hot-electron cooling mechanism via the combination of optical-phonon emission, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (d) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel c. Here, fast decay due to the electron-optical-phonon coupling is followed by slower decay via optical-to-acoustic phonon coupling. The former component shows up very strongly in the TA signal as a consequence of the strongly superlinear relation between the TA signal ΔT/T and the change in carrier temperature ΔTe.

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    Figure 3

    Figure 3. Characterization of suspended high-quality graphene. (a) Sketch of graphene suspended on a holey carbon film. (b) Scanning electron microscopy images of suspended graphene on holey carbon, showing relatively large hole sizes and high yield. (c) TEM image of the suspended graphene, showing the absence of disorder. (d) Plot of 2D peak frequency ω2D as a function of G peak frequency ωG. Dashed lines represent the expected dependence in the strain-free (red dot-dot-dashed line) and doping-free (blue dot-dashed line) material. (e) Fermi energy EF distribution extracted from vector decomposition of peaks positions in panel d, (51) and centered at |EF| ≈ 0.18 eV. (f) Obtained distribution of 2D-peak widths, indicating a mobility of >17 000 cm2 V–1 s–1, following calculations of ref (43).

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    Figure 4

    Figure 4. Hot-carrier cooling dynamics of suspended graphene. (a) Transient transmission ΔT/T map at time zero, showing individual holes where graphene is suspended, acquired with pump tuned at 3.1 eV (400 nm) and probe at 1.55 eV (800 nm). (b) ΔT/T dynamics (colored dots) for suspended graphene at five different pump fluences from 3 to 38 μJ/cm2. The positive ΔT/T results from the pump-induced carrier heating that leads to decreased interband conductivity due to Pauli blocking, and thus decreased absorption of the NIR probe light. The colored lines are the calculated ΔT/T dynamics, based on the intrinsic cooling mechanism where hot electrons cool via the combination of emission of optical phonons, continuous rethermalization of the electron distribution, and coupling of optical to acoustic phonons. (c) Dynamical evolution of the electron temperature Te, corresponding to the calculated ΔT/T dynamics in panel b. Here, a fast decay due to electron-optical-phonon coupling is followed by a slower decay due to optical-to-acoustic phonon coupling.

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    Figure 5

    Figure 5. Hot-carrier cooling dynamics in high-quality graphene. (a) Process of electronic cooling explained through schematics of the carrier density N as a function of carrier energy for three electron temperatures (1200, 800, and 400 K). Cooling occurs through a combination of (i) optical phonon emission by electrons with energy >0.16 eV above the chemical potential (red-shaded area), (ii) rethermalization of the electronic distribution, and (iii) anharmonic coupling of optical phonons to acoustic phonons. (b) Calculated “instantaneous” cooling time for a given initial electron temperature for three different Fermi energies. (c) Calculated cooling time as a function of lattice temperature TL for a very small ΔTe and EF = 0.03 eV. For panels b and c, cooling occurs through optical phonon emission and continuous rethermalization of the electronic system. The hot-phonon bottleneck is not included.

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      Castilla, Sebastian; Terres, Bernat; Autore, Marta; Viti, Leonardo; Li, Jian; Nikitin, Alexey Y.; Vangelidis, Ioannis; Watanabe, Kenji; Taniguchi, Takashi; Lidorikis, Elefterios; Vitiello, Miriam S.; Hillenbrand, Rainer; Tielrooij, Klaas-Jan; Koppens, Frank H. L.
      Nano Letters (2019), 19 (5), 2765-2773CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Although the detection of light at THz frequencies is important for a large range of applications, current detectors typically have several disadvantages in terms of sensitivity, speed, operating temp., and spectral range. Graphene was used as a photoactive material to overcome all of these limitations in 1 device. A novel detector for far-IR radiation that exploits the photothermoelec. (PTE) effect was introduced, based on a design that employs a dual-gated, dipolar antenna with a gap of ∼100 nm. This narrow-gap antenna simultaneously creates a pn junction in a graphene channel located above the antenna and strongly concs. the incoming radiation at this pn junction, where the photoresponse is created. This novel detector has an excellent sensitivity, with a noise-equiv. power of 80 pW/√(Hz) at room temp., a response time <30 ns (setup-limited), a high dynamic range (linear power dependence over >3 orders of magnitude) and broadband operation (measured range 1.8-4.2 THz, antenna-limited), which fulfills a combination that is currently missing in the state-of-the-art detectors. From the agreement obtained between expt., anal. model, and numerical simulations, a solid understanding of how the PTE effect gives rise to a THz-induced photoresponse, which is very valuable for further detector optimization was reached.
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    10. 10
      Viti, L.; Purdie, D. G.; Lombardo, A.; Ferrari, A. C.; Vitiello, M. S. HBN-Encapsulated, Graphene-Based, Room-Temperature Terahertz Receivers, with High Speed and Low Noise. Nano Lett. 2020, 20, 3169– 3177,  DOI: 10.1021/acs.nanolett.9b05207
      10
      HBN-Encapsulated, Graphene-based, Room-temperature Terahertz Receivers, with High Speed and Low Noise
      Viti, Leonardo; Purdie, David G.; Lombardo, Antonio; Ferrari, Andrea C.; Vitiello, Miriam S.
      Nano Letters (2020), 20 (5), 3169-3177CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Uncooled terahertz photodetectors (PDs) showing fast (ps) response and high sensitivity (noise equiv. power (NEP) < nW/Hz1/2) over a broad (0.5-10 THz) frequency range are needed for applications in high-resoln. spectroscopy (relative accuracy ~ 10-11), metrol., quantum information, security, imaging, optical communications. However, present terahertz receivers cannot provide the required balance between sensitivity, speed, operation temp., and frequency range. Here, we demonstrate uncooled terahertz PDs combining the low (~ 2000 kB μm-2) electronic sp. heat of high mobility (>50 000 cm2 V-1 s-1) hexagonal boron nitride-encapsulated graphene, with asym. field enhancement produced by a bow-tie antenna, resonating at 3 THz. This produces a strong photo-thermoelec. conversion, which simultaneously leads to a combination of high sensitivity (NEP ≤ 160 pW Hz-1/2), fast response time (≤3.3 ns), and a 4 orders of magnitude dynamic range, making our devices the fastest, broad-band, low-noise, room-temp. terahertz PD, to date.
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    11. 11
      Liu, M.; Yin, X.; Ulin-Avila, E.; Geng, B.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang, X. A Graphene-Based Broadband Optical Modulator. Nature 2011, 474, 64– 67,  DOI: 10.1038/nature10067
      11
      A graphene-based broadband optical modulator
      Liu, Ming; Yin, Xiaobo; Ulin-Avila, Erick; Geng, Baisong; Zentgraf, Thomas; Ju, Long; Wang, Feng; Zhang, Xiang
      Nature (London, United Kingdom) (2011), 474 (7349), 64-67CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Integrated optical modulators with high modulation speed, small footprint and large optical bandwidth are poised to be the enabling devices for on-chip optical interconnects. Semiconductor modulators have therefore been heavily researched over the past few years. However, the device footprint of Si-based modulators is of the order of millimeters, owing to its weak electrooptical properties. Ge and compd. semiconductors, however, face the major challenge of integration with existing Si electronics and photonics platforms. Integrating Si modulators with high-quality-factor optical resonators increases the modulation strength, but these devices suffer from intrinsic narrow bandwidth and require sophisticated optical design; they also have stringent fabrication requirements and limited temp. tolerances. Finding a complementary metal-oxide-semiconductor (CMOS)-compatible material with adequate modulation speed and strength has therefore become a task of not only scientific interest, but also industrial importance. Here the authors exptl. demonstrate a broadband, high-speed, waveguide-integrated electroabsorption modulator based on monolayer graphene. By elec. tuning the Fermi level of the graphene sheet, the authors demonstrate modulation of the guided light at frequencies over 1 GHz, together with a broad operation spectrum that ranges from 1.35 to 1.6 μm under ambient conditions. The high modulation efficiency of graphene results in an active device area of merely 25 μm2, which is among the smallest to date. This graphene-based optical modulation mechanism, with combined advantages of compact footprint, low operation voltage and ultrafast modulation speed across a broad range of wavelengths, can enable novel architectures for on-chip optical communications.
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    12. 12
      Romagnoli, M.; Sorianello, V.; Midrio, M.; Koppens, F. H. L.; Huyghebaert, C.; Neumaier, D.; Galli, P.; Templ, W.; Ferrari, A. C. Graphene-Based Integrated Photonics for Next-Generation Datacom and Telecom. Nat. Rev. Mater. 2018, 3, 392– 414,  DOI: 10.1038/s41578-018-0040-9
      12
      Graphene-based integrated photonics for next-generation datacom and telecom
      Romagnoli, Marco; Sorianello, Vito; Midrio, Michele; Koppens, Frank H. L.; Huyghebaert, Cedric; Neumaier, Daniel; Galli, Paola; Templ, Wolfgang; D'Errico, Antonio; Ferrari, Andrea C.
      Nature Reviews Materials (2018), 3 (10), 392-414CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
      A review: Graphene is an ideal material for optoelectronic applications. Its photonic properties give several advantages and complementarities over Si photonics. For example, graphene enables both electro-absorption and electro-refraction modulation with an electro-optical index change exceeding 10-3. It can be used for optical add-drop multiplexing with voltage control, eliminating the current dissipation used for the thermal detuning of microresonators, and for thermoelec.-based ultrafast optical detectors that generate a voltage without transimpedance amplifiers. Here, we present our vision for graphene-based integrated photonics. We review graphene-based transceivers and compare them with existing technologies. Strategies for improving power consumption, manufacturability and wafer-scale integration are addressed. We outline a roadmap of the technol. requirements to meet the demands of the datacom and telecom markets. We show that graphene-based integrated photonics could enable ultrahigh spatial bandwidth d., low power consumption for board connectivity and connectivity between data centers, access networks and metropolitan, core, regional and long-haul optical communications.
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    13. 13
      Muench, J. E.; Ruocco, A.; Giambra, M. A.; Miseikis, V.; Zhang, D.; Wang, J.; Watson, H. F. Y.; Park, G. C.; Akhavan, S.; Sorianello, V.; Midrio, M.; Tomadin, A.; Coletti, C.; Romagnoli, M.; Ferrari, A. C.; Goykhman, I. Waveguide-Integrated, Plasmonic Enhanced Graphene Photodetectors. Nano Lett. 2019, 19, 7632– 7644,  DOI: 10.1021/acs.nanolett.9b02238
      13
      Waveguide-Integrated, Plasmonic Enhanced Graphene Photodetectors
      Muench, Jakob E.; Ruocco, Alfonso; Giambra, Marco A.; Miseikis, Vaidotas; Zhang, Dengke; Wang, Junjia; Watson, Hannah F. Y.; Park, Gyeong C.; Akhavan, Shahab; Sorianello, Vito; Midrio, Michele; Tomadin, Andrea; Coletti, Camilla; Romagnoli, Marco; Ferrari, Andrea C.; Goykhman, Ilya
      Nano Letters (2019), 19 (11), 7632-7644CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      We present a micrometer scale, on-chip integrated, plasmonic enhanced graphene photodetector (GPD) for telecom wavelengths operating at zero dark current. The GPD is designed to directly generate a photovoltage, is made of chem. vapor deposited single layer graphene, and has an external responsivity of ∼12.2V/W with a 3dB bandwidth of ∼42GHz. We utilize Au split-gates to electrostatically create a p-n-junction and simultaneously guide a surface plasmon polariton gap-mode. This increases light-graphene interaction and optical absorption and results in an increased electronic temp. and steeper temp. gradient across the GPD channel. This paves the way to compact, on-chip integrated, power-efficient graphene based photodetectors for receivers in tele and datacom modules.
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    14. 14
      Hafez, H. A.; Kovalev, S.; Deinert, J. C.; Mics, Z.; Green, B.; Awari, N.; Chen, M.; Germanskiy, S.; Lehnert, U.; Teichert, J.; Wang, Z.; Tielrooij, K. J.; Liu, Z.; Chen, Z.; Narita, A.; Müllen, K.; Bonn, M.; Gensch, M.; Turchinovich, D. Extremely Efficient Terahertz High-Harmonic Generation in Graphene by Hot Dirac Fermions. Nature 2018, 561, 507– 511,  DOI: 10.1038/s41586-018-0508-1
      14
      Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions
      Hafez, Hassan A.; Kovalev, Sergey; Deinert, Jan-Christoph; Mics, Zoltan; Green, Bertram; Awari, Nilesh; Chen, Min; Germanskiy, Semyon; Lehnert, Ulf; Teichert, Jochen; Wang, Zhe; Tielrooij, Klaas-Jan; Liu, Zhaoyang; Chen, Zongping; Narita, Akimitsu; Muellen, Klaus; Bonn, Mischa; Gensch, Michael; Turchinovich, Dmitry
      Nature (London, United Kingdom) (2018), 561 (7724), 507-511CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Multiple optical harmonic generation-the multiplication of photon energy as a result of nonlinear interaction between light and matter-is a key technol. in modern electronics and optoelectronics, because it allows the conversion of optical or electronic signals into signals with much higher frequency, and the generation of frequency combs. Owing to the unique electronic band structure of graphene, which features massless Dirac fermions1-3, it has been repeatedly predicted that optical harmonic generation in graphene should be particularly efficient at the technol. important terahertz frequencies4-6. However, these predictions have yet to be confirmed exptl. under technol. relevant operation conditions. Here we report the generation of terahertz harmonics up to the seventh order in single-layer graphene at room temp. and under ambient conditions, driven by terahertz fields of only tens of kilovolts per cm, and with field conversion efficiencies in excess of 10-3, 10-4 and 10-5 for the third, fifth and seventh terahertz harmonics, resp. These conversion efficiencies are remarkably high, given that the electromagnetic interaction occurs in a single at. layer. The key to such extremely efficient generation of terahertz high harmonics in graphene is the collective thermal response of its background Dirac electrons to the driving terahertz fields. The terahertz harmonics, generated via hot Dirac fermion dynamics, were obsd. directly in the time domain as electromagnetic field oscillations at these newly synthesized higher frequencies. The effective nonlinear optical coeffs. of graphene for the third, fifth and seventh harmonics exceed the resp. nonlinear coeffs. of typical solids by 7-18 orders of magnitude7-9. Our results provide a direct pathway to highly efficient terahertz frequency synthesis using the present generation of graphene electronics, which operate at much lower fundamental frequencies of only a few hundreds of gigahertz.
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    15. 15
      Soavi, G.; Wang, G.; Rostami, H.; Purdie, D. G.; De Fazio, D.; Ma, T.; Luo, B.; Wang, J.; Ott, A. K.; Yoon, D.; Bourelle, S. A.; Muench, J. E.; Goykhman, I.; Dal Conte, S.; Celebrano, M.; Tomadin, A.; Polini, M.; Cerullo, G.; Ferrari, A. C. Broadband, Electrically Tunable Third-Harmonic Generation in Graphene. Nat. Nanotechnol. 2018, 13, 583– 588,  DOI: 10.1038/s41565-018-0145-8
      15
      Broadband, electrically tunable third-harmonic generation in graphene
      Soavi, Giancarlo; Wang, Gang; Rostami, Habib; Purdie, David G.; De Fazio, Domenico; Ma, Teng; Luo, Birong; Wang, Junjia; Ott, Anna K.; Yoon, Duhee; Bourelle, Sean A.; Muench, Jakob E.; Goykhman, Ilya; Dal Conte, Stefano; Celebrano, Michele; Tomadin, Andrea; Polini, Marco; Cerullo, Giulio; Ferrari, Andrea C.
      Nature Nanotechnology (2018), 13 (7), 583-588CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
      Optical harmonic generation occurs when high intensity light (>1010 W m-2) interacts with a nonlinear material. Elec. control of the nonlinear optical response enables applications such as gate-tunable switches and frequency converters. Graphene displays exceptionally strong light-matter interaction and elec. and broadband tunable third-order nonlinear susceptibility. Here, we show that the third-harmonic generation efficiency in graphene can be increased by almost two orders of magnitude by controlling the Fermi energy and the incident photon energy. This enhancement is due to logarithmic resonances in the imaginary part of the nonlinear cond. arising from resonant multiphoton transitions. Thanks to the linear dispersion of the massless Dirac fermions, gate controllable third-harmonic enhancement can be achieved over an ultrabroad bandwidth, paving the way for elec. tunable broadband frequency converters for applications in optical communications and signal processing.
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    16. 16
      Soavi, G.; Wang, G.; Rostami, H.; Tomadin, A.; Balci, O.; Paradisanos, I.; Pogna, E. A. A.; Cerullo, G.; Lidorikis, E.; Polini, M.; Ferrari, A. C. Hot Electrons Modulation of Third-Harmonic Generation in Graphene. ACS Photonics 2019, 6, 2841– 2849,  DOI: 10.1021/acsphotonics.9b00928
      16
      Hot Electrons Modulation of Third-Harmonic Generation in Graphene
      Soavi, Giancarlo; Wang, Gang; Rostami, Habib; Tomadin, Andrea; Balci, Osman; Paradisanos, I.; Pogna, Eva A. A.; Cerullo, Giulio; Lidorikis, Elefterios; Polini, Marco; Ferrari, Andrea C.
      ACS Photonics (2019), 6 (11), 2841-2849CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Hot electrons dominate the ultrafast optical and electronic properties of metals and semiconductors and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power-law expected for a third harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency converters, can be affected by changes in the electronic temp., which might occur due to increase of absorbed optical power or Joule heating.
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    17. 17
      Deinert, J.-C.; Iranzo, D. A.; Perez, R.; Jia, X.; Hafez, H. A.; Ilyakov, I.; Awari, N.; Chen, M.; Bawatna, M.; Ponomaryov, A. N.; Germanskiy, S.; Bonn, M.; Koppens, F. H. L.; Turchinovich, D.; Gensch, M.; Kovalev, S.; Tielrooij, K.-J. Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics. ACS Nano 2021, 15, 1145– 1154,  DOI: 10.1021/acsnano.0c08106
      17
      Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics
      Deinert, Jan-Christoph; Alcaraz Iranzo, David; Perez, Raul; Jia, Xiaoyu; Hafez, Hassan A.; Ilyakov, Igor; Awari, Nilesh; Chen, Min; Bawatna, Mohammed; Ponomaryov, Alexey N.; Germanskiy, Semyon; Bonn, Mischa; Koppens, Frank H. L.; Turchinovich, Dmitry; Gensch, Michael; Kovalev, Sergey; Tielrooij, Klaas-Jan
      ACS Nano (2021), 15 (1), 1145-1154CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Nonlinear optics is an increasingly important field for scientific and technol. applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and a small material footprint. Ideally, the material system should allow for chip integration and room-temp. operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light-matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear optical conversion efficiency. Here, we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3 x 10-8 m2/V2, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to a third-harmonic signal with an intensity that is 3 orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ~ 1% using a moderate field strength of ~ 30 kV/cm. Finally, we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the ninth harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for com. viable, CMOS-compatible, room-temp., chip-integrated, THz nonlinear conversion applications.
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    18. 18
      Gabor, N. M.; Song, J. C.; Ma, Q.; Nair, N. L.; Taychatanapat, T.; Watanabe, K.; Taniguchi, T.; Levitov, L. S.; Jarillo-Herrero, P. Hot Carrier-Assisted Intrinsic Photoresponse in Graphene. Science 2011, 334, 648– 652,  DOI: 10.1126/science.1211384
      18
      Hot Carrier-Assisted Intrinsic Photoresponse in Graphene
      Gabor, Nathaniel M.; Song, Justin C. W.; Ma, Qiong; Nair, Nityan L.; Taychatanapat, Thiti; Watanabe, Kenji; Taniguchi, Takashi; Levitov, Leonid S.; Jarillo-Herrero, Pablo
      Science (Washington, DC, United States) (2011), 334 (6056), 648-652CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      We report on the intrinsic optoelectronic response of high-quality dual-gated monolayer and bilayer graphene p-n junction devices. Local laser excitation (of wavelength 850 nm) at the p-n interface leads to striking six-fold photovoltage patterns as a function of bottom- and top-gate voltages. These patterns, together with the measured spatial and d. dependence of the photoresponse, provide strong evidence that nonlocal hot carrier transport, rather than the photovoltaic effect, dominates the intrinsic photoresponse in graphene. This regime, which features a long-lived and spatially distributed hot carrier population, may offer a path to hot carrier-assisted thermoelec. technologies for efficient solar energy harvesting.
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    19. 19
      Tielrooij, K.-J.; Piatkowski, L.; Massicotte, M.; Woessner, A.; Ma, Q.; Lee, Y.; Myhro, K. S.; Lau, C. N.; Jarillo-Herrero, P.; van Hulst, N. F.; Koppens, F. H. L. Generation of Photovoltage in Graphene on a Femtosecond Timescale through Efficient Carrier Heating. Nat. Nanotechnol. 2015, 10, 437– 443,  DOI: 10.1038/nnano.2015.54
      19
      Generation of photovoltage in graphene on a femtosecond timescale through efficient carrier heating
      Tielrooij, K. J.; Piatkowski, L.; Massicotte, M.; Woessner, A.; Ma, Q.; Lee, Y.; Myhro, K. S.; Lau, C. N.; Jarillo-Herrero, P.; van Hulst, N. F.; Koppens, F. H. L.
      Nature Nanotechnology (2015), 10 (5), 437-443CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
      Graphene is a promising material for ultrafast and broadband photodetection. Earlier studies have addressed the general operation of graphene-based photothermoelec. devices and the switching speed, which is limited by the charge carrier cooling time, on the order of picoseconds. However, the generation of the photovoltage could occur at a much faster timescale, as it is assocd. with the carrier heating time. Here, the authors measure the photovoltage generation time and find it to be faster than 50 fs. As a proof-of-principle application of this ultrafast photodetector, the authors use graphene to directly measure, elec., the pulse duration of a sub-50 fs laser pulse. The observation that carrier heating is ultrafast suggests that energy from absorbed photons can be efficiently transferred to carrier heat. To study this, the authors examine the spectral response and find a const. spectral responsivity of between 500 and 1,500 nm. This is consistent with efficient electron heating. These results are promising for ultrafast femtosecond and broadband photodetector applications.
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    20. 20
      Iglesias, J. M.; Pascual, E.; Martín, M. J.; Rengel, R. Relevance of Collinear Processes to the Ultrafast Dynamics of Photoexcited Carriers in Graphene. Phys. E 2020, 123, 114211,  DOI: 10.1016/j.physe.2020.114211
      20
      Relevance of collinear processes to the ultrafast dynamics of photoexcited carriers in graphene
      Iglesias, Jose Manuel; Pascual, Elena; Martin, Maria J.; Rengel, Raul
      Physica E: Low-Dimensional Systems & Nanostructures (Amsterdam, Netherlands) (2020), 123 (), 114211CODEN: PELNFM; ISSN:1386-9477. (Elsevier B.V.)
      The importance of interband transitions on the ultrafast relaxation process in photoexcited pristine graphene is evaluated by means of an ensemble Monte Carlo simulator. Impact ionization and Auger recombination in the collinear limit are considered, together with phonon-induced generation and recombination and intraband scattering mechanisms. The results show that collinear impact ionization is dominant in the first 100 fs, creating an important excess carrier population that is finally eliminated in the picosecond scale, together with the photoexcited population, by Auger and optical phonon-assisted recombination. The hot phonon effect is also important, stimulating phonon absorption and indirectly reducing the net collinear recombination in the hundreds of femtosecond range. The substrate type is an important factor, appeasing collinear impact ionization via screening and creating addnl. cooling channels that speed up the relaxation process. The results evidence that interband collinear generation processes are crit. to explain the fastest stages of the relaxation process in graphene.
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    21. 21
      Tomadin, A.; Hornett, S. M.; Wang, H. I.; Alexeev, E. M.; Candini, A.; Coletti, C.; Turchinovich, D.; Kläui, M.; Bonn, M.; Koppens, F. H. L.; Hendry, E.; Polini, M.; Tielrooij, K.-J. The Ultrafast Dynamics and Conductivity of Photoexcited Graphene at Different Fermi Energies. Sci. Adv. 2018, 4, eaar5313,  DOI: 10.1126/sciadv.aar5313
      There is no corresponding record for this reference.
    22. 22
      Fong, K. C.; Wollman, E. E.; Ravi, H.; Chen, W.; Clerk, A. A.; Shaw, M. D.; Leduc, H. G.; Schwab, K. C. Measurement of the Electronic Thermal Conductance Channels and Heat Capacity of Graphene at Low Temperature. Phys. Rev. X 2013, 3, 41008,  DOI: 10.1103/PhysRevX.3.041008
      22
      Measurement of the electronic thermal conductance channels and heat capacity of graphene at low temperature
      Fong, Kin Chung; Wollman, Emma E.; Ravi, Harish; Chen, Wei; Clerk, Aashish A.; Shaw, M. D.; Leduc, H. G.; Schwab, K. C.
      Physical Review X (2013), 3 (4), 041008CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      The ability to transport energy is a fundamental property of the two-dimensional Dirac fermions in graphene. Electronic thermal transport in this system is relatively unexplored and is expected to show unique fundamental properties and to play an important role in future applications of graphene, including optoelectronics, plasmonics, and ultrasensitive bolometry. Here, we present measurements of bipolar thermal conductances due to electron diffusion and electron-phonon coupling and infer the electronic sp. heat, with a min. value of 10kB (10-22 J/K) per square micron. We test the validity of the Wiedemann-Franz law and find that the Lorenz no. equals 1.32 × (π2/3)(kB/e)2. The electron-phonon thermal conductance has a temp. power law T2 at high doping levels, and the coupling parameter is consistent with recent theory, indicating its enhancement by impurity scattering. We demonstrate control of the thermal conductance by elec. gating and by suppressing the diffusion channel using NbTiN superconducting electrodes, which sets the stage for future graphene-based single-microwave photon detection.
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    23. 23
      Kampfrath, T.; Perfetti, L.; Schapper, F.; Frischkorn, C.; Wolf, M. Strongly Coupled Optical Phonons in the Ultrafast Dynamics of the Electronic Energy and Current Relaxation in Graphite. Phys. Rev. Lett. 2005, 95, 187403,  DOI: 10.1103/PhysRevLett.95.187403
      23
      Strongly Coupled Optical Phonons in the Ultrafast Dynamics of the Electronic Energy and Current Relaxation in Graphite
      Kampfrath, Tobias; Perfetti, Luca; Schapper, Florian; Frischkorn, Christian; Wolf, Martin
      Physical Review Letters (2005), 95 (18), 187403/1-187403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Ultrafast charge carrier dynamics in graphite has been investigated by time-resolved terahertz spectroscopy. Anal. of the transient dielec. function and model calcns. show that more than 90% of the initially deposited excitation energy is transferred to a few strongly coupled lattice vibrations within 500 fs. These hot optical phonons also substantially contribute to the striking increase of the Drude relaxation rate obsd. during the first picosecond after photoexcitation. The subsequent cooling of the hot phonons yields a lifetime est. of 7 ps for these modes.
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    24. 24
      Hale, P. J.; Hornett, S. M.; Moger, J.; Horsell, D. W.; Hendry, E. Hot Phonon Decay in Supported and Suspended Exfoliated Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 121404,  DOI: 10.1103/PhysRevB.83.121404
      24
      Hot phonon decay in supported and suspended exfoliated graphene
      Hale, P. J.; Hornett, S. M.; Moger, J.; Horsell, D. W.; Hendry, E.
      Physical Review B: Condensed Matter and Materials Physics (2011), 83 (12), 121404/1-121404/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Near IR pump-probe spectroscopy was used to measure the ultrafast dynamics of photoexcited charge carriers in monolayer and multilayer graphene. The authors observe 2 decay processes occurring on 100-fs and 2-ps time scales. The 1st is attributed to the rapid electron-phonon thermalization in the system. The 2nd time scale is due to the slow decay of hot phonons. Using a simple theor. model the authors calc. the hot phonon decay rate and show that it is significantly faster in monolayer flakes than in multilayer ones. The authors observe this enhanced decay rate in both supported and suspended flakes and thereby demonstrate that it has an intrinsic origin. Possible decay mechanisms, such as flexural phonons, that could cause such an enhancement are discussed.
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    25. 25
      Mounet, N.; Marzari, N. First-Principles Determination of the Structural, Vibrational and Thermodynamic Properties of Diamond, Graphite, and Derivatives. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 205214,  DOI: 10.1103/PhysRevB.71.205214
      25
      First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives
      Mounet, Nicolas; Marzari, Nicola
      Physical Review B: Condensed Matter and Materials Physics (2005), 71 (20), 205214/1-205214/14CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      The structural, dynamical, and thermodn. properties of diamond, graphite and layered derivs. (graphene, rhombohedral graphite) are computed using a combination of d.-functional theory total-energy calcns. and d.-functional perturbation theory lattice dynamics in the generalized gradient approxn. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the assocd. elastic consts. and phonon dispersions. Both the C33 elastic const. and the Γ to A phonon dispersions are brought to close agreement with available data once the exptl. c/a is chosen for the calcns. The vibrational free energy and the thermal expansion, the temp. dependence of the elastic moduli and the sp. heat are calcd. using the quasiharmonic approxn. Graphite shows a distinctive in-plane neg. thermal-expansion coeff. that reaches its lowest value around room temp., in very good agreement with expts. Thermal contraction in graphene is three times as large; in both cases, bending acoustic modes are responsible for the contraction, in a direct manifestation of the membrane effect predicted by Lifshitz over 50 years ago. Stacking directly affects the bending modes, explaining the large numerical difference between the thermal-contraction coeffs. in graphite and graphene, notwithstanding their common phys. origin.
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    26. 26
      Mihnev, M. T.; Kadi, F.; Divin, C. J.; Winzer, T.; Lee, S.; Liu, C.-h.; Zhong, Z.; Berger, C.; Heer, W. A. D.; Malic, E.; Knorr, A.; Norris, T. B. Microscopic Origins of the Terahertz Carrier Relaxation and Cooling Dynamics in Graphene. Nat. Commun. 2016, 7, 11617,  DOI: 10.1038/ncomms11617
      26
      Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene
      Mihnev, Momchil T.; Kadi, Faris; Divin, Charles J.; Winzer, Torben; Lee, Seunghyun; Liu, Che-Hung; Zhong, Zhaohui; Berger, Claire; de Heer, Walt A.; Malic, Ermin; Knorr, Andreas; Norris, Theodore B.
      Nature Communications (2016), 7 (), 11617CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier-carrier interactions and carrier-phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent expts. on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of obsd. signals within phenomenol. frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated exptl. and theor. program, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modeling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amts. of disorder and with either high or low doping levels. The theory reproduces the obsd. dynamics quant. without the need to invoke any fitting parameters, phenomenol. models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier-carrier scattering, which maintains a thermalized carrier distribution, and carrier-optical-phonon scattering, which removes energy from the carrier liq.
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    27. 27
      Bistritzer, R.; MacDonald, A. H. Electronic Cooling in Graphene. Phys. Rev. Lett. 2009, 102, 206410,  DOI: 10.1103/PhysRevLett.102.206410
      27
      Electronic Cooling in Graphene
      Bistritzer, R.; MacDonald, A. H.
      Physical Review Letters (2009), 102 (20), 206410/1-206410/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Energy transfer to acoustic phonons is the dominant low-temp. cooling channel of electrons in a crystal. For cold neutral graphene we find that the weak cooling power of its acoustic modes relative to their heat capacity leads to a power-law decay of the electronic temp. when far from equil. For heavily doped graphene a high electronic temp. is shown to initially decrease linearly with time at a rate proportional to n3/2 with n being the electronic d. The temp. at which cooling via optical phonon emission begins to dominate depends on graphene carrier d.
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    28. 28
      Song, J. C. W.; Reizer, M. Y.; Levitov, L. S. Disorder-Assisted Electron-Phonon Scattering and Cooling Pathways in Graphene. Phys. Rev. Lett. 2012, 109, 106602,  DOI: 10.1103/PhysRevLett.109.106602
      28
      Disorder-assisted electron-phonon scattering and cooling pathways in graphene
      Song, Justin C. W.; Reizer, Michael Y.; Levitov, Leonid S.
      Physical Review Letters (2012), 109 (10), 106602/1-106602/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We predict that graphene is a unique system where disorder-assisted scattering (supercollisions) dominates electron-lattice cooling over a wide range of temps., up to room temp. This is so because for momentum-conserving electron-phonon scattering the energy transfer per collision is severely constrained due to a small Fermi surface size. The characteristic T3 temp. dependence and power-law cooling dynamics provide clear exptl. signatures of this new cooling mechanism. The cooling rate can be changed by orders of magnitude by varying the amt. of disorder providing means for a variety of new applications that rely on hot-carrier transport.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsVKiurrI&md5=92c2c95fea2e7eb6631a9c1dde329f8c
    29. 29
      Betz, A. C.; Jhang, S. H.; Pallecchi, E.; Ferreira, R.; Fève, G.; Berroir, J.-M.; Plaçais, B. Supercollision Cooling in Undoped Graphene. Nat. Phys. 2013, 9, 109– 112,  DOI: 10.1038/nphys2494
      29
      Supercollision cooling in undoped graphene
      Betz, A. C.; Jhang, S. H.; Pallecchi, E.; Ferreira, R.; Feve, G.; Berroir, J.-M.; Placais, B.
      Nature Physics (2013), 9 (2), 109-112CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      Carrier mobility in solids is generally limited by electron-impurity or electron-phonon scattering, depending on the most frequently occurring event. Three-body collisions between carriers and both phonons and impurities are rare; they are denoted supercollisions. Elusive in electronic transport they should emerge in relaxation processes as they allow for larger energy transfers. This is the case in undoped graphene, where the small Fermi surface drastically restricts the allowed phonon energy in ordinary collisions. Using elec. heating and sensitive noise thermometry we report on supercollision cooling in diffusive monolayer graphene. At low carrier d. and high phonon temp. the Joule power P obeys a PTe3 law as a function of electronic temp. Te. It overrules the linear law expected for ordinary collisions which has recently been obsd. in resistivity measurements. The cubic law is characteristic of supercollisions and departs from the Te4 dependence recently reported for doped graphene below the Bloch-Grueneisen temp. These supercollisions are important for applications of graphene in bolometry and photo-detection.
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    30. 30
      Graham, M. W.; Shi, S.-F.; Wang, Z.; Ralph, D. C.; Park, J.; McEuen, P. L. Transient Absorption and Photocurrent Microscopy Show that Hot Electron Supercollisions Describe the Rate-Limiting Relaxation Step in Graphene. Nano Lett. 2013, 13, 5497– 502,  DOI: 10.1021/nl4030787
      30
      Transient Absorption and Photocurrent Microscopy Show That Hot Electron Supercollisions Describe the Rate-Limiting Relaxation Step in Graphene
      Graham, Matt W.; Shi, Su-Fei; Wang, Zenghui; Ralph, Daniel C.; Park, Jiwoong; McEuen, Paul L.
      Nano Letters (2013), 13 (11), 5497-5502CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Using transient absorption (TA) microscopy as a hot electron thermometer, disorder-assisted acoustic-phonon supercollisions (SCs) best describe the rate-limiting relaxation step in graphene over a wide range of lattice temps. (Tl = 5-300 K), Fermi energies (EF = ± 0.35 eV), and optical probe energies (∼0.3-1.1 eV). Comparison with simultaneously collected transient photocurrent, an independent hot electron thermometer, confirms that the rate-limiting optical and elec. response in graphene are best described by the SC-heat dissipation rate model, H = A(Te3 - Tl3). The authors' data further show that the electron cooling rate in substrate-supported graphene is twice as fast as in suspended graphene sheets, consistent with SC model prediction for disorder.
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    31. 31
      Alencar, T. V.; Silva, M. G.; Malard, L. M.; de Paula, A. M. Defect-Induced Supercollision Cooling of Photoexcited Carriers in Graphene. Nano Lett. 2014, 14, 5621– 5624,  DOI: 10.1021/nl502163d
      31
      Defect-Induced Supercollision Cooling of Photoexcited Carriers in Graphene
      Alencar, Thonimar V.; Silva, Mychel G.; Malard, Leandro M.; de Paula, Ana M.
      Nano Letters (2014), 14 (10), 5621-5624CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Defects play a fundamental role in the energy relaxation of hot photoexcited carriers in graphene, thus a complete understanding of these processes are vital for improving the development of graphene devices. Recently, it was theor. predicted and exptl. demonstrated that defect-assisted acoustic phonon supercollision, the collision between a carrier and both an acoustic phonon and a defect, is an important energy relaxation process for carriers with excess energy below the optical phonon emission. Here, the authors studied samples with defects optically generated in a controlled manner to exptl. probe the supercollision model as a function of the defect d. The authors present pump and probe transient absorption measurements showing that the decay time decreases as the d. of defect increases as predicted by the supercollision model.
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    32. 32
      Graham, M. W.; Shi, S. F.; Ralph, D. C.; Park, J.; McEuen, P. L. Photocurrent Measurements of Supercollision Cooling in Graphene. Nat. Phys. 2013, 9, 103– 108,  DOI: 10.1038/nphys2493
      32
      Photocurrent measurements of supercollision cooling in graphene
      Graham, Matt W.; Shi, Su-Fei; Ralph, Daniel C.; Park, Jiwoong; McEuen, Paul L.
      Nature Physics (2013), 9 (2), 103-108CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      The cooling of hot electrons in graphene is the crit. process underlying the operation of exciting new graphene-based optoelectronic and plasmonic devices, but the nature of this cooling is controversial. We ext. the hot-electron cooling rate near the Fermi level by using graphene as a novel photothermal thermometer that measures the electron temp. (T(t)) as it cools dynamically. We find the photocurrent generated from graphene p-n junctions is well described by the energy dissipation rate CdT/dt = -A(T3-Tl3), where the heat capacity is C = αT and Tl is the base lattice temp. These results are in disagreement with predictions of electron-phonon emission in a disorder-free graphene system, but in excellent quant. agreement with recent predictions of a disorder-enhanced supercollision cooling mechanism. We find that the supercollision model provides a complete and unified picture of energy loss near the Fermi level over the wide range of electronic (15 to ∼ 3,000 K) and lattice (10-295 K) temps. investigated.
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    33. 33
      Tielrooij, K.-J.; Hesp, N. C. H.; Principi, A.; Lundeberg, M. B.; Pogna, E. A. A.; Banszerus, L.; Mics, Z.; Massicotte, M.; Schmidt, P.; Davydovskaya, D.; Purdie, D. G.; Goykhman, I.; Soavi, G.; Lombardo, A.; Watanabe, K.; Taniguchi, T.; Bonn, M.; Turchinovich, D.; Stampfer, C.; Ferrari, A. C.; Cerullo, G.; Polini, M.; Koppens, F. H. L. Out-of-Plane Heat Transfer in van der Waals Stacks through Electron-Hyperbolic Phonon Coupling. Nat. Nanotechnol. 2018, 13, 41– 46,  DOI: 10.1038/s41565-017-0008-8
      33
      Out-of-plane heat transfer in van der Waals stacks through electron-hyperbolic phonon coupling
      Tielrooij, Klaas-Jan; Hesp, Niels C. H.; Principi, Alessandro; Lundeberg, Mark B.; Pogna, Eva A. A.; Banszerus, Luca; Mics, Zoltan; Massicotte, Mathieu; Schmidt, Peter; Davydovskaya, Diana; Purdie, David G.; Goykhman, Ilya; Soavi, Giancarlo; Lombardo, Antonio; Watanabe, Kenji; Taniguchi, Takashi; Bonn, Mischa; Turchinovich, Dmitry; Stampfer, Christoph; Ferrari, Andrea C.; Cerullo, Giulio; Polini, Marco; Koppens, Frank H. L.
      Nature Nanotechnology (2018), 13 (1), 41-46CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
      Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior elec. and optoelectronic properties. Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier d. and lattice temp., and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.
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    34. 34
      Principi, A.; Lundeberg, M. B.; Hesp, N. C.; Tielrooij, K. J.; Koppens, F. H.; Polini, M. Super-Planckian Electron Cooling in a van der Waals Stack. Phys. Rev. Lett. 2017, 118, 126804,  DOI: 10.1103/PhysRevLett.118.126804
      34
      Super-Planckian electron cooling in a van der Waals stack
      Principi, Alessandro; Lundeberg, Mark B.; Hesp, Niels C. H.; Tielrooij, Klaas-Jan
      Physical Review Letters (2017), 118 (12), 126804/1-126804/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Radiative heat transfer (RHT) between macroscopic bodies at sepns. that are much smaller than the thermal wavelength is ruled by evanescent electromagnetic modes and can be orders of magnitude more efficient than its far-field counterpart, which is described by the Stefan-Boltzmann law. In this Letter, we present a microscopic theory of RHT in van derWaals stacks comprising graphene and a natural hyperbolic material, i.e., hexagonal boron nitride (hBN). We demonstrate that RHT between hot carriers in graphene and hyperbolic phonon polaritons in hBN is extremely efficient at room temp., leading to picosecond time scales for the carrier cooling dynamics.
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    35. 35
      Yang, W.; Berthou, S.; Lu, X.; Wilmart, Q.; Denis, A.; Rosticher, M.; Taniguchi, T.; Watanabe, K.; Fève, G.; Berroir, J.-m.; Zhang, G.; Voisin, C.; Baudin, E.; Plaçais, B. A Graphene Zener-Klein Transistor Cooled by a Hyperbolic Substrate. Nat. Nanotechnol. 2018, 13, 47– 52,  DOI: 10.1038/s41565-017-0007-9
      35
      A graphene Zener-Klein transistor cooled by a hyperbolic substrate
      Yang, Wei; Berthou, Simon; Lu, Xiaobo; Wilmart, Quentin; Denis, Anne; Rosticher, Michael; Taniguchi, Takashi; Watanabe, Kenji; Feve, Gwendal; Berroir, Jean-Marc; Zhang, Guangyu; Voisin, Christophe; Baudin, Emmanuel; Placais, Bernard
      Nature Nanotechnology (2018), 13 (1), 47-52CODEN: NNAABX; ISSN:1748-3387. (Nature Research)
      The engineering of cooling mechanisms is a bottleneck in nanoelectronics. Thermal exchanges in diffusive graphene are mostly driven by defect-assisted acoustic phonon scattering, but the case of high-mobility graphene on hexagonal boron nitride (hBN) is radically different, with a prominent contribution of remote phonons from the substrate. Bilayer graphene on a hBN transistor with a local gate is driven in a regime where almost perfect current satn. is achieved by compensation of the decrease in the carrier d. and Zener-Klein tunnelling (ZKT) at high bias. Using noise thermometry, we show that the ZKT triggers a new cooling pathway due to the emission of hyperbolic phonon polaritons in hBN by out-of-equil. electron-hole pairs beyond the super-Planckian regime. The combination of ZKT transport and hyperbolic phonon polariton cooling renders graphene on BN transistors a valuable nanotechnol. for power devices and RF electronics.
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    36. 36
      Caldwell, J. D.; Kretinin, A. V.; Chen, Y.; Giannini, V.; Fogler, M. M.; Francescato, Y.; Ellis, C. T.; Tischler, J. G.; Woods, C. R.; Giles, A. J.; Hong, M.; Watanabe, K.; Taniguchi, T.; Maier, S. A.; Novoselov, K. S. Sub-Diffractional Volume-Confined Polaritons in the Natural Hyperbolic Material Hexagonal Boron Nitride. Nat. Commun. 2014, 5, 5521,  DOI: 10.1038/ncomms6221
      There is no corresponding record for this reference.
    37. 37
      Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722– 726,  DOI: 10.1038/nnano.2010.172
      37
      Boron nitride substrates for high-quality graphene electronics
      Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J.
      Nature Nanotechnology (2010), 5 (10), 722-726CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
      Graphene devices on std. SiO2 substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielecs. that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal BN (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice const. similar to that of graphite, and has large optical phonon modes and a large elec. bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by a mech. transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO2. These devices also show reduced roughness, intrinsic doping and chem. reactivity. The ability to assemble cryst. layered materials in a controlled way permits the fabrication of graphene devices on other promising dielecs. and allows for the realization of more complex graphene heterostructures.
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    38. 38
      Wang, L.; Meric, I.; Huang, P.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 2013, 342, 614– 617,  DOI: 10.1126/science.1244358
      38
      One-Dimensional Electrical Contact to a Two-Dimensional Material
      Wang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R.
      Science (Washington, DC, United States) (2013), 342 (6158), 614-617CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal B nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality elec. contact. Here, the authors report a contact geometry in which the authors metalize only the 1-dimensional edge of a 2-dimensional graphene layer. In addn. to outperforming conventional surface contacts, the edge-contact geometry allows a complete sepn. of the layer assembly and contact metalization processes. In graphene heterostructures, this enables high electronic performance, including low-temp. ballistic transport over distances longer than 15 μm, and room-temp. mobility comparable to the theor. phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2-dimensional materials.
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    39. 39
      Banszerus, L.; Janssen, H.; Otto, M.; Epping, A.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Neumaier, D.; Stampfer, C. Identifying Suitable Substrates for High-Quality Graphene-Based Heterostructures. 2D Mater. 2017, 4, 025030,  DOI: 10.1088/2053-1583/aa5b0f
      39
      Identifying suitable substrates for high-quality graphene-based heterostructures
      Banszerus, L.; Janssen, H.; Otto, M.; Epping, A.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Neumaier, D.; Stampfer, C.
      2D Materials (2017), 4 (2), 025030/1-025030/8CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
      We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chem. vapor deposited (CVD) graphene-based heterostuctures on a large no. of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By applying a hBN-assisted, contamination free, dry transfer process for CVD graphene, high-quality heterostructures with low doping densities and low strain variations are assembled. The Raman spectra of these pristine heterostructures are sensitive to substrate-induced doping and strain variations and are thus used to probe the suitability of the substrate material for potential high-quality graphene devices. We find that the flatness of the substrate material is a key figure for gaining, or preserving high-quality graphene.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXnsVyisbk%253D&md5=8131404c329940e3012bf8e0fa8ba4bd
    40. 40
      Banszerus, L.; Sohier, T.; Epping, A.; Winkler, F.; Libisch, F.; Haupt, F.; Watanabe, K.; Taniguchi, T.; Müller-Caspary, K.; Marzari, N.; Mauri, F.; Beschoten, B.; Stampfer, C. Extraordinary High Room-Temperature Carrier Mobility in Graphene-WSe2 Heterostructures. arXiv:1909.09523 http://arxiv.org/abs/1909.09523 (accessed December 25, 2020).
      There is no corresponding record for this reference.
    41. 41
      Backes, C.; Abdelkader, A. M.; Alonso, C.; Andrieux-Ledier, A.; Arenal, R.; Azpeitia, J.; Balakrishnan, N.; Banszerus, L.; Barjon, J.; Bartali, R.; Bellani, S.; Berger, C.; Berger, R.; Ortega, M. M.; Bernard, C.; Beton, P. H.; Beyer, A.; Bianco, A.; Bøggild, P.; Bonaccorso, A. Production and Processing of Graphene and Related Materials. 2D Mater. 2020, 7, 022001,  DOI: 10.1088/2053-1583/ab1e0a
      41
      Production and processing of graphene and related materials
      Backes, Claudia; Abdelkader, Amr M.; Alonso, Concepcion; Andrieux-Ledier, Amandine; Arenal, Raul; Azpeitia, Jon; Balakrishnan, Nilanthy; Banszerus, Luca; Barjon, Julien; Bartali, Ruben; Bellani, Sebastiano; Berger, Claire; Berger, Reinhard; Ortega, M. M. Bernal; Bernard, Carlo; Beton, Peter H.; Beyer, Andre; Bianco, Alberto; Boeggild, Peter B.; Bonaccorso, Francesco; Barin, Gabriela Borin; Botas, Cristina; Bueno, Rebeca A.; Carriazo, Daniel; Gomez, Andres Castellanos; Christian, Meganne; Ciesielski, Artur; Ciuk, Tymoteusz; Cole, Matthew T.; Coleman, Jonathan; Coletti, Camilla; Crema, Luigi; Cun, Huanyao; Dasler, Daniela; De Fazio, Domenico; Diez, Noel; Drieschner, Simon; Duesberg, Georg S.; Fasel, Roman; Feng, Xinliang; Fina, Alberto; Forti, Stiven; Galiotis, Costas; Garberoglio, Giovanni; Garcia, Jorge M.; Garrido, Jose Antonio; Gibertini, Marco; Goelzhaeuser, Armin; Gomez, Julio; Greber, Thomas; Hauke, Frank; Hemmi, Adrian; Hernandez-Rodriguez, Irene; Hirsch, Andreas; Hodge, Stephen A.; Huttel, Yves; Jepsen, Peter U.; Jimenez, Ignacio; Kaiser, Ute; Kaplas, Tommi; Kim, Hokwon; Kis, Andras; Papagelis, Konstantinos; Kostarelos, Kostas; Krajewska, Aleksandra; Lee, Kangho; Li, Changfeng; Lipsanen, Harri; Liscio, Andrea; Lohe, Martin R.; Loiseau, Annick; Lombardi, Lucia; Lopez, Maria Francisca; Martin, Oliver; Martin, Cristina; Martinez, Lidia; Martin-Gago, Joseangel; Martinez, Jose Ignacio; Marzari, Nicola; Mayoral, Alvaro; Mcmanus, John; Melucci, Manuela; Mendez, Javier; Merino, Cesar; Merino, Pablo; Meyer, Andreas P.; Miniussi, Elisa; Miseikis, Vaidotas; Mishra, Neeraj; Morandi, Vittorio; Munuera, Carmen; Munoz, Roberto; Nolan, Hugo; Ortolani, Luca; Ott, Annak; Palacio, Irene; Palermo, Vincenzo; Parthenios, John; Pasternak, Iwona; Patane, Amalia; Prato, Maurizio; Prevost, Henri; Prudkovskiy, Vladimir; Pugno, Nicola; Rojo, Teofilo; Rossi, Antonio; Ruffieux, Pascal; Samori, Paolo; Schue, Leonard; Setijadi, Eki; Seyller, Thomas; Speranza, Giorgio; Stampfer, Christoph; Stenger, Ingrid; Strupinski, Wlodek; Svirko, Yuri; Taioli, Simone; Bkteo, Kenneth; Testi, Matteo; Tomarchio, Flavia; Tortello, Mauro; Treossi, Emanuele; Turchanin, Andrey; Vazquez, Ester; Villaro, Elvira; Whelan, Patrick R.; Xia, Zhenyuan; Yakimova, Rositza; Yang, Sheng; Yazdi, G. Reza; Yim, Chanyoung; Yoon, Duhee; Zhang, Xianghui; Zhuang, Xiaodong; Colombo, Luigi; Ferrari, Andrea C.; Garcia-Hernandez, Mar
      2D Materials (2020), 7 (2), 022001CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)
      We present an overview of the main techniques for prodn. and processing of graphene and related materials (GRMs), as well as the key characterization procedures. We adopt a 'hands-on' approach, providing practical details and procedures as derived from literature as well as from the authors' experience, in order to enable the reader to reproduce the results.
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    42. 42
      Neumann, C.; Banszerus, L.; Schmitz, M.; Reichardt, S.; Sonntag, J.; Taniguchi, T.; Watanabe, K.; Beschoten, B.; Stampfer, C. Line Shape of the Raman 2D Peak of Graphene in van der Waals Heterostructures. Phys. Status Solidi B 2016, 253, 2326– 2330,  DOI: 10.1002/pssb.201600283
      42
      Line shape of the Raman 2D peak of graphene in van der Waals heterostructures
      Neumann, Christoph; Banszerus, Luca; Schmitz, Michael; Reichardt, Sven; Sonntag, Jens; Taniguchi, Takashi; Watanabe, Kenji; Beschoten, Bernd; Stampfer, Christoph
      Physica Status Solidi B: Basic Solid State Physics (2016), 253 (12), 2326-2330CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The Raman 2D line of graphene is widely used for device characterization and during device fabrication as it contains valuable information on, e.g., the direction and magnitude of mech. strain and doping. Here, we present systematic asymmetries in the 2D line shape of exfoliated graphene and graphene grown by chem. vapor deposition. Both graphene crystals are fully encapsulated in van der Waals heterostructures, where hexagonal boron nitride and tungsten diselenide are used as substrate materials. In both material stacks, we find very low doping values and extremely homogeneous strain distributions in the graphene crystal, which is a hall mark of the outstanding electronic quality of these samples. By fitting double Lorentzian functions to the spectra to account for the contributions of inner and outer processes to the 2D peak, we find that the splitting of the sub-peaks, 6.6±0.5cm-1 (hBN-Gr-WSe2) and 8.9±1.0cm-1 (hBN-Gr-hBN), is significantly lower than the values reported in previous studies on suspended graphene.
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    43. 43
      Robinson, J. A.; Wetherington, M.; Tedesco, J. L.; Campbell, P. M.; Weng, X.; Stitt, J.; Fanton, M. A.; Frantz, E.; Snyder, D.; VanMil, B. L.; Jernigan, G. G.; Rachael, L. M. W.; Eddy, C. R.; Gaskill, D. K. Correlating Raman Spectral Signatures with Carrier Mobility in Epitaxial Graphene: A Guide to Achieving High Mobility on the Wafer Scale. Nano Lett. 2009, 9, 2873– 2876,  DOI: 10.1021/nl901073g
      43
      Correlating Raman Spectral Signatures with Carrier Mobility in Epitaxial Graphene: A Guide to Achieving High Mobility on the Wafer Scale
      Robinson, Joshua A.; Wetherington, Maxwell; Tedesco, Joseph L.; Campbell, Paul M.; Weng, Xiaojun; Stitt, Joseph; Fanton, Mark A.; Frantz, Eric; Snyder, David; Van Mil, Brenda L.; Jernigan, Glenn G.; Myers-Ward, Rachael L.; Eddy, Charles R.; Gaskill, D. Kurt
      Nano Letters (2009), 9 (8), 2873-2876CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The authors report a direct correlation between carrier mobility and Raman topog. of epitaxial graphene (EG) grown on silicon carbide (SiC). The authors show the Hall mobility of material on SiC(0001) is highly dependent on thickness and monolayer strain uniformity. Addnl., the authors achieve high mobility epitaxial graphene (18100 cm2/(V s) at room temp.) on SiC(0001‾) and show that carrier mobility depends strongly on the graphene layer stacking.
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    44. 44
      Kang, K.; Abdula, D.; Cahill, D. G.; Shim, M. Lifetimes of Optical Phonons in Graphene and Graphite by Time-Resolved Incoherent Anti-Stokes Raman Scattering. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 165405,  DOI: 10.1103/PhysRevB.81.165405
      44
      Lifetimes of optical phonons in graphene and graphite by time-resolved incoherent anti-Stokes Raman scattering
      Kang, Kwangu; Abdula, Daner; Cahill, David G.; Shim, Moonsub
      Physical Review B: Condensed Matter and Materials Physics (2010), 81 (16), 165405/1-165405/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We report lifetimes of optical phonons (OPs) in graphene and graphite measured by time-resolved anti-Stokes Raman scattering. Lifetimes in graphite and monolayer graphene are 2.4 and 1.2 ps, resp. For graphite and graphene with more than five layers, the lifetimes decrease with increasing temp. as ∼1/T, indicating the dominance of anharmonic processes in the decay of the OP population. The decrease in lifetime with decreasing no. of layers suggests an addnl. decay channel through which excitations in graphene interact directly with lattice vibrations of the a-SiO2 substrate.
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    45. 45
      Lui, C. H.; Mak, K. F.; Shan, J.; Heinz, T. F. Ultrafast Photoluminescence from Graphene. Phys. Rev. Lett. 2010, 105, 127404,  DOI: 10.1103/PhysRevLett.105.127404
      45
      Ultrafast Photoluminescence from Graphene
      Lui, Chun Hung; Mak, Kin Fai; Shan, Jie; Heinz, Tony F.
      Physical Review Letters (2010), 105 (12), 127404/1-127404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Since graphene has no band gap, photoluminescence is not expected from relaxed charge carriers. The authors have, however, obsd. significant light emission from graphene under excitation by ultrashort (30-fs) laser pulses. Light emission occurs across the visible spectral range (1.7-3.5 eV), with emitted photon energies exceeding that of the excitation laser (1.5 eV). The emission exhibits a nonlinear dependence on the laser fluence. In 2-pulse correlation measurements, a dominant relaxation time of tens of femtoseconds is obsd. A 2-temp. model describing the electrons and their interaction with strongly coupled optical phonons can account for the exptl. observations.
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    46. 46
      Wang, H.; Strait, J. H.; George, P. A.; Shivaraman, S.; Shields, V. B.; Chandrashekhar, M.; Hwang, J.; Rana, F.; Spencer, M. G.; Ruiz-Vargas, C. S.; Park, J. Ultrafast Relaxation Dynamics of Hot Optical Phonons in Graphene. Appl. Phys. Lett. 2010, 96, 081917,  DOI: 10.1063/1.3291615
      46
      Ultrafast relaxation dynamics of hot optical phonons in graphene
      Wang, Haining; Strait, Jared H.; George, Paul A.; Shivaraman, Shriram; Shields, Virgil B.; Chandrashekhar, M. V. S.; Hwang, Jeonghyun; Rana, Farhan; Spencer, Michael G.; Ruiz-Vargas, Carlos S.; Park, Jiwoong
      Applied Physics Letters (2010), 96 (8), 081917/1-081917/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      Using ultrafast optical pump-probe spectroscopy, the authors study the relaxation dynamics of hot optical phonons in few-layer and multilayer graphene films grown by epitaxy on Si carbide substrates and by CVD on Ni substrates. In the 1st few hundred femtoseconds after photoexcitation, the hot carriers lose most of their energy to the generation of hot optical phonons which then present the main bottleneck to subsequent cooling. Optical phonon cooling on short time scales is independent of the graphene growth technique, the no. of layers, and the type of the substrate. Av. phonon lifetimes in the 2.5-2.55 ps range were found. The authors model the relaxation dynamics of the coupled carrier-phonon system with rate equations and find a good agreement between the exptl. data and the theory. The extd. optical phonon lifetimes agree very well with the theory based on anharmonic phonon interactions. (c) 2010 American Institute of Physics.
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    47. 47
      Wu, S.; Liu, W. T.; Liang, X.; Schuck, P. J.; Wang, F.; Shen, Y. R.; Salmeron, M. Hot Phonon Dynamics in Graphene. Nano Lett. 2012, 12, 5495– 5499,  DOI: 10.1021/nl301997r
      47
      Hot Phonon Dynamics in Graphene
      Wu, Shiwei; Liu, Wei-Tao; Liang, Xiaogan; Schuck, P. James; Wang, Feng; Shen, Y. Ron; Salmeron, Miquel
      Nano Letters (2012), 12 (11), 5495-5499CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The dynamics of hot phonons in supported, suspended, and gated monolayer graphene was studied by using time-resolved anti-Stokes Raman spectroscopy. We found that the hot phonon relaxation is dominated by phonon-phonon interaction in graphene, and strongly affected by the interaction between graphene and the substrate. Relaxation via carrier-phonon coupling, known as Landau damping, is ineffective for hot phonons which are in thermal equil. with excited carriers. Our findings provide a basis for better management of energy dissipation in graphene devices.
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    48. 48
      Bonini, N.; Lazzeri, M.; Marzari, N.; Mauri, F. Phonon Anharmonicities in Graphite and Graphene. Phys. Rev. Lett. 2007, 99, 176802,  DOI: 10.1103/PhysRevLett.99.176802
      48
      Phonon Anharmonicities in Graphite and Graphene
      Bonini, Nicola; Lazzeri, Michele; Marzari, Nicola; Mauri, Francesco
      Physical Review Letters (2007), 99 (17), 176802/1-176802/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The authors det. from 1st principles the finite-temp. properties - linewidths, line shifts, and lifetimes - of the key vibrational modes that dominate inelastic losses in graphitic materials. In graphite, the phonon linewidth of the Raman-active E2g mode decreases with temp.; such anomalous behavior is driven entirely by electron-phonon interactions, and does not appear in the nearly degenerate IR-active E1u mode. In graphene, the phonon anharmonic lifetimes and decay channels of the A'1 mode at K dominate over E2g at Γ and couple strongly with acoustic phonons, highlighting how ballistic transport in C-based interconnects requires careful engineering of phonon decays and thermalization.
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    49. 49
      Zhang, J.; Lin, L.; Sun, L.; Huang, Y.; Koh, A. L.; Dang, W.; Yin, J.; Wang, M.; Tan, C.; Li, T.; Tan, Z.; Liu, Z.; Peng, H. Clean Transfer of Large Graphene Single Crystals for High-Intactness Suspended Membranes and Liquid Cells. Adv. Mater. 2017, 29, 1700639,  DOI: 10.1002/adma.201700639
      There is no corresponding record for this reference.
    50. 50
      Lin, L.; Zhang, J.; Su, H.; Li, J.; Sun, L.; Wang, Z.; Xu, F.; Liu, C.; Lopatin, S.; Zhu, Y.; Jia, K.; Chen, S.; Rui, D.; Sun, J.; Xue, R.; Gao, P.; Kang, N.; Han, Y.; Xu, H. Q.; Cao, Y. Towards Super-Clean Graphene. Nat. Commun. 2019, 10, 1912,  DOI: 10.1038/s41467-019-09565-4
      50
      Towards super-clean graphene
      Lin Li; Zhang Jincan; Sun Luzhao; Jia Kaicheng; Peng Hailin; Liu Zhongfan; Zhang Jincan; Li Jiayu; Sun Luzhao; Su Haisheng; Cao Yang; Tian Zhongqun; Ren Bin; Li Jiayu; Rui Dingran; Kang Ning; Xu H Q; Li Jiayu; Wang Zihao; Novoselov K S; Xu Fan; Liu Chang; Lopatin Sergei; Zhu Yihan; Han Yu; Chen Shulin; Sun Jingyu; Sun Jingyu; Xue Ruiwen; Gao Peng; Peng Hailin; Liu Zhongfan
      Nature communications (2019), 10 (1), 1912 ISSN:.
      Impurities produced during the synthesis process of a material pose detrimental impacts upon the intrinsic properties and device performances of the as-obtained product. This effect is especially pronounced in graphene, where surface contamination has long been a critical, unresolved issue, given graphene's two-dimensionality. Here we report the origins of surface contamination of graphene, which is primarily rooted in chemical vapour deposition production at elevated temperatures, rather than during transfer and storage. In turn, we demonstrate a design of Cu substrate architecture towards the scalable production of super-clean graphene (>99% clean regions). The readily available, super-clean graphene sheets contribute to an enhancement in the optical transparency and thermal conductivity, an exceptionally lower-level of electrical contact resistance and intrinsically hydrophilic nature. This work not only opens up frontiers for graphene growth but also provides exciting opportunities for the utilization of as-obtained super-clean graphene films for advanced applications.
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    51. 51
      Lee, J. E.; Ahn, G.; Shim, J.; Lee, Y. S.; Ryu, S. Optical Separation of Mechanical Strain from Charge Doping in Graphene. Nat. Commun. 2012, 3, 1024,  DOI: 10.1038/ncomms2022
      51
      Optical separation of mechanical strain from charge doping in graphene
      Lee Ji Eun; Ahn Gwanghyun; Shim Jihye; Lee Young Sik; Ryu Sunmin
      Nature communications (2012), 3 (), 1024 ISSN:.
      Because of its superior stretchability, graphene exhibits rich structural deformation behaviours and its strain engineering has proven useful in modifying its electronic and magnetic properties. Despite the strain-sensitivity of the Raman G and 2D modes, the optical characterization of the native strain in graphene on silica substrates has been hampered by excess charges interfering with both modes. Here we show that the effects of strain and charges can be optically separated from each other by correlation analysis of the two modes, enabling simple quantification of both. Graphene with in-plane strain randomly occurring between -0.2% and 0.4% undergoes modest compression (-0.3%) and significant hole doping on thermal treatments. This study suggests that substrate-mediated mechanical strain is a ubiquitous phenomenon in two-dimensional materials. The proposed analysis will be of great use in characterizing graphene-based materials and devices.
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    52. 52
      Malard, L. M.; Mak, K. F.; Neto, A. C.; Peres, N.; Heinz, T. F. Observation of Intra-and Inter-Band Transitions in the Transient Optical Response of Graphene. New J. Phys. 2013, 15, 015009,  DOI: 10.1088/1367-2630/15/1/015009
      52
      Observation of intra- and inter-band transitions in the transient optical response of graphene
      Malard, Leandro M.; Mak, Kin Fai; Castro Neto, A. H.; Peres, N. M. R.; Heinz, Tony F.
      New Journal of Physics (2013), 15 (Jan.), 015009CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
      The transient optical cond. of freely suspended graphene was examd. by femtosecond time-resolved spectroscopy using pump excitation at 400 nm and probe radiation at 800 nm. The optical cond. (or, equivalently, absorption) changes abruptly upon excitation and subsequently relaxes to its initial value on the time scale of 1 ps. The form of the induced change in the optical cond. varies strongly with excitation conditions, exhibiting a crossover from enhanced to decreased optical cond. with increasing pump fluence. We describe the graphene response in terms of transient heating of the electrons, with the characteristic relaxation time of the transient cond. reflecting the cooling of the electron system and the strongly coupled optical phonons through emission of lower energy phonons. The change in the optical cond. is attributed to a combination of induced absorption from intra-band transitions of the photo-generated carriers and bleaching of the inter-band transitions by Pauli blocking. The former effect, which corresponds to the high-frequency wing of the Drude response, dominates at low pump fluence. In this regime of a limited rise in the electron temp., an increase in the optical cond. is obsd. At high pump fluence, elevated electron temps. are achieved. The decrease in the inter-band bleaching then dominates the transient response, the intra-band contribution being overwhelmed despite an increase in the Drude scattering rate with temp. The temporal evolution of the optical cond. in all the regimes can be described within a model including the intra- and inter-band contributions with a time-varying electronic temp. An increased Drude scattering rate is inferred for high electron temp. and mechanisms for this enhancement are considered. The calcd. scattering rate for interactions of the carriers with zone-center and zone-edge optical phonons agrees well with the rates obtained from expt.
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    53. 53
      Huang, L.; Gao, B.; Hartland, G.; Kelly, M.; Xing, H. Ultrafast Relaxation of Hot Optical Phonons in Monolayer and Multilayer Graphene on Different Substrates. Surf. Sci. 2011, 605, 1657– 1661,  DOI: 10.1016/j.susc.2010.12.009
      53
      Ultrafast relaxation of hot optical phonons in monolayer and multilayer graphene on different substrates
      Huang, Libai; Gao, Bo; Hartland, Gregory; Kelly, Michelle; Xing, HuiLi
      Surface Science (2011), 605 (17-18), 1657-1661CODEN: SUSCAS; ISSN:0039-6028. (Elsevier B.V.)
      Hot carrier cooling in few-layer and multilayer epitaxial graphene on SiC, and CVD grown graphene transferred onto a glass substrate was studied by transient absorption spectroscopy and imaging. Coupling to the substrate was found to play a crit. role in charge carrier cooling. For both multilayer epitaxial graphene and monolayer CVD graphene, charge carriers transfer heat predominantly to intrinsic in-plane optical phonons of graphene. At high pump intensity, a significant no. of optical phonons are accumulated, and the optical phonon lifetime presents a bottleneck for charge carrier cooling. This hot phonon effect did not occur in few-layer epitaxial graphene because of strong coupling to the substrate, which provided addnl. cooling channels. The limiting charge carrier lifetimes at high excitation densities were 1.8 ± 0.1 ps and 1.4 ± 0.1 ps for multilayer epitaxial graphene and monolayer CVD graphene, resp. These values represent lower limits on the optical phonon lifetime for the graphene samples.
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    54. 54
      Laitinen, A.; Kumar, M.; Oksanen, M.; Plaçais, B.; Virtanen, P.; Hakonen, P. Coupling between Electrons and Optical Phonons in Suspended Bilayer Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 121414,  DOI: 10.1103/PhysRevB.91.121414
      54
      Coupling between electrons and optical phonons in suspended bilayer graphene
      Laitinen, Antti; Kumar, Manohar; Oksanen, Mika; Placais, Bernard; Virtanen, Pauli; Hakonen, Pertti
      Physical Review B: Condensed Matter and Materials Physics (2015), 91 (12), 121414/1-121414/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Using elec. transport expts. and shot noise thermometry, we investigate electron-phonon heat transfer rate in a suspended bilayer graphene. Contrary to monolayer graphene with heat flow via three-body supercollision scattering, we find that regular electron-optical-phonon scattering in bilayer graphene provides the dominant scattering process at electron energies ⪆0.15 eV. We det. the strength of these intrinsic heat flow processes of bilayer graphene and find good agreement with theor. ests. when both zone edge and zone center optical phonons are taken into account.
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    55. 55
      Viljas, J.; Heikkilä, T. Electron-Phonon Heat Transfer in Monolayer and Bilayer Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 245404,  DOI: 10.1103/PhysRevB.81.245404
      55
      Electron-phonon heat transfer in monolayer and bilayer graphene
      Viljas, J. K.; Heikkila, T. T.
      Physical Review B: Condensed Matter and Materials Physics (2010), 81 (24), 245404/1-245404/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      The authors calc. the heat transfer between electrons to acoustic and optical phonons in monolayer and bilayer graphene (MLG and BLG) within the quasiequil. approxn. For acoustic phonons, the temp.-power laws of the electron-phonon heat current for BLG differ from those previously derived for MLG and note that the high-temp. (neutral-regime) power laws for MLG and BLG are also different, with a weaker dependence on the electronic temp. in the latter. In the general case the authors evaluate the heat current numerically. Probably a measurement of the heat current could should be used for an exptl. detn. of the electron-acoustic-phonon coupling consts., which are not accurately known. However, in a typical expt. heat dissipation by electrons at very low temps. is dominated by diffusion and the authors est. the crossover temp. at which acoustic-phonon coupling takes over in a sample with Joule heating. At even higher temps. optical phonons begin to dominate. The authors study some examples of potentially relevant types of optical modes, including, in particular, the intrinsic in-plane modes and addnl. the remote surface phonons of a possible dielec. substrate.
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    56. 56
      Sohier, T.; Calandra, M.; Park, C.-H.; Bonini, N.; Marzari, N.; Mauri, F. Phonon-Limited Resistivity of Graphene by First-Principles Calculations: Electron-Phonon Interactions, Strain-Induced Gauge Field, and Boltzmann Equation. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 125414,  DOI: 10.1103/PhysRevB.90.125414
      56
      Phonon-limited resistivity of graphene by first-principles calculations: electron-phonon interactions, strain-induced gauge field, and Boltzmann equation
      Sohier, Thibault; Calandra, Matteo; Park, Cheol-Hwan; Bonini, Nicola; Marzari, Nicola; Mauri, Francesco
      Physical Review B: Condensed Matter and Materials Physics (2014), 90 (12), 125414/1-125414/18, 18 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We use first-principles calcns., at the d.-functional-theory (DFT) and GW levels, to study both the electron-phonon interaction for acoustic phonons and the "synthetic" vector potential induced by a strain deformation (responsible for an effective magnetic field in case of a nonuniform strain). In particular, the interactions between electrons and acoustic phonon modes, the so-called gauge-field and deformation potential, are calcd. at the DFT level in the framework of linear response. The zero-momentum limit of acoustic phonons is interpreted as a strain of the crystal unit cell, allowing the calcn. of the acoustic gauge-field parameter (synthetic vector potential) within the GW approxn. as well. We find that using an accurate model for the polarizations of the acoustic phonon modes is crucial to obtain correct numerical results. Similarly, in the presence of a strain deformation, the relaxation of at. internal coordinates cannot be neglected. The role of electronic screening on the electron-phonon matrix elements is carefully investigated. We then solve the Boltzmann equation semianalytically in graphene, including both acoustic and optical phonon scattering. We show that, in the Bloch-Gruneisen and equipartition regimes, the electronic transport is mainly ruled by the unscreened acoustic gauge field, while the contribution due to the deformation potential is negligible and strongly screened. We show that the contribution of acoustic phonons to resistivity is doping and substrate independent, in agreement with exptl. observations. The first-principles calcns., even at the GW level, underestimate this contribution to resistivity by ≈30%. At high temp. (T>270 K), the calcd. resistivity underestimates the exptl. one more severely, the underestimation being larger at lower doping. We show that, besides remote phonon scattering, a possible explanation for this disagreement is the electron-electron interaction that strongly renormalizes the coupling to intrinsic optical-phonon modes. Finally, after discussing the validity of the Matthiessen rule in graphene, we derive simplified forms of the Boltzmann equation in the presence of impurities and in a restricted range of temps. These simplified anal. solns. allow us the ext. the coupling to acoustic phonons, related to the strain-induced synthetic vector potential, directly from exptl. data.
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    57. 57
      Betz, A. C.; Vialla, F.; Brunel, D.; Voisin, C.; Picher, M.; Cavanna, A.; Madouri, A.; Fève, G.; Berroir, J. M.; Plaçais, B.; Pallecchi, E. Hot Electron Cooling by Acoustic Phonons in Graphene. Phys. Rev. Lett. 2012, 109, 056805,  DOI: 10.1103/PhysRevLett.109.056805
      57
      Hot electron cooling by acoustic phonons in graphene
      Betz, A. C.; Vialla, F.; Brunel, D.; Voisin, C.; Picher, M.; Cavanna, A.; Madouri, A.; Feve, G.; Berroir, J.-M.; Placais, B.; Pallecchi, E.
      Physical Review Letters (2012), 109 (5), 056805/1-056805/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liq. helium temp. We observe the electronic temp. T ∞ V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on T ∞ √V behavior at high bias, which corresponds to a T4 dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation anal. of the two regimes we ext. accurate values of the electron-acoustic phonon coupling const. Σ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the redn. of Σ, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.
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    58. 58
      Massicotte, M.; Soavi, G.; Principi, A.; Tielrooij, K. J. Hot Carriers in Graphene-Fundamentals and Applications. Nanoscale 2021, 13, 8376– 8411,  DOI: 10.1039/D0NR09166A
      58
      Hot carriers in graphene - fundamentals and applications
      Massicotte, Mathieu; Soavi, Giancarlo; Principi, Alessandro; Tielrooij, Klaas-Jan
      Nanoscale (2021), 13 (18), 8376-8411CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
      A review. Hot charge carriers in graphene exhibit fascinating phys. phenomena, whose understanding has improved greatly over the past decade. They have distinctly different phys. properties compared to, for example, hot carriers in conventional metals. This is predominantly the result of graphene's linear energy-momentum dispersion, its phonon properties, its all-interface character, and the tunability of its carrier d. down to very small values, and from electron- to hole-doping. Since a few years, we have witnessed an increasing interest in technol. applications enabled by hot carriers in graphene. Of particular interest are optical and optoelectronic applications, where hot carriers are used to detect (photodetection), convert (nonlinear photonics), or emit (luminescence) light. Graphene-enabled systems in these application areas could find widespread use and have a disruptive impact, for example in the field of data communication, high-frequency electronics, and industrial quality control. The aim of this review is to provide an overview of the most relevant physics and working principles that are relevant for applications exploiting hot carriers in graphene.
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    59. 59
      Block, A.; Liebel, M.; Yu, R.; Spector, M.; Sivan, Y.; de Abajo, F. G.; van Hulst, N. F. Tracking Ultrafast Hot-Electron Diffusion in Space and Time by Ultrafast Thermomodulation Microscopy. Sci. Adv. 2019, 5, eaav8965,  DOI: 10.1126/sciadv.aav8965
      There is no corresponding record for this reference.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.0c10864.

    • Hyperbolic cooling model, cooling dynamics probed with terahertz pulses, topography of encapsulated graphene, electron mobility of WSe2-encapsulated graphene, Raman characterization of WSe2-encapsulated graphene, fully encapsulated vs semiencapsulated graphene, differential reflectance of WSe2-encapsulated graphene, cooling due to lateral heat diffusion, cooling via disorder-assisted acoustic phonon scattering, cooling via optical phonons (PDF)


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