Hot Electron Cooling by Acoustic Phonons in Graphene

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Hot Electron Cooling by Acoustic Phonons in Graphene

A. C. Betz, F. Vialla, D. Brunel, C. Voisin, M. Picher, A. Cavanna, A. Madouri, G. Fève, J.-M. Berroir, B. Plaçais, and E. Pallecchi

Phys. Rev. Lett. 109, 056805 – Published 2 August 2012

See Synopsis: Electrons in Graphene Beat the Heat

Abstract

We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature $T \propto V$ at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on $T \propto \sqrt{V}$ behavior at high bias, which corresponds to a $T^{4}$ dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant $Σ$ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of $Σ$ , not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.

Received 12 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.056805

Synopsis

Electrons in Graphene Beat the Heat

Published 2 August 2012

Graphene researchers show the leakage of heat from electrons to sound vibrations is small enough to allow for sensitive light detectors.

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Authors & Affiliations

A. C. Betz¹, F. Vialla¹, D. Brunel¹, C. Voisin¹, M. Picher², A. Cavanna², A. Madouri², G. Fève¹, J.-M. Berroir¹, B. Plaçais^1,*, and E. Pallecchi^1,†

¹Laboratoire Pierre Aigrain, ENS-CNRS UMR 8551, Universités P. et M. Curie and Paris-Diderot, 24, rue Lhomond, 75231 Paris Cedex 05, France
²Laboratoire de Photonique et Nanostructures, CNRS-UPR20 CNRS, Route de Nozay, 91460 Marcoussis Cedex, France

^*bernard.placais@lpa.ens.fr
^†Present address: Laboratoire de Photonique et Nanostructures, 91460 Macoussis Cedex, France.

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Issue

Vol. 109, Iss. 5 — 3 August 2012

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Images

Figure 1
Shot noise measurement scheme with a sketch of the sample the electrical environment. The bias resistance is $R_{bias} = 4732 Ω$ . The samples and the cryogenic low-noise amplifier are cooled at 4.2 K. The scanning electron microscope pictures refer to samples BN1 and CVD1: BN1 consists of an exfoliated graphene flake (red), deposited on an exfoliated hBN platelet (green), itself deposited on a $Si / {SiO}_{2}$ used as a back gate. CVD1 was fabricated from CVD grown graphene deposited on $Si / {SiO}_{2}$ . Both samples are contacted with Pd electrodes (yellow).Reuse & Permissions
Figure 2
(a) Typical excess noise $S_{I}^{m} (V)$ spectra in sample BN1; it is a white noise with a superimposed $1 / f$ contribution and fitted by $S_{I}^{m} = S_{I} + C / f$ laws (solid lines). (b) and (c) show the $I (V)$ and $S_{I} (V)$ data for different gate voltages in sample BN1 from which we deduce $T_{e}$ . The circles point out the $I (V)$ and $S_{I} (V)$ values of the spectra shown in (a).Reuse & Permissions
Figure 3
Electronic temperature in sample BN1 as function of voltage bias for a set of gate voltages. $T_{e} = S_{I} V / (4 k_{B} I)$ is deduced from the $S_{I} (V)$ and $I (V)$ data shown in Figs. 2c, 2b. Unlike $S_{I} (V)$ , $T_{e} (V)$ is nearly independent of gate voltage and closely follows the $T_{e} \propto \sqrt{V}$ law (black solid line) expected for 2D phonons. A $T_{e} \propto V^{2 / 5}$ law (dashed line) is also plotted to highlight the difference with a standard 3D-phonons mechanism. Deviations from $T_{e} \propto \sqrt{V}$ law are observed at low bias where a $T_{e} \propto V$ behavior is found.Reuse & Permissions
Figure 4
(a) and (b) Electron temperature of sample CVD1 (a) and BN1 (b) plotted as $T_{e}^{4} (V) / P$ , where $P$ is the Joule heating per unit area $P = V^{2} / R L W$ . The plateau at high bias is at a value $T_{e}^{4} / P ≃ 1 / Σ$ . The dip at low $V$ is due to electron heat diffusion to the leads. Dashed lines are one-parameter fits with $Σ$ as a free parameter. (c) $Σ$ as a function of carrier density $n_{s}$ for samples BN1 and BN2.Reuse & Permissions
Figure 5
(a) Raman shift of the 2D band of a graphene sample similar to CVD1, as function of the cryostat temperature $T_{0}$ . The slope is $(- 0.051 \pm 0.008) {cm}^{- 1} K^{- 1}$ . Excitation laser at 532 nm, $P = 25 kW {cm}^{- 2}$ . No laser power dependence was observed in this range. (b) Raman shift of the 2D band as function of the bias voltage for $T_{0} = 100 K$ (triangles) and $T_{0} = 300 K$ (full circles). The slopes are $(- 0.3 \pm 0.3)$ and $(- 0.9 \pm 0.3) {cm}^{- 1} V^{- 1}$ , respectively. The bias-induced phonon heating is therefore below $30 K / V$ . Similar results and conclusions were drawn from measurements on the $G$ band (not shown).Reuse & Permissions

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