Hot carrier and hot phonon coupling during ultrafast relaxation of photoexcited electrons in graphene

Abstract

We study, by means of a Monte Carlo simulator, the hot phonon effect on the relaxation dynamics in photoexcited graphene and its quantitative impact as compared to considering an equilibrium phonon distribution. Our multi-particle approach indicates that neglecting the hot phonon effect significantly underestimates the relaxation times in photoexcited graphene. The hot phonon effect is more important for a higher energy of the excitation pulse and photocarrier densities between 1 and 3 × 10 12 cm −2 . Acoustic intervalley phonons play a non-negligible role, and emitted phonons with wavelengths limited up by a maximum (determined by the carrier concentration) induce a slower carrier cooling rate. Intrinsic phonon heating is damped in graphene on a substrate due to additional cooling pathways, with the hot phonon effect showing a strong inverse dependence with the carrier density. * Electronic mail: raulr@usal.es; Copyright 2016 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Appl. Phys. Lett. 108, 043105 (2016) and may be found at http://dx. Graphene features, among other properties, large carrier mobility at room temperature along with gapless linear energy spectra for electrons and holes, that results in a linear optical absorption with virtually no photon wavelength restriction,[1] making it a promising material for the development of a wide range of highly efficient photonic and optoelectronic applications, including those operating in the terahertz range. [2-4] Consequently, an intense effort has been made in the recent years in order to get a good understanding of the carrier dynamics involved during and after photoexcitation [5][6][7][8][9][10][11][12][13][14] from a purely theoretical approach and also from an experimental point of view (pump-probe differential transmission spectroscopy) accompanied by means of various modelling techniques. Right after photoexcitation, an ultrafast thermalization of the carriers takes place driven by Coulomb dual carrier scattering. [13,15,16] Simultaneosly, the carriers partially cool by transferring their energy to the graphene and substrate lattices by means of phonon cascade emissions. [5,8,11,16] As a result, a hot thermal distribution of electrons and holes is achieved in tens of fs. [7,8,10] Later processes involve the cooling of the carriers as a consequence of scattering with phonons in the tail of the energy distribution, at the same time that recombination leads the system towards the full thermodynamic equilibrium. [5,11] Several authors remark the importance that the hot phonon (HP) effect would have on this dynamics. [6,7,17] The ensemble Monte Carlo (EMC) technique has been employed to study the influence of HP on the static transport properties of monolayer graphene under high-field conditions. [18] This method has been proven also to be worthy in the study of ultrafast carrier dynamics in a sub-ps time scale in other m...

Ultrafast relaxation of hot phonons in graphene-hBN heterostructures

“…When the temperatures of the carriers and optical phonon bath equalize, this cooling channel slows down and this is termed as the Hot Phonon (HP) bottleneck. 5,[9][10][11][12][13] Cooling through direct acoustic phonon emission is not viable because of a vanishingly small phase space for such a scattering process. 14 The hot optical phonons cool down through anharmonic decay to acoustic phonons which are subsequently absorbed into the substrate.…”

“…12,[15][16][17] Theoretical predictions and experiments place the hot optical phonon lifetime in graphene, graphite, and carbon nanotubes in the 1-5 ps range. 5,9,[18][19][20][21] The buildup of optical phonons is detrimental to device performance and the HP bottleneck has been invoked to explain current saturation and negative differential conductance in graphene and carbon nanotubes. 10,11,22 The HP bottleneck also affects the photoresponse 23 of optoelectronic devices.…”

Harmonic Extraction in Graphene: Monte Carlo Analysis of the Substrate Influence

“…Furthermore, it must be taken into account that the instantaneous ensemble-averaged velocity is formed by the regular contribution, which consists of odd harmonics of the fundamental frequency due to the collective carrier response, and the fluctuating noise components in the whole frequency range. In an attempt of understanding the physical mechanisms related, it is a priority to examine both contributions [ 12 ]. The efficiency of graphene for high-order harmonic generation has already been revealed [ 4 ], and tunable resonances characterised by large Q-factors have been observed in the THz regime [ 13 ]; on the other hand, we have previously evidenced the potentiality of free-standing graphene, concluding that it is possible to reach the THz range in alike conditions than III–V materials [ 5 ]; however, attending to the actual requirements of the experimental works, it is important to develop these analyses for monolayer graphene on different substrates.…”

“…The efficiency of graphene for high-order harmonic generation has already been revealed [ 4 ], and tunable resonances characterised by large Q-factors have been observed in the THz regime [ 13 ]; on the other hand, we have previously evidenced the potentiality of free-standing graphene, concluding that it is possible to reach the THz range in alike conditions than III–V materials [ 5 ]; however, attending to the actual requirements of the experimental works, it is important to develop these analyses for monolayer graphene on different substrates. Ensemble Monte Carlo (MC) simulations [ 12 ] have been used for this aim, such modelling tools being highly convenient for determining and studying parameters such as velocity correlation function or noise temperature [ 14 ]. The great advantage of the MC procedure is that the sources of fluctuations are intrinsically assimilated through the stochastic nature of the different scattering events.…”

Influence of temperature on the displacement threshold energy in graphene

“…The same formalism has been applied to materials other than graphene, including MoS 2 17,18 and hBN 19,20 , although in non-metallic specimens inelastic excitations play an important role 19,21,22 . Excitation lifetimes in graphene have been established 23–25 to be in the order of 10 −15 to 10 −12 s, while typical beam currents used in STEM correspond to on average one electron passing through the sample every nanosecond. Therefore, any excited states are expected to relax between the electron impacts, and for vacancy creation in pristine graphene, only the knock-on mechanism needs to be considered 16 .…”