Super-Planckian thermal radiation between 2D phononic hBN monolayers

https://doi.org/10.1016/j.ijthermalsci.2021.107315Get rights and content

Abstract

Near-field radiation heat transfer (NFRHT) in two-dimensional (2D) hexagonal boron nitride (hBN) monolayer and its composite symmetric-based structure was investigated. Contrary to three-dimensional (3D) materials, the splitting of modes (in 2D materials) into the longitudinal optical (LO) and transverse optical (TO) phononic modes disappears at the Γ-point even in some polar materials. The conductivity of atomic thin hBN monolayer depends on the LO phonon frequency under the long wavelength limit. Exploiting such concept, the electromagnetic local density of states (EM-LDOS) accounting for the near-field radiation spectrum was evaluated in free-space close to an interface with the hBN monolayer as well as composite structures. An intense narrow peak of LDOS was found in the case of hBN monolayer caused by the surface phonon polariton (SPhP) resonance. This peak was modified in the case of hBN-graphene composite due to hybridization, which strongly depends on two factors – the distance of observer (in vacuum) from interface and graphene Fermi energy. It was found that the flux density between monolayer hBN gets 2.8-fold enhanced as compared to the monolayer graphene configuration under 0.11 eV Fermi energy applied at a vacuum gap of 15 nm. The possibility of tuning Fermi energy has great potentials in designing thermally controlled devices.

Introduction

The emitter and receiver placed together at the subwavelength-sized gap results in tunneling phenomenon through the coupling of evanescent modes, thereby enhancing the radiation heat transfer above Planck's blackbody radiation limit. Such type of modes, comprised of surface plasmon polaritons (SPPs) and/or surface phonon polaritons (SPhPs), cause flux radiation [[1], [2], [3], [4], [5]]. Investigators have reported the near-field heat flux amplification for wide range of applications in energy management [[6], [7], [8], [9]]. The details of progress and challenges for near-field radiation at subwavelength scales have been discussed in Refs. [[10], [11], [12], [13], [14], [15]].

PhPs supported by polar materials are effectively responsible for radiative heat transfer over nanoscale range at the terahertz and infra-red frequencies. They exhibit the capability of hybridization coupling with photons. The confinement of light over tinny volume is possible through materials exhibiting such properties. Within the context, nanostructured thin films have led to extreme confinement by reducing its thickness, in which the values of in- and out-of-plane wave vectors of polaritons get enhanced [[16], [17], [18], [19]]. Due to these remarkable features, PhPs have attracted attention among researchers for energy management applications, especially in designing qualitative emitters for efficient radiative heat transfer [[20], [21], [22], [23]].

The van der Waals heterostructures play significant roles in varieties of optoelectronic devices [[24], [25], [26]]. Among several other polar materials, the newly reported monolayer two-dimensional hexagonal boron nitride (2D-hBN) has great potentials [27]. Within the context, electron screening and Coulomb interaction give rise to the separation of phononic modes in the form of longitudinal optical (LO) and transverse optical (TO) modes, depending on the dimensionality and momentum [[28], [29], [30]]. Such a splitting disappears at certain point, referred to as the zone center (or the Γ-point); the gradient remains finite for the LO dispersion. Moreover, the polarization charge density, confined in the monolayer, is vanishing for the TO mode due to the presence of orthogonality between the direction of propagation and polarization. In the LO case, however, it is non-zero, which causes the electric field to exist over long range. Consequently, the electron-phonon Frohlich interaction significantly affects the transport features of monolayers and their heterostructures. In fact, the dispersion property of optical phonon is influenced by the dipole-dipole interaction term [[31], [32], [33]]. Screening in layered materials can be illustrated by exploiting the dielectric constant of bulk material. This can be described by the effective screening length, and can be determined by using the first-principles [34]. In this context, the effect of screening in van der Waals heterostructures on optical phonon modes is of great concern as the polarization strength, describing the slope of LO dispersion, affects the electronic transport properties through layers [35].

In this work, we propose monolayer hBN structure mimicking graphene [36] along with its heterostructure for the local density of states (LDOS) [37] in the near-field radiation heat transfer (NFRHT) application. The monolayer hBN material is characterized by the long wavelength range-based conductivity, which depends on the environmental dielectric constant and LO frequency [38]. According to electronic smearing obeying the density-functional perturbation theory [39], graphene-coated hBN is considered as bulk dielectric [40] with the environment screening function as εgra=5.5. In this situation, the conductivities of both the monolayer hBN and monolayer graphene are added together. Based on this concept, the determination of LDOS and radiative flux for atomic thin hBN layer along with its composite heterostructure have not been reported yet. With this viewpoint in mind, we take monolayer hBN, monolayer graphene, bulk pure silicon and their composite heterostructures, in order to evaluate the LDOS in vacuum from interfaces considering different structural configurations. It essentially describes the rate of spontaneous emission and black body spectral density which are significantly affected by the presence of interferences due to the incidence and reflected waves, and the surface modes. Consequently, the density of states becomes a space-dependent function [41]. Also, we determine the radiation flux density for different structures, as stated above.

Section snippets

Theoretical formulation

In electrodynamic applications, the electromagnetic (EM) conductivity has significant importance, and is helpful to determine the dielectric response of monolayer hBN in calculating its scattering characteristics; it is given as [38].σhBN(ω)=4iε0εenωωTOvgωTO2ω2iωτ1

Here εen denotes the average permittivity of materials present below and above monolayer, ε0 is the free-space permittivity, τ1 is the phonon dissipation rate and the other quantities are chosen asvg=3.6×104 m/s and ωTO=1387cm−1.

Results and discussion

Fig. 1b and c shows the frequency dependence of the real and imaginary parts of conductivity, respectively, as evaluated using eq. (1). For computations, we choose four different values of loss rate τ1, viz. 5 cm−1, 10 cm−1, 15 cm−1 and 20 cm−1. The loss will significantly affect the EM response of the monolayer material and heat transfer. We observe that increasing the value of τ1 causes reduction in the conductivity of material (Fig. 1b). It is worth mentioning that the waves will propagate

Conclusion

The heat flux can be enhanced through the 2D LO phonons-based thin film, giving rise to the opportunity of achieving greater heat energy. The evaluated LDOS patterns exhibit a narrow peak due to phononic resonance in thin hBN layer, and the hybridization coupling is effective within a distance of 100 nm in vacuum from the interface. The flux density between symmetric thin layers of hBN is 3 orders of magnitude higher than the black body radiation, and 2.8-fold higher than the monolayer graphene

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The authors are grateful to the partial supports from NSFC (61775195 and 62075196), NSFC of Zhejiang Province (LR15F050001 & LZ17A040001) and the National Key Research and Development Program of China (No. 2017YFA0205700). Also, the authors are indebted to anonymous reviewers for their constructive comprehensive comments on the work.

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