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Abstract
Graphene has attracted great interest due to its superior and unique physical properties. The strong light‐matter interaction with ultrafast and broadband photoresponse of graphene has allowed for the development of state‐of‐the art optical components, such as photodetectors and optical modulators, making this material very promising for ultrafast optical communications. However, so far, light emission from graphene has remained elusive, although this would open the door towards obtaining atomically thin, flexible and transparent light sources and graphene‐based on‐chip interconnects. In this chapter, we review experimental results and techniques of the electrically driven light emission from graphene in the infrared and visible spectrum range.
Keywords
- Graphene
- light emission
- power dissipation
- high electric field
- Phonon temperature
1. Introduction
In order to obtain bright thermal radiation from gapless graphene, the radiative electron–hole recombination process is not enough due to the ultrafast energy relaxation that occurs through electron–electron (∼10 fs) and electron–phonon (∼1 ps) interactions. On the other hand, graphene's superior mechanical strength, high‐temperature stability and non‐equilibrium electron temperature, compared to lattice temperature, may enable the efficient thermal radiation under high electric field. However, the thermal radiation from electrically biased graphene is significantly influenced by the substrate. Especially, dominant vertical heat dissipation through underlying substrate, and extrinsic scattering effects, such as charged impurities and the surface polar optical phonon, limit the thermal radiation efficiency of graphene.
Freely suspended structure enables the dramatic suppression of undesirable vertical heat dissipation and extrinsic scattering effects by substrate, and much more promising to yield efficient and brighter thermal radiation from graphene in the infrared to visible range. Furthermore, the emitted light from suspended graphene interacts with the reflected light from the separated substrate surface, resulting in interference effects that can be used to tune the radiation spectrum of this material. Electro‐thermal engineering will allow obtaining advanced graphene light emitters for atomically thin, flexible and transparent lighting and ultrafast optical interconnects. In this chapter, we will provide an overview of the thermal radiation from electrically biased graphenes in the infrared and visible spectrum range.
2. High electric field transport in graphene on substrate
Graphene's superior electronic [1], mechanical [2] and thermal [3] properties can be used for high mobility field‐effect transistors (FETs) [4] and mechanical resonators [5]. In the case of electronic devices, as shown in Figure 1a, that depicts a graphene FET, the applied electric field applied by the source-drain voltage generates a Joule self‐heating effect, which leads to a change of its electronic transport behaviour or device failure, in some cases [6]. For carbon nanotubes (CNTs), the observed electronic transport characteristics have been explained by heat transports along the CNT channels and between CNTs and the substrates [7]. There have been reports on the heat dissipation from graphene devise in a diffusive regime, where the chemical potential changes along the graphene channel. A direct method to study the heat dissipation is to accurately measure the temperature during device operation (see Sections 2.1–2.3). The temperature measurement of graphene on a substrate biased by a source–drain voltage has been performed in four ways: (1) shift of Raman peaks [8–11]; (2) thermal scanning imaging [11]; (3) thermal radiation [9, 10, 12] and (4) ratio of the Stoke/anti‐Stoke intensities in Raman spectroscopy [9, 10, 13]. Methods (1) and (2) are sensitive to the acoustic phonon (AP) temperature (
The Fourier's law for thermal conductance is:
where
Figure 2 shows a summary of temperature increase (ΔT) of graphene devices on substrates, as a function of electrical power density, determined by various temperature measurement techniques. The closed, opened and half‐closed scattered points show the acoustic,
The detailed measurement techniques can be found in the legend of Figure 2. For each sample, one can obtain the
In order to treat the heat transfer from graphene on a substrate into the surrounding environment, as shown in Figure 1b, let us first consider a one‐dimensional heat equation along the graphene channel [12]:
where
2.1. Electron temperature of graphene
Thermal radiation can be observed for graphene devices on a substrate under high electric field, which is attributed to the electrically driven spontaneous emission from hot electrons of graphene [9, 10]. The thermalized charge carriers under electric field emit electromagnetic radiation, according to Planck's law, as a grey body:
where
The
2.2. Optical phonon temperature of graphene
Raman spectroscopy is a well‐known technique for the characterization of a number of layers, doping level, mechanical strain and temperature of graphene. In particular, for graphene devices under high electric field, Raman spectroscopy accurately provides the phonon temperature and population. In typical Raman spectroscopy, spontaneous Raman effects are due to the inelastic light scattering, with optical phonon modes of the material being determined by measurement. The resulting inelastic scattered of excited photon emits or absorbs optical phonons. The Stoke process involves the creation of extra optical phonons (
In graphene, the phonon population for zone centre optical phonons can be estimated from the G peak signal intensity of the Raman spectra, which is proportional to phonon populations with effective temperature, and follows from the Bose‐Einstein distribution. Raman signal intensity ratio of the anti‐Stoke (
where
2.3. Acoustic phonon temperature of graphene
The Raman spectrum of graphene also exhibits a downshift of the Raman peak position with increasing temperature. This is due to the anharmonic coupling effect and anharmonic temperature of secondary phonons into G mode phonon decay and a thermal expansion effect [16]. Empirically, the down shift of the G peak can be measured as a linear function of
where
2.4. Non‐equilibrium phonon population in graphene
As discussed in Sections 2.1–2.3, accurate measurements of graphene temperature provide a deep understanding of the heat dissipation mechanism and electron‐phonon interaction in biased graphene devices. Direct comparison of
In the case of CNTs, non‐equilibrium phonon distributions have been measured when electrically biased, as high‐energy optical phonons have larger populations than low‐energy phonons, such as radial‐breathing mode and acoustic phonons [7, 18].
Similarly to what was found with CNTs, non‐equilibrium phonon populations in electrically biased graphene on a substrate have been observed. Table 1 and Figure 3 [9, 10] showed that the elevated
Experimental results show that strong electron‐optical phonon coupling enables the equilibrium of the electron and optical phonon temperature, whereas an energy relaxation bottleneck to low‐energy phonons results in the non‐equilibrium phonon population. Furthermore, strong coupling with surface polar optical phonons and substrate acoustic phonons provides an extra electronic energy relaxation path, resulting in the effective cooling of acoustic phonons of graphene, under high electric field. Therefore, non‐equilibrium optical phonon temperature (
where
where
3. Infrared light emission from graphene on substrate
Graphene has unique electronics and phonon states under high electric field, such as decoupled electrons and low‐energy phonon temperature [9, 13]. These make graphene an efficient material as thermal radiation source, determined only by
Previous studies of infrared light emission from graphene were accomplished by graphene FETs on a substrate under high electric field [9, 10, 12]. Due to the self‐heating effect of graphene under electrical bias, only a small fraction (<10-6) of energy is converted into light and most of the energy is dissipated into the substrate and metal contact. The extracted
In graphene FETs, charge carrier density profiles are determined by applied electric field and gate voltage. According to the self‐consistent electrical‐thermal model of charge and heat transport in graphene, the minimum charge carrier density spatial location is the cross‐point of the Fermi level across the charge neutrality point. The hot spot position of the infrared image directly reveals the spatial location of the charge neutrality point along the graphene channel, as shown in Figure 5a and b. In some case, the stationary hot spot of infrared light emission, even under variation of gate voltages and source‐drain bias, is attributed to the defects of graphene and trapped charges in the substrate [10, 12, 14].
Spontaneous thermal radiation is governed by the Fermi's golden rule, and the transition rate is determined by the optical density of the environment. This was shown in Ref. [19], through an optical micro cavity controlled graphene infrared light source, with emission around 925 nm,. Due to the strong light‐matter interaction of atomically thin graphene and the optical confinement effect, micro‐cavity structures enable the control of 20‐fold enhancement of photocurrent generation, which is spectrally selective near infrared thermal radiation. The thermal radiation confinement effect inhibits spontaneous thermal radiation wavelengths larger than the resonant wavelength of the optical cavity. The optical cavity‐induced suppression of the radiative thermal radiation also leads to the self‐heating effect in graphene, which is affected by non‐radiative heat transfer through the substrate, metal electrodes and radiative heat transfer.
4. High electric field transport in suspended graphene
As discussed in the previous section, high electric field transport of graphene on a substrate is affected by the substrate and environmental conditions. Limited thermal radiation efficiency and electron temperature are due to the dominant heat dissipation to the substrate and extrinsic scattering effects, such as electron‐hole puddle, trapped charges [20] and surface polar phonon [21]. According to some authors [22, 23], suspended graphene shows ultrahigh mobility and fractional quantum Hall effect at low temperature, with low electric field. Therefore, in order to observe the intrinsic properties of graphene under high electric field, suspended structures are essential.
In suspended graphene, the self‐heating effect plays a role due to significantly reduced heat dissipation through the substrate. Thermally induced charge carriers, saturation velocity, charge carrier mobility and thermal conductivity of graphene are significantly affected by the applied electric field and temperature.
In the clean limit of suspended graphene, under high electric field as shown in Figure 6a–c, the total charge carrier density of graphene is dominated by thermally induced charge carriers (
where
The current density
where
where
For a self‐consistent electrical‐thermal calculation of suspended graphene, the heat diffusion equation for the temperature profile (
where
Using a self‐consistent electrical‐thermal calculation in suspended graphene, as shown in Figure 6d, clean samples show the saturation behaviour under high electric field. This implies that high charge carrier mobility of suspended graphene devices have a larger temperature dependence (
In contrast with suspended CNTs, suspended graphene does not show a negative differential conductance, due to the linear increase of density of states in 2D, whereas CNTs have strong 1D phonon scattering, resulting in a negative differential conductance [7].
Along the temperature profile of suspended graphene, drift velocity and charge carrier density are affected by current density. Theoretically, saturation velocity of graphene was predicted as
Suspended graphene is well known as a material having the highest thermal conductivity at room temperature (
5. Bright visible light emission from suspended graphene
Graphene has a great potential as an efficient thermal radiation light source due to its superior mechanical strength, high‐temperature stability, high current density and non‐equilibrium phonon modes. However, previous reports regarding the thermal radiation of supported graphene [9, 10, 12, 19] have been limited to the near infrared light emission range, and extremely small fractions of electrical power are converted into the photons (∼10-6). The main reason for the limited performance of graphene light emitters supported on a substrate is the dominant heat dissipation through the substrate, and significant hot carriers cooling by dominant extrinsic scattering origins, such as charged impurities, trapped charges and surface polar phonons. In the case of freely suspended graphene, these issues can be ignored. Therefore, suspended structures are promising for the observation of bright, efficient light emission radiation approaching the intrinsic properties.
There are several methods that can be used for the synthesis of suspended graphene structures. One is wet‐etching of a sacrificial layer after metallization onto the graphene. The other procedure is the transfer of patterned graphene onto pre‐fabricated trench substrate. In order to increase the fabrication yield and prevent the collapse of graphene, a critical point dryer process is important. Suspended graphene structures are fabricated using mechanically exfoliated graphene or large‐scale graphene grown by the CVD method. Figure 7a shows the obtained suspended graphene devices [25].
In order to observe light emission from suspended graphene under electrically bias, an experimental set‐up, similar to that shown in Figure 7b, is used under vacuum (∼10-5 Torr), at room temperature. In addition, to get clean graphene channel and reliable contact resistance, a slow current‐induced annealing process [29] is essential. Suspended graphene exhibits bright visible light at the centre of the graphene channel once the applied bias voltage exceeds the critical field (0.5 ∼ 1.0
Y.D. Kim et al. [25] also demonstrated multiple visible light emission from a large‐scale suspended graphene array, which was fabricated from large‐scale CVD graphene. The synthesis of a large‐scale, robust and bright visible light emitter array from CVD graphene will allow obtaining graphene‐based flexible and transparent lighting and display modules. Furthermore, complementary metal‐oxide‐semiconductor (CMOS) compatibility of graphene technology will enable a hybrid graphene‐photonic platform for ultrafast optical communications.
The radiation spectrum from electrically biased suspended graphene over a trench of depth (
These multiple emission peaks in the visible range and significant modulation by trench depth can be understood by interference effects between the light emitted directly from the suspended graphene and light reflected from the substrate as shown in Figure 8b. When we neglect the light reflection and absorption by the graphene, the interference effect on thermal radiation is given by:
where
Based on thermal radiation with interference effect (Eq. 13), electron temperature of suspended graphene was extracted, as shown in Figure 8a (solid line) and approaches 2800 K. The light emission peak in the visible range rapidly increases with the applied electric field above a critical field (∼0.4
Raman spectroscopy provides an accurate measurement of acoustic phonons, optical phonon population and the temperature under applied electric field, as described in Sections 2.2 and 2.3. However, bright thermal radiation from electrically biased suspended graphene becomes significantly stronger than the Raman signal above ∼1500 K. In order to estimate the temperature profiles and thermal conductivity, self‐consistent numerical simulation of electrical and thermal transport is used, as described in Section 4. From numerical simulation based on the electrical transport data, thermal conductivity at the centre of the suspended graphene channel decreases from
Effectively localization of hot electron in suspended graphene by unique electronic and thermal properties enables bright visible light emission. Based on the Stefan–Boltzmann law from measured electron temperature, as shown in Figure 8e, thermal radiation efficiency was estimated as
An electrically driven graphene light emitter has great advantages, such as being atomically thin, broadband emission, radiation spectrum tunability, surface and self‐emission all with a simple structure. Furthermore, ultrafast and broadband electrical and optical response of graphene has enabled the development of a nanoscale ultrafast light emitter. We expect to obtain atomically thin, flexible and transparent light sources and on‐chip optical interconnects for communications based on graphene.
Acknowledgments
The authors thank J. Hone, Y.D. Park and G. Arefe. YDK was supported by Grants from ONR (N00014‐13‐1‐0662 and N00014‐13‐1‐0464) and DE-SC0012592. MB was supported by Grants from the National Research Foundation of Korea (NRF‐2012‐M3C1A1‐048861, NRF‐2015R1A2A1A10056103) funded by the Korean government.
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