Revealing the ultrafast spontaneous emission in plasmon-enhanced monolayer semiconductor nano-light sources

Compact optical interconnects have been considered as a promising solution/platform for on-chip communication and information processing with modulation bandwidth and energy efficiency superior to traditional electrics.^1–3 With high output power and fast modulation speed, lasers are generally considered as candidate light sources for building efficient optical links.^4–6 However, downscaling the lasers to subwavelength scale brings additional challenges, including high lasing threshold and gain compression effects. On the other hand, previously ignored light-emitting diodes (LEDs) are recently proposed as a suitable alternative to the lasers with higher energy efficiency and lower fabrication requirements.^7–10 By coupling the light-emitting materials to optical nanocavities with extreme light confinement,^11,12 their slow intrinsic spontaneous emission rate can be largely enhanced by the Purcell effect.^13–18 The Purcell-enhanced nano-light sources show potential modulation speed comparable with or even faster than the lasers.^9,19 With a smaller footprint and simpler structure, such nanoLEDs are not limited by lossy cavities and can efficiently operate at room temperature without a threshold or gain compression.⁹ 

Developing Purcell-enhanced nanoLEDs with modulation speed faster than the lasers (>50 GHz) requires a spontaneous emission lifetime less than several picoseconds and even sub-picoseconds. This requirement is hard to be achieved using traditional emitters (such as molecules and quantum dots) with nanosecond-scale spontaneous emission lifetime. Even after the efficient coupling to the optical nanocavities with large Purcell enhancement, the lifetime is still at the range of several to hundreds of picoseconds.^14,15,17,19 In contrast, transition metal dichalcogenides (TMDs) are recently demonstrated to have distinctive optical and optoelectronic properties, including strong exciton effect.²⁰ This makes the TMDs a powerful candidate for LEDs' sources with high quantum yield and intrinsic spontaneous emission lifetime down to few picoseconds.^21,22 The total decay lifetime of excitons in TMDs can be further accelerated by plasmonic nanocavities to even tens of femtoseconds.^18,23,24 However, such an ultrafast decay lifetime within ∼100 nm diameter is hard to be characterized using conventional time-resolved techniques. Zhang et al. developed a method to determine the ultrafast total decay rate in nanocavities through simultaneously obtaining photoluminescence (PL) and Raman spectra.¹⁸ Yet, the radiative decay channel remains unrevealed, hampering the development of such kind of ultrafast light source toward practical applications.

In this work, we constructed a Purcell-enhanced ultrafast spontaneous light source by coupling a monolayer WSe₂ to the gap region of a nanocube-over-mirror (NCOM) nanocavity. In this hybrid nanosystem, the gap plasmon mode is tailored to match the excitons of WSe₂ spatially and spectrally, reaching a moderate plasmon–exciton coupling with 40.1 meV Rabi splitting. Enabled by such measurable coupling strength and PL enhancement, we developed a practical model to determine the radiative lifetime of the hybrid nanosystem. The results show that the radiative lifetime can be controlled from ∼20 ps to 350 fs in the nanocavity, indicating the potential modulation bandwidth up to 440 GHz. In addition, our light sources also show high brightness with more than 300 times enhanced quantum yield compared to the bare WSe₂. Our results not only manifest the potential of developing a bright spontaneous emission source with superior modulation bandwidth but also practically promote the further quantitative study of femtosecond-scale ultrafast emission beyond the time-resolved fluorescence spectroscopy limit.

The illustration of the NCOM nanocavity-WSe₂ hybrid is shown in Fig. 1(a). (Details about the samples are shown in supplementary material Section 1 and Section 7.) By situating an 85 nm Ag nanocube over an ultrasmooth Au film, the NCOM nanocavity was constructed. The nanogap between the nanocube and the Au film consists of a 4 nm Al₂O₃ layer and monolayer WSe₂. The size of the nanocube and the thickness of the Al₂O₃ layer are selected to ensure that the plasmon is in resonance with excitons in WSe₂.²³ The fundamental plasmon mode of the NCOM nanocavity is located in the gap region, providing considerable electric field enhancement to enhance light–matter interaction.^15,23Figure 1(c) shows the simulation on the electric field distribution of the fundamental plasmon mode in the gap region using a full wave finite element method. (Details are shown in supplementary material Section 7.) The xy-plane electric field distribution at emission wavelength (750 nm) has a field enhancement up to 80 times. Figure 1(d) shows the PL (excited by 633 nm laser) and dark-field (DF) scattering characterization of the NCOM nanocavity-WSe₂ hybrid when the nanocavity plasmon and excitons are in resonant. The mode splitting of the scattering spectra and great PL enhancement are simultaneously achieved in a single nanocavity-WSe₂ hybrid. This indicates that the plasmon–exciton coupling is at the border between strong and weak coupling regimes, where the PL brightness reaches its maximum.²⁵ The electric field enhancement at excitation wavelength (633 nm) has negligible effect on the PL process, because the excitation wavelength is away from the resonant with the emission wavelength. (Details are shown in supplementary material section 2.) Thus, the PL enhancement is mainly contributed from the emission enhancement.

To map the energy dispersion of the hybrid for quantifying the plasmon–exciton coupling, we gradually deposited Al₂O₃ layers over the sample to continuously shift the wavelength of the plasmon resonance.²³ (Details are shown in supplementary material Section 3.) We collected the dark-field scattering spectra from the single NCOM nanocavity-WSe₂ hybrid to eliminate the deviation coming from the statistics on different samples.^26,27Figures 2(a) and 2(b) show the experimental and simulated mapping of dark-field scattering of the single NCOM nanocavity-WSe₂ hybrid under every Al₂O₃ deposition thickness (from 4 to 32 nm). So, we can quantify the strength g of the coupling between excitons (resonant at $E0$⁠) and nanocavity mode (resonant at $Ecav)$ according to the Jaynes–Cummings model.^28,29 The energy of the hybrid states is $E±=12(E0+Ecav)±g2+14δ2$⁠, where $δ=Ecav−E0$ is the detuning between excitons and nanocavity mode. By fitting the dark-field scattering data in Fig. 2(a) with the coupled-oscillator model, we can map the energy dispersion of the hybrids to quantify the coupling strength. (Details about the fitting are shown in supplementary material Section 3.) The resulting energy dispersion in Fig. 2(c) shows avoided-crossing behavior, and we can get Rabi splitting $Ω=2 g=40.1 meV$⁠. In addition, the full-widths at half-maximum of the plasmon (⁠ $γcav)$ and the excitons (⁠ $γ0)$ are 119.8 and 42.8 meV, respectively. So, the Rabi splitting achieved (∼40.1 meV) is smaller than 1/2 $γcav+γ0$⁠,³⁰ which means that the coupling achieved here does not exceed the strong coupling condition.

To check the light-emitting capability of the NCOM nanocavity-WSe₂ hybrid, we perform the PL experiment. The PL can be enhanced only at the WSe₂ region within the nanocavity. Yet, the area of WSe₂ overlapped with the NCOM nanocavity (⁠ $Scav$⁠) is much smaller than which we collected (⁠ $S0$⁠). So, the real enhancement factor (EF) of the PL emitted from WSe₂ enhanced by the nanocavity should be calculated according to $EF=Icav−I0I0S0Scav$⁠, where $Icav$(⁠ $I0)$ represents the PL counts with (without) the nanocube. As shown in Fig. 2(d), the PL can be enhanced by a factor of 1350 when the excitons and nanocavity mode are almost in resonant (for 16.5 nm Al₂O₃ coating over the sample). By collecting the PL spectra of the nanocavity-WSe₂ hybrid at every Al₂O₃ deposition thickness, we get the relation between the PL enhancement against the detuning. The results show that the PL enhancement can be controlled from 26 to 1350 times through continuously changing the detuning with the Al₂O₃ deposition method. The PL imaging results also demonstrate the great light-emitting capacity of the nanocavity-WSe₂ hybrid. (Details are shown in supplementary material Section 4.)

Benefiting from the extreme confined plasmon mode, the total decay lifetime of the excitons in TMDs can be accelerated down to tens of femtosecond by the NCOM nanocavities.¹⁸ This indicates an ultrafast Purcell-enhanced spontaneous emission beyond the limit of time-resolved fluorescence spectroscopy.^31,32 Therefore, developing an experimental method to evaluate and prove the radiative decay lifetime is as significant as achieving it in such hybrids composed of plasmonic nanocavities and monolayer TMDs.

We have quantified the 2g (40.1 meV), $γ cav$ (119.8 meV), $η 0$ (0.065%), and the $γ PL/ γ 0 PL$ [Fig. 2(d)] based on the measured dark-field scattering and PL spectra. After simulating the enhancement of the excitation $γ exc/ γ 0 exc$ at every energy detuning [Fig. 3(a)], we can deduce the radiative lifetime of the nanocavity-WSe₂ hybrids according to Eq. (3). As shown in Fig. 3(a), the radiative lifetime can be controlled from ∼20 ps to 350 fs when changing the energy detuning by in situ scanning the plasmon resonances. The minimum radiative lifetime is ∼350 fs when the nanocavity mode and the excitons are nearly on resonance. Such a spontaneous emission source exceeds a nearly 3 THz emission rate, which is much faster than the former nanocavity-quantum dot hybrids (90 GHz).¹⁷ We further calculate the modulation bandwidth of the nanocavity-WSe₂ hybrid according to the relation $f 3 dB ≈ 1 2 π 1 ( 1 / γ cav ) 2 + ( 1 / γ r ) 2$⁠.¹⁹ The maximum modulation bandwidth exceeds 440 GHz. Such a modulation speed is much superior to the semiconductor lasers, indicating the possible applications with no need for coherent light such as short-distance on-chip or intra-chip communications.⁹ 

Apart from the radiative lifetime, the quantum yield is another important parameter to quantify the light-emitting devices. So, we then measure the quantum yield $η$ of the nanocavity-WSe₂ hybrid according to the method introduced in Eq. (4). As shown in Fig. 3(b), the quantum yield reaches as high as 20.8%, which is enhanced by more than 300 times compared to WSe₂ on quartz. The $η$ of WSe₂ is effectively controlled by the spectrally tunable nanocavity from 0.4% to 20.8%. The coupling strength of the plasmon–exciton coupling in plasmonic nanocavities will be increased if decreasing the mode volume of the nanocavity mode, leading to the enhancement of the quantum yield. Yet, the smaller mode volume results in the stronger nonradiative decay of the excitons, because they are closer to the metals. Therefore, the maximum quantum yield will be likely obtained before entering the strong coupling regime, i.e., in the intermediate coupling regime. That is why such a magnificent quantum yield enhancement can be obtained in our nanocavity-WSe₂ hybrids.

In conclusion, we achieved a high-speed and efficient light-emitting source based on plasmonic nanocavities-WSe₂ hybrids. The exciton–plasmon coupling is in the intermediate regime to obtain an extreme usage of the radiative enhancement instead of the nonradiative channel. The quantum efficiency is demonstrated to be 20.8%, which is over 300 times to the bare monolayer WSe₂. By simultaneously obtaining the coupling strength and the PL enhancement in a single nanocavity, the radiative lifetime of the hybrid is evaluated to be 350 fs with theoretical modulation bandwidth up to 440 GHz. Such a high-speed spontaneous nano-light source is crucial to build up nanoLEDs faster than the lasers.