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Light–matter interaction in a microcavity-controlled graphene transistor

Graphene has extraordinary electronic and optical properties and holds great promise for applications in photonics and optoelectronics. Demonstrations including high-speed photodetectors, optical modulators, plasmonic devices, and ultrafast lasers have now been reported. More advanced device concepts would involve photonic elements such as cavities to control light–matter interaction in graphene. Here we report the first monolithic integration of a graphene transistor and a planar, optical microcavity. We find that the microcavity-induced optical confinement controls the efficiency and spectral selection of photocurrent generation in the integrated graphene device. A twenty-fold enhancement of photocurrent is demonstrated. The optical cavity also determines the spectral properties of the electrically excited thermal radiation of graphene. Most interestingly, we find that the cavity confinement modifies the electrical transport characteristics of the integrated graphene transistor. Our experimental approach opens up a route towards cavity-quantum electrodynamics on the nanometre scale with graphene as a current-carrying intra-cavity medium of atomic thickness.


Supplementary Information
Supplementary Figure S1 | Angular distribution of microcavity-controlled thermal emission. a, Schematic showing the graphene layer placed between the two cavity mirrors. Also indicated are the maximum angle of detection and the angular distribution of the emitted light. b, Emission wavelength as a function of emission angle. No light emission can be observed for θ > 23°. c, On-axis transmission (red) and thermal emission (black) spectrum measured on the same device as a function of wavelength and emission angle, respectively. The maximum thermal emission intensity is observed at 5° while the collimated thermal emission lobe has an angular width of 12° (FWHM). Plotted is the temperature of graphene as function of injected electrical power density, in comparison with data taken from the literature 11,12 . The temperature-values are extracted by fitting the measured, free-space thermal emission spectra of a reference graphene transistor (with the same dielectric layers and metal contacts, but without cavity mirrors) to a model of a two-dimensional blackbody. Estimation at which rate heat is radiatively dissipated through cavity-controlled thermal light emission the measured light intensity is converted into an energy flux. By summing the measured photon flux in the spectral window of the cavity resonance and taking into account the detection conditions, we obtain the integrated energy flow that emanates from the device area of 1µm 2 at each bias point. Above threshold at 4V or 80kW/cm 2 , respectively, the device emits thermal photons having energy of 1.3eV (λ~925nm) which is equivalent to an overall heat transfer at a rate of 4.8x10 6 eV/s.

Simulation and experimental verification of resonance wavelength and cavity-Q
The microcavity resonance is determined by the thickness of the Si 3 N 4 and Al 2 O 3 layers, i.e. the total thickness of the intra-cavity medium. In our case the Si 3 N 4 layer thickness is fixed at 50nm while the thickness of the second intra-cavity medium Al 2 O 3 can be freely adjusted. To determine the Al 2 O 3 thickness to grow, we modeled the cavity resonance within a transfer matrix approach, i.e. a plane wave propagates through this multilayered cavity system and the electric field is evaluated at each boundary (see Supplementary Figure S7a). From the simulations we infer the proper

Microcavity-controlled thermal emission -angular distribution
We now analyze the angular distribution of the cavity-confined thermal light emission. According to reference 18, the following equation relates the emission wavelength λ to the emission angle θ with respect to the cavity normal (see Supplementary Figure S1), where L is the geometrical mirror spacing (or cavity length), n pol is refractive index of the intra-cavity medium, m is the mode order (m=1 in this case), and Δφ is the phase shift associated with light absorption in the metallic mirrors. The microscope objective used in our measurements has a numerical aperture of NA=0.8. This corresponds to a maximum detection angle of θ max =53.1° with respect to the cavity normal (see Supplementary Figure S1). For the device discussed in the main manuscript (see Figs.3,4), having an on-axis (θ=0) resonance wavelength of 925nm, the shortest wavelength that can be collected is hence 556nm. The measured microcavity-controlled emission spectra typically level of at around 850nm and have a spectral width of 40nm (FWHM), which translates into an angular distribution of θ=12° (FWHM), with an intensity maximum occurring at θ max =5° (see Supplementary Figure S1). This demonstrates that the cavity-coupled thermal emission of graphene is radiated into a narrow lobe and that off-axis emissions coupled to guided modes are insignificant.

Estimating temperature effects in a microcavity-controlled graphene transistor
At high source-drain bias, the saturation current density j sat in graphene depends on the self-heating of the graphene layer 22 . The degree of self-heating is determined by the thermal coupling of graphene to its environment. A measure for the thermal coupling is the thermal conductance r. Within the self-heating model the saturation current is proportional to the square root of the thermal conductance, We extract a lower bound for the thermal conductance r 0 in our graphene transistors by fitting in Supplementary Figure S2 the measured spectra of the free space, nonconfined thermal radiation to the following expression j sat / r 0.5 which delivers r 0 =0.4 kW/(cm 2 K).
We now estimate the temperature modifications ΔT associated with the optical confinement based on the expression We assume that j sat =j-j sat,0 for j > j sat,0 and that relative changes in the thermal conductance r can be captured through the relative changes of the saturation current As reference saturation current j sat,0 , we choose the current density at the intersection between regimes I. and II. (see Supplementary Figure S4).
The resulting temperature modifications for the cavity emitter discussed in Figs. 3, 4 of the main manuscript are plotted in Supplementary Figure S4. As compared to graphene in free, non-confined space, the modifications of saturation current suggest temperature modifications as high as ΔT=100K.