Switching of Photonic Crystal Lasers by Graphene

Supporting Information For:

Switching of Photonic Crystal Lasers by Graphene Min-Soo Hwang, Ha-Reem Kim, Kyoung-Ho Kim, Kwang-Yong Jeong, Jin-Sung Park, JaeHyuck Choi, Ju-Hyung Kang, Jung Min Lee, Won Il Park, Jung-Hwan Song, Min-Kyo Seo, Hong-Gyu Park

This file includes: Methods Supplementary Figures S1–S3 Supplementary References

S1

Methods Numerical simulations. We used finite-element method (FEM) (COMSOL) to calculate transmittance and cavity modes in Figures 1b and 2f. To obtain the optical conductivity of graphene as a function of the gate voltage Vg, the following theoretical model was employed.S1-S3 The Fermi level (EF) of the electrons in graphene is given by

EF = hν F π ( Cg e ) Vg − V0

(1)

where νF, Cg, and V0 are the Fermi velocity (~0.9 × 106 m/s), the effective capacitance per unit area, and the offset voltage for charge neutrality, respectively.S2 The optical conductivity of graphene is defined by σgraphene = σintra + σinter. In turn, the change in EF alters the optical conductivities of intra- (σintra) and inter- (σinter) band transitions:

σ intra (ω ) =

  2 EF e 2γ i log  2 cosh  2 −1 2π h ω + iτ   γ

σ inter (ω ) = H (ω ) −

2ω

π

∫

∞

0

   

H (ω ′) − H (ω ) dω ′ ω ′2 − ω 2

(2)

with H (ω ) =

 hω + 2 EF   hω − 2 EF   e2   tanh   + tanh   8h  γ γ     

(3)

where e, γ, and τ are the electron charge, the broadening of the inter-band transition, and the free carrier scattering rate (5 × 10−13 s), respectively.S2,S3 The parameters used in our simulations were Cg = 14.4 mF/m2, V0 = 0.9 V, and γ = 150 meV.S2 For calculating the transmittance in Figure 1b, a monolayer graphene sheet was placed between glass (n = 1.4) and ion gel (n = 1.4). The system was irradiated by a normally incident 1550-nmwavelength light beam, from the ion gel to the glass. The monolayer graphene with optical conductivity of σgraphene was modeled as an effective surface current sheet in the FEM simulation. The intensity of the transmitted light was detected in the glass for different Vg. In the three-dimensional FEM simulation in Figure 2f, the structural parameters of the PhC cavity were determined based on the SEM image of a fabricated cavity (inset, Figure 2b), as follows: the lattice constant, the radii of the regular air holes, and the six nearest neighbor holes S2

around the cavity were 440, 132, and 84 nm, respectively. The six nearest neighbor holes were shifted by 53 nm relative to their original positions. The thicknesses of the InGaAsP slab, SiO2 layer, and ion gel were 250 nm, 100 nm, and 2 µm, respectively. The refractive indices of the InGaAsP slab, SiO2 layer, and ion gel were set to 3.2, 1.4, and 1.4, respectively.S4,S5

Device fabrication. The PhC structures were fabricated using electron-beam lithography and chemically assisted ion-beam etching in a wafer that consisted of a 250-nm-thick InGaAsP slab/800-nm-thick InP sacrificial layer/InP substrate. After removing the PMMA electron-beam resist, the InP sacrificial layer was selectively wet-etched using a diluted HCl solution at room temperature. A 100-nm-thick SiO2 layer was deposited on the PhC structures by plasmaenhanced chemical vapor deposition (PECVD). Next, a monolayer graphene sheet was synthesized on a Cu substrate using the chemical vapor deposition (CVD). A PMMA layer was coated on the graphene, and the PMMA/graphene sheet was detached from the Cu substrate by successive wet-etching. Then, the PMMA/graphene layer floating on water was uniformly transferred to the PhC structures.S6 Electron-beam lithography and thermal evaporation were performed for fabricating 5-nm-thick Ti/200-nm-thick Au contacts on the graphene sheet. The remaining PMMA was removed by rinsing with acetone. The entire sample including the graphene-PhC structures was moved and attached to the glass substrate with two large Ti/Au contacts.

Finally,

to

fabricate

ion

gels,

we

used

poly(vinylidene

fluoride-co-

hexafluoropropylene), 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide, and acetone as the polymer, ionic liquid, and solvent, respectively.S7 The weight ratio among the polymer, ionic liquid, and the solvent was kept to 1:4:7. Spin-coated ion gels on a silicon substrate were placed in a vacuum oven at 80°C for 24 hours, to remove the residual solvent. The ion gels were cut with a razor blade and then, transferred onto the graphene-PhC structures using tweezers. The leakage current between the two electrodes was measured to be 1.0 V).S8

S5

Figure S2. Measured PL spectra of the graphene-integrated double-cavity PhC laser of Figure 4, with varying gate voltages of the left and right graphene layers, left Vg and right Vg. The incident peak pump power was fixed at 3.23 mW. (a) As the left Vg increased from 0 to 1.0 V and the right Vg was fixed at 0 V, only the peak intensity at 1525.0 nm increased significantly. All of the peak intensities were normalized by the maximal intensity at (left Vg, right Vg) = (1.0 V, 0 V). (b) As the right Vg increased from 0 to 1.0 V and the left Vg was fixed at 0 V, only the peak intensity at 1513.0 nm increased significantly. All of the peak intensities were normalized by the maximal intensity at (left Vg, right Vg) = (0 V, 1.0 V). These measurements show the independent controls of the lasing peaks at 1525.0 nm and 1513.0 nm by gating the left and right graphene, respectively.

S6

Figure S3. Electric field intensity profiles in the double-cavity PhC structures, calculated using FEM simulations. Based on the SEM image in Figure 4b, the structural parameters of the simulation were as follows: the radius of regular air holes was 123 nm, the lattice constant was 440 nm, and the radii of reduced holes around the left and right cavities were 73 nm and 77 nm, respectively. In addition, the thicknesses of the PhC slab, SiO2 layer, and ion gel were set to 250 nm, 100 nm, and 2 µm, respectively. Graphene was not considered in this simulation. The calculated field profiles show the strong confinement of the hexapole mode (a) in the left PhC cavity at a wavelength of 1523.0 nm and (b) in the right PhC cavity at a wavelength of 1514.0 nm. The resonant wavelength in each cavity agrees well with the measured one in Figure 4. The simulation result indicates that the coupling effect between the two PhC cavities is negligibly small. Scale bar, 1 µm.

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Supplementary References S1. Falkovsky, L. A. J. Phys. Conf. Ser. 2008, 129, 012004. S2. Majumdar, A.; Kim, J.; Vuckovic, J.; Wang, F. Nano Lett. 2013, 13, 515–518. S3. Emani, N. K.; Chung, T.-F.; Kildishev, A. V; Shalaev, V. M.; Chen, Y. P.; Boltasseva, A. Nano Lett. 2013, 14, 78–82. S4. Kang, J.-H.; Kim, S.-K.; Jeong, K.-Y.; Lee, Y.-H.; Seo, M.-K.; Park, H.-G. Appl. Phys. Lett.

2011, 98, 2–4. S5. Thareja, V.; Kang, J.-H.; Yuan, H.; Milaninia, K. M.; Hwang, H. Y.; Cui, Y.; Kik, P. G.; Brongersma, M. L. Nano Lett. 2015, 15, 1570–1576. S6. Li, X.; Cai, W.; An, J.; Kim, S.; Nah, J.; Yang, D.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; Banerjee, S. K.; Colombo, L.; Ruoff, R. S. Science 2009, 324, 1312–1314. S7. Lee, K. H.; Kang, M. S.; Zhang, S.; Gu, Y.; Lodge, T. P.; Frisbie, C. D. Adv. Mater. 2012, 24, 4457–4462. S8. Cho, J. H.; Lee, J.; He, Y.; Kim, B.; Lodge, T. P.; Frisbie, C. D. Adv. Mater. 2008, 20, 686– 690.

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