Graphene is appearing more often in a broad range of technological innovations. The Nobel prize-winning material is formed by a single layer of carbon atoms configured like the vertices of a molecular-scale hexagonal chicken wire. It has fascinating electronic and optical properties and has been proposed for novel applications, such as transparent electrodes for touch screens and solar cells, a platform for lithium ion batteries, and saturable absorbers for pulse lasers.
The hexagonal lattice structure of graphene leads to a linear structure in the electron bands—the range of energies the electrons in graphene can have. The linear band structure allows direct and strong coupling between light and relativistic electrons. As a result, the optical absorption of graphene is frequency-independent for a broad spectral range from visible to infrared.1, 2 The overall absorption of layered graphene is proportional to the number of layers. Each layer absorbs πα=2.293%, where α is the fine-structure constant (), in which e is the electronic charge, ℏ is Planck's constant divided by 2π, and c is the velocity of light. This strong coupling over the entire visible spectrum means that graphene can be seen by the naked eye, despite the fact that it contains only one layer of atoms.
The strong light absorption of graphene can be modulated by electrical gating, a process known as charge doping (see Figure 1). In ideal graphene, there is zero ‘band gap’ in the electronic structure. Because graphene is formed by a monolayer of carbon, its density of states is very low compared with bulk materials. Therefore, even a small charge accumulation can effectively shift the position of the Fermi level (the highest occupied molecular orbital at 0K). For example, take a sheet of graphene under the illumination of incident photons with energy ℏν (where ν is the light frequency). If the sheet is uncharged, the Fermi level is in the middle of the band structure, close to the touch-point of the bands where the electrons behave as massless Dirac fermions (the Dirac point and the incident light can excite the electrons). However, when the graphene sheet is positively charged, its Fermi level drops. If the charging is sufficient for it to drop to under −ℏν/2 below the Dirac point, there is no electron available for the interband transition, and hence no optical absorption. When the graphene sheet is negatively charged, the Fermi level rises. If the Fermi level rises to more than ℏν/2 above the Dirac point, there is no state available to accept optically excited electrons, and the absorption is again zero.
Figure 1. The band structure of graphene under different gate voltages. (Left) When graphene is positively charged, the Fermi level (Ef) is lowered. There is no electron available for the interband transition. (Middle) When the bias voltage is low, the incident light can excite electrons. (Right) When graphene is negatively charged, the Fermi level is higher than half of the photon energy, so there is no state available for the electrons to be excited to. Therefore the absorption in this case is zero.
Light can assume two different forms, propagating or evanescent. Both forms have electrical components and can interact with graphene. As explained above, a single layer of graphene absorbs 2.293% of a propagating wave that is incident normal to its surface. However, the absorption can be drastically increased if the wave is incident parallel to graphene's surface. Evanescent light decays exponentially with distance and is found in the vicinity of light waveguides or metal surfaces in which surface plasmons (collective oscillations of electrons) are excited.
Figure 2. Schematic illustration of the fabrication process for the double layer graphene modulator. We start with a silicon waveguide on a silicon-on-insulator (SOI) wafer (a and c). A graphene sheet (G) prepared by chemical vapor deposition is mechanically transferred on top of the waveguide, and oxide-plasma etching is used to define the active regions (b and d). A thin layer of gate oxide (aluminum oxide, Al2O3) prepared by atomic layer deposition (e and g), and the second graphene layer is then transferred and defined (f and h). Si: Silicon. SiO2: Silicon oxide. Al: Aluminum. Au: gold. The gold structures are electrodes.
In our group, we demonstrated the first graphene optical modulator by integrating graphene layers with a silicon waveguide, using a fabrication process described in the literature3, 4 (see Figure 2). The graphene-based modulator is prepared on a silicon-on-insulator (SOI) wafer. First, waveguides are prepared by standard electron-beam lithography and deep reactive-ion etching. The active region contains two layers of graphene sheet separated by a thin oxide layer, which in our case is a 7nm thick layer of aluminum oxide (Al2O3) prepared by atomic layer deposition. Graphene sheets prepared by standard chemical vapor deposition method are then transferred to the chip, covering all regions of the device. After the electrode is defined, a thin layer of polymethyl methacrylate is used to protect the graphene on the top of the waveguide and between the electrodes and the waveguide. The rest of the graphene is removed by oxygen plasma.
Figure 3. Static response of a double-layer graphene modulator. Length of the device: 40μm; working wavelength: 1.537μm. (Lower insets) The band structures of two graphene layers at different drive voltages. Ef: Fermi energy.
Drive voltages are added between the two graphene layers. When the drive voltage is zero, the device is in the ‘OFF’ state, since undoped graphene is opaque. A non-zero drive voltage upshifts the Fermi level in one layer and downshifts the other. Both shifts contribute to making the material transparent, so that the device is in the ‘ON’ state. A static response and a modulation depth (a change in transmissivity) of 6.5dB is achieved in a 40μm-long device (see Figure 3).
We achieved an operation speed of 1.2GHz with a modulation depth of 3dB in an ambient environment. This speed is only limited by the huge contact resistance existing in our device, which we expect can be improved by orders of magnitude in the future. By incorporating multilayer graphene sheets, the modulation efficiency can be further increased. In addition, the flexibility of graphene sheets could also lead to a new family of soft photonic devices when integrated with flexible substrates and plastic waveguides,5 or novel geometries such as a core–shell modulator for nano-optical cables. The recent development of large-scale graphene synthesis and transfer techniques6 has ensured its compatibility with the existing integrated electronics platform. Our future work will look into improving the contact resistance, the use of multilayer graphene, and applications of the system in flexible optoelectronics.
We acknowledge funding from the National Science Foundation Nano-scale Science and Engineering Center (NSF-NSEC) for Scalable and Integrated Nano Manufacturing (SINAM) (grant No. CMMI-0751621).
University of California, Berkeley
Ming Liu completed his PhD studies in 2010 at the University of California, Berkeley, and has worked as a postdoctoral researcher in Xiang Zhang's group since then. His research focuses on novel materials for optoelectronics and clean energy.
Mechanical Engineering Department, University of California, Berkeley
Xiang Zhang is the inaugural Ernest S. Kuh Endowed Chaired Professor at the University of California, Berkeley, and the director of the National Science Foundation Nanoscale Science and Engineering Center. He is also a faculty scientist at the Lawrence Berkeley National Laboratory.
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