Graphene for Microwaves

Transcription

1 T hese days, electronics are moving toward faster, smaller, more efficient, yet cost effective, solutions. In doing so, the limits of what materials are currently available within the technologies are frequently reached. Because of this, the hunt for new materials that are endowed with disruptive, enhanced properties and a high degree of compatibility with standard processes, has become paramount. In this difficult quest, graphene has shown proven results as an emblematic protagonist, seeming to answer many needs. Characterized by superior electric and mechanical performance, it is also quite compatible with conventional manufacturing techniques. Hence graphene may become a key enabling material, paving the way for a new generation of high-speed nanoscale electronics with consequences and breakthroughs similar to that of silicon s in the last few decades. This article will try to encompass the evolution of this fascinating material, beginning with early observations and moving into the practical microwave applications that are envisioned for its bright future. IS FO SU CU E FE SED AT UR E What Is? is a graphite monolayer with a thickness of only 0.34 nm. It is formed from carbon atoms in a sp2 hybridization state, arranged such that each carbon atom is covalently bonded to three others. So, graphene is a planar for Microwaves Mircea Dragoman, Dan Neculoiu, Daniela Dragoman, George Deligeorgis, G. Konstantinidis, Alina Cismaru, Fabio Coccetti, and Robert Plana Mircea Dragoman (mircea.dragoman@nano-link.net) and Alina Cismaru are with the National Institute for Research and Development in Microtechnology (IMT-Bucharest), P.O. Box , Bucharest, Romania. Dan Neculoiu is with Politehnica University of Bucharest, Electronics Dept., 1-3 Iuliu Maniu Av., Bucharest, Romania. Daniela Dragoman is with the University of Bucharest, Physics Dept., P.O. Box MG-11, Bucharest, Romania. George Deligeorgis, Fabio Coccetti, and Robert Plana are with LAAS CNRS, 7 Avenue du Colonel Roche, Toulouse Cedex 4, France. G. Konstantinidis is with the Foundation for Research & Technology Hellas (FORTH) P.O. Box 1527, Vassilika Vouton, Heraklion , Crete, Greece. DIGITAL STOCK Digital Object Identifier /MMM December /10/$ IEEE 81

2 Drain n + Si Gate Source SiO 2 Figure 1. Field-effect-transistor-like structure based on graphene. Resistance (Ω) (a) 20 μm (b) Frequency (GHz) S 11 (db) at 2,420 mv S 21 (db) at 2,420 mv S 11 (db) at 2,500 mv S 21 (db) at 2,500 mv S 11 (db) Reference S 21 (db) Reference (c) Resistance (Left) (L) 0.02 Capacitance (Right) (R) Voltage (d) Capacitance (pf) Figure 2. coplanar waveguide (a) graphene (courtesy of Industries), (b) graphene coplanar waveguide, (c) scattering parameters under different dc bias, and (d) equivalent circuit up to 65 GHz. [(b) and (c) reprinted with permission from G. Deligeorgis, M. Dragoman, D. Neculoiu, D. Dragoman, G. Konstantinidis, A. Cismaru, and R. Plana, Appl. Physics Letters 95, no. 7, pp /1-3, Aug. 2009, Copyright 2009, American Institute of Physics.] nanomaterial with a honeycomb lattice formed from two interpenetrating triangular sublattices [1]. is encountered in many carbon-based materials. A simple example is graphite, which is formed by a very large number of stacked graphene monolayers. Another example is the single wall carbon nanotube (CNT), which is simply a rolled-up graphene sheet. is a two-dimensional (2-D) crystal, and a native 2-D gas of charged particles. In many devices, graphene is deposited on a SiO 2 layer with a typical thickness of 300 nm, which is grown over a doped silicon substrate. In this configuration, the silicon substrate acts as a backgate, which shifts the Fermi energy level in graphene and produces a surface charge density n 5e 0 e d V g /te > av g, where e 0 is the air dielectric permittivity of air, e d is the dielectric permittivity of SiO 2, t is the thickness of the SiO 2 layer and the gate V g voltage. The gate-induced carriers can be seen as resulting from an electrical doping, analogous to the chemical doping typically used for semiconductor devices. So, in graphene, the electrons and holes are electrically induced by applying a positive or a negative voltage on a gate. After graphene deposition on the Si/SiO 2 structure, electrodes are patterned on graphene to implement certain devices. Figure 1 shows a field effect transistor (FET)-like structure based on graphene. Although this structure is very simple, it can be used for many graphene devices. was isolated for the first time in 2004 using the mechanical exfoliation of highly ordered pyrolytic graphite (HOPG) with an adhesive tape, followed by the release of graphene flakes on Si/SiO 2 after tape removal [2]. HOPG is a stacked three-dimensional (3-D) structure consisting of vertically arranged graphene sheets. Fragments of peeled HOPG are engineered to fall directly on the Si/SiO 2 interface and are immobilized on the Si/SiO 2 due to Van der Waals forces. This appears to be a rudimentary way to obtain graphene, but, even now, this method is successfully applied to obtain graphene flakes with dimensions up to 1 mm having a low rate of defects. The fabrication method described above was accompanied by another important discovery regarding the visibility of graphene [3]. is visible with an optical microscope if the incident white light is filtered by a green, blue, or other-colored filter, depending on the thickness of SiO 2 [4]. In these conditions, graphene was seen using a simple microscope, as shown in Figure 2(a). Although there are, presently, a multitude of methods to visualize graphene [5], graphene monolayer and other nanostructures formed by successive layers of graphene, such as bilayer, trilayer, or multiple layers of graphene, are quite well distinguished with a microscope using optical reflection and optical contrast spectroscopy. Even their thicknesses can be determined with high accuracy [6]. 82 December 2010

3 TABLE 1. Methods to Produce. Starting Material Brief Description of the Method Yield Quality Area Highly ordered Pyrolytic graphite Silicon carbide Repetitive peeling highly ordered pyrolytic graphite Reduction of silicon atoms at high temperature Low Very high Small Low Medium Large (3 4 inches wafers) oxide Oxide dispersion into hydrazine High Medium Large Gas mixture (CH 4 and H 2 ) Chemical vapor deposition Very high High Very large (30 inches) Starting from graphene mechanical exfoliation with adhesive tape, in only a few years the growth methods of graphene on metal or semiconductor substrates have evolved up to advanced chemical vapor deposition (CVD) techniques [7]. There are presently four main methods to produce graphene (see Table 1). The first one is the mechanical exfoliation with adhesive tape from HOPG, which has a low yield but the highest quality to date, the second is the epitaxial growth of graphene on a silicon carbide (SiC) substrate, which must be heated at temperatures greater than 1,000 ºC [8]. The third method is based on graphene oxide (GO), which is dispersed in hydrazine and deposited on various substrates as a uniform film that contains single- or few-layer graphene [9]. The last method, which among all seems to be the most promising from a yield and reproducibility point of view, is the grapheneraphene produced using CVD techniques. Based on this technique, a graphenebased microelectricalmechanical system (MEMS) switch was also fabricated and tested [10]. The CVD technique was successfully used for roll-to-roll production of 76.2-cm (30-in) graphene films on flexible copper substrates, with applications in flexible electronics, such as touch screens where graphene film is used as a transparent electrode [11]. can be washed using solvents such as acetone and isopropanol without damage. However, the use of ultrasonic agitation or aggressive cleaning agents must be avoided. In addition, optical lithography or particle lithography techniques to process semiconductors are also applicable to graphene devices. has amazing physical properties, and it is often termed the wonder material. The carrier mobility measured in various devices is 8,000 10,000 cm 2 V 1 s 1 at room temperature, but could become as high as cm 2 V 1 s 1 in suspended graphene [12]. The mean-free path for ballistic carrier transport is nm at room temperature, while graphene resistivity depends significantly on the gate voltage. The dispersion relation in graphene is linear for both electrons and holes for small energies E and has the simple form E 56 h k v F, where v F is the Fermi velocity and k 5 ik x 1 jk y denotes the wavenumber of the charge carriers. The linear dispersion relationship consists of two lines that are crossing at a point called the Dirac point. Far from the Dirac point, the carrier transport is unipolar, while in the Dirac region it is ambipolar and strong recombination processes take place. The linear dispersion relation is similar to that of photons propagating in a vacuum, but the significance of this relation is very different. In graphene, the linear relation between the energy and the wavenumber means that the effective mass of charge carriers is practically zero, so that the transport of electrons and holes is ballistic, that is, without any collision in the device if its length is less than the mean-free path, in which case the charge carriers behave as waves instead of particles. These waves are slow and propagate with the Fermi velocity v F = 10 6 m/s > c/300. In contrast, the photons propagate with the speed of light in vacuum, c. The analogy between the ballistic transport of electrons and electromagnetic waves is a rich concept used in many areas of electronics, optoelectronics, and electromagnetism [13]. Moreover, graphene is considered to be the strongest material ever known with an elastic stiffness of 340 N/m and a Young modulus of 1.5 TPa [14]. The very impressive mechanical and electrical properties of graphene are summarized in Table 2. The following shows how we can use these properties for the advancement of microwave devices. Microwave Devices Based on is a hot topic in nanoelectronics in the area of transistors [15], spin valve devices [16], photodetectors [17], single-electron transistors [18], and solar cells [19], but few works have been reported up to now in the area of microwave applications. The reason is that microwave devices and circuits are fabricated up to 100 GHz using GaAs, SiGe, InP, or high-resistivity silicon, which are mature technologies implemented in semiconductor fabrication plants. Therefore, the microwave devices and circuits are based on the above-mentioned semiconductor technologies, which, in their turn, are rapidly improved. December

4 TABLE 2. s Main Properties. Paramerer Value and Units Obervations Thermal conductivity 5,000 W/mK Better thermal conductivity than in most crystals Young modulus 1.5 TPa Ten times greater than in steel Mobility 40,000 cm 2 V 21 s 21 At room temperature (intrinsic mobility) maximum mobility: 200,000 cm 2 V 21 s 21 Mean free path (ballistic transport) As a result, nanomaterials such as nanoparticles, nanowires, and CNTs are not widespread in microwaves, although important progress was made regarding CNT microwave devices [20], and even a nanoradio was recently demonstrated [21]. Another reason for the absence of nanomaterials, in particular, CNTs, in microwaves is that their impedance is greater than 10 kv and, thus, these materials are difficult to match with the 50 V required by microwave circuits equipment. One solution for decreasing CNT impedance to 50 V [22] uses dielectrophoresis to arrange in parallel thousands of nanotubes, but this procedure has a low reproducibility. Therefore, graphene may be a viable solution to replace the single wall CNT thin film, which consists of thousands of nanotubes, the total number of which is difficult to control. For instance, in [23] a coplanar waveguide (CPW) deposited on graphene was fabricated and characterized up to 65 GHz, and the equivalent circuit of the CPW was developed in [24]. The CPW graphene device is shown in Figure 2(b). Source (Au) Gate (Au) IHT-RWTH SiO µm µm Drain (Au) SEI 0.5 kv 10,000 1 μm WD 9.2 mm Figure 3. FET transistor of Aachen group (Figure 1 from [27]). on suspended graphene < 400 nm At room temperature Fermi velocity c/ ,000,000 m/s At room temperature A graphene monolayer was fabricated by Industries and positioned over a 300 nm SiO 2 layer grown on an n-doped silicon substrate. The monolayer can be optically recognized, as shown in Figure 2(a). A graphene flake is rather small to pattern the entire CPW on and the CPW dimensions cannot be made smaller due to the impedance required by the testing equipment, which is 50 V, and the pitch of the probe tips, which is 150 µm. To solve this problem, in the graphene region we have patterned the three electrodes of CPW to cover entirely the graphene [see Figure 2(b)], and outside the graphene region we enlarged the electrodes on the SiO 2 substrate to fit with the probe tips requirements. The technology to fabricate the CPW is quite complex and involves a combination of various deposition techniques and electron beam lithography. The main geometrical parameters of the CPW graphene are: the central electrode width is 4.3 µm; the distance between the central electrode and the ground is W = 1.7 µm; the width of the ground electrodes is 8.4 µm; and the overall length of the CPW on graphene is around 80 µm. S parameters measurements have shown that these are shifted as a function of the dc voltage applied on the CPW between the central electrode and its ground electrodes. The applied dc voltages are between 22.5 V and 12.5 V (with 1 on the center conductor of the CPW). From these S parameter measurements [see Figure 2(c)], an equivalent circuit consisting of a resistance R and a capacitance C connected in parallel was extracted. We have found that the resistance is tunable as a function of the applied dc voltage in the range V while the capacitance was around 1 pf. These results were valid up to 7 GHz because, at higher frequencies, the doped silicon substrate becomes very lossy. Very recently, we have replaced the doped silicon substrate with a highresistivity substrate and the above results regarding the tunable resistance around 50 V were obtained up to 65 GHz for a similar bias voltage range. However, this time, the resistance varied in the range of V for biases between 26 V and 6 V, while the capacitance remained almost constant, around 60 ff [see Figure 2(d)]. Now, the equivalent circuit is valid in the range GHz [23]. The 50 V impedance of graphene is a result of its physical properties. More precisely, in graphene, which is a 2-D gas, the conductivity is quantized (has a finite minimum value) [25], while in a CNT, which is a one-dimensional (1-D) gas, the conductance is quantized (varies in steps), and thus the resistance step of 84 December 2010

5 6.3 kv cannot be decreased. Because of this, packing of CNTs in high density arrays or bundles has become a major research topic aiming to lower the impedance of electrical interconnects. After we have understood that graphene is a nanomaterial that can be used in microwave applications due to its tunable 50 V impedance, we have started to build a radio frequency (RF) graphene transistor [26]. FETs are, at present, the main device application of graphene. In principle, the first graphene FETs have used as gates a doped substrate, as shown in Figure 1, but the top-gate configuration is the main configuration used up to now. is the FET channel and is terminated with two electrodes: source (S) and drain (D). The current between source and drain is controlled by a gate electrode separated from graphene by a dielectric. Among the first graphene transistors we describe is the top-gate graphene transistor with a SiO 2 dielectric [27] reported by AMICA and Aachen University in 2007 and shown in Figure 3. In the following three years, the cut-off frequency of graphene FET transistors has increased from a few gigahertz to 100 GHz [28]. This is due to improvements in the fabrication technology, which allows a decrease in the gate length and the use of dielectrics that, when deposited on graphene, do not destroy its atomic lattice and do not introduce defects, which decrease the mobility. Moreover, graphene FETs MRG-FORTH S D G S SEI 30.0 kv 1,100 WD 10.0 mm 10 μm (a) After we have understood that graphene is a nanomaterial that can be used in microwave applications due to its tunable 50 V impedance, we have started to build an RF graphene transistor. fabricated on graphene flakes are now replaced by graphene FETs fabricated on an entire wafer, as reported by the IBM team in [28]. Other important results regarding FET graphene transistors working in microwaves are found in [29] and [30]. Our graphene FET transistor is displayed in Figure 4(a) and(b). To fabricate it, a flake of graphene monolayer was deposited over a 300 nm SiO 2 grown on high-resistivity silicon by Industries. It is a strange fact that graphene exfoliated from HOPG is of better quality than the epitaxial or even CVD-grown graphene, but the explanation is simple. The exfoliated graphene is a native graphene sheet and has a low rate of defects, while graphene growth by any methods is accompanied by a much greater defect density. The fabrication of our transistor is described in detail in [26] and will not be repeated here. It combines various deposition techniques with electron beam lithography. We have used an organic gate dielectric a poly(methyl methacrylate) (PMMA) layer with a thickness of 200 nm. The relevant dimensions of the graphene FET are: gate length L G nm, sourcedrain distance L 5 2 µm and source/drain width W 5 40 µm. A maximum stable gain greater than one was measured up to 5 GHz, while the cutoff frequency is eight times larger. The value of the cut-off frequency was calculated according to the conventional definition that applies for an FET, taking into account the geometry of this particular double gate version. The mobility was determined from the drain current versus gate voltage characteristic and was found to be 8,000 cm 2 /Vs at room temperature and far from S G CPW Lines (b) Figure 4. (a) Microwave graphene field effect transistor with polymethyl methacrylate dielectric gate. (b) Top view of the entire transistor. (Reprinted from [26] with permission. Copyright 2010, American Institute of Physics.) D Maximum Stable Gain V DS = 2 V V DS = 3 V Frequency (GHz) Figure 5. Maximum stable gain for the field effect transistor of Figure 4. December

6 the Dirac point. This value is eight times greater than in silicon. Other microwave applications of graphene are multipliers [31], even though here the progress is slower than in the case of graphene FETs. Conclusions nanoelectronics is an emerging area of research. The 2010 Nobel Prize for physics was awarded to A. Geim and K. Novoselov [1] for the discovery of graphene and its unexpected physical properties, paving the way for many new applications in the area of nanoelectronics, nanooptics, and solid state physics. The most-studied microwave device is the graphene transistor [15], which, in only three years, has reached a cutoff frequency of 100 GHz. As consequence of this impressive development, the prediction that a THz graphene FET transistor will soon be demonstrated is quite realistic. Moreover, graphene multipliers and other microwave graphene devices are expected to follow the graphene FET development dynamics and reach 100 GHz in few years. Acknowledgments The authors acknowledge the support of the project NANO-HF financed by the Ministry of Education and Research of Romania and the European Laboratory LEA SMART MEMS. Alina Cismaru also acknowledges the support of the Sectoral Operational Programme Human Resource Development (SOPHRD) under the contract number POSDRU/89/1.5/S/ The authors thank Industries for the fabrication of graphene used in their research. References [1] A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater., vol. 6, no. 3, pp , Mar [2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, V. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science, vol. 306, no. 3696, pp , Oct [3] P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, Making graphene visible, Appl. Phys. Lett., vol. 91, no. 6, pp /1 3, Aug [4] D. S. Abergel, A. Russel, and V. I. 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