A graphene based frequency quadrupler

Benefit from exceptional electrical transport properties, graphene receives worldwide attentions, especially in the domain of high frequency electronics. Due to absence of effective bandgap causing off-state the device, graphene material is extraordinarily suitable for analog circuits rather than digital applications. With this unique ambipolar behavior, graphene can be exploited and utilized to achieve high performance for frequency multipliers. Here, dual-gated graphene field-effect transistors have been firstly used to achieve frequency quadrupling. Two Dirac points in the transfer curves of the designed GFETs can be observed by tuning top-gate voltages, which is essential to generate the fourth harmonic. By applying 200 kHz sinusoid input, arround 50% of the output signal radio frequency power is concentrated at the desired frequency of 800 kHz. Additionally, in suitable operation areas, our devices can work as high performance frequency doublers and frequency triplers. Considered both simple device structure and potential superhigh carrier mobility of graphene material, graphene-based frequency quadruplers may have lots of superiorities in regards to ultrahigh frequency electronic applications in near future. Moreover, versatility of carbon material system is far-reaching for realization of complementary metal-oxide-semiconductor compatible electrically active devices.

Scientific RepoRts | 7:46605 | DOI: 10.1038/srep46605 is enough for the purpose of frequency tripling. We have reported a pure frequency tripler with ultrahigh output signal purity (> 94%) with only one GFET for the first time 33 . The CVD grown graphene with micron scale graphene flakes interspersed on the surface was used as the channel material of the GFET. A W-shaped transfer curve was obtained due to different doping levels of the single layer graphene and the bilayer graphene in the channel. In order to achieve a high performance frequency quadrupler with our reported device structures, lots of work optimizing synthesis conditions would be required to achieve a more perfect W-shaped transfer curve with two symmetrical Dirac points. In this work, a much simpler method was carried out to realize a tunable W-shaped transfer curve with two Dirac points. More specifically, a dual-gated GFET with a W-shaped transfer curve was firstly used to achieve frequency quadrupling. With an input of 200 kHz sinusoid signal, about half of the output signal radio frequency (RF) power is concentrated at desired 800 kHz. Moreover, in suitable operation areas, our devices can also work as high performance frequency doublers and frequency triplers, respectively. Compared with the first reported graphene-based frequency tripler 26 , this work shows a remarkable improvement in operation bandwidth with a relative simple device configuration. The simple device structure and potential superhigh carrier mobility of graphene make this graphene-based frequency quadrupler prospective for ultrahigh-frequency electronic applications in the future. Complementary metal-oxide-semiconductor (CMOS) compatible fabrication processes give these carbon material-based devices a chance to replace traditional silicon material in analog circuit, especially in RF applications.

Results and Discussion
Structure design and device fabrication. The V-shaped transfer curves can be obtained easily in GFETs if homogeneous graphene material is used as the channel material 7 . Total channel resistance (R total ) can be written as 34 : where R C is the metal/graphene contact resistance (nearly a constant) 35 , W and L are the width and the length of the channel, respectively, μ is the mobility of the charge carrier, n 0 is the electron-hole puddle 36 concentration (a constant), e is the electron charge, and n is gate (V G ) dependent charge carrier concentration which can be described by: where, ε and t are the permittivity and thickness of the dielectric layer and V Dirac is the gate voltage of charge neutrality point. Hence n equals to zero with V G reaching V Dirac , and the minimal drain current of the V-shaped transfer curve can be obtained as R total reaches the peak value. However, if inhomogeneous graphene, such as a graphene PN junction 37 , is used in the FET channel, then equation (1) will be replaced by: as two graphene parts are connected in series. Here, L 1 and L 2 are the length of the N-type doping graphene and P-type doping graphene, respectively. μ 1 and μ 2 are the carrier mobility in the two regions. As equation (2), the charge carrier concentrations in the two different regions can be given by: where V Dirac1 and V Dirac2 are the Dirac voltage of N-type region and P-type region, respectively. With different values of V Dirac1 and V Dirac2 , two maxima will be discovered in R total at gate voltages of V Dirac1 and V Dirac2 . Figure 1a and b sketchily display formation of the W-shaped transfer curve in a single GFET with two different graphene parts connected in series as the channel material. In Fig. 1a, due to different doping levels, gate voltages for resistance maxima in graphene 1 (red line) and graphene 2 (blue line) are different. The black line with two resistance maxima is the total channel resistance of GFET. Since the drain current is inversely proportional to the total channel resistance, a W-shaped transfer curve with two conductance minima can be obtained, which is shown in Fig. 1b. Figure 1c shows how GFETs with W-shaped transfer curves can work as frequency quadruplers. The device can generate four-cycle waveform at V out with one-cycle input V in . Therefore, a frequency quadrupler can be realized with only one GFET if two different graphene parts with different doping levels, such as graphene PN junctions, are formed in the channel.
Although no effective bandgap, graphene-based PN junctions find their applications in electronic 38,39 and optoelectronic fields 40,41 . Stable graphene PN junctions can be obtained by electrostatic doping 42,43 , chemical doping 44,45 , substrate engineering 46 and photoinduced doping 47,48 . Among these methods, electrostatic doping method is tunable in real time by applying variable gate voltages 42,43 . In our case, a tunable doping method is aspired for the purpose of achieving a tunable W-shaped transfer curve. Therefore, a narrow top gate (TG) is utilized to dope the underneath graphene with electrostatic field and form PN junctions in the graphene channel of Scientific RepoRts | 7:46605 | DOI: 10.1038/srep46605 GFET. A dual-gated GFET is designed and fabricated to achieve frequency quadrupling function for the first time since the dual-gated GFET structure can modulate charge transport characteristics in graphene films efficiently 34 . In this case, the total channel resistance can be derived as: where L is the channel length, L TG is the length of the TG, and the charge carrier concentrations in graphene under the TG and away from the TG can be given by: where ε 1 , ε 2 and t 1 , t 2 are the permittivities and thicknesses of the back gate (BG) dielectric layer and TG dielectric layer, respectively, V Diarc BG is the Dirac voltage of the channel graphene without TG and V BG is the BG voltage. The peak value of R total can be obtained by setting either equation (7) or equation (8) to zero. Therefore, a W-shaped transfer curve with two Dirac points can be achieved with this dual-gated GFET structure. The values of the two Dirac voltages can be obtained from equation (7) and equation (8), respectively, which are shown as: Hence the newly arising Dirac voltage V BG1 is tunable with variable TG voltages and a linear relation can be observed from equation (9).
The three-dimensional schematic of the dual-gated GFET-based frequency quadrupler is shown in Fig. 2a. The P ++ silicon with the SiO 2 cover layer works as global BG. The narrow Ti/Au finger with Al 2 O 3 bottom layer is utilized as local TG. With suitable TG voltage, the one-cycle input electronic signals applying to global BG can result in the four-cycle output signals at the drain electrode. The circuit implementation of the frequency quadrupler is displayed in Fig. 2b. A common-source topology is used for dual-gated GFET in this frequency quadrupler. At first, a suitable voltage V TG is applied to the TG to achieve electrostatic doping in the underneath graphene. Direct-current (DC) voltage V BG is applied to BG to bias the working point of the frequency quadrupler, while an alternating current (AC) sinusoidal input signal V in is added to V BG . V S is connected to the ground. High performance bias tee is utilized to apply DC bias and extract the output RF power.
The detailed device fabrication process of dual-gated GFETs is schematically illustrated in Fig. 2c-h. A heavily doped silicon chip was used as the substrate and global BG (Fig. 2c). Then the silicon wafer was put into an atmospheric thermal oxidation furnace with a temperature of 1000 °C for 3 h. A 100 nm-thick SiO 2 layer working as the dielectric layer of BG was formed on the surface of the silicon substrate (Fig. 2d). Then the commercial CVD grown graphene film was transferred onto the surface of the thermal oxidization SiO 2 layer after the copper foil being etched away. The photolithography and O 2 plasma etching were successively used to fabricate the patterned graphene channel (50 μ m * 20 μ m) that works as the active region (Fig. 2e). The Ti (10 nm)/Au (200 nm) films working as metal contacts were competed by lift-off in acetone after the photolithography and thermal evaporated processes (Fig. 2f). In order to obtain the dielectric layer for TG, 40 nm Al 2 O 3 dielectric was generated on the graphene films successfully by atomic layer deposition (ALD) (Fig. 2g). Here, it should be noted that before the ALD process, a 1 nm Al seed layer was deposited on the graphene surface with electron beam evaporation. After deposition of the Al 2 O 3 dielectric layer, photolithography and wet etching processes were carried out to etch the Al 2 O 3 layer on the surface of the contact pads. At last, the Ti (10 nm)/Au (200 nm) films working as TG were finished by lift-off in acetone after the photolithography and thermal evaporated processes (Fig. 2h). As the fabrication temperatures of these processes mentioned above are lower than 200 °C, CMOS compatible fabrication process is achieved 49 . Characterization of the fabricated device. Before deposition of the Al 2 O 3 dielectric layer, Raman spectrum (Fig. 3a) of graphene was obtained utilizing a 532 nm excited laser with incident power of 5 mW and laser spot diameter of 20 μ m. Intensity ratio of 2D/G is 3, indicating monolayer nature of the CVD graphene sample. The almost invisible D band suggests high quality of the graphene film. Figure 3b shows the optical micrograph of the fabricated dual-gated GFET-based frequency quadrupler. The channel length and width of fabricated GFET   Fig. 3c. The boundary of the buried graphene layer can be discovered with easiness because of high electrical conductivity of graphene. Figure 4 shows the DC transfer curves of dual-gated GFET with different TG voltages. BG voltage V BGS (V BG -V S ) swept from − 30 V to 0 V and bias voltage V ds (V D -V S ) was set at 1 V. By decreasing TG voltage V TGS (V TG -V S ) from − 1 V to − 8 V, the second obvious Dirac point is arising. When V TGS was set at − 1 V, only one Dirac point at about − 21 V is discovered, indicating homogenization of the whole graphene channel and heavy n-type doping of the original graphene. When V TGS was decreased to − 8 V, two clear conductance minima can be found at the BG voltages of about − 21 V and − 4 V, respectively. Occurrence of the second Dirac point at − 4 V indicates formation of soft n-doped graphene underneath TG. The inset shows relationship between location of the newly formed Dirac point and TG voltages and illustrates that new Dirac voltage is approximately a linear function of TG voltage, which agrees well with equation (9). With decrease of TG voltage, an increasing number of holes will be injected into the graphene layer underneath TG due to capacitance effect, which results in decrease of the doping level of graphene. As the doping level of original heavy n-type graphene away from TG in the channel remains unchanged, a constant Dirac voltage at − 21 V (in agree with equation (10)) can be discovered. An interesting phenomenon is that the new Dirac point becomes obvious with decrease of V TGS . In other words, the total area of the soft n-doped graphene increases with decrease of V TGS . Therefore, resistance of this part graphene plays a growing important role in the total channel resistance. The reason is that TG can dope the graphene near the TG edges due to edge effect of the capacitor structure and the total doping range increases when V TGS decreases (increase in absolute value). Nonlinear behaviour in the inset at lower V TGS is another result of edge effect proposed above. Therefore, with narrow TG for underneath graphene electrostatic doping, obvious inhomogeneous graphene could be formed in the FET channel and a W-shaped transfer curve was obtained with dual-gated GFET.

Static response of the device.
Dynamic response of the device. Figure 5 shows the measured AC performances of our dual-gated GFET based frequency quadrupler. In the AC measurements, the V TGS was set at − 8 V and the V ds was set to 1 V. The capacitor C from a bias tee was used to block the DC signal from the output V out . A 200 kHz sinusoidal input (V BGS ranges from − 22 V to − 2 V) was applied to the BG to initiate the frequency quadrupling. In principle, a pure frequency quadrupler (nearly 100% spectrum purity) can be achieved when two symmetric conductance minima arise in the operation area simultaneously, which is sketchily shown in Fig. 1c. In other words, a higher symmetrical factor in the working area can result in a higher output power of the fourth harmonic. The relative output RF power spectrum is obtained through the Fourier transform of the output real time RF signals. With these data, it is found that about 50% of the output RF power is concentrated at the desired 800 kHz. Compared with the useful frequency, these undesired output frequency components (about 25% at the fundamental frequency, about 12% at the second harmonic and about 12% at the third harmonic) play a minor role. In order to investigate the RF conversion efficiency of the frequency quadrupler, the RF input power was obtained. As the total capacitance of the dual-gated GFET is about 18 pF, the total RF input power is about 1.7 mW. The quadrupled output power is 2.4 μ W, which means that a RF conversion efficiency of 0.14% is achieved in this frequency quadrupler. Relative low RF power conversion efficiency is attributed to the large parasitic capacitance of the fabricated GFET. Here, noticeably for the first time a GFET based frequency quadrupler is reported. Moreover, the simple dual-gated GFET based frequency quadruplers provide perfect illustration of versatility of graphene material once again.
A frequency multiplier with simple structure and tunable multiplication factor may have lots of superiorities for RF electronic applications due to low cost and high integration. In our case, dual-gated GFET can also work as high performance frequency doublers or frequency triplers with a suitable operation area. Figure 6a shows relative output RF power spectrum of working dual-gated GFETs as frequency doublers (V TGS = − 6 V and V BGS ranged from − 10 V to − 2 V) and about 78% of output RF power is concentrated at useful 400 kHz, with an input of 200 kHz. Figure 6b presents AC performances of working dual-gated GFETs as frequency triplers, where V TGS was set to − 8 V and V BGS swept from − 15 V to − 1 V. About 79% of total RF power is concentrated at 600 kHz with 200 kHz input. Therefore, dual-gated GFET can work as high performance frequency doublers, frequency triplers and frequency quadruplers by choosing suitable operation areas. This is the first time that a multi-mode frequency multiplier is reported.
With potential ultrahigh carrier mobility and high saturation velocity, graphene can response to high frequency signals completely. Hence large RC time constant of the device structure is major obstacle to improvement of operation bandwidth of graphene based device. Therefore, performance of graphene based devices can be enhanced significantly if an optimized fabrication process is carried out to decrease both parasitic capacitance and output resistance. More clearly, in order to decrease the parasitic capacitance of the GFET-based frequency quadrupler, a highly resistive substrate such as quartz assisting with a local BG technique is preferred. On the other hand, both contact resistance and channel resistance make contribution to output resistance of GFET. A polymeric residue-free graphene fabrication process 50 can be carried out to reduce contact resistance. Channel resistance can be decreased by fabricating GFET with nanoscale channel length and large W/L ratio. In order  to investigate limitation of operation frequency of dual-gated GFET-based frequency quadrupler, a developed device structure is designed and proposed. The channel width and length of newly designed GFET are 10 μ m and 1 μ m, respectively. A local BG with width of 1 μ m is located at the bottom of the channel. A SiO 2 gate dielectric layer with thickness of 90 nm is formed between BG and the graphene channel. With this structure, time constant of about 1.74 ps (R of about 200 Ω and C of about 8.7 fF) can be obtained, indicating cut-off frequency of about 92 GHz and 368 GHz generated output signal. Under a 1 V bias voltage, required carrier mobility of graphene is only 3680 cm 2 /Vs, which can be achieved easily due to ultrahigh intrinsic carrier mobility of graphene material. Hence graphene-based frequency quadruplers have great potential to generate ultrahigh frequency signals and could find its roles easily in ultrahigh frequency electronic applications in near future.
Here, we summarize potential superiorities that dual-gated GFET offers as a new device for RF applications.
(1) A multi-mode frequency multiplier. The zero band gap of graphene enables tunable electronic transport polarity. In this work, a narrow top gate was utilized to dope underneath graphene with electrostatic field, and a tunable transfer curve was achieved with one GFET. With the tunable transfer curve, GFET can work as high performance frequency doubler, frequency tripler and frequency quadrupler. (2) High multiplication factor. Without any additional filter system, it is impossible to achieve a frequency multiplier with high multiplication factor by using traditional nonlinear electronic devices because output power of the high-order harmonic is much smaller than the low-order harmonic. In this work, a graphene based frequency quadrupler with about 50% power purity was realized with dual-gated GFET. Developing idea proposed in this work, a frequency multiplier with multiplication factor of 2 * N (N > 2) can be realized by fabricating N-1 top gates in the GFET channel. With superhigh carrier mobility of graphene, this graphenebased frequency multiplier will play an important role in the ultrahigh-frequency electronic applications, such as signal generator for THz. (3) Low cost. The cost-effective high performance CVD graphene material can be available with rapid improvement of the synthetic technology. Simplicity of the GFET structure results in low fabrication cost. Furthermore, the demand of this multi-mode frequency multiplier increasing rapidly as communications would become indispensable nowadays.

Conclusion
In summary, a novel dual-gated GFET based high performance frequency quadrupler is presented. Benefit from electrostatic doping effect of the narrow TG to the underneath graphene, a W-shaped transfer curve was obtained with only one GFET. With this new type nonlinear I-V feature, a graphene-based frequency quadrupler was achieved. This device can also operate as high performance frequency doublers and frequency triplers. To the best of our knowledge, it is the first reported multi-mode graphene based frequency multiplier in the world. The potential ultrahigh carrier mobility of the graphene, together with simplicity of the device structure and CMOS compatible fabrication processes makes the dual-gated GFET based frequency quadrupler one of the most captivating candidates for future ultrahigh-frequency electronics, especially RF applications.

Methods
We characterized the fabricated device at room temperature in ambient conditions. The DC characteristics of the dual-gated GFET were measured by a Keithley 1602B semiconductor analyzer. Both Agilent 33250A signal generator and Agilent MSO-X 3034A mixed signal oscilloscope were used to obtain AC characteristics of the graphene based frequency quadrupler.